- Email: [email protected]
Lift-generated vortex wakes of subsonic transport aircraft
Progress in Aerospace Sciences 35 (1999) 507}660
Lift-generated vortex wakes of subsonic transport aircraft Vernon J. Rossow* NASA Ames Research Center, Mail Stop N247-2, Mowett Field, CA 94035-1000, USA
Contents 1. Introduction 1.1. Justi"cation 1.2. Background 1.2.1. Literature 1.2.2. Modi"cation of vortex wakes 1.2.3. Ground-based experiments 1.3. Scope of the paper 2. In-trail spacing of aircraft at airports 2.1. Flight experiments 2.2. Experiments with #ight simulators 2.3. Possibilities for wake-vortex accommodation 3. Lift and circulation 4. Simple estimate for vortex-induced loads 4.1. Description of #ow "eld 4.2. Analysis 4.3. Comparison with other methods 4.4. Applications 5. Span loading and vortex structure 5.1. Introduction 5.2. Description of Betz' analysis 5.3. Invariants for motion of vortices 5.4. Rollup equations 5.5. Vortex-wake examples 5.6. Vortex wakes with multiple pairs 5.7. Extended-Betz methods 5.8. Inverse-Betz method 5.9. Region of applicability 6. Design of non-hazardous vortex wakes 6.1. Introduction 6.2. Hypothetical non-hazardous wake con"gurations 6.2.1. Tailored loading 6.2.2. Sawtooth loading 6.3. Experimental veri"cation 6.3.1. Ground-based experiments 6.3.2. Swirl velocity 6.3.3. Span loading 6.3.4. Measured rolling moment 6.3.5. Predicted rolling moment
509 509 511 511 512 513 515 516 516 519 523 523 526 526 528 530 533 536 536 536 538 539 540 540 543 544 546 546 546 546 546 549 550 550 550 553 555 557
* Tel.: #1-650-604-4570; fax.: #1-650-604-3489. E-mail address: [email protected] (V.J. Rossow) 0376-0421/99/$ - see front matter. Published by Elsevier Science Ltd. PII: S 0 3 7 6 - 0 4 2 1 ( 9 9 ) 0 0 0 0 6 - 8
7.
8.
9.
10.
6.4. Application of sawtooth loading to aircraft 6.4.1. Ground-based tests 6.4.2. Flight tests Mutually induced instabilities in single pair 7.1. Introduction 7.2. Numerical method 7.3. Vortex-pair instability 7.3.1. Introduction 7.3.2. Isolated vortex 7.3.3. Vortex pair; waves in phase, "03 7.3.4. Vortex pair; waves out-of-phase, "1803 7.3.5. Vortex pair; intermediate phase angles, 03( (1803 7.3.6. Concluding remarks on the e!ect of phase Multiple pair instabilities 8.1. Introduction 8.2. Overview of #ight tests 8.3. Estimate of steady-state span loadings 8.4. Two-dimensional simulation of wakes 8.5. Three-dimensional simulation of wakes: B-747 8.6. Three-dimensional simulation of wakes: L-1011 8.7. Concluding remarks on multiple vortex pairs Wake alleviation by wing "ns 9.1. Introduction to wing "ns 9.2. Experimental setup in 40;80 ft Wind Tunnel 9.3. Test results 9.3.1. General comments 9.3.2. Fin angle of attack 9.3.3. Spanwise location 9.3.4. Chord of "n 9.3.5. Height of "n 9.3.6. Circular-arc planform 9.3.7. Multi-element "ns 9.3.8. Fins with blown #ap 9.4. Discussion of "n con"gurations 9.5. E!ect of rectangular "ns on span loading 9.6. Concluding remarks on wing "ns Measurements in 80;120 ft Wind Tunnel 10.1. Introduction
559 559 563 571 571 575 576 576 576 576 578 581 581 582 582 583 584 585 587 588 590 590 590 591 593 593 593 593 594 594 594 596 597 597 598 598 599 599
508
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
10.2. Experimental setup in 80;120 ft Wind Tunnel 10.3. Test procedures 10.4. Comparison of data from two large wind tunnels 10.5. E!ect of span ratio on rolling moments 10.6. Rolling-moment results: conventional landing con"gurations 10.6.1. E!ect of yaw of the wake-generating model 10.6.2. E!ect of angle of attack of the wake-generating model 10.7. Rolling-moment results: alleviated landing con"gurations 10.7.1. E!ect of span of trailing-edge #aps 10.7.2. E!ect of wing "ns 10.8. Measured spanwise distributions 10.8.1. Overview of data 10.8.2. Up- and down-wash velocity distributions 10.8.3. Diagnosis of velocity measurements 10.8.4. Lift and rolling-moment loads 11. Validation of vortex-lattice method 11.1. Introduction 11.2. Applicability of vortex-lattice method 11.3. Comparison of predicted and measured loads 11.3.1. Lift 11.3.2. Rolling moment 11.4. Assessment of assumptions 12. Wake energy, span e$ciency and span loading 12.1. Introduction 12.2. Estimated span loadings 12.3. Analysis of downwash data 12.3.1. Vortex structures 12.3.2. Span-load distributions from isolated vortex structures 12.3.3. Discussion of retrieved span loadings 12.4. Wake hazard and induced-drag 13. Vortex decay 13.1. Introduction 13.2. Natural decay
600 602 603 604 605 605 606 606 607 608 609 609 611 612 614 614 614 615 615 615 617 617 620 620 620 621 621 622 623 625 627 627 629
13.2.1. Simple models for decaying vortices 13.2.2. Numerical simulations 13.3. Observations of decay 13.3.1. Swirl velocity 13.3.2. Vortex-induced rolling moment 14. Tests for similitude in vortex structures 14.1. Introduction 14.2. Oseen/Lamb/Squire structure 14.3. Ho!man}Joubert structure 14.4. Sample results from similitude tests 15. Vortex instabilities 15.1. Introduction 15.2. Small-scale vortex instabilities 15.3. Large-scale vortex instabilities 15.3.1. Stability of single vortex pair 15.3.2. Stability of multiple vortex pairs 15.4. Vortex injection by use of wing "ns 16. Turbulence injection 16.1. Introduction 16.2. Wingtip spoiler 16.3. Wingtip spline 16.4. Flight spoilers already on aircraft 16.5. Atmospheric turbulence 17. Wake-vortex avoidance schemes 17.1. Introduction 17.2. Vortex Advisory System (VAS) 17.3. Aircraft Vortex Spacing System (AVOSS) 18. Simpli"cation of vortex-avoidance systems 18.1. Overview 18.2. Flight corridor of small cross-section 18.2.1. Accuracy of global positioning system (GPS) 18.2.2. Vortex transit times 18.3. Straight or curved #ight corridors 18.4. Relocation of #ight corridors 18.5. Atmospheric data monitoring 19. Remarks on status of research References
629 630 631 631 632 632 632 633 633 634 636 636 637 638 638 639 640 640 640 641 642 643 643 643 643 644 645 646 646 647 647 647 649 650 652 652 653
Abstract The #ow "elds of vortices, whether buoyancy-driven or lift-generated, are fascinating #uid-dynamic phenomena which often possess intense swirl velocities and complex time-dependent behavior. As part of the on-going study of vortex behavior, this paper presents a historical overview of research conducted on the structure and modi"cation of the vortices generated by the lifting surfaces of subsonic transport aircraft. Although primarily presented from an experimental point of view, the derivation and use of relatively compact theoretical formulations and concepts are included. Experience with lift-generated wakes has shown that they are so complex that progress requires application of a combined theoretical and experimental research program, because either alone often leads to incorrect conclusions. The primary purpose of the research to be described is to "nd a way to reduce the hazard potential of lift-generated vortices shed by subsonic transport aircraft in the vicinity of airports during landing and takeo! operations. The information presented points out that the characteristics of lift-generated vortices are related to the aerodynamic shapes that produce them and that various arrangements of surfaces can be used to produce quite di!erent vortex structures. It is concluded that a satisfactory aerodynamic solution to the wake-vortex problem at airports has not yet been found, but a reduction in the impact of the wake-vortex hazard on airport capacity may soon become available through wake-vortex avoidance concepts currently under study. Published by Elsevier Science Ltd.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
509
Nomenclature AR b c C * C J e G(r/b ) ¸ M p PQ
aspect ratio wing span wing chord lift coe$cient ("¸/qS) rolling-moment coe$cient ("M/qSb) span e$ciency circulation parameter, Eq. (70) lift rolling moment acceleration in roll ratio of roll accelerations ("p /p , B "C /C B ) J J q dynamic pressure ("o; /2) r radius S wing planform area t time ; free-stream velocity u, v, w velocity components in x, y, z directions = Kirchho!}Routh path function x distance in #ight direction y distance in spanwise direction z distance in vertical direction X, >, Z (x/b, y/b, z/b)
1. Introduction 1.1. Justixcation The capacity of an airport is governed by such factors as the number and arrangement of runways available, the landing and takeo! distances required for arriving and departing aircraft, and the hourly distribution of those activities. Capacity is also limited by the fact that the spacing between aircraft must be large enough to insure that safety is not compromised on the ground nor in the air. While aircraft are in the air during approach and departure, the in-trail spacings are now larger than needed for other factors because it is based on the hazard posed by the lift-generated wakes of aircraft that have previously used the airspace (Fig. 1). The hazard posed is an aerodynamic one wherein the swirl velocities in wake vortices are strong enough to cause an encountering aircraft to roll uncontrollably. The problem comes about because vortices decay or decompose so slowly that the hazard they pose now governs airport capacity. The impact of the hazard posed by vortex wakes is most apparent near airports where aircraft numbers and density are concentrated for landing and takeo!. Furthermore, aircraft are constrained to certain #ight corridors for their approach to the airport and for landing on
a c C d
angle of attack point vortex circulation bound circulation aileron angle of de#ection
Subscripts av averaged over time at a given point cl centerline value cs constant-swirl velocity in core f following wing or probe g wake-generating model ir irrotational part max maximum on one side of centerline mi minimum at a given point mx maximum at a given point o centerline value r rectangular loading ro rotational part s vortex sheet sb solid-body rotation in core v vortex w wing
a runway. On departure from an airport, aircraft also take o! from a given runway so that vortices shed by aircraft during and after rotation, and during climb, can pose a hazard to following aircraft. In such situations, if an encounter occurs, the wake penetration is again nearly aligned with a vortex axis rather oriented in an acrossaxis path (Fig. 1). For the foregoing reasons, the Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) have supported the study of vortex wakes for over 30 years. In this program, research e!orts have been devoted to the study of the fundamental physics of lift-generated vortices, to the magnitude of the hazard they pose to aircraft, to possible means for avoiding them, and to methods for making vortex wakes decompose more quickly. The hazard posed by vortex wakes appears in di!erent forms depending on how following aircraft encounter them. As shown in Fig. 1, an aircraft #ying across the vortices experiences strong and rapid changes in up- and down-loads that may damage the aircraft or cause it to lose control. Analyses of across-trail and in-trail penetrations were made by McGowan [1] in the early part of the wake program, and it was found that the in-trail encounter was the hazard that had the most signi"cant impact on airport capacity. McGowan also studied across-wake
510
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 1. Possible encounters with lift-generated wake by a following aircraft [228]. (a) wing of rectangular planform at several angles of attack; (b) wings with various planforms; a "53.
encounters and found that they could also pose a vertical-load hazard. However, across-wake encounters are not likely to occur on approach or departure. As a consequence, almost all of the research e!orts have been directed at wake penetrations nearly parallel to the vortex axes. As illustrated in Fig. 1, when following aircraft penetrate a vortex wake at a location not near vortex centers, the aircraft experiences up- or down-loads depending on which part of the wake is encountered. These disturbances are usually modest in amplitude and, even though they are of a sustained nature, most aircraft can accommodate the up- or down-draft that the vortices generate. If, however, the following aircraft penetrates the vortex wake near the centerline of a vortex shed by a preceding aircraft that is larger, the follower experiences an overpowering rolling moment due to the swirling #ow "eld of the vortex. If the encounter occurs near the ground, or the subsequent loss of control is catastrophic, the following aircraft may impact the ground. As a consequence, the study of vortex wakes has focussed on the hazard posed by the rolling-moment intensity of vortex wakes. Since vortex wakes of aircraft are persistent and can be hazardous, following aircraft must delay their arrival until the vortex wakes shed by previous aircraft have either descended below or been blown out of the #ight corridor by the wind, or decayed to a harmless level. For these reasons, current minimum separation distances (Table 1) were set for circumstances when instrument #ight rules (IFR) apply. Under visual #ight rules (VFR), the #ight crew receives advisory information on tra$c and wake vortices, and is then free to choose their own spacing, which is usually close to that speci"ed in Table 1. The minimum IFR distances listed in Table 1 for the various weight classes of transport aircraft are based primarily on observations of the lifetime and motion of
wake vortices at airports. The distances listed indicate the amount of time needed for the vortices to decay to a harmless level in ground e!ect or to move downward and/or sideways so that they are well outside of the #ight corridor of any following aircraft. It is to be noted that larger separation distances are speci"ed for small aircraft (including business types) following larger aircraft to insure a comparable margin of safety for the smaller aircraft, which are more susceptible to over-powering vortex-induced rolling moments. The added distance allows more time for the vortices to move farther out of and away from the #ight corridor, and to decay. Since the separation guidelines must allow for worst-case conditions, they tend to be conservative. The spacings listed in Table 1 were modi"ed in 1996 to provide weight categories that better re#ect the weights of aircraft that currently use airports in the United States; Table 2 [2]. Also, the B-757 aircraft was placed in a category by itself that lies between that of heavy and large
Table 1 Terminal Radar Minimum Separation Distances; Gessow [25] Type of following aircraft (km) Small2 Large2 Heavy2
Generator Large Heavy Separation (n mile) (km) (n mile) (km) (n mile)
Small
5 5 5
3 3 3
7 5 5
4 3 3
11 9 5
Less than or equal to 5.67 Mg (12,500 lb). 5.67}140 Mg (12,500}300,000 lb). Greater than or equal to 140 Mg (300,000 lb).
6 5 4
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 Table 2 U.S. Separation Standards; Hinton [2] After July 1996 Reduced ROT Documented. (Distances in n mile) Following aircraft
Heavy
Leading aircraft B-757 Large
Small
Heavy Large Small
4 5 5, 6T
4 4 5
2.5 2.5 2.5
2.5 2.5 3, 4T
Table 3 Approximate Separation time intervals; Hinton [2] Based on standard separation, constant airspeed of 120 knots (Small), 140 knots (757/Large) & 160 knots (Heavy). Following Aircraft
Heavy
Leading aircraft B-757 Large
Small
Heavy
90 90
106 90
72 56
94 56
Large
129 145
103 103
64 64
86 64
Small
150 188
150 171
90 120
75 75
leading aircraft. Since air tra$c controllers can more accurately control the time rather than distance between aircraft, Table 3 lists spacing in seconds between aircraft at the outer marker (upper number) and at threshold (lower number). Two sets of numbers are required, because aircraft travel at di!erent velocities in the approach corridor for a runway. As more information and as conditions change, the values listed in Tables 2 and 3 will probably change again. Other countries have also changed the data in Table 1, and some now use spacing criteria di!erent from that listed in Tables 2 and 3. Based on factors such as runway occupancy time after touchdown, and before lift-o!, the minimum safe separation distance between aircraft in the airport environment, and especially while in the #ight corridors during landing and takeo!, is estimated to be about 2 n mile
511
(nautical miles). One goal of wake-vortex research is to "nd a way to reduce or avoid the wake-vortex hazard so that all landings and takeo!s can be carried out with an in-trail spacing of 3 n mile. If such a reduction were put into practice without an e!ective avoidance scheme, the likelihood of a vortex-wake encounter would increase unacceptably, because less time is allowed for the wake to move out of the way and to decay. Since most aircraft cannot now safely enter the newly formed wakes of larger aircraft, methods must be developed for either reducing wake velocities to a safe level, or to avoid vortex wakes. The con"gurations of generating and following aircraft that need to be treated are those used for landing or takeo! wherein their #aps are deployed and landing gear are extended. Furthermore, since the penetrating aircraft is either landing or taking o!, the nearness of the ground will limit the acceptable unexpected coherent rolling motion caused by a vortex encounter. Lastly, since the #ight velocities of aircraft in the approach and departure corridors are between 130 and 200 knots, analysis of the #uid dynamics of the vortices and the #ow "elds surrounding the aircraft can assume the air to be incompressible. 1.2. Background 1.2.1. Literature The literature on the hazard posed by lift-generated vortices is quite limited up through the early 1960s. One of the "rst papers written about the possible hazard posed by the wakes of large aircraft appeared when the DC-6 was put into service in about 1950. Bleviss [3] estimated the decay rates of the various wake components, and concluded that the so-called propeller wash spread quickly enough that it could be considered nonhazardous to other aircraft #ying more than several spans behind the generating aircraft. He noted, however, that the lift-generated vortices in the wake decay so slowly that they persist for some distance behind the generating wing, and could pose a hazard to following aircraft. The study of lift-generated vortices as a hazard to following aircraft intensi"ed during the 1960s and early 1970s, because the size di!erences between large and small aircraft landing at airports was becoming larger rapidly, and more wake-vortex-induced accidents began to occur. Several investigations by Kraft [4], McGowan [1], Rose and Dee [5], Robinson and Larson [6], Wetmore and Reeder [7], and Zwieback [8] were carried out from 1960 to 1964 to de"ne the vortex-wake structure and to estimate the loads imposed on a penetrating aircraft as it enters the wake from di!erent directions. The results showed that the loads imposed by a wake may overpower the control capability, and may exceed the structural limits of the penetrating aircraft. Based on #ight test results, and on estimates of vortex decay by use of Lamb's vortex model [9], the time
512
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
required for the wake to decay to a safe level was estimated to be far in excess of 3 min (i.e., 6}9 n mile at landing velocity). In order to better understand the structure and slow rate of decay of lift-generated vortices, measurements of the wake velocities were made in #ight by Kraft [4] in 1955 with a P-51 (= "8800 lb) as the wake-generating aircraft, and with two larger aircraft as the probe aircraft (= "13,480 and 16,400 lb). In addition to obtaining some of the "rst in-#ight measurements of vortex structure, it was found that the strength of the vortices did not decrease appreciably for about 35 s behind the generating aircraft, and that the propeller wake is not detectable at distances in excess of about 1000 ft behind the aircraft. The apparently rather slow decay of the vortices seemed to depend on the atmospheric structure present at the time of the #ight tests. The data-reduction techniques developed for these experiments are similar to those used in other ground-based [10] and #ight [11] investigations of wake vortices. When several axial penetrations were made into the wake, the pilot found that it was di$cult to maintain a precise course, and that the vortices caused disturbances similar to severe atmospheric turbulence. No mention was made of overpowering vortex-induced roll excursions, probably because the penetrating aircraft was about twice as large as the generating aircraft. Breakup of the wake began about 60 s after the vortex lines became very sinuous from motions brought about by atmospheric eddies. It was also noted that the sinuous shape of the vortices made it di$cult for the pilot to "nd and stay in the vortices for prolonged measurements. During the 1960s, the FAA began an extensive #ight program to study the nature of, and hazard posed by, wake vortices shed by subsonic transport aircraft in service at the time [12}21]. One of the objectives of the #ight program was to obtain direct measurements of the vortex structures shed by a wide variety of aircraft. Data on the structure of the vortices were obtained by #ying various subsonic transport aircraft well o! to the side of an instrumented tower so that the wind would blow the shed vortices across the instrumented tower for a measurement of their velocity and pressure. Intentional penetrations by following aircraft of vortex wakes shed by a lead aircraft were also carried out at a safe altitude to determine when overpowering rolling moments occurred, and to obtain estimates for the separation distances listed in Table 1. About the time that the #ight tests were being carried out by Garodz et al. [12}21], interest in the characteristics of wake vortices shed by transport aircraft was increasing rapidly and various workshops and summary articles appeared in the literature. Although not devoted directly to the rolling-moment hazard posed by liftgenerated vortices, an excellent background summary of the #uid dynamics of vortices appeared in Vol. 7 of the Progress in Aeronautical Sciences as edited by
Kuechemann [22]. In order to stimulate interest in, and to summarize the current status of, research on the subject of lift-generated vortices, a symposium was held in 1970 that resulted in the publication of proceedings that provides an excellent background survey and introduction into the wake-vortex hazard problem at airports [23]. Also, during the 1970s, the Federal Aviation Administration (FAA) and National Aeronautical and Space Administration (NASA) began intensive groundbased and #ight-research programs into the nature of and solution to the wake-vortex hazard problem. As a consequence of the large increase in the study of vortices, a number of conferences have been held since the late 1960s that produced very informative proceedings [23}30]. Furthermore, a number of summary articles have appeared in various publications [16,31}36]. A good status report of the work on wake-vortex research in Russia at TsAGI is provided by Vyshinsky [37]. The photographs of various #ow phenomena, including some good ones of vortices, in a book by Van Dyke [38] is recommended for intuitive guidance. In addition, two bibliographies by Hallock [39,40] provide a complete listing of titles, authors, and abstracts available at the time of publication. Rather than put out a new ever larger book of abstracts, an internet address has now been established by Hallock that includes all of the listings in an on-line bibliography which is updated regularly; i.e., 1www.volpe.dot.gov/wv2. Although research on rotorcraft technology provides some valuable information that also applies to the vortices shed by aircraft in linear #ight (e.g., [41}43]), the large volume of other articles on the aerodynamics, noise, etc., of the vortices shed by helicopter rotor blades along a circular path will not be discussed. 1.2.2. Modixcation of vortex wakes Since the objective of the research on wake vortices is either to modify them so that they are harmless, or to avoid them, the types of equipment to be used to achieve these objectives is not straightforward. If the objective is to change vortex wakes, the existing structure of vortex wakes should "rst be determined before steps directed at changing the vortices can be undertaken. As will be seen in the survey literature listed in the foregoing paragraph, the magnitude and the nature of the hazard posed by wake vortices were "rst studied by use of #ow visualization, by analysis, and in #ight [5,8,12}21,37,44}55]. Even though the structure of lift-generated vortices had not been fully de"ned, and the hazard completely evaluated, research e!orts intensi"ed greatly toward the development of methods for producing benign vortices or that would promote more rapid decomposition of vortex wakes than achieved through natural decay [25,56,57]. Addition of turbulence to the vortex wakes of aircraft was the "rst option considered because excess turbulence
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
in the ambient #uid was known to disrupt or prevent the formation of laboratory vortices. Therefore, when the FAA/NASA wake vortex program was started in the early 1970s, turbulence injection (or addition of turbulence to the wake by means of various devices) was the "rst method tried. An overview will be given in Section 16 of the e!orts made to promote the rapid disintegration of vortex wakes by use of turbulence-producing devices on the generating aircraft. At about the same time, the mutually induced instability of a vortex pair was analyzed by Crow [49] which called attention to a mechanism that brings about closed loops in the vortex pair. After formation, the vortex loops gyrate about to produce mixing in the wake on a scale equal to or larger than the wingspan of the wake-generating aircraft. Many variations on the general approach to turbulence injection and to mutually induced instabilities were postulated and tried. Some that appeared to be e!ective at reducing the wake hazard continue to be studied [58}71]. Various wake-vortex dispersion mechanisms are listed below in approximately the chronological order in which they were tried. The listing is somewhat arbitrary and is not intended to include all of the concepts investigated. 1. 2. 3. 4. 5. 6. 7.
Spoiler and spline devices. Wingtip blowing. Forward or reverse thrust of the engines. Flight spoilers already on aircraft. Wingtip turbine. Span loading. Wing "ns.
Results from investigations on some of these devices are presented in various conference proceedings [25,27}30]. If any of the con"gurations tried under item 4 had been successful, it might not have been necessary to signi"cantly modify the aircraft, i.e., if the required #ightspoiler equipment already on board the aircraft proved to be adequate. Application of some of the other concepts listed could require extensive modi"cation of the wakegenerating aircraft, which would reduce the attractiveness of the alleviation concept. The use of span loading on the wake-generating wing and of wing "ns to deintensify the vortices are discussed in sections to follow. Not included in the foregoing list is the decay due to self-generated turbulence in the #ow "eld of the wake itself, and the ambient turbulence present in the #ow "eld ahead of the aircraft through which it #ies (i.e., atmospheric turbulence). A number of papers on the characteristics and structure of unmodi"ed decaying wakes were also written [72}86]. The early research work de"ned the nature of the hazard posed by vortex wakes when an aircraft makes an in-trail encounter with a vortex wake. The primary con-
513
cern soon became one of the magnitude and the persistence of the rolling-moment hazard. Therefore, analytical and ground-based studies concentrated on the decay of vortices, and the #ight measurements concentrated on #ow visualization and on intentional penetration of the vortices by a following aircraft. It was found that the cross-sectional region of the wake that is hazardous to a following aircraft is small, and di$cult or impossible to "nd without some sort of #ow visualization to indicate where the vortex centers are located [12}21,50,58,59]. The primary reason for deliberate penetrations into a vortex core by an aircraft was to determine whether or not enough control was available on board the penetrator aircraft for it to proceed through to a safe landing at an airport. It was found that the measurements in #ight tended to be qualitative and to have a large amount of scatter among the results, because the vortices to be penetrated were sinuous in shape and the response of the aircraft to the vortex #ow "eld was often an intensely dynamic one. It was then realized that an understanding of the vortex structure, its decay, and potential hazard require improved measurements of vortex wakes as a function of time or distance behind the wake-generating aircraft. It was also concluded that this kind of data could best be obtained in ground-based experiments, where the test conditions could be better controlled at a more modest cost. This paper presents an overview of experiments directed at the understanding, evaluation, and possible modi"cation of vortex wakes. The introduction of various theoretical tools will be made to illustrate their use as a guide for the experiments, and to the interpretation of the results obtained. Reference to #ight test results will be made for comparison with ground-based results, and to show how they helped to guide the ground-based experiments. 1.2.3. Ground-based experiments The distribution of the swirling velocity in vortex wakes is the characteristic of most importance for a determination of the in-trail hazardous nature of the wake. When research e!orts were expanded in ground-based facilities, a signi"cant portion of the e!ort was devoted to the development of improved methods for measuring the velocity distribution in the #ow "eld of the wake [25,27]. It was found that wake vortices tended to meander rapidly enough that it was di$cult to obtain measurements of the velocity distribution with enough accuracy to test various theories. One solution to the problem was to mount a hot-"lm anemometer on the end of a rotating arm for a rapid survey of vortex wakes, and thereby eliminate the problem with vortex meander (e.g., [10,87,88]). Di$culties with the test equipment and with data reduction prompted the search for other simpler and less-intrusive test techniques. The subsequent
514
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
development of laser-velocimetry provided a good technique for obtaining test data in both wind tunnels and in water tow tanks (e.g., [60,61,80,87}100]). Measurements made with laser velocimeters made pioneering discoveries in the decay characteristics of vortex wake (e.g., [90}93]). Of particular signi"cance at the time was the "nding that the maximum swirl velocity in a vortex changed negligibly at "rst, and then decayed roughly as the inverse of the square root of time (i.e., as t\ , Fig. 2). It was assumed that the behavior of the entire vortex would be about the same as the maximum swirl velocity. The #at or nearly zero decay region of the vortices in Fig. 2 is referred to as the plateau region. The similarity of the decay rates of vortices shed by various wings prompted Iversen [101] to study a wide variety of measurements of wake vortices. Scaling parameters were then derived to collapse the data into a narrow band (Fig. 3). The small "gure on the upper right-hand side of Fig. 3 presents the functional dependence used in the horizontal scale. In summary, the measurements in water tow tanks con"rmed that the self-generated decay of lift-generated vortices is far too slow to be of use for the reduction of the in-trail spacings currently being used between aircraft in the vicinity of airports. For example, based on the data in Fig. 2, the vortex wake of a heavy aircraft like the B-747 would not even begin to decay until the desired spacing of 3 n mile has been reached or exceeded. The di$culties with accurately measuring velocity distributions, and then translating them into rolling moments, led to the development of the following-wing technique [102]. The simplicity of the method and the approximately good agreement with rolling moments determined by use of measured velocity distributions [10] was soon adopted as not only satisfactory, but the preferred instrument for the determination of the rolling-moment hazard posed by a vortex wake. The follow-
ing-wing technique has the virtue that it integrates the swirl velocity distribution over a portion of the #ow "eld to yield an indication of the net rolling moment. The entire vortex wake can then be surveyed for the nature of the rolling-moment hazard without the need for an elaborate measurement technique and data reduction process for the determination of the rolling moment. Research showed that for most wings of interest the rolling moment depends primarily on the span of the follower, and is relatively independent of taper and sweep. When measurements from ground-based facilities are compared with those in #ight, the agreement is generally quite good. The precision of the comparisons are compromised however, because the #ight measurements are taken during a dynamic encounter, whereas the wind tunnel or water tow tank results are measured with "xed following wings [55,103]. It was decided thereafter that the best way to test the rolling moment intensity in a vortex wake during a #ight experiment is to approach the vortex center from below, so that the pilot had good visual contact with the vortex location, and so that he can then guide the aircraft upward quickly through a region at or near the vortex center. The penetrating aircraft then experiences imposed roll accelerations of short duration without much change in velocity or intended trajectory [104]. Data reduction is thereby simpli"ed greatly, and the test results improved. Measurements made in wind tunnels and in air or water tow tanks also improved with time as various techniques were re"ned. It was "rst found to be essential that the wake-generating model be mounted on a slender aerodynamically clean strut fastened to the top rather than to the bottom of the fuselage or centerbody. The vortex wake of the wake-generating model then moves away from the wake of the support strut to minimize the interference of the strut with the vortex wake being
Fig. 2. Water tow-tank results for the maximum swirl velocity as a function of downstream distance; ; "6.8 ft/s (2.07 m/s) Ci!one and Orlo! [91].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
515
Fig. 3. Correlation of maximum swirl velocity in lift-generated vortices as a function of downstream distance; Iversen [101].
studied [10,105,106]. Also, it was found earlier that the complications caused by the motion of the vortex centers (brought about by non-uniformities in the airstream) cause the wake to have a time-dependent character that depends on the facility being used. Special techniques must be used, therefore, if reliable results are to be obtained. One technique used with some success is to measure the maximum, minimum and time-averaged quantities of the parameters of interest during a certain measurement interval [106]. 1.3. Scope of the paper An overview is presented on the theoretical models used to guide the tests on vortex wakes with various items of equipment and facilities used to obtain data. Reference to equipment and test techniques are given only as needed to help explain the nature of the results. The paper attempts to summarize work carried out from about 1970 to the present time. Much of the work to be
described was sponsored by the FAA/NASA wakevortex program. Along with the experimental results to be described, various theoretical methods are presented to show how they have guided the test programs, and have helped to interpret the data obtained. Applicable theoretical models provide a guide for the experimentation, so that tests can be carried out in a systematic way rather that by random testing. Analysis of the data obtained is then also expedited, and the dynamics of vortex wakes better understood. It is also shown how the theoretical relationships between measured parameters can be used to not only test the theory, but also to determine the "delity of the test equipment and techniques used. Experimental results from water and air tow facilities, wind tunnels, #ight and #ight simulators are included. The overall theme of the results to be described is the evaluation, reduction and avoidance of the rolling-moment hazard posed by the vortex wakes of subsonic transport aircraft which are generally con"gured in their landing con"guration with #aps and slats deployed, and landing gear extended.
516
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
The objective of the theoretical and experimental research to be discussed is to diagnose vortex wakes, so that the dynamics of their generation, persistence, modi"cation, and demise are understood and predictable by use of analytical relationships or by numerical analysis. In such a process, experiments need to be conducted to "nd when and how simpli"ed models of vortex wakes break down or fail to apply, and how to develop improved models for the #ow "eld. Experiments are most e!ective and useful when they are used to test particular theoretical models or analyses as part of an e!ort to improve the models or to develop new ones. In this way, it should become possible to modify or tailor the structure of vortex wakes to achieve the characteristics desired.
2. In-trail spacing of aircraft at airports 2.1. Flight experiments The scienti"c study of lift-generated vortices began with the introduction of vortex-lift concepts by Lanchester and Prandtl in the early 1900s. As mentioned previously, the possible hazard posed to small aircraft by the vortex wakes of much larger aircraft was "rst analyzed by Bleviss [3] when the DC-6 was put into service in the early 1950s. Somewhat later, several theoretical studies were made of the consequences that could occur if aircraft inadvertently encountered a vortex wake [1,5,107}109]. These papers and other unpublished estimates of the hazard posed by lift-generated vortices prompted increased e!ort on the subject. In the late 1960s, e!orts were started on the development of guidelines that would recommend in-trail separation distances between aircraft on approach and departure at airports. Probably, the primary reason for the increased e!ort was the increasing size di!erences between large and small transport aircraft that were being put into service. Since very few results were available from groundbased facilities or theoretical tools, and because the safety requirements dictated a maximum reliability of the results at the earliest possible time, it was decided to determine the information by conducting #ight tests. The objective was to produce a table (e.g., Tables 1}3) that would indicate to aircraft operators the minimum spacing between aircraft that would insure against hazardous encounters with vortex wakes on approach and departure from airports. The e!orts are described in a number of papers [4,6,8,12}21,44}48,50,53,55,66,67,110}122]. The material presented here provides a brief description of the process and some results, but does not go into the many interesting discoveries made during this early study of purposeful encounters made by aircraft with vortex wakes. The intent of this presentation, which is taken largely from Andrews et al. [44}46], Condit and Tracy [117] and Hallock and Burnham [122], is to indicate
how the "rst separation guidelines in Table 1 were obtained, and how they have changed in the United States (Tables 2 and 3). The test program of the 1960s included a wide variety of aircraft that included large military and a variety of subsonic transport aircraft along with small aircraft such as a Lear Jet and a Cessna-210. A graphical presentation of the aircraft used in the study reported by Andrews et al. [44] illustrates the variety of aircraft pairs, and the separation distances at which vortex encounters were tested (Fig. 4). All penetrations were made possible by injecting some type of smoke, vaporized oil, or powder from the wake-generating aircraft into the vortices, so that they were visible to following aircraft. Without some sort of #ow visualization, the trailing vortices were almost impossible to "nd. As illustrated in Fig. 5, the penetrations were made from directly aft of the wakegenerating aircraft to minimize the induced structural loads, and to best simulate the kinds of in-trail encounters to be expected on approach and departure from an airport. During the encounter, the pilot of the following aircraft tried to position his aircraft in the center of a vortex (made visible by #ow visualization) and to hold it there. Hence, only the core region of the vortices were speci"cally probed for hazard. For aircraft smaller than the semi-span of the wake-generator, a penetration of one vortex probably covers the most hazardous region in the wake. If, however, the penetrating aircraft is on the order of the same size as the wake-generating airplane, the most hazardous location in the wake is theoretically not at the center of a vortex. Observations of the #ight path of probe aircraft as they encounter a vortex wake made it
Fig. 4. Summary of aircraft used in wake vortex #ight program; Andrews et al. [44].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 5. Procedure used to probe the vortex wake of a generator aircraft; Andrews et al. [44].
apparent that a large part of the entire wake region is probed by test aircraft as it attempts to "nd and stay in the center of a vortex, and to recover from a vortex upset. The procedures used to determine the hazard posed by the vortex wake of one aircraft when another aircraft penetrates it were of two types. The initial test procedure was to position the aircraft at the maximum separation distance at which the vortex trail was visible, and then proceed to #y in or near the center of the vortices until a speci"ed minimum separation distance was reached (Fig. 5). The second method was to position the probe aircraft at a pre-arranged separation distance, and to then evaluate the response characteristics for a period of approximately 2 min. In both cases, the task of the pilot was to maintain the wings of the aircraft level, and to return to the center of the vortex as soon as possible
517
following an upset. In order to expedite the program and to provide a margin of safety for potential upset recovery, the tests were conducted at 2591 and 3810 m (8500 and 12,500 ft) altitudes. The wake-generating aircraft were #own at speeds from 130 to 170 knots, which is considered normal for terminal-area operations. The speed of the probe aircraft was generally comparable with that of the generator. The tests were observed and recorded on video tape, and the relative locations of the aircraft pairs were recorded on a digital system. As stated by Andrews et al. [44], the primary objective of the foregoing vortex-encounter program is to determine a ratio of the maximum vortex-induced roll-acceleration response of the probe airplane to the maximum roll-control power of the probe airplane as a function of separation distance. The rationale for separation distance assumes that when the maximum control power of the probe aircraft is equal to the induced rolling moment from the vortex wake of the generating aircraft, the separation from the generating aircraft is considered to be a safe minimum (Fig. 6). The straight lines in Fig. 6, and in "gures to follow, represent the upper envelope of data for the maximum roll accelerations experienced during all encounters. The quantity p with the subscript &measured' in Fig. 6 represents the roll acceleration of the penetrating aircraft. When the subscript is d , the
quantity represents the roll-acceleration capability of the penetrating aircraft when full-aileron de#ections are used. A safe encounter then assumes that aileron de#ections are applied instantly as needed when a vortex-wake encounter occurs. Results from Andrews et al. [44] for other aircraft are presented in Figs. 7 and 8. As explained in the foregoing paragraphs, the #ightdetermined separations are based on deliberate encounters with the most intense regions of a vortex wake. It is
Fig. 6. Method used to determine aircraft separation distances: C-5A as wake-generating aircraft, DC-9 as probe aircraft, landing con"guration; Andrews et al. [44].
518
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 7. Proposed aircraft separation distances when in landing con"guration; Andrews et al. [44].
Fig. 8. Summary of separation criteria; Andrews et al. [44].
noted that the separation guidelines listed in Table 1 are sometimes smaller than the safe encounter distances found in the various references. Since su$cient time or distance is allowed between aircraft during landing or takeo!, a vortex is usually not encountered, because they have moved downward and/or sideways too far from the #ight corridors to be a hazard. Experience with the recommended spacings during instrument #ight conditions indicates that the spacings listed are indeed adequate for most purposes. Somewhat later, and as indicated by Hinton [2,123,124], for an unknown reason vortex encounters behind some aircraft were more fre-
quent than most of the rest of the #eet, e.g., the B-757. For this reason, and because the aircraft was close to the 300,000 lb division between large and heavy aircraft, a special category was assigned to the B-757, and other changes were made as well (Table 2). It should be noted in Table 2 that the weight limits on the various aircraft categories have also been changed. An added complication are the two numbers, and the letter ¹, listed in the leading-aircraft blocks for heavy and large categories when the following aircraft is small. The "rst of the two numbers indicates the recommended minimum spacing between aircraft at the outer marker (about 7}10 n mile
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
from the end of the runway), and the second number with the letter ¹ attached is the recommended minimum spacing between aircraft at runway threshhold. Hinton [2] presents Table 3 in order to call attention to the fact that separation distances should be based on time rather than on distance, because vortices move and decay as a function of time. Therefore, when leading and following aircraft approach airports at di!erent velocities, the spacings (in time and distance) between aircraft often changes between the outer marker and touchdown on the runway. Although it was well known that vortex wakes descend behind the wake-generating aircraft, uncertainty existed as to how quickly and how far down the wakes would descend. It was found in various #ight tests that wakes would frequently descend below the wake-generating aircraft by at least 500 ft, and often as much as 1000}1500 ft while they were visible. Analysis of both the motion of vortex wakes and the hazardous region around them by Burnham and Hallock [27,28,39,40,112}116,122,125], indicates that the speci"ed spacings provide safe passage under most conditions. They also determined that the roll control available by use of aileron de#ection on board a penetrating aircraft should be at least twice the vortex-induced rolling moment posed by the wake of a leading aircraft. The factor of two provides enough control to not only overcome the vortex-induced rolling moment, but allows enough spare control so that the aircraft can be returned to its normal attitude when its intended #ight path has been disturbed. If such a criterion were imposed on the #ight data shown in Figs. 6 and 7, the horizontal lines used for acceptable separation distances would be drawn at p /p "0.5
B rather than at 1.0, as shown in the "gures. 2.2. Experiments with yight simulators Further information on what is considered by pilots as a safe or acceptable level of hazard was determined by use of #ight simulators. The information summarized here was developed in #ight simulators at NASA Ames and Langley Research Centers and by analysis of that data. The tests in the simulators were carried out to obtain safely, and at modest cost, more information on the levels of acceptable vortex-induced motions, and to obtain repeatable data on excursions caused by wakevortex encounters. Tests were conducted with piloted ground-based simulators [54,104,108,109,126}132] which included not only the dynamics of vortex encounters, but also the e!ects of atmospheric turbulence on the perception of hazard by the pilots while occupied with the usual piloting duties associated with the airport environment. Also, the experiments were planned so that the wake-vortex encounters were unexpected rather than deliberate. The forces and moments on the probe aircraft were computed at each increment of time by use of
519
a strip-theory type of analysis that was fast enough to provide data on a real-time basis for the six degrees of freedom of motion. The piloting task was to #y a 33 glide slope towards a landing with an abort capability if desired. The pilots who had previous #ight experience with wake-vortex encounters reported that the simulations were quite realistic and a good representation [54,129]. Also, the simulations were judged to be a useful and valid method for establishing hazard criteria. After a number of simulated encounters had been #own under both visual #ight conditions (VFR) and instrument #ight conditions (IFR), the separation of occurrences into hazardous and non-hazardous categories correlated best with maximum roll or bank angle [54,129,130,132]. The data used to infer boundaries between hazardous and non-hazardous conditions is reproduced in Fig. 9 for a range of altitudes and bank angles. The boundaries are summarized in Fig. 10 for both IFR and VFR. It was concluded from the simulations that under IFR conditions, a roll angle of more than 5}73 is perceived as hazardous at altitudes of 200 ft or less. The primary reason given by the pilots for rating an encounter as hazardous was proximity of the ground, and subsequent altitude loss caused by the encounter. Two more values can be inferred from the data of Sammonds and Stinnett [129] when they divide their roll acceleration data (reproduced in Fig. 11) into two groups. In the "rst (Fig. 11a), the entry angle into the vortex is held constant while the vortex strength is varied. In the second (Fig. 11b), the data for a given vortex strength are plotted as a function of maximum bank angle while the entry angle into the vortex is varied. Even though some sort of relationship appears to exist in the data, extrapolation to low values of bank angle can only be done in an approximate fashion. Therefore, lines drawn through the center of the data points, or along the upper or lower edges of the data scatter, provide an estimate of the roll acceleration not to be exceeded if the encountering aircraft is to roll no more than 53 or so. If such a connection and the extrapolation are valid, the values estimated for maximum acceptable roll acceleration due to a vortex encounter appear to range from about 0.8 rad/s to about 1.6 rad/s. In order to be conservative, the 0.8 rad/s value is chosen as representative of maximum tolerable values for p . A value for the roll-control ratio PQ can be calculated for aircraft by using the appropriate value for p . From Tinling [130], typical values B (Table 4) for the roll control acceleration range from about 0.6 rad/s for large aircraft to 1.8 rad/s for small aircraft [104]. Since the Lear Jet characteristics were used for the following aircraft in the ground-based simulations, the appropriate value (Table 4) for p is B 1.15 rad/s. The corresponding value for the roll control ratio, PQ , is then (0.8/1.15) or about 0.7 for the Lear Jet, which is not signi"cantly greater than the value of 0.5
520
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 9. Data for maximum bank angle from simulated encounters for all entry conditions tested-VFR; Sammonds et al. [129].
Fig. 10. Summary of data from simulated encounters indicating the boundaries between hazardous and non-hazardous conditions for all entry conditions tested with a Lear Jet and a B-707/720 aircraft; Sammonds et al. [54].
recommended by Burnham [113,115] and by Rossow and Tinling [104]. A similarly well-de"ned boundary between hazardous and non-hazardous conditions was not found for either roll rate or roll acceleration, e.g., Fig. 12. It may be that since the vortex intensity was for larger aircraft (C"92.9}185.8 m/s (1000}2000 ft/s)), the roll velocities and accelerations that occurred in the simulations did
not go to low enough values to completely de"ne a boundary. In the absence of enough data at the lower values of roll acceleration to de"ne a sharp boundary between hazardous and non-hazardous roll accelerations, the available encounters are extrapolated to the low altitudes of interest for separation guidelines. When such an extrapolation is made (Fig. 12), the maximum tolerable roll acceleration is estimated to be about
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
521
Fig. 11. Data for maximum roll acceleration from simulated encounters for all entry conditions tested under VFR conditions; Sammonds et al. [129]. (a) Data for constant vortex strength (C"92.9 m/s (1000 ft/s)), variable entry angle into vortex. (b) Data for constant encounter angle (W"$103, h"!103), variable vortex strength.
1.6 rad/s, which exceeds the value of 1.15 rad/s capability of the Lear Jet used in the simulation. Since the acceptable value exceeds the capability of the aircraft, either the extrapolation in Fig. 12 is invalid or roll acceleration is an insensitive indicator of hazard. A value for PQ between 0.5 and 1.0 appears to be of about the correct magnitude, because Smith [55] reported that pilots of the T-37B probe aircraft placed the safe separation distance behind a B-747 alleviated con"guration at about 5.5 n mile. At that distance, the max-
imum measured rolling moment was about 0.6 of the aileron capability of the T-37B probe. A similar "gure for the non-alleviated wake of the B-747 is a more uncertain, because the data do not go beyond the 13 n mile distance that was judged by the pilot to be safe. However, data at the 10}11 n mile distance scatters from about PQ "0.4}0.8. Since these #ight tests were all VFR and at altitude, it is not clear how they are related to the more delicate situation that exists with IFR conditions and low altitude [104]. The foregoing results are in agreement
522
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Table 4 Aircraft roll-control characteristics [104] Aircraft
Wing span (ft)
Available roll control, c B J
Roll-control power, p B (rad/s)
Cessna 210 T-37B Lear Jet PA-30 DC-9 B-737 B-727 Convair 990 B-707 B-747
36.6 33.8 34.0 36.0 89.4 93.0 108.0 118.0 145.8 195.7
0.056 0.060 0.047 * 0.067 0.097 0.092 0.059 0.080 0.068
* * 1.15 1.87 0.97 * 0.62 * * *
with the value of 0.5 estimated for PQ by Burnham [113] while carrying out a study of wake-alleviation requirements. The "nding that a vortex encounter is considered non-hazardous if the maximum roll excursion is below a certain value prompted studies by Johnson and Rediess [127], Johnson et al. [128], Tinling [130}132] of the feasibility and e!ectiveness of an automatic control system on maximum roll angle. It was observed that since the simulator experiments were designed to make the vortex encounter unexpected, the pilot response during a typical encounter "rst consisted of a time delay of
about 0.4 s. During this time delay, the aircraft undergoes the initial accelerations induced by the velocity "eld of the vortex. The pilot then applies roll control in proportion to the perceived roll rate. Based on the pilot response, it was reasoned that a considerable reduction in roll excursion could be achieved if an automatic system was used to command immediate aileron action. A numerical analysis was then carried out by Tinling [131] which showed that when the full amount of roll control is used with an automatic system, and when the parameter PQ is less than one, the angle of roll can be kept within acceptable limits. An illustration of the e!ectiveness of an automatic control system is presented in Fig. 13 for a range of roll accelerations. It is apparent that the on-board capability of the following aircraft can increase the value of the roll-control ratio PQ , which is required to qualify a wake as non-hazardous, or acceptably alleviated. If the on-board response is minimal, the value of PQ that is required could be as low as the 0.4 value estimated on one of the #ight tests. If the on-board capability is maximized, the acceptable value for PQ could approach 1.0. In summary, the foregoing estimates for PQ , which include the response time of the pilots, range from 0.4 to 0.8. Hence, a single approximate value for PQ that is recommended as a general rule for all aircraft is that PQ 40.5 for a manageable wake encounter. When this value is combined with typical values for the maximum aileron-control capability contained in Table 4, it appears that the vortex-induced rolling-moment coe$cients should not exceed about C "0.03. J
Fig. 12. Data from simulated encounters illustrating variation of maximum bank angle with maximum roll acceleration due to the vortex; Sammonds et al. [129].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 13. Estimate of maximum bank angle due to vortex encounters for several levels of roll-control authority for automatic system based on numerical analysis; Tinling [131]. (a) without circulation; (b) circulatory #ow only; (c) with correct circulation for Kutta}Joukowsky condition.
2.3. Possibilities for wake-vortex accommodation Consideration is given here to the currently available possibilities for achieving the reduction in wake-vortex hazard potential needed to satisfy the requirement that C 40.03 for all following aircraft. The magnitude of the J problem is illustrated by noting that the wake vortices trailing from a B-747 can induce a rolling moment on a Lear Jet type following aircraft about equal to C "0.12 at 1}2 n mile behind the generating aircraft J [60,61]. Hence, an accommodation of some sort by a factor of about 4 must be made. If 2 n mile separation distances are to be achieved, following aircraft must either: (1) avoid wake encounters; or (2) increase its rollcontrol power to the point where an acceptable attitude can be maintained throughout any wake that might be in the #ight corridor. If the wake-generating aircraft is to solve the wake-spacing problem, design of its lifting surfaces must be carried out so that the intensity of the swirling velocities in the wakes are so benign that current control capabilities are su$cient. Each of these possibilities has its own set of di$culties. For example, wake avoidance at the 2}3 n mile separation requires special restraints on the #ight paths of wake-generating and following aircraft so that, as they use the same #ight corridor, the vortex wakes move quickly away, so that approach and departure can be made safely. Several prospective avoidance systems are described in the last part of this paper. None has been
523
developed to the degree needed for application at this time. The second possibility mentioned above is to increase the roll-control power on board the penetrating aircraft in order to maintain attitude control throughout any vortex wake encounter. Such a change appears impractical, because it would require large changes in the characteristics of the aircraft. Since transport aircraft are designed for e$ciency in cruise, they cannot be readily adapted to special requirements (which may degrade cruise performance) to cope with occasional situations during landing and takeo!. For example, an increase in the roll control power of an aircraft by a factor of 4 would require major changes in the wing and aileron design. Since the aileron rolling-moment capability typical of current transport aircraft is about C B "0.06, an upJ grade to over 0.2 would be a major undertaking, and would probably be found to be an impractical solution. Not only are large changes required in the wing structure, but the mechanisms must also apply such large roll-control forces rapidly enough to maintain control the instant a vortex is encountered. The combination of large control surfaces and rapid de#ection for a variety of #ight circumstances poses di$cult design problems for a large #eet of transport aircraft and does not appear to be a satisfactory approach to a solution. When the FAA/NASA wake-vortex research program was started in the early 1970s, the most attractive solution at that time was to alleviate the rotary velocities in the lift-generated wakes to the degree where the rollingmoment coe$cients induced on any following aircraft would be negligible compared with the roll-control capability on board the aircraft. As mentioned previously, this requires roughly a four-fold reduction in the rotary velocities of the wake. This goal has been found to be very di$cult to achieve, even when other considerations such as e$ciency and cost of implementation are not included. Also, any penalties imposed by the alleviation scheme on e$ciency and costs of implementation should be small in comparison with the savings generated by higher airport capacities, which are estimated at from 20 to 40% for busy airports with a large percentage of aircraft tra$c concentrated in the heavy category. Nevertheless, research results found so far indicate that the foregoing goal is reachable. Further research may present solutions that ful"ll all of the characteristics needed for a satisfactory wing design. Information in the following sections provides a history of the work carried out so far on the alleviation of the hazard posed by vortex wakes.
3. Lift and circulation In order to discuss the structure and modi"cation of lift-generated vortices, a brief overview of the concepts behind lift on, and the vortices shed by, a wing of "nite
524
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
span, along with some de"nitions for certain terms will be given in this section. The theory of lift began with the visualization of the #ow "eld around wings. These observations led Lanchester and Prandtl to the vortex theory of lift wherein the strength of the vortex is called its circulation, C. Wing theory begins with the circulation around an airfoil (usually considered a two-dimensional #ow "eld) which is brought about by designing the airfoil with a sharp trailing edge to insure a clean departure of the streamlines over the top and along the bottom of the airfoil, and thereby bring about circulation and lift. Without circulation, the streamlines around the airfoil would tend to #ow around the sharp trailing edge (Fig. 14a). If the #ow "eld associated with circulation (Fig. 14b) is added to the #ow "eld in Fig. 14a, the #uid #ows smoothly o! of the top and bottom of the airfoil past the sharp trailing edge (Fig. 14c). In practice, circulation is produced by the sharp trailing edge on the airfoil. Since the air is not able to make the sharp turn at the trailing edge, the #ow separates from the upper and lower surfaces of the airfoil smoothly rather than making the sharp turn (Fig. 14c). The modi"cation of the #ow "eld from Fig. 14a to 14c is theoretically and mathematically equivalent to adding circulation to the #ow "eld around the airfoil (the Joukowsky hypothesis [133]). The circulation required is the amount which is just su$cient to cause the streamlines that wet the airfoil to depart the airfoil at its sharp trailing edge as shown in Fig. 14c [134]. Di!erent amounts of lift are produced by changing the angle of attack of the airfoil relative to the free-stream velocity. An increase in lift is obtained, because more circulation is required on the airfoil to bring about a smooth departure of the streamlines at the sharp trailing edge of the airfoil. The #ow "eld of a wing is produced by placing airfoil sections side by side to form a three-dimensional lifting
surface of "nite size. If all of the airfoil sections are of the same size, a wing of rectangular planform is produced (Fig. 15). Trailing vortices could then be considered to begin at the wing surface. It is more convenient, however, to have the circulation symbolically continue through the wing from wingtip to wingtip (Fig. 15). At the wingtips, the vortices enter the air and are swept downstream behind the wing to form the trailing vortices. Similarly, the vortices far behind the wing are considered to be joined by a segment of the vortex passing across the wake between the two downstream ends of the trailing vortices that were generated when the aircraft lifted o! the runway (Fig. 15). In the same way, the two ends of the vortices are also joined by an across-stream vortex as the aircraft lands and reduces its wing lift to zero. After the vortices are generated, and as time passes, all of the vortex lines associated with the entire #ight of an aircraft mix with the surrounding air and di!use so that, after several minutes, air motions due to the vortices are usually indistinguishable from local winds and the turbulence they generate. As mentioned previously, one purpose of the wake-vortex research program is to "nd out how fast the vortices lose their identity, and how to accelerate the process. In Fig. 15 it is assumed that the lift on each airfoil section across the span of the wing is the same so that all of the circulation bound in the wing trails downstream from each wingtip. A constant lift across the span of the wing is, however, not possible. Since the span of the wing is "nite, the ends of the wing allow the high-pressure air on the bottom of the wing to #ow around the wingtips to the low-pressure region on the top (Fig. 16). As a consequence, the circulation bound to each airfoil section decreases from the centerline of the wing to the wingtips, where the lift vanishes. Rather than all of the circulation being trailed or shed only from the wingtips as shown
Fig. 14. Flow "eld around airfoil; Talay [134].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
525
or by Stokes' theorem [133]
C" (v dy#w dz), !
Fig. 15. Vortex pattern shed by wing with rectangular loading; Talay [134].
in Fig. 15, circulation is now shed all along the trailing edge of the wing. Also, the total lift on the wing is then a summation of the circulation bound to each of the airfoil sections. The lift may be written as an integration of the circulation bound in the wing along its span as
>@ C(y) dy. (1) \@ Since the lift varies across the span of the wing, and the bound circulation is shed all along the trailing edge of the wing, a vortex sheet is formed that begins at the wing trailing edge and extends downstream behind the wing. The local strength of the vortex sheet, c(y), is given by the gradient of the bound circulation as Lift"o;
dC(y) . c(y)" dy
(2)
As the distance behind the wing increases, the vortex sheet rolls up from the wingtips drawing more and more of the vortex sheet at inboard stations into the rolled-up vortex to form a pair of oppositely rotating trailing vortices. Since the circulation is shed in a sheet that extends over the span of the wing, it is then also distributed or spread over the cross-section of each trailing vortex. Circulation shed throughout a cross-section of the wake, rather than as a thin sheet at the trailing edge of the wing, is referred to as vorticity. The amount of vorticity, X, at a given point in the #uid is de"ned by the gradients in the velocity components at the point [9,133] de"ned by
(3)
where C is the path along which the integration is carried out, and that encloses the area A. The circulation, C, determined by Eq. (3) represents the total strength of all the vortex "laments that pass within the contour C. If the contour is made large enough to include the vortex sheets shed by both sides of the wing, the total circulation within the contour is zero, because equal amounts of positive and negative vorticity are included. The port and starboard vortex sheets are connected by across-stream vortices bound in the wing which produced lift. The circulation and the vorticity in a vortex are given a direction by use of the rule wherein the "ngers of the right hand are placed around the vortex, so that the "ngers point in the direction of swirl. The thumb then indicates the direction of the vorticity or circulation. In twodimensional or planar #ow, counter-clockwise (i.e., increasing meridian angle) swirl is denoted as positive circulation, and clockwise swirl as negative circulation. The foregoing illustrations become complex when the wakes of subsonic transports are considered. First, as stated previously, the lift on the wing is not constant between the wingtips, but varies continuously from a maximum near the centerline of the wing to zero at the wingtips (Fig. 16). Secondly, the wing con"guration during landing and takeo! is not necessarily simple in shape, but usually consists of a system of #aps, slats and ailerons (Fig. 17). The #aps are used to produce large values of lift at low angles of attack during low approach and departure velocities, and the slats to prevent #ow separation at the leading edge of the wing. Hence, circulation is shed or trailed in several sheets that are not necessarily adjacent, and that extend from the wing trailing edge downstream. Multiple vortex sheets form because the wing is not a #at continuous trailing edge, but rather one with partialspan #aps, that leave spanwise gaps for openings through which engine exhaust passes rearward for undisturbed
X";U where U is the local velocity vector. The circulation is found by integrating the vorticity over a chosen area, A, which is usually placed at a cross-section of a stream tube. Since the streamwise component of the vorticity and circulation are of most interest in the study of vortex wakes, the expression for the x-component is written as
C"
Rw Rv ! dy dz Ry Rx
Fig. 16. E!ect of "nite span on loading of wing; Talay [134].
526
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 17. Typical #ap and aileron assembly on wing; Talay [134].
thrust, i.e., exhaust gates (Fig. 17). When the wing has such a complex shape, #ow visualization (e.g., by use of smoke) makes the wake "rst appear to be composed of one or more continuous sheets that vary in strength, and contort to "t the wing trailing edge. A small distance behind the wing, the vortex sheet appears to be composed of several pairs of separate vortices (Fig. 18a). At larger distances behind the wing, the vortices usually blend or merge into a single vortex pair, and to stay that way (Fig. 18a and b). As the vorticity leaves the wing trailing edge, the swirling motion in the vortices smears and scrubs the distribution of vorticity, so that discontinuities in the shape of the vortex sheet, and in vortex strength across the span of the wing, are smoothed out into the "nal vortex structure. As the vortices age, the originally straight lines become distorted by low-velocity aircurrents to produce a sinuous shape in the vortices (Fig. 18). The experiments and analyses to be described use a coordinate system that places the uniform free stream in the positive #x direction, the horizontal direction across the airstream in the #y direction, and #z in the vertical direction. The wing is assumed to be centered on the x-axis and to be lifting in the #z direction. In general, the #uid in which the vortices are embedded is assumed to be incompressible.
4. Simple estimate for vortex-induced loads From the outset of the wake-vortex research program, a desire was often expressed for a relationship that would de"ne the maximum or worst-case value for the rolling moment induced on a following wing by a vortex of a given strength, i.e., circulation. The "rst part of that problem is simple, because the most hazardous vortex is one that has all of its circulation concentrated at its
center, i.e., a point vortex. All other vortex structures have smaller swirl velocities over some portion of their radius, which makes them less hazardous. A worst-case situation also requires that the encountering wing captures the most intense part of the vortex #ow "eld. This occurs when the vortex center and wing centerline are aligned. It remains then to derive an estimate for the worst-case rolling moment. Such a relationship has been found in closed form for the encounter of a #at wing of "nite span with a line vortex when the wing is moving in a direction parallel to the axis of the line vortex [135]. A line vortex is de"ned as a vortex structure wherein all of the circulation in the vortex is concentrated at its axis. In a two-dimensional #ow "eld, the cross-section of the vortex #ow "eld would then appear as a point vortex wherein the swirl velocity is given by v "C/2pr. The F solutions found are shown to yield realistic results for all types of interactions and to provide simple closed-form expressions for the various #ow "eld parameters. After the #ow "eld and its idealizations are described, the steps used to obtain a solution are presented along with several applications of the results. 4.1. Description of yow xeld The problem being considered here (Fig. 19) assumes that the axis of the vortex is aligned with the #ight direction of the encountering wing [135]. The vortex is assumed to have a circulation of C , and to be positive when it has counter-clockwise rotation from a pilot's viewpoint. The vortex is located at a distance r from the centerline of the wing at an elevation angle of h relative to the spanwise direction of the wing, where the subscript sv is used to denote quantities related to the vortex in the slit plane where the wing and its vortex wake appear as a slit looking upstream (Fig. 20). The surface that encounters the vortex is shown in Fig. 19 as a #at
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
527
Fig. 18. Photograph of oil vapor mist used to visualize rollup of vortex wake from wing of B-747 aircraft when landing #aps are deployed and landing gear stowed; Corsiglia et al. [61]. (a) First photo. (b) 20 s later.
rectangular wing for simplicity, but the analysis treats the wing as a lifting line and does not specify its shape. In the computation, it is assumed that the wake trailing from the lifting line remains as a #at sheet. The procedure used to obtain the solutions presented here is patterned after the transverse-#ow method described in Chapter V of Munk [136], wherein the #ow about the wake is con-
sidered as two-dimensional in order to determine the vorticity distribution in the wake. Munk used this method to derive elliptic loading as the most e$cient for a given span, and to analyze other lifting systems of "nite span. The shape of the wing needed to achieve the #ow"eld boundary conditions is not included in the analysis (e.g., Chapter II of Munk [136]).
528
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
these expressions when the signs of multiple-valued square roots had to be chosen. A very satisfactory scheme was then found by "rst squaring both Eqs. (5a) and (5b) and then combining the results in such a way as to eliminate the dependence on h . As a result, a quadratic equation was generated for the quantity, (r#a/r), as (r#a/r)!r(r#a/r)!2a(2a!y#z)"0. (6)
Fig. 19. Diagram of #ow "eld for encounter of wing with a nearby vortex [135].
Fig. 20. Mapping of slit in physical plane into a circle [135].
4.2. Analysis Since the wake shed by the encountering wing is assumed to remain as a #at sheet, the #ow "eld far downstream of the wing in a plane transverse to the #ight direction can be treated as two-dimensional. If the vortex wake is taken to be a slit of vanishingly small separation between the upper and lower surfaces (Fig. 20), it can be mapped from a circle into a slit by the function f "f #a/f
(4)
or y "y (1#a/r),
(5a)
z "z (1!a/r),
(5b)
where y "r cos h , z "r sin h , and r"y#z. Eqs. (5a) and (5b) are simple to apply when the mapping process goes from the circle to the slit plane. In the other direction, which happens to be the one necessary for the present analysis, the procedure is more complex. Several attempts were "rst made to invert Eqs. (4) and (5) directly, but they all resulted in unmanageable expressions which also became ambiguous when the mapping did not involve the "rst quadrant. Further di$culty also arose in
Solution of Eq. (6) for the quantity inside the parantheses yields another quadratic equation in terms of r which is again easily solved. The quantity r is then found by taking the square root obtained from the solution of the second quadratic equation. In each of these steps, the positive sign is chosen for the square root to be sure that r remains positive. After r has been found, h is found by use of Eqs. (5a) and (5b). In the computations for the mapping, a point on or just outside of the circle or slit is always taken slightly in excess of the circle radius (i.e., above or below the slit that represents the wake) to be certain that the point in question is mapped into the #ow "eld and not into the inside of the circle or slit. Since the #ow "eld is linear, the contributions of any number of vortices can be superimposed. For the present, however, consider a single vortex passing somewhere near a wing and its wake (Figs. 19 and 20). If the circle in the mapped plane is to be a boundary, an image vortex must be placed inside the circle at the same angle, h , as the impinging vortex and at the radius, r "a/r , from the center of the circle. An additional vortex of the same strength as the impinging vortex must be placed at the center of the circle, so that the net circulation inside the circle vanishes. Since both a positive and negative vortex are added to the #ow "eld inside the circle, the net circulation upstream and far downstream of the wing are both equal to the magnitude of the circulation in the impinging vortex. If a vortex had not been added at the center of the circle, the net or total circulation in the transverse #ow "eld far downstream of the wing would be zero. The complex potential for the cross-stream #ow "eld is then given by U"(iC/2p)ln[f (f !f )/(f !a/fM )], (7) where no tangency or Kutta condition is speci"ed at the edges of the wake. The solution given by Eq. (7) yields the potential and stream function when separated into real and imaginary parts. The velocity components are found by taking the complex derivative of Eq. (7). The velocity on the surface of the slit is then found from the circumferential velocity on the surface of the circle as v "(v sin h !w cos h )/2 sin h . The vorticity in the wake is found from
(8)
c (y )"v ) !v ) .
(9)
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Substitution of the various derived quantities into Eq. (9) yields the vorticity distribution for the wake in terms of the wing span, b , or the radius of the circle, a"b /4, and the location of the impinging vortex in the circle plane as
C c(y )" 4pa sin h
r !a 2! r #a!2ar cos(h !h ) r !a ! , (10) r #a!2ar cos(h #h ) where a position on the slit is related to a corresponding one on the circle by
y "2a cos h . (11) The span loading on the encountering or following wing is obtained by integration of the intensity of the vortex wake, c (y ), for the bound circulation, C(y ), or W C(y )"! c(y) dy \@ to yield
C C(y )"! p
(r #a) h !tan\ tan[(h !h )/2] (r !a) (r #a) !tan\ tan[(h #h )/2] . (12) (r !a) When Eq. (12) is used to compute the span loading, the arc tangents sometimes switch quadrants at improper values of the arguments. If the arc tangents do not make a smooth transition between quadrants, unwanted discontinuities and errors occur in the loading. This di$culty can be eliminated by combining the two arc tangent functions through the use of trignometric identities so that Eq. (12) becomes
C C(y )"! p
(r #a) sin h ; h !tan\ . (r #a)cos h !2ar cos h (13) Now that the circulation bound in the wing is known, the lift and torque induced on the wing by the vortex can also be found by integration of the equations,
¸"!o;
@
\@ @
C(y ) dy ,
(14a)
y C(y ) dy . (14b) \@ The integrations are carried out by "rst transforming them to the circle plane. Integration by parts is then used to conform the integrals to "t those listed in standard integral tables. By this technique, the coe$cients of lift M"!o;
529
and rolling moment induced on the following or encountering wing by a vortex are found as [135] C "!AR (C /b ; )(b /b )(a/r )cos h , (15) * C "(b /b )(a/r )cos 2h , (16) J where a positive value of lift is taken as upward. The rolling-moment coe$cient is taken as positive when the torque is in the same direction as the rotation direction of the impinging vortex. An equation for the drag due to lift that corresponds to Eqs. (15) and (16) was not derived, because the integrations were not obvious and an evaluation of drag is not needed as much as lift or rolling moment. Eqs. (15) and (16) are of value, because they indicate the dependence of the induced lift and rolling moment on the signi"cant parameters for an encounter; namely, the span ratio, aspect ratio, vortex strength, and the location of the vortex relative to the wing centerline. It should be noted that Eqs. (7)}(16) are given in terms of the location of the vortex in the circle plane even though the quantities represented apply to the slit or physical plane. Transformation back and forth between the two planes is relatively easy by use of Eqs. (5) and (6). The maximum values predicted by the transverse-#ow method for lift and rolling moment are given by setting r equal to a, the radius of the circle, and h equal to zero for the maximum lift, and equal to 903 for maximum rolling moment [135]: C ) "[AR ](C /b ; )(b /b ), (17a) * C ) "[AR /8](C /b ; )(b /b ). (17b) J The magnitude of the two maximums in Eqs. (17) are noted to be the same except for a factor of eight. The two formulas are quite accurate for small aspect ratios (i.e., less than one), but quickly become less accurate as aspect ratio increases above one. It has been pointed out by Jones [137] that the lift-curve slope for a wing of small aspect ratio is given by dC /da"pAR/2, and that, at * larger aspect ratios, more accuracy is obtained with another relationship given by dC /da"2pAR/(pAR#2), (18) * where the quantity AR is the aspect ratio of the wing, p is the ratio of the semi-perimeter of the wing to its span, and dC /da is the lift-curve slope of the encountering wing * (e.g., p. 95 of Jones [137]). It is therefore recommended that the quantity, 2dC /da/p be substituted for AR in* side the square brackets in both Eqs. (17a) and (17b). In Eq. (17a) for the lift, the functions in Eq. (18) are based on the full span of the following wing. However, in Eq. (17b) for the rolling-moment coe$cient, the functions in Eq. (18) should be based on half of the span of the following wing [135]. It is reasoned that the entire wing is in either an upwash or downwash for maximum lift, but when the
530
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
maximum rolling moment occurs, only half of the wing is in an upwash and half is in a downwash. The change in vertical velocity at the wing centerline is simulated in Eq. (18) by use of half of the following wing for evaluation of the various parameters it contains. 4.3. Comparison with other methods The solutions derived by use of Munk's transverse#ow method are now applied to several problems to illustrate the accuracy of the predictions by comparing them with the vortex-induced loads predicted by a vortex-lattice method on a #at wing of rectangular planform [135]. Since the shape of the wing is not speci"ed by the theory, there is some question as to how the results presented here should be tested. If the wing is cambered and/or twisted to redirect the rotary #ow of the impinging vortex, the results could be made to agree exactly, because the assumptions would be the same. However, a di!erent wing shape must then be used for each vortex strength and location. It seems best then to compare the present predictions on the basis of a #at wing of rectangular planform which does not "t any particular aircraft, but is representative of many wing shapes in use. The methods available to be used in the comparison range from quite simple strip-theory type analyses to fairly involved "nite-di!erence methods. Of these, the two methods to be used here are a modi"ed strip theory which incorporates features suggested by Munk [136], Jones [137] and Maskew [138], and a vortex-lattice method developed by Hough [139]. Both methods assume that the wake is not changing with time, and that the penetrating wing is "xed at some point in the wake so that the #ow "eld can be treated as steady state. The di!erences between these two prediction schemes for the maximum torque on a following wing were found to be small compared with the uncertainties usually experienced in obtaining test data. Since the span-load distribution predicted by strip theory is directly proportional to the local upwash without any redistribution of vorticity, it is not useful for comparison with the load or vorticity distributions. Hence, the modi"ed strip theory will be used only to derive equations for the lift and torque induced on the wing when the vortex is at its most e!ective or intense location for each quantity. The vortex-lattice method will be used to make more detailed comparisons. The "rst of the two quantities to be derived with the modi"ed strip theory is the lift induced on an encountering wing when the vortex impinges on the wing at a distance y from the wing centerline. Since the impinging vortex is a potential vortex, and has no core, the velocity distribution is given by v "C /2pr. F
(19)
Integration of the lift distribution when the vortex is in the z"0 plane yields C ) "[1/(1#3/AR )](C /b ; )(b /b ) * ;ln[(y !b /2)/(y #b /2)], (20) where the aspect ratio function inside the "rst set of brackets arises from the empirical correction for strip theory as suggested by Jones [137]. Similarly, the rolling moment induced by the vortex on the encountering wing is found by integration of the torque to yield C ) "[1/(1#6/AR )](C /b ; )(b /b ) J ;+1#0.5 ln[(y !b /2)/(y #b /2)],. (21a) The empirical aspect-ratio function derived by Jones, Eq. (18), di!ers slightly from quantities inside the brackets in Eqs. (20) and (21a), (21b) re#ecting the fact that the maximum torque location for the vortex puts half of the wing in an upwash and half in a downwash #ow "eld, making the e!ective aspect ratio half as large as when the vortex impinges at the wingtip [136]. Note that both Eqs. (20) and (21a) become in"nite when the vortex impinges on either wingtip, i.e., y "$b /2. This characteristic makes it di$cult to use these equations for #ow "elds that contain point or line vortices, because the answer may depend on the proximity of a vortex to a control point. Vortex-lattice methods present a similar di$culty whenever a point vortex falls on or too near a control point, and therefore are also not useful for #ow "elds that contain point vortices. When the vortex impinges on the wing centerline, the lift vanishes and the rolling-moment coe$cient takes on the "nite value [135] C ) "[1/(1#6/AR )](C /b ; )(b /b ). (21b) J It is to be noted that the strip-theory result, Eq. (21b), has the same form as predicted by the transverse-#ow theory, Eqs. (17a) and (17b), except for the aspect ratio function. It is for this reason that in each of these equations, the dependency on AR is indicated by square brackets to emphasize where the functional di!erence between various theories appears to be concentrated. Since the strip theory result for maximum rolling moment and vortexlattice theory have been found to be in good agreement with experiments [10], the results obtained with the transverse-#ow method need to be examined in more detail to "nd out how well they compare with the loads on #at wings of rectangular planform. The vortex-lattice method of Hough [139] makes possible an evaluation of the accuracy of the transverse-#ow predictions for the vortex-induced span loadings and the integrated parameters. Since the vortex-lattice method is a numerical procedure, the velocity distribution of the vortex must not contain in"nite values in case a control point inadvertently falls on or near the center of a vortex.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
531
Fig. 21. Variation of lift and rolling moment coe$cients with spanwise distance along a line just above the vortex center [135].
In order to cover such a possibility and still have a vortex structure that approximates a potential vortex, the vortex used in the comparisons was a Rankine vortex [9] with a small but "nite core of radius, r "0.001b (Fig. 21a). Even though a small core is speci"ed for the vortex, the vortex-lattice solution responds as if the core were as large as the distance to the control point nearest the center of the vortex. Such an approximation does not always a!ect the results signi"cantly, but may be responsible for some of the di!erences between the two predictions. The wing used for the vortex-lattice computation has a rectangular planform and has no twist or camber. As expected, all of the expressions derived for the wing}vortex interaction indicate a linear relationship with the dimensionless vortex strength. Such a relationship is expected in the absence of #ow separation or other #ow anomalies that lead to nonlinear characteristics. Such a well-behaved linear characteristic for the other parameters like the span ratio, b /b , and the aspect ratio of the following wing, AR , is not necessarily expected. Hence, these variations will now be investigated. The lift and rolling moment predicted by the transverse-#ow method, and the vortex-lattice method, are "rst compared in Fig. 21 as the wing is given locations along a line just above the horizontal axis of the vortex. As mentioned previously, the vortex used in the vortexlattice computation was given a core of radius, r "0.001b (Fig. 21a). Even with this precaution, un realistically large positive and negative values of lift and rolling moment occurred at locations along the y-axis
whenever the vortex center was too near a control point of a wing panel or lattice. For this reason, a dashed curve for the vortex-lattice prediction is not presented in Fig. 21 for y/b values between !0.05 and #0.05. Outside of this region, no portion of the wing is near the vortex center, so the vortex-lattice method does not have di$culty, and the two predictions are in good agreement. Of course, the closed-form expressions derived here have no di$culty with nearness to the center of a point vortex. The span ratio parameter, b /b , was chosen as the next part of Eqs. (15) and (16) to be studied, because all of the equations predict a linear dependence of lift and torque on it. The comparison in Fig. 22a indicates that the relationship is indeed not only linear, but the rolling moments are in very good agreement when the vortex center and the wing centerline are aligned. However, when the vortex impinges on the wingtip (Fig. 22b), the agreement is not as good even though the transverse-#ow and vortex-lattice methods both predict a linear relationship with b /b . The reason for the lack of agreement is not obvious, but as mentioned previously, may be caused by the dependence of the vortex-lattice method on the nearness of the control points to the vortex center. The "nite mesh size of the vortex-lattice method may also contribute to the di!erence but probably not signi"cantly. Next, the e!ect of aspect ratio on the lift and rolling moment predicted by the two methods are compared in Fig. 23. Once again, the quantities are evaluated at the
532
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 22. Variation of lift and rolling-moment coe$cients with the inverse of the span ratio as predicted by transverse-#ow and vortex-lattice methods [135]; C /b ; "0.1.
vortex locations that yield maximum values for each. As observed in Fig. 21, the lift has a maximum whenever a wingtip is at the vortex center. The magnitude of the rolling moment maximum predicted by the transverse#ow method is the same at the wingtips as at the wing centerline (Eq. (16)). The comparisons in Fig. 23 show that the linear relationship predicted by the transverse#ow method is not con"rmed by the vortex-lattice results. As anticipated by the assumptions made in the transverse-#ow theory, the two predictions are in agreement with one another at low values of AR . As AR increases however, the transverse-#ow method increas-
Fig. 23. Variation of lift and rolling-moment coe$cients with aspect ratio of following wing as predicted by transverse-#ow and vortex-lattice methods [135]; C /b ; , b /b "0.2.
ingly overpredicts the loading. Such a result points out that the encountering wing needs a large chord if, as assumed in the theory, the wing is to turn the rotary #ow "eld of the vortex so that it does not penetrate the wake. Hence, even though the theory of the transverse-#ow method did not specify the planform of the wing nor its twist and camber, it did require that the wing should be of a size and shape that would de#ect the rotating airstream around the wing. As indicated in Fig. 23, one possible design that accomplishes the #ow diversion is a wing with a large chord or small aspect ratio. According to the results of the comparison, the required amount
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
of turning is apparently provided by the #at rectangular wing used in the vortex-lattice examples when its aspect ratio is below about one. The transverse-#ow result can be corrected by the simple aspect-ratio function, Eq. (18), derived by Jones [137], but the results are not exact. Trial-and-error attempts were then used to develop a function of AR that would bring the two predictions into more precise agreement. A function that corrects for lift when the vortex is aligned with a wingtip is given by F (AR )"[1#0.5AR ] tan(0.6AR ). (22a) * A function that corrects the rolling moment prediction when the vortex is aligned with the wing centerline is given by F (AR )"[1#1.6AR ] tan(0.4AR ). (22b) J If Eqs. (22a) and (22b) are used instead of the simple AR parameter in Eqs. (17) and (18), the straight lines presented in Fig. 22 for the transverse-#ow method are converted into curved lines that lie within a line width of the vortex-lattice results. However, when Eqs. (22a) and (22b) were applied to other locations of the vortex relative to the wing to obtain the span loading, lift, and rolling moment, the agreement with vortex-lattice theory was not nearly as good. Some of the discrepancies may be due to failures of the vortex-lattice method to represent some aspects of the aerodynamic interaction process. When both predictive methods are applied in circumstances where their respective assumptions are not violated, the two results agree. In the cases considered, they agree well only when the aspect ratio is small. In order to further illustrate the character of the transverse-#ow results, the span loadings are compared with vortex-lattice results in Fig. 24 for AR "1.0 when the
533
vortex is aligned with the wing centerline and with the wingtip. Once again the vortex center is not near enough to a vortex-lattice control point to yield unrealistic results, but the loading may also not be accurately represented. Note that the agreement is quite good except for the lift magnitude when the vortex impinges on the wingtip. Such a di!erence is expected when the comparisons in Fig. 23 are examined at low values of AR . In general, it is recommended that the proper aspect ratio be used in the lift-curve slope function given by Eq. (18), and the discussion that follows it. 4.4. Applications Several examples of problems that can be treated by use of the results of the transverse-#ow method (Eqs. (15) and (16)) are now presented to illustrate applications. The author's primary interest was to have available a simple, quick means for the calculation of the contours of constant lift and torque for any system of point vortices; e.g., one that represents a lift-generated wake. In order to illustrate such a capability, the contours for a single or isolated vortex are "rst presented in Fig. 25. Such a computation is relatively simple, because they are known in closed form from Eqs. (15) and (16). In the case of two or more vortices, a predictor/corrector method is used to generate the contours. The contours for a pair of point vortices are presented in Fig. 26 for both lift and rolling moment in order to illustrate application to the simplest of lift-generated wakes. Obviously, the results in Figs. 25 and 26 are easily extended by superposition to any number and arrangement of point vortices, thereby providing the tools sought at the beginning of the investigation. In order to illustrate the technique and to check the accuracy of the
Fig. 24. Comparison of spanwise loading as predicted by the transverse-#ow and vortex-lattice methods [135]; C /b ; "0.1, b /b "0.5, AR "1.
534
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 25. Predictions by transverse-#ow method of the contours of equal lift and rolling-moment coe$cients as induced on a following wing by a point vortex [135].
Fig. 26. Predictions by transverse-#ow method of the contours of equal lift and rolling-moment coe$cients as induced on a following wing by a pair of point vortices [135]; b /b "1.
approximation of vortex structure by any number of point vortices, the structure of a Rankine vortex core is simulated with 19 point vortices (Fig. 27). Comparison is then made with the vortex-lattice method by assuming a continuous distribution of velocity in the vortex, so that the computation does not have di$culty. In order to indicate the accuracy of the point-vortex approximation, and of Eqs. (15) and (16), the two predictions are compared in Fig. 27 along a line through the center of the vortical region. Since the agreement is quite good, the example illustrates the e!ectiveness with which a system of point vortices can be used to represent a continuous distribution of vorticity. The wiggles in the transverse#ow prediction are small-scale versions of the #uctuations shown in Fig. 21 for a single vortex. As the number
of vortices used to simulate a given vortex structure increases, the amplitude and length of the wiggles decreases. Another example which illustrates the use of Eqs. (15) and (16) for estimating lift and torque throughout a vortex wake is presented in Fig. 28. A system of 40 point vortices is used to represent the lift-generated wake of an elliptically loaded wing. The contours of constant torque are presented at several time intervals or distances downstream of the wing trailing edge as noted in the "gure. The technique developed to produce Fig. 28 makes it possible to evaluate the wake hazard as a function of time for a wide variety of lifting con"gurations. In the cases studied so far, it was found that the maximum rolling moment induced on a following wing by a vortex system
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
535
Fig. 27. Lift and rolling moment on a wing as it traverses through a vortex with a core of radius r "b . Transverse-#ow method uses a system of point vortices to simulate the continuous distribution of vorticity in the Rankine vortex used in the vortex-lattice method [135]; C /b ; "0.1, b /b "0.5, AR "1.0.
Fig. 28. Contours of equal rolling-moment coe$cient at various instants of time as the wake shed by an elliptically-loaded wing rolls up [135]; C /b ; "0.1, b /b "0.5, AR "1.0.
536
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
does not change appreciably during the time history of the wake even though the contours change somewhat. This result is not expected to be true for all wakes, because the maximum value of the gradient in vertical velocity is not an invariant of vortex systems. It should also be noted that the maximum torque predicted is larger than any of those measured in wind tunnels for two reasons. First, viscous e!ects di!use the high energy concentrated in the vortex cores. Secondly, most of the wakes measured were shed by wings with slats and #aps that shed some turbulence which tends to di!use the cores of vortices and reduce the induced torque. In all of these examples, note that even though wiggles occur in the contours due to the "nite number of point vortices used in the simulation, the predicted torque always provides realistic values when the vortex impinges on any part of the encountering wing. This attribute makes the foregoing results usable in a wide variety of circumstances not possible with strip or vortex-lattice theories, unless special precautions are taken to avoid the proximity of vortex centers to control points. If the aspect ratio of the following wing is to be much greater than one, an empirical adjustment, such as Eq. (18), should be made to the results predicted by the transverse-#ow method to improve the quantitative accuracy of the method for aspect ratios much above one. These comparisons also add con"dence in the ability of vortex-lattice methods to properly represent rearrangement of the velocity and vorticity in the #ow "elds produced by the interaction of a wing with a vortex. The comparisons also demonstrate that the closed-form expressions derived by Munk's transverse #ow-"eld method are quantitatively very good at small aspect ratios. At higher aspect ratios, a correction factor like the one in Eq. (18) needs to be applied to the lift-curve slope for the shape and aspect ratio of the encountering wing to improve the accuracy of the predictions.
5. Span loading and vortex structure 5.1. Introduction A relationship between the span loading on the wakegenerating wing, and the structure of the vortices it sheds was "rst derived by Betz [140]. Although not utilized after its introduction until around 1970, it is one of the most signi"cant theoretical tools available for the understanding of wake-vortex generation, and for the design of experiments conducted in support of wake-vortex research programs. The importance and applicability of Betz' formulation was identi"ed and called to the attention of researchers by Donaldson and his associates as a part of the interpretation of #ight data, and of e!orts
to analytically and numerically treat the dynamics and decay of lift-generated vortex wakes [32,141,142]. Before the derivation of Betz' method is presented, the assumptions made and the process used to derive the equations are discussed. The vortex invariants for the time-dependent motion of two-dimensional (or point) vortex systems [9] are presented, because the invariants are needed in the derivation, and because they are useful for a wide variety of purposes that relate to the study of vortex systems. An overview will then be presented of extensions to the basic Betz method that have been made, and experiments conducted to determine the reliability of the method. Section 6 will describe how the simple Betz relationships can be used to design vortex wakes that are less hazardous. 5.2. Description of Betz' analysis Betz' method [140] relates the two-dimensional inviscid structure of the lift-generated vortex sheet shed at the trailing edge of a wing to the structure of the fully developed vortices far behind the wing. As such, the method does not concern itself with the time-dependent motion of the initially nearly #at vortex sheet shed at the trailing edge of a lifting wing as it rolls up into the fully developed axially symmetric vortices located far behind the wake-generating wing (Fig. 29). The analysis is treated as a two-dimensional one between an initial time and a "nal time. The assumption of axial-symmetry for the rolled-up vortices is approximately valid when the portion of the wing wake being analyzed is far enough in the spanwise direction from the opposite vortex, so that the "nal Tre!tz-plane streamlines do not deviate far from circular (Fig. 30a). The invariants for two-dimensional timedependent vortex systems are used to relate the radius at which a portion of the circulation in the vortex sheet at the trailing-edge of the wing is deposited in the fully developed vortex. In the strictest sense, the invariants require that all of the vortices or vorticity in the #ow "eld be included in its evaluation. The Betz method [140], however, and the analyses to follow, apply the invariants to only certain portions of the vortex system at a time. Justi"cation for such an assumption at the station far downstream from the wing is made by noting that the swirl velocity in an axially symmetric vortex depends only on the circulation contained within the radius where the velocity is being determined. Since the streamlines are then concentric circles, circulation outside of the radius does not in#uence the velocity which is given by v "C(r)/2pr, F
(23)
where C(r) is the circulation inside the circular streamline. As mentioned in the previous paragraph, much of the simplicity of the basic-Betz method results from the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
537
Fig. 29. Conceptual process used by Betz' method to derive equations for rollup of vortex sheet [147].
Fig. 30. Streamlines for the #ow"eld of point vortices designated by "lled symbols.
assumptions made in the analysis. First, the span loading at the wingtip being analyzed is assumed to be far from the vorticity being shed by the opposite side of the wing, so that the streamlines in the rolled-up vortex can be approximated by concentric circles (Fig. 30a). If the circulation and rolled-up vortex on the opposite side are included in the analysis, the streamlines would be o!set laterally as illustrated for two point vortices in Fig. 30b. The second equal and opposite vortex in the #ow "eld also causes the vortex pair to move downward due to the mutual induction of the velocity "eld of the two vortices. If this downward motion is included in the analysis,
the streamlines associated with the vortex pair, and the circulation distribution, are con"ned to a vortex oval (Fig. 30c) [9]. In Fig. 30b and c, the spanwise distance between the vortices is kept the same to illustrate the di!erences in the streamline arrangements. When the vortex pair moves downward, the streamlines are no longer perfect circles. Also, the approximate centers of rotation are o!set laterally, only a small amount and not by nearly the amount that takes place when the vortices are held in place (Fig. 30b). It is believed that a great deal of the success of the Betz method comes about because the
538
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
streamlines, although not perfect circles, are nearly circular and much more concentric in Fig. 30c than they are in Fig. 30b. Therefore, when a vortex sheet is rolled up, circulation associated with each streamline is distributed throughout a region of the #ow "eld enclosed by the oval. These complications are all assumed to be negligible in Betz' method, but should be kept in mind when applications are made to situations where unusual results occur. Since the in#uence of the opposite vortex fades linearly with the distance between the vortex centers, some sort of in#uence is present throughout the rollup. The in#uence is probably truly negligible only near the center of a vortex where high rotational velocities dominate. Another restrictive assumption in the basic Betz' method is that the vortex sheet shed by the wing rolls up in an orderly fashion from the wingtip inboard. In such a process, successive layers of the vortex sheet are wrapped around the center and previous wrappings of the vortex (Fig. 29). It is found from the study of experimental and idealized hypothetical span loadings that the vortex sheet shed by a wing usually does roll up from the wingtip inboard in an orderly fashion. If such an orderly rollup is to occur, not only must the span loading increase monotonically from the wingtip inboard, but the strength of the vortex sheet that it sheds must also have its maximum intensity at the wingtip and then decrease monotonically from the wingtip inboard [32,142}147]. Extensions to the basic Betz method that provide an approximate remedy for span loadings that violate this criterion will be discussed in a section to follow. 5.3. Invariants for motion of vortices The invariants for the time-dependent motion of twodimensional vortex systems relate a given function or state at a given time (i.e., at the wing trailing edge), to the state of the system at another time (i.e., at a station far behind the wing) [9]. In order to facilitate the analysis to follow, the invariants presented in various texts are now written for vortex sheets that are approximated by N point vortices whose strengths are given by, c , and locations by (y , z ). The equations are written as G G G [147]. Conservation of circulation: , C "C " c "constant. G G
(24)
Conservation of "rst moment of circulation: , y C " c y "constant, , G G G
(25a)
, z C " c z "constant. , G G G
(25b)
Conservation of second moment of circulation: , J " c [(y !y )#(z !z )]"constant. G G , G , G Conservation of angular moment of circulation: , M " c [(y !y )w !(z !z )v ] G G , G G , G G ,\ , c c " G H"constant. 2p G HG> Conservation of energy:
(26)
(27)
o ,\ , = "! c c ln[(y !y )#(z !z )] G H G H G H 4p G HG> "constant. (28) In Eqs. (24)}(28), and those to follow, the subscript s is used to denote quantities in the across-stream (or Tre!tz) plane located at the trailing edge of the wake-generating wing where the vortex sheet begins, and the circulation is spread out as a thin sheet. The subscript v is used to denote quantities at the Tre!tz plane located far downstream from the wing where the vortices in the wake are assumed to be fully rolled up into an axially symmetric vortex (Fig. 29). The subscript w is used to refer to the wing, and to quantities associated with the span loading. Eqs. (26) and (27) are written so that the centroid of circulation (y , z ) is used as the reference location on , , which the second moment and angular moment are computed in order to put the equations in the forms needed for the rollup analysis. The equations are still applicable even if another reference location is used. The spanwise and vertical velocity components in Eq. (27) for the ith vortex are given by 1 , v "! [c (z !z )]/[(y !y )#(z !z )], G G H G H G H G 2p H (29a) 1 , w "# [c (y !y )]/[(y !y )#(z !z )]. G G G H G H G H 2p H (29b) The function = for the energy in Eq. (28), which is often referred to as the Kirchho!}Routh path function, is sometimes written with a positive sign. The negative sign is correct, however, because it represents the variable portion of the kinetic-energy content (usually designated by ¹) of the #ow "eld. When the integration over the #ow "eld is carried out to determine the energy, the positive part is found to be a constant. The positive part is also found to become in"nitely large when the area of integration is expanded to include the core region of the point vortices and the region at very large radius.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Since the in"nite parts are constant with time, they are usually left out of any analysis of time-dependent vortex motions. Since an equation for the energy of a system of concentric vortex rings in the rolled-up vortex plane is not available, it is derived by integration of the equation for the kinetic energy of the #uid between the rings [147]. Since the fully developed vortex is assumed to be axially symmetric, the energy, ¹ , is given by o ¹" v2pr dr, (30) 2 F where the swirl velocity for (r (r(r ) is given by L\ L L\ c G. v " (31) FL 2pr G The integration for the energy in the #ow "eld goes from the radius of one vortex ring to the next (Fig. 31). Since the circulation from a given point vortex is spread over an annulus of zero thickness, no energy is contributed by the ring itself. Furthermore, it appears that no energy is expended by the process which distributes the circulation contained in the point vortex around the annulus. Since the "rst point vortex is deposited at the center of the rolled-up vortex at zero radius, the "rst integral in Eq. (30) is given by
o P c o dr" c[ln(r )!ln(r) ]. ¹ " (32) L 2 2pr P 4p In Eq. (32), the contribution to the energy by the term that goes to in"nity as rP0 is constant with time, and is therefore ignored. Similarly, the contribution to the
539
energy by the #uid outside of the radius of the outermost ring also goes to in"nity at the upper limit of integration. Once again, it is constant with time and is ignored. The symbol = (rather that ¹ ) is used to denote the time-invariant portion of the kinetic energy in the #ow "eld of the vortex sheet, because it does not contain the in"nite contributions to the invariant for energy. Similarly, the parameter = is used to denote the "nite quantities for the energy in the #ow "eld of the rolled-up vortex. The "nite and variable parts of the energy of the rolled-up vortex where the point vortices are deposited are then
o cln(r )#(c #c )ln(r /r ) = " 4p #(c #c #c )ln(r /r )#2 L\ L # c ln(r /r )! c ln(r ) . (33) G L L\ G L G G Eq. (33) is the axially symmetric version of the energy equation, Eq. (28), which is needed in discussions to follow for the development of rollup equations for vortex wakes. The foregoing equations apply to the invariants of the time-dependent motion of two-dimensional point vortices in an inviscid, incompressible #uid. The corresponding integral forms of the equations for vortex sheets are obtained by substituting
dC(s) c" ds, G ds
(34)
where s is the distance along the vortex sheet. The summation over the point vortices is then changed into an integration along the vortex sheet. 5.4. Rollup equations
Fig. 31. Idealized #ow "eld with point vortices spread over concentric annuluses to illustrate computation of energy in rolled-up plane [147].
In this section, the basic-Betz rollup method is derived by use of the "rst three invariants (i.e., Eqs. (24)}(26)) written in integral form as suggested by Eq. (34). The distance s along the vortex sheet is taken as y , because the vortex sheet is initially approximately #at so that its variation in height, z , is ignored. It is emphasized here that the vortex invariants strictly apply only when all of the circulation in the #ow "eld is included in the various summations. If such a requirement is strictly enforced, and the vortex invariants are applied to the vortex system as a whole, very little information is obtained, because Eqs. (24) and (26) vanish, and because the "ve summations usually contain a much larger number of unknowns than the "ve equations are able to ful"ll. Therefore, Betz' method achieves a solution for the rollup problem by specifying that the invariants be applied progressively to portions of the #ow "eld, so that the number of unknowns does not exceed the number of equations
540
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
available as each vortex-sheet element is incorporated into the rolled up vortex for a solution. For this purpose, the summation is made over only a portion, n (beginning with n"1) of the vortices (or segments of vortex sheets) in the #ow "eld rather than all of the segments as given by N. It is found that the results achieved by Betz' method are in good agreement with experiment, even though the invariants are applied to only certain portions of the vortex system at a time. Good results are achieved because the assumptions made, and the guidelines given by Betz [140], are approximately valid for the way that the invariants are applied. When the vortex invariants are applied to portions of the vortex system, it is noted in Eq. (24) that the portion of the vortex sheet that has been incorporated into the vortex by Betz' method is also equal to the circulation bound in the wing at that spanwise station (i.e., C (y )"C (y )), so that the two can be used interchange L L ably. The center of the rolled-up vortex is located at the centroid of circulation (y , z ). The conservation of circuL L lation as it is transferred from its location at y in the G vortex sheet behind the wing into the fully developed vortex far behind the wing is now written as
W dC(y ) G dy (35) G dy @ G where the integration begins at the wingtip and then proceeds inwardly to the point y successively, until the L centerline of the span loading is reached. The radius, r , G that encloses the circulation in the vortex is related to the corresponding spanwise station on the wing, y , by the G second moment of circulation written for the spanwise station on the wing as C (r)"C (y)"
W dc(y ) G [(y !y )#(z !z )] dy G G G G G dy @ G and at the rolled-up vortex as J(y)"
(36a)
W dc(r ) G r dr . (36b) dr G G @ G At each stage of the rollup, the second moment of circulation is conserved as each segment of vortex sheet is transferred to the rolled-up vortex which requires that J (r )"J (y ). If the second moments of circulation in the G G two planes are the same at each point on the span, the di!erence between two successive segments is also the same. As the number of vortex sheet segments or elements are added to the summation by stepwise increases in n, the incremental increase in the second moment becomes J(r)"
*J "J !J "c r L L L\ LL and,
(37a)
*J "J !J . L L L\
(37b)
Therefore, when increments in the second moment of circulation for the two planes are equated, *J "*J , L L the radius at which the circulation, c , from the nth vortex L is deposited is given by
1 r" , (38) (J !J ) L L L\ c L where the circulation contained in the nth vortex is spread over an annulus or ring of zero thickness at the radius r . The relationship between r and y that corresL L L ponds to Eq. (38) is then [145,147] r ""y (y )!y " L L L Eq. (39) may also be written as
(39)
(40)
v "C (r )/2pr . F L L
(41)
1 WL r "! C (y) dy. L C (y ) L @ The swirl velocity in the vortex is given by
5.5. Vortex-wake examples In order to gain an understanding of how the structure of the rolled-up vortex changes with variations in span-load distribution, a series of cases were calculated by use of Eqs. (39)}(41) [145]. The function used for the various span-load distributions on the wake-generating wing is C (>)/C "(1!>,)+, (42) where >"2y/b . The z"0 plane is de"ned as the hori zontal plane through the vortex sheet at the trailing edge of the wing, and/or center of the fully developed vortex. Fig. 32 presents the spanwise loading, circulation, and vertical velocity for the rolled-up vortex for several values of N and M, assuming that rollup begins at the wingtip as postulated in the original Betz theory. Instead of plotting C (r)/C and v as a function of R"2r/b , the F results are presented at their position on the >"2y/b axis to better illustrate their relative location spanwise to other vortices that may be in the wake. The curves for the velocity in these "gures and in those to follow, terminate at the edges of the region where vorticity is located so that the velocity distributions in the irrotational parts of the #ow "eld are not presented. 5.6. Vortex wakes with multiple pairs Before discussing extended-Betz methods, several simple examples are presented to indicate the complications that can arise when the vortex wakes of aircraft with #aps deployed are analyzed. The examples presented in Figs. 33}35 for three di!erent span loadings were chosen to illustrate the e!ect of span loading, or the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
541
Fig. 32. Examples of fully developed vortices that form behind various span loadings [145] represented by C (y)/C "[1!(2y/b ),]+, by assuming that vortices roll up from the wingtip. (a) N"2.0, M"0.5. (b) N"2.0, M"1.0. (c) N"1.0, M"1.0. (d) N"2.0, M"2.0. (e) N"0.5, M"1.0. (f) N"1.0, M"2.0.
vortex sheet strength, on sheet division and rolled-up structure of the "nal vortex wake. The method used to simulate the time-dependent motion of the vortex wake was introduced and demonstrated by Rosenhead [148] and Westwater [149]. (For more background information on the use of two-dimensional point vortices to represent vortex wakes, see the appendix of Ref. [148].) The method uses point vortices in the Tre!tz plane to represent the segments of the vortex sheet across the span. The velocity components of the various vortices are determined by the velocities induced by the other vortices in the #ow "eld. The displacement of each vortex is calculated by use of the average velocity between time steps, and then iterating for the "nal locations. The point vortices were not given a "nite core size as is often done to limit the motion of the vortices when they are close together [65]. The dimensionless
label with each of the plots for the three cases correspond roughly to 0, 5, and 10 spanlengths behind the wakegenerating wing. The axes have been shifted downward in all cases, so that the vortex locations remain in the "eld of view. Elliptic loading (C(y)/C "[1!(2y/b)] ) is chosen "rst to demonstrate how the vortex sheet rolls up from the wingtip inboard without sheet division (Fig. 33). In contrast, a vortex sheet of constant strength (as shed by an isolated triangularly loaded wingtip, (C(y)/C " 1!(2y/b)), rolls up from each end so that the vortex sheet is divided in half to form two vortices of equal strength, and structure (Fig. 34). (The port side of the wake is left blank to emphasize the one-sided character of the example.) It is to be noted in Fig. 34 that four point vortices in the center of the vortex sheet are represented by open rather than "lled symbols. From the movement
542
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 33. Time-dependent rollup of vortex sheet shed by elliptic loading; 26 point vortices on each side used in simulation [147].
of these four vortices, it becomes clear that, as expected, a single vortex sheet of constant strength divides at its center to form two equal vortices. If however, the vortex sheet is shed by an entire wing that is triangularly loaded, the inboard ends of the vortex sheets from the port and starboard sides of the wake are now adjacent and opposite in sign. The two sheets of constant and opposite strength now in#uence the division process, so that the two rolled-up vortices are not of equal magnitude or structure (Fig. 35). Rather, the in#uence of the vorticity on the opposite side of the centerline causes the division point of the two vortex sheets to be o!set, so that all four of the point vortices at the center of each sheet are incorporated into the outboard vortices, to form two vortex pairs of unequal strength. One guideline sometimes used for sheet division suggests that sheet division be chosen at those spanwise
Fig. 34. Time-dependent rollup of vortex sheet shed by isolated wingtip with triangular loading, i.e., vortex sheet of constant strength; 26 point vortices used in simulation [147].
locations where the up- or down-wash velocities vanish. Such a criteria is also inadequate, because such a guideline indicates that three rather than four point vortices join the outboard vortex, which is not what occurs. The results in Figs. 34 and 35 demonstrate that the rollup process does depend (sometimes weakly) on all of the vorticity in the #ow "eld. Approximate vortex structures can still be derived, however, if vortices outside of the rollup region do not signi"cantly in#uence the dynamics of the sheet motion, and certainly do not dominate it. The examples in Figs. 33}35 have a far simpler rollup process than the vortex sheets shed by wings with #aps deployed, and with wing mounted engines (e.g., Figs. 17 and 18). If the drag of the wing and its high-lift elements, and the thrust of the engines, are added to the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
543
vortices approach one other closely because the velocity is singular at the center of a point vortex. Nevertheless, point-vortex representations can provide useful insights and quantitative estimates if used properly. 5.7. Extended-Betz methods
Fig. 35. Time-dependent rollup of vortex sheet shed by triangular loading, i.e., two adjacent vortex sheets of constant and opposite strength; 26 point vortices on each side used in simulation [147].
self-induced convection of the circulation in the wake, the formation of the "nal con"guration of vortices is even more complicated, thereby requiring more extensions of the basic-Betz method than discussed here. It is also important to note that the use of point-vortex calculations to simulate the dynamics of vortex wakes is simple, convenient and representative of a number of characteristics of vortex wakes. However, the method does have faults. Firstly, the accumulation of vorticity or circulation into discreet locations prevents simulation of the stretching and spreading of the circulation in a vortex sheet over the spiral shape during the rollup process. It also does not include the slow asymptotic assimilation of the remote weak segments of the sheet into the "nal vortex structure. The point-vortex representation also sometimes yields unrealistic motions when two or more
The double-valued curve in Fig. 32e is a consequence of choosing the circulation shed at the wingtip as the rollup center. If Betz's method is modi"ed, or extended, so that rollup centers are based on the details of the span-load distribution (rather than always "xing it at the wingtip), more realistic vortex structures are found for more general span loadings. An attempt was made to "nd exact relationships for the locations of the starting points for the vortex centers, and for the points in the vortex sheets where circulation divides between two adjacent vortices, but the desired relationships were not found [147]. It was found that none of the vortex invariants, including the one for energy, produce any kind of indication as to when a rollup process is proceeding correct physically or not. It then becomes necessary to assume a roll-up sequence, as Betz did, or to determine the proper sequence by introduction of other mathematical techniques. It is possible, however, to identify some simple, approximate guidelines for these parameters that usually produce realistic vortex structures for complex vortex wakes [10,95,142,146]. The extensions applied by Donaldson et al. [142] and by Rossow [145,147] to the basic formulation of Betz [140] treat two aspects of the rollup procedure that were not considered in the original analysis. The "rst relates to the division of vortex sheets for rollup into multiple vortices on each side of the centerline. Once the vortex sheet has been properly divided, the second aspect concerns how, and in what sequence, the vorticity in the vortex sheet should be layered around the center of each rolled-up vortex in the wake. Guidelines presented in the foregoing references recommend that the vortex sheet be divided for separate vortices at locations where the initial vortex sheet ends, passes through zero (or has minimum strength), and/or where the self-induced vertical velocity passes through zero. The centers, about which each vortex begins its wrapping sequence of vorticity, are chosen at those locations where the vortex sheet ends, and/or where the sheet has a maximum strength. When the vortex center is located at the ends of a sheet segment, it forms a single spiral as it progresses from its originally nearly #at structure to the "nal axially symmetric fully developed vortex. When a vortex center is located somewhere in the middle of a vortex sheet segment, and not at an end, vorticity is incorporated into the rolled-up vortex from both sides of the chosen center; that is, the sheet rolls up as a double-layered spiral. For example, dc (y)/dy is in"nite at the wingtip for elliptic loading and c (y) is also in"nite there. For the
544
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
triangularly loaded case, the derivative dc (y)/dy is in" nite at both wingtips and at midspan, because c (y) is discontinuous there. In Figs. 32e and f, the strength of the inboard or wing root portion of the vortex sheet is a maximum and the vortex strength would, in fact, be discontinuous across the junction of the left and right wings, so that rollup is estimated to begin at center span rather than at the wingtip in both of those cases. The parabolic and contoured loadings shown in Figs. 32b and d have their maximum values of c (y), respectively, at the tip and about halfway out to the wingtip. As already mentioned for parabolic loading, the wingtip is chosen as the rollup site, because c (y) is discontinuous there, being "nite for y4b/2 and zero for y5b/2. If two or more vortices are produced on each side of the wing, the vortex sheet is divided into rollup segments at those places where c (y), or its derivative, is zero. For example, in triangular loading, the sheet is divided at y"b/4, so that the two vortices are of equal strength. The computations presented in Figs. 33}35 show that such an estimate is not exact. In order to perform the calculations for vortices originating at several places along the semispan, Eq. (40) is rewritten so that rollup begins at the estimated rollup site, y"y , as
1 WL r" [C (y)!C (y )]dy . L C (y )!C (y ) L W
(43)
If the rollup site occurs at the midpoint of the sheet, Eq. (43) is applied to the two segments of the sheet separately, and the two resulting curves for C (r ) are added. That is, L it is assumed that the two parts of the sheet roll up within
one another without interacting. The "nal variation of C (r )"[C (r )" !C (r )" ] is then used in Eq. (41) L L L for the determination of the swirl velocity in the vortices. The center of the vortex is, of course, located at the centroid of the segment. Fig. 36 shows the application of these techniques to the four cases that do not have the entire rollup beginning at the wingtip. An interesting and convincing application of the rollup rules for the extended-Betz method was made by Corsiglia and Orlo! [95] by use of a scanning laser velocimeter to survey the wake 1.5 spans behind a 0.03 scale model of a B-747 in a wind tunnel. The comparisons made in Figs. 37 and 38 indicate quite good agreement of the predicted vortex strengths with those measured in the wind tunnel. The modi"ed or adjusted span loadings were made as an approximation to the loss of lift to be expected, due to #ow separation on the various lifting elements, and to account for the fact that the vortexlattice calculation did not account for the presence of the fuselage on the aircraft model. The adjustments made to the vortex-lattice solution and to the span loadings indicate that judgements are required if the simple technique introduced by Betz is to be used successfully [95]. It must also be recognized that the vortex cores identi"ed by Corsiglia and Orlo! a short distance behind the wakegenerating model will merge with one another as the wake ages to form a single vortex pair.
5.8. Inverse-Betz method As experimental data began to accummulate for the velocity distributions in vortex wakes, a need arose for
Fig. 36. Examples of fully developed vortices for the same span loadings presented in Fig. 32c}f, but with rollup beginning points determined by rules for multiple vortex wakes [145]. (a) N"1.0, M"1.0. (b) N"2.0, M"2.0. (c) N"0.5, M"1.0. (d) N"1.0, M"2.0.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
545
a theoretical relationship that would make it possible to go from the measured velocities back to the span loading that generated the wake. One need for such a relationship is the desirability to go backwards to "nd out how turbulent and viscous e!ects modi"y vortices as they age, and also to "nd out how vortex mixing modi"es vortices in the near term of their history. Such a reverse or inverse method adapted from the original Betz method has been labeled the inverse-Betz method [146]. Naturally, the inverse method is based on the same assumptions as the direct- or basic-Betz method. The derivation begins with the expression that relates the radius, r , in the L vortex to the spanwise station on the wing, y , where the L increment in circulation is "rst deposited in the vortex sheet shed by the wing. From Eq. (40), the relationship between r and y for the starboard or right wing may be L L written as
Fig. 37. Comparison of maximum vortex circulation from vortex-lattice theory and the axisymmetric model for the measured velocities; B-747 (303, 03) con"guration with gear stowed; Corsiglia et al. [95].
1 WL r "! C (y) dy. L C (y ) L @ Since the circulation in the vortex, C (r ) contained L within the radius r is equal to that shed by the wing L between its tip at b/2 and the element of circulation at y being transferred, the conservation of circulation L yields C (r )"C (y ). Eq. (21a), (21b) can then be L L written as
d WL d [r C (r )]" C (y) dy dr L L dr L L @ dy "!C (y ) L L dr L so that dy r dC (r ) L. ! L"1# L dr C (r ) dr L L L On integration from the wingtip inboard, one form of the inverse-Betz relationship between y and r is given L L by
PL r dC (r) b dr. !y "r # L L C (r) dr 2
(44)
A simpler form of Eq. (44) is obtained by writing the circulation as C (r )"2pr v , so that, in terms of L L F measured quantities,
Fig. 38. Comparison of maximum vortex circulation from vortex-lattice theory and the axisymmetric model for the measured velocities; B-747 (303, 303) con"guration with gear stowed; Corsiglia et al. [95].
b PL d(rv ) F. !y "r # L L 2 v F
(45)
Application of both the basic- and inverse-Betz methods will be presented in a section to follow on experimental veri"cation.
546
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
5.9. Region of applicability The simplicity of both the direct- and the inverserollup methods results from the assumptions that the vortex is completely rolled up, and that the rollup process is inviscid and orderly. These two assumptions then limit the downstream interval over which the theories apply. The upstream end of the region of applicability begins where the rollup of the vortex sheet is largely completed, and can be estimated by use of inviscid, timedependent rollup calculations. Results such as those presented in Figs. 18 and 33 for the numerical estimates of the time required for a major part of the rollup process to be completed indicate that a major part of the rollup process behind many wings can be considered as practically complete within three to "ve span lengths behind the generating wing. The e!ect of viscosity and turbulence on the core of the vortex has recently been added as another extension of the Betz method [150]. Their method appears to be able to account for some of the di!erences between the basic Betz method and experiment in the core region of the vortices. The downstream end of the region of applicability is the distance at which viscous and turbulent decay of the vortex has modi"ed its structure to the extent that the inviscid theory no longer approximates it. An estimate for this limit can be obtained from the data of Ci!one and Orlo! [91] wherein a so-called plateau region is identi"ed (Fig. 2). Within this plateau region, they found that the vortex maximum swirl velocity decays very little, but is followed by a region where the vortex decays roughly as t\ . Based on these considerations, the region of applicability of the Betz method lies between about three span lengths and the downstream end of the plateau region for simple span-load distributions. If the span loading is complicated enough that multiple vortex pairs are shed, and that persist into the far "eld, the Betz methods do not, of course, apply with a great deal of accuracy.
6. Design of non-hazardous vortex wakes 6.1. Introduction It was reasoned that, since Betz' method [140] made a direct theoretical relationship between the span loading on the wake and the vortex wake that it sheds, it may be possible to design the span loading, so that the vortex wake of the wing is non-hazardous. In such an endeavor, it is assumed that a span loading will produce a vortex con"guration that is non-hazardous, and that is stable to three-dimensional disturbances even though it is derived by use of a two-dimensional/Tre!tz-plane method. A di$culty then arises in that the de"nition of a nonhazardous wake is not a straight-forward process.
Since clearly de"ned guidelines were not available nor identi"ed, it was assumed that the span loading should be such that the vortex wake that it sheds should simply not roll up, but maintain its shape until some outside disturbance causes the wake organization to be disrupted and possibly to decompose and decay quickly [151]. 6.2. Hypothetical non-hazardous wake conxgurations Two wake con"gurations were designed by use of the non-rollup criterion [151]. The "rst vortex wake design was produced by specifying that the initial vortex system shed by each wingtip should rotate as a solid body or sheet (Fig. 39a). The resulting span loading is very similar to those designed by Jones [152] to have a minimum induced drag for a given span and wing-root bending moment. In fact, Jones' designs initially rotate more closely to a solid sheet than the design selected here, but both rotational motions break down rather quickly due to in#uence of the rest of the wake, and due to the plane of the rotating sheets moving out of the original design plane. Since the span loading was tailored to produce a vortex wake with certain characteristics, any span loading of this type is referred as `tailored loadinga. The second hypothetical wake-vortex con"guration [151], designed by the foregoing method, assumed that all of the vortex elements would translate downward at the same velocity (Fig. 39b). At "rst, it seemed that the resulting span loading should be elliptic. Further consideration indicated that the vortex sheet shed by elliptic loading does move downward at the same velocity everywhere except for the two wingtip vortices, which move upward to start the rollup process. Therefore, another solution is found for the case where all vortices (including the ones at the wingtips) translate downward at the same velocity. When the matrix for the vortex strengths is inverted, it is found that the wake consists of vortices whose strengths alternate in sign, and whose magnitudes oscillate about elliptic loading (Fig. 39b). The span loading that sheds a vortex wake that translates downward as a unit then consists of a square-shaped sawtooth superimposed on top of an elliptically-shaped loading (Fig. 39b). If a large number of point vortices is used to represent the wake, the oscillations in magnitude are smaller than if a small number of vortices is used, but the oscillations appear to persist inde"nitely. Any span loading with large spanwise oscillations in its loading is referred to as `sawtooth loadinga. 6.2.1. Tailored loading The time-dependent characteristics of the foregoing two wakes were "rst studied by approximating the three-dimensional dynamic problem with the two-dimensional time-dependent motion of point-vortices in the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
547
Fig. 39. Two span-load distributions designed so that their vortex wakes do not roll up in the conventional sense but stay in approximately the same shape as when shed [151]. (a) Tailored loading. (b) Sawtooth loading.
Tre!tz plane [133]. It is assumed that the wake is initially a #at sheet as it leaves the trailing edge of the wing. The time-dependent motions of the vortices are then assumed to move as if they are in a two-dimensional system where small-scale three-dimensional distortions in the vortex con"gurations are suppressed. In order to provide an illustration of the method with a familiar span loading, the technique is presented in Fig. 40 for elliptic span loading, which may be considered an extension of the
results presented in Fig. 33. The shapes of the vortex lines are determined by connecting the locations of the vortices at each time step wherein time and distance behind the wake-generating wing are assumed to be equivalent, as the Tre!tz plane moves downstream with the free-stream velocity. It is noted in Fig. 40 that the wake rolls up from the wingtips inboard to form a pair of counter-rotating vortices typical of most wings that have conventional span loadings.
Fig. 40. Point-vortex simulation in Tre!tz plane of wake structure by elliptically loaded wing [151]. (a) Span load and vortex velocity distributions. (b) Wake structure.
548
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Since the strengths of the point vortices used to represent the rotating array are all of the same sign, a span loading for a wing is designed by use of an array for each wingtip (Fig. 41a). The space allowed between the two arrays is arbitrary and allows a uniform loading over the center part of the wing where the fuselage is located. The ratio of the parts of the wing designed to rotate to the total span of the wing is considered as the amount tailored. For example, the span loading Fig. 41a is tailored over 0.9 or 90% of its span, thereby making it approximately triangular. Since the arrays were designed to rotate when they were isolated from the rest of the wing, the calculations were carried out to obtain a more realistic estimate for the wake dynamics that might occur in an experiment. The initial downward velocity of the vortex arrays that represent the vortex wake are also shown in Fig. 41a. As shown in Fig. 41b, the rotation of the two vortex sheets persists in its idealized form for a rotation of about 903 before the sheets break up into parts that rollup separately. If the initial conditions for pure rotation are disturbed by displacing a point vortex in the vertical direction, the orderly part of the rotation is a!ected sooner, but the wake structure at later times does not appear qualitatively to be much di!erent from that shown in Fig. 41b. If the gap between the two rotating arrays is increased from 10% of the span to a larger value, the arrays rotate more independently; however, the vorticity is then spread over a smaller part of the span, resulting in a concentration of shed vorticity and a more intense wake. Note in Fig. 41a that the centerline circulation of tailored loadings must be increased above that required for an elliptically loaded wing of the same span in order to have the two wings carry the same lift. Any such increase adds to the hazard posed by the wake
which must also be overcome by any alleviation developed by the tailored design. If the number of point vortices used to represent the rotating array is allowed to increase inde"nitely, the circulation distribution in the wake becomes continuous and is given by dC(y) 4C c(y)"! "$ [1!(2y/b)] , dy pb
(46a)
where C is the centerline circulation required for a given lift. The bound circulation in the wing is then C C(y)"C(!b/2)#$ (2y/b)[1!(2y/b)] p ;sin\(2y/b)#p/2].
(46b)
By use of the extended-Betz method, the radius in the vortex where a sheet segment is deposited is given by 2r/b">!2C [(1!>) !1]/[3p[C(>)!C(0)]], (46c) where >"4[y]/b¹ , and ¹ is the fraction of the wing that is tailored. The circulation C (r) contained in the vortex at radius r is then C (r)"2C (y) (46d) because the vortex sheet rolls up about its center rather than from an end [151]. The center of a vortex on each side of the wing is located at the centroid of the circulation in the tailored loading on the wing which is at the center of each rotating sheet. The circumferential velocity in the vortices is again given by v "C (r)/2pr. F
Fig. 41. Span loading tailored so that vortex wake shed by each wingtip rotates as a rigid sheet [151]; corresponds to span loading for minimum wing-root bending moments [152]. (a) Span load and vortex velocity distributions. (b) Wake structure.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
In an e!ort to obtain an estimate for how accurately Betz's extended method predicts the rollup of the wake, a comparison is made of the circulation distributions in various vortices. For reference, the Betz distributions for rectangular and elliptic loadings are presented as dashed lines in Fig. 42. The circulation distribution in the rolledup vortex for 90% tailored loading as predicted by the extended-Betz method is shown as a solid line (Eqs. (46a)}(46d)). The stepped curve for the radial distribution of circulation as predicted by the Tre!tz-plane simulation at the dimensionless time equal to 3, was determined from the numerical data by increasing the circulation from zero at the centroid as each point vortex is passed while the radius increases. The radial distance of each point vortex from the centroid of circulation is used as the abscissa at which the circulation takes a stepwise increase. The Tre!tz-plane and extended-Betz methods are noted to be in good agreement; no doubt, somewhat because the span loading is not complicated. 6.2.2. Sawtooth loading The point vortices in a vortex wake that has been designed to translate downward as a unit, alternate in sign across the span (Fig. 43). If the circulation in the vortices across the span are added together, they sum to zero circulation. A single array can therefore be used to represent the entire wake of a lifting wing. When the vortex distribution is integrated across the span to determine the bound circulation (or span loading) on the wing, the discontinuous or stepped curve shown in Fig. 43a is obtained. Such a loading could be interpreted as an approximation to the loading achieved by de#ecting
549
Fig. 42. Radial distribution of circulation in wake vortices shed by 90% tailored loading as predicted by time-depending Tre!tz-plane method and by extended-Betz rollup theory [151].
a large number of #aps upward and downward across the span of the wing. As expected, the speci"ed downward motion of the vortices in the array is achieved when the time-dependent calculations are carried out, i.e., the "rst part of Fig. 43b. If, however, the initial condition of one or more of the vortices is disturbed (e.g., by displacing the "fth vortex vertically a small amount), the speci"ed motion breaks down quickly into the chaotic motion shown in the latter part of Fig. 43b. The unequal strengths of the vortices cause the various pairs of vortices in the wake to orbit in a seemingly random motion to promote mixing in the
Fig. 43. Span loading designed so that vortex wake shed by each wingtip initially moves downward as a rigid sheet [151]. (a) Span load and vortex velocity distributions. (b) Wake structure.
550
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
wake on a large scale. Mixing of this kind suggests rapid dispersion of the circulation throughout the wake so that the entire wake would tend to be neutralized quickly in a real #uid. It was also found that smaller amounts of sawtooth loading could be added to conventional loadings to also theoretically induce large mixing motions of vortices in the wake. The foregoing idealized concepts served as a basis for the experimental program by suggesting span loadings for vortex wakes that were either less hazardous at the outset or that would become less hazardous more quickly than conventional designs. The next section will discuss some experimental results designed to test some of the conceptual relationships identi"ed between span loading on the wing and the vortex wake that it sheds. 6.3. Experimental verixcation In 1972, the wake-vortex research program began conducting wake-vortex experiments in wind tunnels [10,60}63,87,88,95,96,153,154], in water tow tanks [61,89}93,96,102,155}158] and in #ight [4,11}21,44}48, 50,55,58,59,119,159,160]. The material to be presented in this section is devoted to experiments designed to investigate tailored and sawtooth type span loadings [58}61,90}93,95,112,125,159,160] to determine their effectiveness for the reduction of the hazard posed by vortex wakes. 6.3.1. Ground-based experiments Wind tunnel tests in the 40;80 ft (12.2 m;24.4 m) Wind Tunnel at NASA Ames were carried out to study the characteristics of vortex wakes shed by lifting wings of conventional and of special design [10]. The test setups used to measure the velocity distribution in the vortex, and to measure the rolling moment on a following wing are illustrated in Figs. 44a and b. Both experimental setups generated the vortex wake to be studied by use of a swept wing whose planform was typical of those used on subsonic transports and that had seven #aps on each side of the centerline which could be adjusted in 53 increments (Fig. 45). The large number of #aps allowed the span loading on the wing to be changed from a cruise condition, when all of the #aps are in a stowed, or non-de#ected, position, to those typical of landing, parabolic, and the two unconventional ones described previously and labeled tailored and sawtooth loadings; see table in Fig. 45. The span loadings estimated by means of vortex-lattice theory [139] for the various wing con"gurations at an angle of attack of 83 are presented in Fig. 46. The symbols denote points calculated by the vortex-lattice method. At a distance of 80 ft (24.4 m) downstream of the wakegenerating wing, either a hot-"lm apparatus (Fig. 44a, inset) or a following wing (Fig. 44b, inset) was mounted on a tower that could be positioned horizontally over
a 14 ft (4.27 m) range. In addition, the follower wing could be positioned vertically over a 10 ft (3 m) range. The only encounter direction studied with the setup shown in Fig. 44b was an axial penetration by the following wing set at zero incidence. Most of the tests were conducted at a free-stream velocity of ; "131 ft/s (40 m/s), (q "20.1 lb/ft) corresponding to a Reynolds number of 843,000 based on average wing chord. Several di!erent values of free-stream velocity were used during the rolling-moment tests to obtain moments of a magnitude such that the optimum sensitivity of the balance could be used. 6.3.2. Swirl velocity As shown in Fig. 44a, the hot-wire probe is mounted at the end of a rotating arm of about 7.34 ft (2.24 m) that rotated at 120 rpm, which was rapid enough, so that, in the wind tunnel, the circumferential velocity of the probe dominated the meander velocity of the vortex. Vortex meander comes about because the free-stream velocity in the wind tunnel is not perfectly uniform, since it contains turbulent eddies of di!erent sizes [161,162]. In the 40;80 ft Wind Tunnel, the vortex meanders over a circle of about 2 in (5 cm) radius at a distance of 80 ft (24.4 m) behind the wake-generating wing (Fig. 47). As a consequence, local lateral velocities in the eddies convect the wake vortices sideways and vertically thereby generating a sinuous shape to the centerline of each of the vortices. Therefore, as the vortex lines are swept downstream by the free-stream velocity, the location of the vortices at a given downstream station meanders randomly about its time-averaged location (Fig. 47). If a stationary probe is located near the center of the meander region, the instantaneous measurement changes from a maximum to zero swirl velocity in a fraction of a second due to the meander of the vortex. An air jet used to calibrate the hot-wire probe is located at the bottom of the arc of the rotating arm, so that a calibration signal is generated on each revolution. It was found that the instrumentation was di$cult to keep properly tuned and the measurements required extensive data reduction techniques [10]. It was concluded that the rotating-arm technique is an e!ective but clumsy method for measuring the instantaneous structure of vortex wakes. The test procedure consisted of moving the tower that supports the rotor arm assembly across the wind tunnel until, as noted on a paper-chart recorder, a maximum occurred in the number of times that the hot-wire probe had encounters with the vortex per unit time. A permanent record of 5 min duration was then made on magnetic tape and paper chart. The data runs for analysis were taken from the magnetic tape, so that the record could be ampli"ed enough to obtain 3}4 signi"cant "gures of accuracy. Five records out of the large number taken during the 5 min were then chosen for analysis on the basis of how close to a vortex
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
551
Fig. 44. Experimental setups in 40;80 ft Wind Tunnel used to make measurements in vortex wake of swept wing model [10]. (a) Three components of velocity. (b) Rolling moment.
center that the hot-wire probe had passed. After the three components of velocity had been determined for the various runs, the motion of the hot-wire probe and the velocity of the vortex center relative to the wind tunnel coordinate system were removed from the hot-wire measurements in order to arrive at a
corrected measurement of the structure of the vortex wake. Since both processes could only be done approximately, the accuracy of the measurements was limited. In order to develop a vortex structure usable for analysis in the various Betz methods, it was also necessary to
552
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 45. Plan view of swept wing used to generate vortex wakes along with #ap settings for various con"gurations [10].
Fig. 46. Span-load distributions on various con"gurations of swept-wing model as predicted by vortex-lattice method [10]; a "83.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 47. Illustration of vortex meander at a given downstream station.
remove the in#uence of the opposite vortex in the pair, whose location is uncertain. Fig. 48 presents the "nal structure of a typical measurement along a curved path that had passed through or near a vortex center. The velocity "eld of the opposite vortex in the pair has been removed, so that the curves shown in Fig. 48 represent the structure of an isolated vortex. It is noted that the measured streamwise component of the velocity di!ers from the free-stream velocity only in the vortex core region and then, by less than 10%. Five such sets of data from "ve di!erent passes of the rotor arm through the vortex wake of the con"guration being tested were then averaged to obtain a representative velocity distribution for the vortex trailed by a particular con"guration of the wake-generating wing (Fig. 49). The data for the various con"gurations has been normalized (divided) by the free-stream velocity and the measured lift coe$cient on the generating wing to remove lift as a variable in the comparisons. It is noted in Fig. 49 that the maximum circumferential velocity, and the radius at which it occurs (i.e., the core radius of the vortex) are di!erent between the various con"gurations tested. As expected, the vortex with the largest core was produced by the swept wing with the #aps de#ected to produce a type of tailored loading. An averaged curve for the swirl velocity shed by the sawtooth loading is not presented, because each pass of the hot-wire probe through the wake yielded a di!erent velocity pro"le with several possible vortex centers. It is believed that the wake consisted of about seven vortex pairs so that a pro"le for the swirl velocity could not be correctly represented by a single vortex pair. Since the data in Fig. 49 for the swirl velocity has had the contribution of the companion vortex removed, the
553
Fig. 48. Example of variation of radial and circumferential velocity components with radius [10]; wing planform tailored 40%, a "123, C "0.85. *
results can be compared with estimates of vortex structure obtained by use of the basic-Betz rollup theory and the computed vortex-lattice solutions obtained for the span loading on the wake-generating wings from Fig. 46. When the measured and Betz-predicted circumferential velocity distributions are compared, the agreement is quite good in the outer parts of the vortex (Fig. 50). The di!erences that often occur near the vortex center are attributed to the choice of how the vortex sheet shed by the wing was assumed to roll up. If a di!erent rollup sequence had been assumed, the agreement could sometimes be improved. For example, in the case of the landing con"guration, the theory should assume that two vortices instead of one formed initially. Two vortices did form near the wing, but the #ow visualization with smoke indicated that these two merged before they reached the measuring station in the wind tunnel. The Betz theory used to predict the vortex structure in Fig. 50 does not account for vortex merging. Also, the method does not account for the boundary layer on the wing that enters the core region near the center of the vortex. The comparison indicates that the direct-rollup theory is adequate for many purposes, because the predictions are quite accurate for the outer part of the vortex, even though they are not always reliable near the center. 6.3.3. Span loading The span loadings predicted by vortex-lattice theory are compared in Fig. 51 with those predicted by the inverse-Betz theory using the measured swirl-velocity distributions. These comparisons were made by adjusting the span loading calculated by the vortex-lattice theory, so that the area under span loading curve is the same as that predicted by the inverse-Betz method. The results
554
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 49. Radial distribution of circumferential velocity as measured in wind tunnel for various con"gurations [10].
Fig. 50. Comparison of measured circumferential velocity in vortices with that predicted by the direct-Betz rollup method [10] using theoretical span-loadings presented in Fig. 46.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
555
Fig. 51. Comparison of span loading predicted by vortex-lattice theory with that predicted by the inverse-rollup theory [10] using measured vortex structures in Fig. 49.
in Fig. 51 show that the inverse theory can recover the span loading on the generating wing fairly accurately. With almost all con"gurations, a di!erence occurs near the wing tip as a result of the "nite core size of the vortex and the solid-body type rotation near r"0 due to the boundary layer on the wing. The magnitude of the distortion in span loading depends on the size of the core, which is in#uenced by the character of the boundary layer on the wing and on the viscous and turbulent shear forces in the vortex itself. In most cases, these distortions appear to be small and to occur largely in the vicinity of the wing tip. The agreement between theory and experiment found for the inverse-Betz method is better, in some cases, than for the direct-Betz method. It is believed that this is caused by the di!erence in the integration process, which tends to suppress inaccuracies for small radii for the inverse-Betz, and to amplify them in the direct-Betz. This di!erence occurs because the integral for the inverse-Betz method, Eq. (45), contains the radius in the numerator, which tends to suppress inaccuracies near the center of the vortex. The equation used for the direct-Betz method, however, Eq. (40), has small values of radius (or C (y)) in the vicinity of the wingtip or vortex center. Therefore, in the direct-Betz, inaccuracies are suppressed at large radii. Examination of the #ow visualization results obtained in the wake shed by a wing designed for sawtooth span loading indicates that the same instability and vortex linking occurs there also. The wake dynamics was most apparent in experiments conducted by Ci!one [91}93] in a water tow tank with a generic wing of 2 ft (61 cm) span with seven #ap segments on each side, i.e., a scaled down version of the wing used in the wind tunnel (Fig. 45). In one case, the #aps were de#ected alternately up and down across the span in order to generate sawtooth loading. It was found that, shortly behind the wing, the vortices formed pairs that executed large across-stream
excursions that "nally led to linking and loop formation, much like some of those shown in Fig. 43b. When a wing with the same shape was tested in the 40;80 ft Wind Tunnel, it was found that the torque on a following wing was much reduced until the lift on the wing became large enough to dominate all of the subvortices from the de#ected #aps. These results indicate that large #ap de#ections are required for large amounts of alleviation at lift coe$cients of interest for landing and takeo!. Hence, such an alleviation scheme becomes unwieldy and ine$cient if the landing #aps are not used judiciously to generate the vortices of opposite sign. When the vortex pairs are of comparable strength, they interact to bring about large excursions and loop formation between vortices so that wake vorticity is quickly dispersed. However, when the angle of attack of the wing is increased to the point where the wing-tip vortex becomes dominant, wake organization is restored causing alleviation to be diminished. It remains therefore, to develop guidelines for the design of lifting surfaces that produce highly dispersive multiple vortex wakes. The penalties associated with these designs can then be evaluated to determine the practicality of such an alleviation scheme. 6.3.4. Measured rolling moment Rolling moment measurements were made with the experimental setup (Fig. 44b) and the wake-generating wing (Fig. 45). As shown in Fig. 44b, the test-section length is su$ciently long to allow separation distances between generator and follower up to about 80 ft (24.4 m). The generator wing is mounted through a strain-gage balance to a "xed strut in order to measure the lift and drag exerted on it by the free stream. The following wing is also mounted onto a strut through a strain-gage balance to measure the rolling moment induced on it by the vortex wake of the leading wing. The strut could be raised and lowered, and moved laterally, to "nd the
556
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
location where the rolling moment was a maximum. The following wings were made of balsa wood to ensure a high-frequency response to the imposed torques of the meandering vortices. The analog signal from the straingage balance was "ltered with a low-pass "lter at 10 Hz to suppress unwanted electrical noise that occurs at higher frequencies. The three wings used as the follower model all had the same chord length, but a di!erent span in order to study the e!ect of the ratio of the span of the follower wing to that of the generator. The procedure for recording a data point started by "rst setting the #aps on the wake-generating wing at the angles desired for the con"guration, and then setting the angle of attack of the wing itself. The vertical and lateral locations of the follower wing were then set, and the wind tunnel conditions established. Since the wind tunnel airstream contains turbulence, the vortex moves about (meanders) causing the rolling moment induced on the following wing to change with time. This time-varying signal was recorded on a light-beam, strip-chart recorder. It was found that a data record of 1 min duration was su$cient to obtain a record wherein a maximum rolling moment for that location occurred at least three times. The procedure was then repeated at successive lateral and vertical positions of the follower wing (at 2}4 in increments) to determine the maximum value of the rolling moment for the entire wake for each test condition and each con"guration. (The nature of the vortex meander was such that the time-averaged rolling moments would be too facility dependent to be of much value, and therefore they were not recorded.) It was reasoned that the maximum &instantaneous' rolling moments would also represent the maximum rolling moment during a sustained vortex encounter. The measured maximum rolling moments on the following wing were converted to coe$cient form through the equation rolling-moment C " , (47) J q Sb where S and b are respectively the planform area and span of the following wing. After the measurements were obtained for the various wing con"gurations, the rolling moment data were plotted as C /C to better compare the various con"guraJ * tions at the same lift (Fig. 52). Such a parameter would theoretically not change with angle of attack if the span loading did not change. However, the #ap settings used in the present test cause some changes in the span loading when the angle of attack changes. As a consequence, the data in Fig. 52 are, in most cases, a function of C . It will be noted that, for comparison purposes, * a con"guration of the generating wing with wingtip spoilers was also tested (Fig. 52). The three parts of Fig. 52 include the e!ect of span ratio b /b on the wake-induced rolling moments. An expected decrease in
Fig. 52. Rolling-moment parameter as a function of lift on a swept-wing generator for various con"gurations [10].
maximum rolling moment with increasing span of the follower wing is not clearly apparent. Also, for the smallest following wing, it was found that sawtooth loading or the addition of a spoiler to the #ap 03 con"guration were both more e!ective than tailoring the wing. Note that aircraft typically have the capability to create a rolling-moment coe$cient of about 0.04}0.06 by use of ailerons. Hence, any imposed torque by a vortex that causes C to exceed about 0.06 will cause the encounterJ ing aircraft to roll even when full counter-roll control is imposed. When the smallest following wing is immersed in the wake of the swept wing con"gured to develop sawtooth loading (Fig. 52a), the generation of multiple vortices in the wake appears to be quite e!ective for reducing the rolling moment at low lift coe$cients. However, a large part of the e!ectiveness disappears as the lift increases above C "0.4, for the #ap settings used in the *
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
experiment. Some alleviation was achieved on the larger follower (b /b "0.29) with sawtooth loading, but not to the extent realized with the smallest following wing. A 2 ft (61 cm) span version of the swept wing was tested by Ci!one and Orlo! [91] by towing the wing through a water tank. Their test showed that the vortices shed by the sawtooth loading at C "0.7 undergo large excur* sions in the wake which are on the order of one-half of the span of the generating wing, and very similar to the excursions predicted in Fig. 43. In the water tow tank tests, the vortex pairs appeared to cause destructive interactions that tended to disperse the wake vorticity rapidly enough to substantially reduce the wake hazard at low angles of attack. At higher angles of attack, the overall lift on the wing seems to dominate the less intense vortices shed by the various #aps, so that vortex excursions are suppressed and a fairly strong single vortex pair then persists in the wake indicating that the vorticity shed by the generating wing is not being dispersed to the desired large amount. 6.3.5. Predicted rolling moment The methods used to predict the rolling moment induced on a wing as it encounters a wake are restricted here to penetrations that are parallel to the axis of the vortex (Fig. 53). The axial velocity in the vortex is assumed to be the same as the free-stream velocity. It is also assumed that the vortex encountered is straight, and that
557
the #uid is incompressible and inviscid. In the cases considered here, the up- and down-wash velocity distributions on the following wing are set equal to the measured circumferential or swirl velocity in the vortex wake (Fig. 49). In order to account for both vortices in a pair, the contributions of the port and starboard vortices are added. Even with these restrictions on the problem, it was not straighforward as to how to proceed with a computation. As background, when the test was conducted in the early 1970s, very little experience was available on the reliability of computational methods for estimating the loads induced on a wing when it encounters a vortex wake. At that time, emphasis was placed on the reliability of simple and quick methods that could be used in #ight simulators to study the #ight dynamics of aircraft as they encounter vortex wakes. Therefore, the analysis of torque or rolling moment on an encountering wing was restricted to the following methods [10]: 1. Two-dimensional strip theory. 2. Strip-theory with empirical lift-curve slope correction. 3. Vortex-lattice theory; #at-wing and #at-wake approximation. The two-dimensional strip theory assumes that the lift on each spanwise element is given by its two-dimensional value, or l(y)"C q c(y)sin a(y), *?
Fig. 53. Theoretical model used to analyze vortex impinging on following wing [10].
(48)
558
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
where C is the two-dimensional lift-curve slope of the *? airfoil section at that spanwise station, sin a(y)+w/; is the #ow inclination relative to the airfoil section at the spanwise station, and c(y) is the local chord of the wing. When the quantity yl(y) is integrated across the span of the wing, the rolling-moment coe$cient becomes
C @ C " *? (w/; )y dy. (49) J b \@ The values presented in Table 5 were found by numerically integrating Eq. (49) after setting w/; equal to the sum of the measured v /; contributions from the port F and starboard vortices. For two-dimensional wings, the lift-curve slope, C , is *? often taken as 2p. As noted in Table 5, the predictions made with Eq. (48) are then generally too large because the local angle of attack at each wing element does not account for the induced angles of attack caused by the vortex wake shed by the following wing as it experiences the #ow "eld of the vortex. A correction for this e!ect can be obtained by adjusting the lift-curve slope for the encountering wing by means of a formula introduced by Jones [137] and a modi"cation to it by Maskew [138]. The formula derived by Jones for wings of general planform is 2p AR , C " *? P AR#2
(50)
where AR is the aspect ratio and P" (semi-perimeter/span) of the wing. Maskew [138] reasoned that the spanwise station on the wing where the vertical velocity vanishes serves the #ow "eld in the same way as a wingtip. The following wing is therefore divided into separate spanwise segments for the computation of the
lift-curve slope by the use of Eq. (50). The strip-theory results presented in Table 5 were obtained by use of the Maskew adjustment to the Jones formula, and were found to be in good agreement with rolling moments calculated by use of vortex-lattice theory for the same upand down-wash distributions. The study showed that such an approximation provides much more realistic lift-curve slopes for the wing when it encounters a vortex wake than the straight two-dimensional strip theory. Comparison of the values calculated by use of the modi"ed strip theory with an empirically adjusted lift-curve slope are noted in Table 5 to be in good agreement with the vortex-lattice theory, which are also in good agreement with the experimental results. The di!erences in Table 5 between the vortex-lattice theory and experiment may be due to any of the following reasons: the way that the measurements of rolling moments were made; di!erences in the vortex velocity data; a combination of both; or unsteady aspects of the wind-tunnel measurements which were assumed negligible. Nevertheless, the foregoing results indicate that either the vortex-lattice theory or the simple strip theory with the lift-curve slope, C , determined by the *? Jones}Maskew formula provides reasonable estimates for the rolling moment induced by a vortex on a wing penetrating a vortex wake of another aircraft. The fairly good agreement between the predicted and measured values in Table 5 also suggests that the steady-state approximation is probably satisfactory for near-axial penetrations of the vortex wake. As experimental equipment and procedures improved, the ability to predict loads induced on wings that encounter vortex wakes was studied further [163]. By use of the empirically adjusted strip theory, the rolling moment and lift induced on a wing were
Table 5 Comparison of predicted and measured rolling-moment coe$cients [10] Con"guration
a
C *
b /b
R
Normalized rolling moment, C /C J * Strip theory
Vortex-lattice theory
Measured
C ?"2p *
Empirical C ? *
Flat-wake approximation
Flaps 0H Flaps 0H plus spoiler Landing Landing plus spoiler Tailored
8H 8H 6H 8H 10H
0.75 0.70 0.85 0.86 0.82
0.29 * * * *
5.84 * * * *
0.092 0.053 0.081 0.081 0.105
0.222 0.184 0.243 0.163 0.246
0.110 0.091 0.120 0.081 0.122
0.109 0.085 0.117 0.071 0.111
Flaps 0H Flaps 0H plus spoiler Tailored
8H 8H 10H
0.75 0.70 0.82
0.14 * *
2.82 * *
0.099 0.023 0.074
0.317 0.154 0.173
0.101 0.049 0.055
0.090 0.038 0.042
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
calculated at a large number of points in the wake. From these points, contours of equal rolling-moment and lift coe$cient were drawn (Fig. 54) for one vortex pair when the ratio of the span of the following wing to that of the wake-generating wing, b /b is 0.29. Only one quadrant is presented because the #ow "eld is symmetrical vertically and anti-symmetrical about the wake centerplane. Although the contours are not as precise as if determined by vortex-lattice theory, they do indicate the nature of the area over which high values of rolling moment occur. As expected, the maximum rolling moment occurs when the encountering wing is centered on the vortex. The area in Fig. 54a inside the contour labeled 0.06 is the region where overpowering rolling moments are to be experienced. Similarly, the results in Fig. 54 indicate that large values of positive and negative lift are induced on the following wing by the vortex wake depending on its location relative to the vortex pair. As expected, the shape of the curves of constant torque and lift change with both the vortex structure and with the span of the following wing. 6.4. Application of sawtooth loading to aircraft 6.4.1. Ground-based tests About the same time that the foregoing preliminary experiments were being carried out, the NASA spaceshuttle program purchased a surplus Boeing 747 subsonic transport aircraft. The ultimate use of the aircraft was to carry the space shuttle from Dryden Flight Research Center, where the space shuttles were expected to land, to Kennedy Space Center where the space shuttles were expected to be launched. Since space-shuttle operations had not yet started, the aircraft was assigned to the wake-vortex program for use in #ight tests. In order to obtain wake data on the B-747, several 0.03 scale models
559
were built for use in ground-based tests at Langley and Ames Research Centers and at the Hydronautics Inc. water tow-tank facility. The standard landing con"guration was "rst tested in the various ground-based facilities to establish a reference hazard against which alleviated con"gurations could be compared, and to establish the kind of agreement to be expected [164]. Since the aircraft had an on-board capability to independently deploy either the inboard or outboard #aps separately, three con"gurations were chosen for consideration during the test program; namely, the standard landing con"guration with all #aps fully deployed (i.e., the (303, 303) con"guration), and two modi"ed-landing con"gurations. One modi"ed landing con"guration had the inboard #aps fully deployed and the outboard #aps stowed (i.e., the (303, 03) con"guration). The third con"guration had the opposite #ap schedule (i.e., the (03, 303) con"guration). Only those #ap settings were chosen, because the ground-based experiments described in the previous section indicated that the tailored-loading concept would not provide the magnitude of alleviation required. Results obtained for wings with sawtooth loading, however, indicated that the concept should be explored [10]. At that time, the computations and some water tow-tank experiments by Ci!one and Orlo! [91,92], and some wind tunnel experiments published later [61,96] indicated that the alleviation mechanism instigated by sawtooth loading was brought about by the large excursions made by vortex pairs that usually ended in a linking of the vortex cores across the pair, i.e., large self-induced across-stream vortex excursions. Uncertainty existed then (and still exists now), however, as to the number of vortex pairs, and the magnitude of vortex strengths required to produce the large-scale mixing, and subsequent wake alleviation needed to decrease in-trail spacings by the amount desired.
Fig. 54. Contours of equal rolling moment and lift induced on a following wing by wake of swept wing with tailored loading [10]; b /b "0.29. (a) Rolling-moment parameter, C /C ; C /C "0.122. (b) Lift parameter, C /C ; C /C "!0.88. J * J * * * * *
560
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
With the foregoing information as background, a decision was made to test the conventional con"guration, and the two sawtooth options that were available by deploying either the inboard or the outboard #aps separately while leaving the other #ap stowed. Since no other span loading options were apparent at the time, the choice was somewhat obvious. The various con"gurations to be tested were designated the conventional landing or #aps (303, 303) con"guration, the modi"ed landing or (303, 03) con"guration, and the (03, 303) con"guration. The span-load distributions estimated for the various con"gurations by use of vortex-lattice theory [60,139] are presented in Fig. 55. It is to be noted that the variations in the span-load distributions achieved by independent #ap de#ections are a substantial portion of the entire lift. Tests with separate B-747 models began in the 40;80 ft Wind Tunnel and in the Hydronautics Water Tow Tank facility at about the same time [60,61]. Somewhat later, tests were also conducted in an air-tow facility (i.e., Vortex Research Facility [66,67,156,164] and in the 14;22 ft (4.42;6.63 m) Wind Tunnel which are both located at Langley Research Center [62,63]. In the water tow tank, the turbulence in the free stream is very near zero at the beginning of a run, and the model is mounted right-side up with a strut attached to the top of the model fuselage. In the 40;80 ft Wind Tunnel, the turbulence level in the free stream is about 0.5%, and the model was at "rst also mounted right-side up. The rightside up mounting of the model in the wind tunnel required that the strut be attached to the bottom of the fuselage so that the vortex wake of the model would mix with the wake of the mounting strut. As a consequence, the "rst results in the wind tunnel for the modi"ed landing or (303, 03) con"guration, were inconsistent. That is, during a given run, the wake-induced rolling moment on a following wing would jump from a level just below that produced by the conventional landing con"guration (i.e., a small amount of alleviation) down to a low level near the one measured in the water tow tank (i.e., a large amount of alleviation), thereby indicating two curves for the same con"guration. It was later discovered in some #ight tests that the reason for the #uctuating rollingmoment results was caused by the in#uence of the mounting strut on the wake-vortex structure. The mechanism by which the viscous wake of the mounting strut in#uenced the vortex wake of the model was not discovered until later [61]. The remedy for the interference from the strut was, of course, to mount the wake-generating model upside down in the wind tunnel so that the vortex wake of the model moves upward away from the viscous wake of the strut holding the model (Fig. 56). As disconcerting as the #uctuating results were, they did provide guidance for the #ight tests. Since the mounting strut added turbulence to the vortex wake along its strut when the generating model is mounted
Fig. 55. Span loading on wing of B-747 model for various #ap settings as computed by vortex-lattice theory; Corsiglia et al. [61].
right-side up, and that resulted in inconsistent results, it was suggested to the #ight-test group that the "rst tests of the (303, 03) con"guration of the B-747 be carried out with all of the landing gear stowed, and with no yaw of the aircraft. After that, the same con"guration should be tested with landing gear extended. The #ight results were consistent with the wind tunnel results in that the alleviation of the (303, 03) con"guration was extensive when the landing gear were stowed, but not nearly as e!ective when any part or all of the landing gear was extended. The same was also true when the aircraft was #own at zero yaw and with yaw. The experiences with the two methods of mounting wake-vortex models in a wind tunnel led to the decision to mount wake-generating models only by use of a streamlined strut attached to the fuselage upper surface,
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
561
Fig. 56. Experimental setup in Ames 40;80 ft Wind Tunnel [61].
so that the model appears upside down in the wind tunnel. By use of the experimental setup shown in Fig. 56, the rolling moments imposed on the following two models are presented in Figs. 57 and 58 as a function of the lift coe$cient on the B-747 subsonic transport model. For conventional #ap con"gurations, the rolling moment on the following model increases nearly linearly with C up * to the beginning of stall on the generator. This result is expected, because, the shape of the span-load distribution is nearly independent of lift over the range of C tested, * and only the magnitude of the loading changes with angle of attack. Since the vortex structure depends directly on the span loading, only the total vortex strength changes with C thereby yielding a nearly linear rela* tionship between C and C . Note in Fig. 57 that the J * various curves for the conventional con"gurations lie on approximately the same line. This implies that there is no major change in the vortex structure (except for magnitude) among the conventional #ap con"gurations. It is noted in Fig. 57 that, at low angles of attack, the wake-induced rolling moments behind the (03, 303) con"guration are greater than those measured for the standard landing con"guration. Analysis of the span-load distribution for the (03, 303) con"guration indicates that such a result is to be expected, because the vortex shed by the wingtip, and by the outboard end of the outboard #ap, merge before the two #ap vortices can interact to create the large excursions that lead to dissipation through linking. Hence, when the two outboard vortices (i.e., wingtip and outboard #ap) merge early in the rollup process, their combined strength dominates the #ow "eld. The combined circulation brings about a stronger and more concentrated vortex than is shed by the standard landing con"guration at the same lift coe$cient. At
Fig. 57. Maximum rolling-moment coe$cients on following wings in wake of B-747 for various #ap settings as measured in 40;80 ft Wind Tunnel [60,61]; x /b "13.
higher angles of attack, the curve for the rolling moment turns over to make the con"guration more appealing. It is believed, however, that this outboard-loaded con"guration at the higher loadings began to stall thereby producing low energy #uid that migrates to the vortex core. The larger core diameter reduces C for following J models of small span. No further consideration was given to the (03, 303) con"guration, because it did not produce a signi"cant reduction in wake-induced rolling moment. In contrast, when the (303, 03) con"guration was tested upside down, so that the vortex and strut wakes did not mix [60,61], it produced a substantial reduction in the rolling moment on the smaller trailing wing (Fig. 58a)
562
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 58. Variation with lift coe$cient of measured maximum rolling-moment coe$cients on following wings in wake of B-747 for two #ap settings with landing gear stowed as measured in 40;80 ft Wind Tunnel [60,61]; x /b "13. (a) b /b "0.2, (b) b /b "0.5.
Fig. 59. Variation with downstream distance of measured maximum rolling-moment coe$cients on following wings in wake of B-747 for two #ap settings with landing gear stowed as measured in 40;80 ft Wind Tunnel, and in Hydronautics Inc. water-tow facility [60,61]. (a) b /b "0.2, (b) b /b "0.5.
and a modest reduction on the larger trailing wing (Fig. 58b). In Fig. 58a, the data from the water tow tank and the wind tunnel for the small following wing are not in good agreement, whereas the data are in good agreement in Fig. 58b for the large following wing. Consideration of the data presented in Fig. 59a indicates that the alleviation mechanism appears to require a di!erent amount of time to go to completion in the two facilities
[61]. That is, the water tow-tank data taken at 14 spans behind the wake-generating wing is seen to be in fair agreement with those measurements for the (303, 303) con"guration, but not for the (303, 03) con"guration. However, at 30 spans downstream and beyond, the water tow-tank data for C is 50% of the (303, 303) J con"guration, which is in agreement with the wind tunnel results.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
563
Fig. 60. Photographs of wake con"gurations shed by B-747 with its inboard #aps fully deployed and with outboard #aps stowed [61]. (a) Landing gear stowed. (b) Landing gear extended.
It is now believed that the time for the alleviation mechanism to be completed is longer in the water tow tank than it is the wind tunnel, because the free-stream turbulence level in the tow tank is near zero, whereas it is about 0.5% in the wind tunnel. It is now known that the alleviation is brought about by a sinusoidal mutually induced instability that involves the two vortices o! the ends of the inboard #ap which eventually go into a linking process between the two vortices (Fig. 60). Since the instability is non-linear, and requires a "nite disturbance to initiate it, wave growth is slow to start in the quiescent tow tank, but begins immediately in the more turbulent environment of the wind tunnel airstream, even with the landing gear extended. If some low energy #uid from the landing gear, or from a wind tunnel strut, is ingested by the vortex cores, the vortices become more rigid, and do not go into a mutually induced instability unless they are given a large input from free-stream turbulence. In quiescent conditions, like the early morning quiet atmosphere present at the time of the #ight tests, the disturbances present to initiate the sinusoisal instability are not strong enough to do so (Fig. 60b). 6.4.2. Flight tests The #ight tests were conducted shortly after sunrise under low wind conditions in an attempt to minimize
atmospheric variations between test days. The #ight experiments were made with the full-scale B-747 aircraft mentioned previously which could be #own with the #ap con"gurations discussed here, with or without the landing gear extended. Both a Lear Jet and a T-37B aircraft were used to probe the vortices of the generator. The span ratio of the smaller of the trailing wings used in the ground-based tests to the span of the B-747 model, are about the same as that of the two probe aircraft relative to the B-747 used in the #ight tests; namely, b /b "0.186. Since the probe aircraft were free to move about in response to the induced velocity "eld of a vortex wake, wake penetrations were often along a path that did not include a vortex center. The vortex encounter data was therefore random in character, and required an interpretation that was less straightforward than with windtunnel data. The #ight and data-interpretation procedures used during the #ight tests are described by Jacobsen and Short [159], Barber et al. [58], Jacobsen and Barber [160], and Smith [55]. Information in those papers will be summarized here in order to give the reader an understanding of the di$culties of the #ight tests and of the nature of the data obtained. A great deal of information on the aircraft used in the tests is contained in the various papers, along with other information on the tests, which will not be described here.
564
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Measurements of the upset, or rolling-moment response, during a wake encounter were made by both probe aircraft, and the measurements of the velocity pro"les through vortex wakes were made with the Lear Jet. The results obtained with the Lear Jet are reported by Barber et al. [58], Jacobsen and Short [159], and Jacobsen and Barber [160], and the T-37B results are reported by Smith [55]. The B-747 aircraft was equipped with smoke (or vaporize oil) generators on each wingtip, and near the outboard edges of both the inboard and outboard #aps, so that the lift-generated vortices would be visible for the pilots of the probe aircraft. When a second series of tests over Rosamond Dry Lake near Dryden Flight Research Center in California were conducted, smoke generators were added at the inboard ends of the inboard #aps. The B-747 aircraft was equipped with a modi"ed Distance-Measuring-Equipment (DME) unit to allow direct measurement of the range to the probe aircraft. The Lear Jet aircraft was instrumented to measure the aircraft motions, and its control surface de#ections. Air speed, altitude, and angles of attack and sideslip were measured by use of an instrumented boom on the nose of the aircraft. A three-component hot-wire anemometer was also mounted on the nose boom for measuring the velocities in the various wakes of the B-747. The data were recorded on magnetic tape on board the aircraft. The response measurements were recorded in digital form, while the hot-wire anemometer measurements were recorded in analog form because of their high-frequency content. More information on the aircraft and test procedures are presented in Barber et al. [58], Jacobsen and Short [159] and Jacobsen and Barber [160]. The #ight tests were conducted at an altitude of approximately 12,500 ft (3800 m) (or 10,000 ft above ground level) at indicated air speeds that ranged from 150 to 180 knots. The gross weight of the wake-generating aircraft ranged from 480,000 to 600,000 lb (217,000 to 272,000 kg), so that the lift coe$cients ranged from 1.0 to 1.4. The test procedure used to obtain measurements was carried out by having a probe aircraft enter the wake at a separation distance large enough to assure safety. While the pilot attempted to keep the aircraft at or near the center of a vortex, the distance behind the wakegenerating aircraft was decreased until judged by the pilot, or through assessment of the loads on the aircraft, to be too hazardous to continue. The resulting motions during the various penetrations were then analyzed to determine the rolling moments imposed on the aircraft. Since the severity of the encounter depends strongly on the location of the probe aircraft relative to the vortex, a large number of encounters was required to ensure that the maximum upsets possible were obtained. Once the data from the large number of upsets had been reduced, an upper bound (or envelope) to the data was constructed and assumed to represent the maximum upset that
a particular wake produces on the probe aircraft. Since the velocity of the probe aircraft was usually higher than that of the B-747, the measured responses were corrected to the velocity of the wake-generating aircraft. Since the response of the probe aircraft usually involved rotation about all three axes, questions were raised as to whether the hazard index should consist of the rolling moment parameter alone, or one that included the three degrees of rotation of the probe aircraft, i.e., yaw, pitch and roll. In order to explore which hazard index was more appropriate, Jacobsen and Short [159] de"ned a spin control parameter written as XQ "[(p /p )#(q /q )#(r /r )] , (51) B B B where the subscript m identi"es the maximum control authority available on the probe aircraft for each rotation direction. The simpler hazard index involves only the ratio determined by dividing the roll acceleration due to the vortex by the roll acceleration brought about by full de#ection of the ailerons, PQ "p /p B or, in terms of rolling moment coe$cient,
(52a)
PQ "C /C B . (52b) J J When the roll-control ratio, PQ , is equal to one, the probe aircraft is able to just hold its own against the vortexinduced rolling moment, if the controls are applied instantaneously as needed. In order to determine which of the two parameters was more signi"cant for the encounter of aircraft with a vortex, Jacobsen and Short [159] reduced the data, so that comparisons could be made by use of both parameters (Fig. 61). The data set chosen for the comparison was obtained with the Lear Jet in the wake of the B-747 in its standard landing or (303, 303) con"guration, with the landing gear stowed, and thrust set for level #ight at C "1.4. It is noted in Fig. 61 that when the encounter * is near the vortex core, as evidenced by the larger control ratios, the combined-axes upsets are not signi"cantly greater than the roll upsets alone, the average increase being about 5%. When the encounter is closer to the edge of the vortex (i.e., lower values of the control ratio) the measurements indicate large upsets can occur in the pitch and yaw axes and they should be included in the probe aircraft response measurements. It is speculated that the spin control ratio would be a more adequate measurement of the response for a non-axial wake encounter. However, since the maximum upsets were of most interest in the program, and the roll-acceleration parameter is much simpler and easier to use, the roll-control ratio, PQ , came into common use rather than the spin-control parameter. Figs. 62}66 are reproduced from Jacobsen and Short [159] to show the large number of encounters that were used to develop rather crude boundaries for the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
565
Fig. 61. Comparison of rolling-moment control ratio with total spin control parameter for Lear Jet aircraft encountering wake of B-747 with #aps (303, 303), gear up, and thrust for level #ight at C "1.4; Jacobsen et al. [159]. *
Fig. 62. Variation with separation distance of rolling-moment coe$cient measured in #ight on Lear Jet aircraft in wake of B-747 at various lift coe$cients (303, 303), gear up, and thrust set for level #ight; Jacobsen et al. [159]. (a) #aps (303, 303), (b) #aps (303, 03).
various con"gurations that were tested. The data in those "gures are summarized in Fig. 67. The vortex-induced upset responses of the Lear Jet determined for several values of the lift coe$cient on the B-747 are shown in Fig. 62, where the vortex-induced
rolling-moment coe$cient, C , is plotted as a function of J the separation distance between the generating and probe aircraft. Even though it is expected that the higher lift coe$cients of the B-747 would produce larger upsets because of the increased circulation in the vortices, no
566
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 63. Variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 for two #ap settings and several lift coe$cients with gear up and thrust set for level #ight; Jacobsen et al. [159].
Fig. 64. E!ect of extension of landing gear on variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 for (303, 03) #ap settings and several lift coe$cients with thrust set for level #ight; Jacobsen et al. [159].
e!ect of the change in C from 1.0 to 1.4 is discernible for * either the normal landing #ap (303, 303) con"guration (Fig. 62a) or for the modi"ed landing (303, 03) con"guration (Fig. 62b). This result disagrees with the wind-tunnel results, but agrees with the #ight tests reported by Smith [55]. Two methods used to make the measurements may
account for some of the di!erences. In the wind-tunnel, the following wings are held "xed, whereas in #ight the probe aircraft is allowed to move in a dynamic encounter. The data in Fig. 62 are replotted in Fig. 63 to show the e!ect of the inboard and outboard #ap con"gurations. It
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
567
Fig. 65. E!ect of engine thrust on variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 with gear retracted for two #ap settings and several lift coe$cients with thrust set for level #ight; Jacobsen et al. [159]. (a) #aps (303, 303), (b) #aps (303, 03).
is noted that the vortex encounters were more severe behind the (303, 303) con"guration. Also, the wake shed by the (303, 303) con"guration was so persistent that, even though the separation distance was twice as large, it was still roughly equivalent to the wake of the (303, 03) con"guration. Included in the "gure are the corresponding wind-tunnel data. The #ight test results con"rm the alleviation of the vortex strength with the (303, 03) con"guration, as measured in the wind tunnel at a scaled separation distance of 0.5 n mile (0.85 km). The #ight-test results, however, do not show the increase in C with lift J coe$cient that was measured in the wind tunnel. The adverse e!ect of extending the landing gear on the (303, 03) con"guration is shown in Fig. 64. This e!ect is also shown in the data of Smith [55]. Included in Fig. 64 for comparison is a dashed line that indicates the upper boundary of the data in Fig. 62a for the gear up (303, 303) con"guration. The e!ect of the de#ected outboard #ap is greater than the e!ect of the landing gear, and both con"guration changes increase the magnitude of the
upset responses in the wake of the (303, 03) alleviated con"guration. The e!ect of engine thrust of the B-747 on the upset response of the Lear Jet probe aircraft is shown in Fig. 65 for three engine settings: (1) all engines at level #ight thrust; (2) the inboard engines at idle thrust and the outboard engines at thrust for level #ight; and (3) the inboard engines at thrust for level #ight and the outboard engines at idle. In general, it appears that the vortex encounter is more severe behind the (303, 303) con"guration with engines at idle than with all engines at level #ight thrust (Fig. 65b). This e!ect is not evident behind the modi"ed landing (303, 03) con"guration, however (Fig. 65b). No de"nitive di!erence is apparent between the con"guration with inboard engines idle, and the con"guration with the outboard engines idle. In the present investigation, no measurements were taken with all engines at idle thrust, but the results by Smith [55] indicate a strong adverse e!ect with all engines idle for the (303, 303) #ap con"gurations of the B-747.
568
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 66. E!ect of sideslip of B-747 with gear retracted on variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 for various #ap settings and several lift coe$cients with thrust set for level #ight; Jacobsen et al. [159].
The e!ect of sideslip angle of the B-747 in the (303, 03) con"guration is presented in Fig. 66 for sideslip angles of about $23. Larger upsets were measured for the case of positive sideslip than for either zero or negative sideslip. It is not known which wing vortex was penetrated during each encounter. Although data are available for only a limited range of separation distances, they indicate that the resulting upset is approximately 50% greater with sideslip than for a comparable separation distance with no sideslip, which is in agreement with the results presented by Smith [55]. The pilots of the probe aircraft reported that, from 4.8 to 8.0 km (3 to 5 n mile) behind the aircraft, the trailing vortices, which were marked by smoke, appeared far more concentrated and well de"ned for the (303, 303) con"guration than for the (303, 03) con"guration. Furthermore, as a result of #ying in the wake at various ranges, they identi"ed a separation requirement which was much greater for the (303, 303) con"guration than for the (303, 03) con"guration. Fig. 67 is a summary of pilot qualitative separation requirement for following aircraft [58,61]. With the landing gear retracted to correspond to the ground-based experiments, the separation requirement was reduced substantially for the (303, 03) con"guration compared with the (303, 303) con"guration (Fig. 67a). Deployment of all or any part of the landing gear, however, increased the separation requirements for all con"gurations and especially for the (303, 03) con"guration. Sideslip was also found to adversely a!ect the wake alleviation when the landing gear was stowed (Fig. 67b). Flow visualization obtained during the #ight test provided some insight into the cause of the landing-gear e!ect. Fig. 60 shows the smoke trails from the B-747 for the (303, 03) con"guration with the landing gear both up and down. With the landing gear up, a well-de"ned
vortex pair is shed from the inboard edge of the inboard #aps, and these vortices undergo large-amplitude mutually induced interactions that lead to linking between the two #ap vortices. When the landing gear is deployed, these same vortices appear to be more di!use, and no instability or wave growth or linking between the two vortices appears to occur. The reason why the (303, 03) con"guration of the B-747 was so adversely a!ected by deployment of landing gear or by yaw was essentially explained by the photographs in Fig. 60. A method for making the alleviation mechanism work under all #ight conditions was, however, not found even though a number of attempts were made to "nd a solution. Therefore, since a simple method is not available to initiate the wave instability in the atmosphere on a consistent basis, the (303, 03) con"guration was considered not useable. It might at "rst seem that, if the (303, 03) con"guration of the B-747 had worked as well with gear down and with yaw as it did in the clean and unyawed condition, a solution would have been available for at least one aircraft in the #eet, and might be applicable to others. Such would not have been the case however, because a study by the Boeing company found that the (303, 03) #ap settings reduced the load carrying capability of the aircraft, because it restricted the travel of the center of gravity of the aircraft. When only the inboard #aps are deployed, the aircraft must be loaded more forward which restricts the available aircraft payload distributions and consequently, the e$ciency of the aircraft would be substantially reduced. The Boeing study also concluded that the reduction in lift for landing, imposed by the (303, 03) #ap settings, required both a higher landing velocity and a higher angle of attack at touchdown. The higher landing velocity would produce more stress and wear on the tires and landing gear, and the higher
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
569
Fig. 67. Pilot qualitative estimate of separation requirement for a Lear Jet or T-37B aircraft following a B-747 in level #ight; Corsiglia et al. [61].
angle of attack would risk more tail dragging incidents. These disadvantages would have rendered the aircraft less useful, so that it would not have been competitive with other aircraft in the market. The velocity in the #ow "eld of the wake shed by the standard landing (303, 303) con"guration was also measured by Jacobsen and Short [159] by use of a threecomponent hot-wire anemometer probe mounted on a nose boom of the Lear Jet probe aircraft. After the motions of the probe aircraft have been removed, the three components of the velocity in the vortex wake at 2.9 n mile (5.4 km) behind the B-747 in its (303, 303)
con"guration are presented in Fig. 68. Velocity measurements were also made at a distance of 2.2 n mile (4.1 km). Since the path of the hot-wire probe through the vortex is uncertain, the measured vortex structures were matched to a Lamb mathematical model for a vortex to aid in the interpretation of the data presented in Fig. 68. The reason for the di!erence in the vertical velocity in the port and starboard vortices in Fig. 69 is attributed to a di!erence in the probe path between the two measurements, and their distances from the vortex centers. It was noted by Jacobsen and Short [159] that their method provided a consistently good representation of
570
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 68. Variation of vertical, lateral and axial velocity components in wake of B-747 in standard landing con"guration as measured with hot-wire probe on Lear Jet aircraft as it traverses wake; Jacobsen et al. [159].
the maximum tangential velocities in the vortices (Fig. 70). Both the decay of the vortices with distance behind the generating aircraft, and the e!ect of raising the outboard #ap can be seen by observing the change in the tangential velocity as given by the vortex models matched to the data. This parameter is plotted in Fig. 70 where both variables have been normalized in the manner suggested by Iversen [101]. The mean line through the data correlated by Iversen is also shown in Fig. 70 as a dashed line. It is evident that the dimensionless maximum velocities for the (303, 303) con"guration are representative
Fig. 69. Velocity components in wake of B-747 standard landing con"guration from hot-wire results using Lamb vortex model to interpret data; Jacobsen et al. [159]. (a) Vertical velocity, (b) Lateral velocity.
Fig. 70. Peak tangential velocity in various wakes of B-747 as measured by hot-wire technique as a function of separation distance; Jacobsen et al. [159].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
of the values for other aircraft used in the correlation. The results also show a marked reduction in peak tangential velocity when the outboard #ap is retracted to produce the (303, 03) con"guration, which is consistent with the response measurements of the probe aircraft, and with results from ground-based experiments.
7. Mutually induced instabilities in single pair 7.1. Introduction The results presented in the previous section, and especially the discussion regarding Fig. 60, indicate the importance of the alleviation that can be achieved if the mutually induced instability can be mobilized for a vortex pair. Therefore, consideration is given in this section to the mutually induced instability for a vortex pair. Some background on the mutually induced instability is "rst presented, and then some computations are described that illustrate the dynamics that come about when a vortex pair is given a variety of initial sinusoidal displacements. As mentioned previously, large-scale vortex instabilities bring about mixing on a scale such that vorticity is rapidly convected not only within the wake but also across the centerplane and into regions beyond the wingtips of the wake-generating aircraft. After such a mutually induced instability has gone to completion, the intense and coherent swirling motions associated with the vortex cores shed by conventional span loadings are thereby rapidly changed into incoherent slowly rotating con"gurations which posed a much reduced wake hazard. The mixing action of the vortex motions also spreads the downwash over an area larger than the wingspan of the wake-generating aircraft which reduces the concentration of the downwash momentum in the wake. Study of the sinusoidal or mutually induced instability was carried out to understand the instability better, and to develop guidelines for the design of lifting systems that bring about a rapid onset and completion of instabilities in the vortex "laments. In the 1950s, the mutually induced instability was identi"ed by Scorer [120,165] in condensation trails left by aircraft #ying at cruise altitudes. At that time, Scorer attributed the instability to buoyancy di!erences along the vortex "laments and not to the mutual induction between the two vortices in the pair. Scorer [120] assumed that the buoyant gas from engine exhaust in the core region of the vortices accumulated at the crest of the waves, thereby making those parts of the "laments more buoyant than the troughs. It was reasoned that the warm exhaust gases would drift along the vortex cores from those parts at lower elevations to the crests of the waves, causing the amplitude of any waviness present along the vortex axes to grow. An explanation for the tilt
571
of the wave planes relative to the vertical was not presented. Photographs taken at 15 s intervals from directly below a typical mutually induced event are presented in Fig. 71 [38,49]. As explained in the caption below the "gure, the vortex cores are made visible by condensation of water vapor in the engine exhaust. Another good sequence of photographs of the instability in a vortex pair is presented by Bisgood et al. [47] for the wake of a Comet aircraft. In each of these sequences, the vortex "laments slowly recede and draw together in a nearly anti-symmetrical and sinusoidal pattern until they connect to form a train of irregularly shaped vortex loops. The loops then become more complex in shape and break up causing the wake to disintegrate into a number of incoherent aerodynamic motions. In a landmark paper, Crow [49] presents the correct explanation for the mutually induced instability for a vortex pair (Fig. 71) by analyzing the time-dependent motion of a vortex pair. His analysis correctly attributes the dynamics of the instability to the self-induced velocity "eld of the vortices on each other when they have waves along their length. The analysis was carried out for the cases when the waves on two vortices of opposite sign were in phase, and out of phase. Crow's analysis explains
Fig. 71. Photographs taken at 15 s intervals from below condensation wake of B-47 in cruise con"guration to illustrate mutually induced instability of a vortex pair (from Crow [49] and Van Dyke [38], courtesy of Meteorology Research, Inc.).
572
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the growth of the waves, their tilt relative to the vertical, and predicts a range of preferred wavelengths for the instability. Observations made of the vortices in the laboratory and those shed by transport aircraft at cruise altitude, and marked by the condensation of exhaust vapors, are in agreement with Crow's predictions [34,47,48,50,58,108,166}169]. Not only were the results of Crow's study of great signi"cance for the understanding of the dynamics of vortex wakes and their demise, but Crow's analysis also provided a method of analysis for the dynamics of various three-dimensional time-dependent motions of systems of vortex "laments. Analyses carried out by Hackett and Evans [170] illustrate how the sinusoidal instability exhibits itself in vortex wakes composed of multiple pairs, in agreement with results expected for sawtooth loadings described previously [90}93,151]. Shortly thereafter, Crow and Bate [74] estimated the time required for the instability waves to be initiated by atmospheric turbulence, and to develop to the point where the wake is estimated to be harmless. They also suggested ways to accelerate the onset of rapid wave growth. In recognition of his contributions to the understanding of the mutually induced instability of a vortex pair, the event is justi"ably often referred to as the Crow instability. At the time of the appearance of Crow's "rst paper on the sinusoidal or mutually induced instability, the e!ect of the structure of the vortices (i.e., radial distribution of swirl velocity) on the growth of the waves was unknown. Widnall et al. [171] studied the in#uence of #ow along the axes of the vortices on the growth of the instability waves. It was found that if axial #ow is part of the vortex structure, it would slow wave growth. The physical reason by which #ow along the axis of the vortices slows wave growth was found to be related to the work required to divert the streamwise momentum in the core into a curved path. An experimental study by Bilanin and Widnall [155] of wave growth when the span loading on the generating wing is given a time-dependent oscillation found that, even though fairly large waves could be induced in a pair of wake vortices, the waves would not grow in amplitude enough to bring about the crosslinking between vortices. Without cross-linking, the vortices remain hazardous, because the destructive part of the process which brings an end to the organization of the wake did not occur. As more experimental and theoretical information accumulated on the initiation, growth and culmination of the mutually induced instability, it became apparent that turbulence in the #ow "eld where the vortices are embedded must be of a size and intensity to initiate the instability. The analysis of Crow and Bate [74] pointed out that wave initiation and growth thrive when atmospheric eddies or disturbances are not only present but of a size large enough to be comparable with the preferred wavelengths for maximum instability. Since then a num-
ber of experiments and analyses have been carried out in order to better de"ne the e!ect of free-stream turbulence on the dynamics of the mutually induced instability [50,80,84,97}99,172}175]. In some of the studies, it was found that su$cient turbulence would initiate vortex breakdown (i.e., a rapid destructive enlargement of the vortex core diameter) before the onset of the mutually induced instability [84]. In some other studies, it was found that low levels of free-stream turbulence caused the vortices to meander with time, but did not observe vortex bursting or the mutually induced instability [89]. An example of informative research that illustrates the progress being made in the experimental study of vortex #ow "elds was carried out by Liu [80,98,99] in a water tow tank. The study observed the dynamics of vortex pairs generated by lifting wings to obtain detailed information on the mechanism at work when a vortex pair interacts with various aspects of the atmosphere such as ambient turbulence, wind shear, strati"cation and the proximity of the ground. The study of ambient turbulence [80] is of particular interest here, because it reports on how a pair of trailing vortices behave as the freestream turbulence is increased from very low values obtainable in water tow tanks to very intense turbulence from a towed grid. The scale and magnitude of the turbulence along with strati"cation of the #uid in the tow tank were changed systematically over a wide range of each parameter. Even though the wake-generating wing is small (5.1 cm chord by 10.2 cm span), interesting and informative results were obtained. Photographs presented by Liu [80] of vortex "laments in plan view at various times after being generated are reproduced with permission in Figs. 72}74. Turbulence generated by the wing itself appears to initiate local small amounts of core bursting even when the tow-tank #uid is quiescent (Fig. 72). The dominant mechanism for destruction of the #ow "eld of the vortex pair, however, is certainly the mutually induced instability. In the presence of turbulence generated by the larger grid, linking is still the dominant mechanism even though core bursting is more apparent on the vortices (Figs. 73a and b). Liu points out that more intense levels of turbulence in the free stream also shortened the preferred wavelength of the mutually induced instability. The core bursting exhibited in Fig. 73 at the locations of maximum amplitude along the waves is also frequently observed in the exhaust-condensation trails behind subsonic transports #ying at cruise altitudes. When the turbulence level is increased even further, as also found by Sarpkaya and Daly [84], core bursting appears to be the dominant mechanism for destruction of the organization of the #ow "eld of the vortex pair (Fig. 74). The e!ect of ambient turbulence was found by Liu to decrease the dominant wavelength for linking as the dissipation rate is increased (Fig. 75). Lui [80] also presents hot-wire data on the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
573
decay characteristic of vortex pairs in a turbulent and strati"ed ambient #uid. When it was observed in the air-tow facility at Langley Research Center that temperature-gradient e!ects in the air basin appeared to have a signi"cant e!ect on test results, Greene [176] carried out an analysis on the e!ect of atmospheric structure on wake decay. In order to obtain simple and useful guidelines, the analysis was one that could be characterized as a global analysis of the problem. That is, details of the vortex structure are set aside in the formulation, and attention is given to an extended model of the vortex oval (Fig. 76). It is "rst assumed that the vortex oval, due to viscosity and turbulence at its periphery, spills circulation from both sides of the oval, so that the enclosing streamline is not symmetrical above and below the vortex oval as shown on the left side of Fig. 76. (When the #ow is inviscid and nonturbulent, spillage does not occur.) The amount of circulation shed or spilled per unit time is then assumed to be proportional to the drag of the equivalent body shown on the right-hand side of Fig. 76. The Brunt}Vaisala frequency, N, is introduced as Fig. 72. Sequential photographs of development of mutually induced instability in a quiescent, neutrally stable water tow tank; linking is initially the sole mode of instability; Liu [98].
N"
g do g ! , o dz a
(53)
where g is the acceleration due to gravity, o the air density, dz the altitude change, and a the speed of sound.
Fig. 73. Sequential photographs of development of mutually induced instability in presence of ambient turbulence generated by large grid; linking is still dominant mode of instability with a few bursting events; Liu [80]; note time scale of wake decay. (a) e*+0.2; (b) e*+0.4.
574
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 76. Equivalent cross-section assumed for vortex pair in analysis of vortex decay in the atmosphere by Greene [176].
Fig. 74. Sequential photographs of development of wake instabilities in presence of stronger ambient turbulence (eH+0.5); both linking and bursting take place and preferred wavelength of mutually induced instability is smaller; Liu [80].
The parameter, N, is the frequency at which a buoyant #uid element at one elevation will oscillate about its equilibrium altitude. The motion of the hypothetical oval (Fig. 76) in the vertical direction is then analyzed to
develop predictions for the dynamics of vortex pairs (such as the mutually induced instability) for a wide variety of circumstances. For a given set of atmospheric conditions, Greene's #ow "eld model has been found to quite accurately interpret the response of a vortex pair with good accuracy in a number of circumstances. These successes include measurements in the air tow facility [176] and some laboratory experiments designed to check the validity of the theory [97]. The applicability of Greene's analysis is especially surprising because, in practice, the vortex oval does not have a velocity discontinuity across the streamline that encompasses the oval so that a shear layer is not generated. Spillage of circulation from both vortices in the pair must then come about, because turbulence eddies generated in the outer layers of the vortices transport circulation through the interface between the
Fig. 75. Variation of the dominant wavelength of vortex-linking instability as dissipation rate increases; Liu [80].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
#ow inside the oval into the freestream of the outer #ow which goes past the oval. It is therefore unexpected that the drag of the cross-section shown on the right-hand side in Fig. 76 would represent so closely the spillage of circulation found in practice. Some recent ground-based experiments and numerical results to test the theoretical relationships indicate remarkably good agreement [97]. The study shows again that models of the global type like Greene's [176] will on occasion provide very useful results even though they are based on #ow models that are quite approximate. Recently, Greene's model has been extended by Kantha [177,178] to provide more realistic modelling of the detrainment of the circulation from the vortex oval and across the interface between the two vortices in the pair by use of the Monin}Obukho! similarity laws. Kantha's model includes ground e!ect and the more rapid decay of the vortices when in the proximity of the ground. It is also designed to simulate the tilt of the oval and vortex bounce. 7.2. Numerical method The numerical technique used to compute the results to be presented is patterned after the incompressible, inviscid technique used by Crow [49]. That is, the wake vortices are broken into straight-line segments that approximate the curved "laments. The shape and locations of the vortex lines are monitored by following the points where adjacent segments or links are connected. The velocity components at these points are calculated as a summation of the separate contributions of all of the vortex links in the #ow "eld } except for the two that touch the point itself, and thereby have indeterminate contributions. Since the velocity contributions induced by the two adjacent links are not included, the vortex lines are essentially cut o! at a distance of one link length, ds, on both sides of the point in question. The length of the link, and consequently the cut-o! distance, are chosen so that the numerical results agree with the velocity of propagation of a vortex ring. That is, the link length, ds, in the present numerical method is adjusted until the velocity of propagation of a vortex ring agrees with the closed-form expression given by Lamb [9] for a ring with a small but "nite core. The core is assumed to have uniform vorticity over a diameter, d , comparable with the vortices trailed by transport aircraft. Agreement is achieved with the present numerical method when ds"0.36d . Based on these values, a link length of ds"0.2b is used throughout the computations to be presented. The symbol, b, is the initial spanwise separation between the vortices. The foregoing guidelines work well for a vortex pair. The spacing guidelines just described become more complex when a vortex wake is composed of more than one vortex pair. In those cases, care must be exercised to be
575
sure that the guideline for link length of ds"0.2b is a maximum and not violated during the dynamic motions of wakes composed of multiple vortex pairs. If such a situation does occur, the closely associated vortices may numerically undergo a local rapid wave growth that might be mistaken for a realistic vortex interaction. This type of rapid wave growth has been studied and found to occur whenever the spacing between vortices decreases, so that a link length approaches half the distance between any two vortices. The resulting instability has been referred to as a spur-type instability and has been shown to be associated with the numerical analysis and not with the #uid mechanics of the vortex interactions [179]. The computations are begun by placing sinusoidally shaped waves of amplitude, a , on the "laments in the G vortex pair so that, at the beginning of each case, the waves on the port (or left) vortex "lament have a phase angle, , between 0 and 1803 relative to the waves on the starboard vortex. For comparison purposes, the initial amplitude, a , of the waves is set by the magnitude G expected at the wingtips when the wake-generating aircraft rolls through an angle b"73. A value of 73 was chosen because that is the magnitude of the oscillations used to study wake alleviation in the #ight tests at Dryden [59,112]. The pitch oscillations used to generate the wave pattern for the in-phase case are assumed to be of a magnitude such that the same displacement magnitude is achieved at the wingtips as when the aircraft undergoes roll oscillations like those used in the #ight tests. Hence, those cases are also given a b label to signal that the amplitude of the waves are comparable. Di!erent initial amplitudes are then taken as multiples, or fractions, of the 73 case. All of the wavelengths are held "xed at six spans, which corresponds roughly to the streamwise length of the oscillations experienced in the #ight experiments. In order to reduce the computation time, only "ve wave cycles were considered in the analysis of each case. The beginning and end of each wave set was blended smoothly into the straight-line portions of the vortices by use of one-quarter cycle of sine-squared variation in the displacement of the vortex links. Flexibility of the wavy portion of the "laments was enhanced by placing two spans of links between the ends of the waves, and the single link that projects o! to the far reaches of the wake. In the "gures to be presented, only the three center waves on each "lament are shown, because they are believed to be insulated well enough from the starting and stopping parts of the waves that they represent the dynamics to be experienced by an in"nite wave train. This conclusion is supported by the fact that a signi"cant di!erence between the shape of the center and of the two adjacent waves on a "lament is not detectable. The strength of the vortices in dimensionless form, C"circulation/b; , is held "xed at 0.1, which approximates transport aircraft in their
576
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
landing con"guration. When a matrix of values has been computed, the results are used to determine the e!ect of the relative phase of the waves on the two vortices in the pair on their wake dynamics. 7.3. Vortex-pair instability 7.3.1. Introduction A systematic study is presented in this section to determine the e!ect of phase on wave ampli"cation, i.e., does a di!erence in phase of the input waves on the port and starboard vortices a!ect the growth rate of the wave amplitude [180]. The study was prompted by #ight-test results obtained with a B-747 and a L-1011 aircraft. Of interest here is the portion of the test devoted to roll- and pitch-oscillation maneuvers by the aircraft to "nd out if the wake hazard increased or decreased as measured with a following aircraft [59]. The #ight results, to be treated in more detail in Section 7.4, indicate that the phase of input waves on the vortices in the wake does have a profound a!ect on the resulting dynamics of the vortices as in#uenced by the mutually induced instability. The signi"cance of the question is apparent when it is noted that turbulence in the atmosphere might in#uence a vortex wake, so that the initial disturbances to the vortices could be in phase, out-of-phase, or somewhere in between. The investigation to be presented considers the entire range of possible phase-angle di!erences between the input waves on the port and starboard vortices. 7.3.2. Isolated vortex Before investigating the dynamics of a vortex pair with initial disturbance waves along their length, the timedependent motion of an isolated vortex is considered when it has displacement waves along its axis [180]. When analyzed by use of the foregoing numerical method, it is found that an isolated vortex "lament with sinusoidal waves impressed on it rotates without much change in shape as time progresses. Fig. 77 illustrates how the rotation rate is a!ected by the amplitude of the waves. In the computations, it is noted that the plane of the input waves rotates counter to the direction of the vortex rotation (i.e., retrograde direction) with no appreciable change in amplitude. Some small distortions do take place at the crests and troughs of the waves. These distortions are largely perpendicular to the plane of the disturbance waves, and oscillate in the fore and aft directions of rotation. That is, the oscillations consist of small changes in the shape of the waves in the direction normal to the wave plane. Since the angle of the wave plane was measured along the line from the crest to the trough, the rotation angles plotted in Fig. 77 re#ect a change in shape together with any change in rotational speed. It is observed in Fig. 77 that when b is 143 or more, the rotation rate is approximately constant with time and with initial amplitude even though the waves do curl
Fig. 77. Variation with time of rotation of plane of sinusoidal waves impressed on an isolated vortex with various initial amplitudes [180].
a little at the crests in the direction perpendicular to the wave plane. At smaller initial wave amplitudes, both short- (b"3.53) and long-term (b"73) variations occur in the apparent rotational rate. These results provide some background characteristics on the rotation rate, and on the changes in wave shape from the initial sinusoidal one in order to help di!erentiate between the various dynamics brought about on the "laments by the mutually induced interactions between the "laments [180]. The primary conclusion is that the plane of sinusoidal waves along the axis of an isolated vortex "lament will rotate in a retrograde direction with little change in shape, i.e., a second vortex is not necessary to induce rotation by the plane of the waves. However, if growth in the wave amplitude is to occur, a second vortex of opposite sign, (so that its wave planes rotate in the opposite direction) must also be present for wave growth. That is, as the wave planes of the port and starboard vortices rotate, the wave troughs are brought closer together, so that those parts of the waves have their amplitudes increased by mutual induction. At the same time, the crests move apart, so that mutual induction is small causing the amplitude of those waves to remain almost unchanged. If the amplitude of the waves on both vortex "laments is very small, the waves on each "lament in a pair rotate without growth. Without the rotation of the wave planes that a wavy vortex "lament induces on itself, it is unlikely that wave growth would occur. 7.3.3. Vortex pair; waves in phase, "03 The initial wave pattern on the "laments for this case could be thought of as having been generated by executing small pitching or plunging motions with the wake-
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
generating aircraft. Fig. 78 presents the shape of the vortex "laments at three di!erent times after the beginning of the event. The dimensionless time, ¹"t; /b, indicated on each "gure, represents the vortex spans of travel of the wake-generating aircraft from the beginning of the event. The wakes are displayed on a 303/303/903 oblique view to yield a three-dimensional perspective of the wake, and as an end view. The end views are plotted at four times the scale used for the oblique views to more clearly indicate the shapes of the vortex planes. The foregoing numerical method was used to calculate a range of input wave amplitudes to study the characteristics of the in-phase wave pattern. These results are summarized in Figs. 79 and 80 for the wave amplitude, A"a/b, and the angle of the wave planes, h. The larger initial amplitudes lead to faster growth rates and to di!erent rotation rates of the wave planes (Fig. 79). The decrease observed in the angle of the wave plane, h, when the time, ¹, exceeds about 80 occurs because of the way that the angle is measured. That is, the measurement is made on a secant from the crest to the trough of the wave, so that as the wave grows rapidly in the trough region,
577
the apparent plane of the wave becomes more vertical. It is also noted in Fig. 79b that, at the smaller initial amplitudes, the wave planes rotate at di!erent rates. However, if b is over 143, the wave planes rotate at about the same rate independently of the initial amplitude. If the dynamics of the interaction were linear, the curves in Fig. 79a would collapse to a single line when plotted as the ratio of the input amplitude, a , rather than G vortex span b. As indicated in Fig. 80, the wave growth is nearly linear with the input amplitude during the initial stages of the event. As time progresses, however, the larger inputs appear to be more productive, because they are the ones that bring the troughs of the waves close together most quickly, so as to bene"t from the large mutual induction brought about by the proximity of the two vortices at those axial stations where the wave troughs occur. Not shown in the "gures are the disconnecting and linking parts of the instability which occur after the numerical simulation has been terminated. As mentioned previously, the present method is not capable of simulating those #uid-dynamic processes. The results in Figs. 79 and 80 illustrate the importance of large
Fig. 78. Oblique and end views of vortex pair which has an initial displacement of sine waves that are in phase [180]; "03, wavelength"6b, initial amplitude"0.23b (b"143).
578
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 79. Wave characteristics as a function of time for various input amplitudes when waves are in-phase [180]; "03.
Fig. 80. Wave amplitude ratio, a/a , as a function of time to test for linearity of the vortex dynamics to input amplitude when input waves G are in-phase [180]; "03.
input-wave amplitudes for consistent and rapid wave growth during the mutually induced instability. 7.3.4. Vortex pair; waves out-of-phase, "1803 The disturbance waves are now initially located on a circular cylinder as if the vortices had been shed by an
aircraft executing a series of roll oscillations. As a consequence, the phase of the waves on the port vortex is shifted one-half cycle, "1803, relative to the waves on the starboard vortex in order to study the out-of-phase or anti-symmetric case. Another representation of the anti-symmetric case could be made by placing the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
"laments in vertical planes rather than on arcs. A number of events were also calculated using such an initial con"guration. It was found that the results di!ered only slightly, and that no di!erence in the stability characteristics appeared. Since the circular-arc con"guration more closely approximates the #ight situation, only those results are presented. The wave shapes at three instances of time are presented in Fig. 81 for a typical event. The wave amplitude is noted to grow as the wave planes rotate in the retrograde direction, as predicted by the stability analysis of Crow [49]. However, at the latest time shown, the wave planes have just passed the horizontal, and are beginning to shrink. It is noted that counter rotation of the two wave planes for this case bring neither the wave troughs nor the crests closer together. Also, the wave tips at the inboard ends are taking on a slight curl which contributes a small amount to the rotation angle and to the amplitude reduction. The results for a series of such events are summarized in Figs. 82a and b by plotting the dimensionless amplitude, A"a/b, and the change in the angle, h, of the wave planes. Fig. 82a illustrates how the wave amplitude "rst grows to a maximum value, which occurs at about ¹"90, and then decreases. At about the same time (Fig. 82b) the wave planes reach the
579
903 rotation angle. Linearity of the wave dynamics for the out-of-phase wave pattern is tested in Fig. 83 by comparing the amplitude history for the various values of b on the basis of the input amplitude. All of the cases fall along a single line, except for the small amplitude case of b"3.53. A similar observation is noted in Fig. 82b for the rotation of the wave planes. The results indicate that an out-of-phase disturbance causes the initially nearly vertical waves to rotate to the horizontal plane and remain there as a stable vortex con"guration. The result is a vortex trail wherein the two vortices appear as a railroad track that waves back and forth sinusoidally in the horizontal plane (Fig. 81). An example from #ight tests of the wake-vortex dynamics associated with the roll-oscillation case is presented in Fig. 84. (The contrast, brightness, background and smoke trails in the photographs were adjusted electronically to better de"ne the vortex trails taken from 16 mm "lm.) The two scenes were taken from frames in motion pictures of the smoke trails taken during the #ight tests conducted by Barber and Tymczyszyn [59]. The initial multiple-pair vortex wake of the L-1011 changes quickly into a single pair of nicely formed vortices. The planes of the vortices, which were initially vertical, then rotate to an approximately horizontal
Fig. 81. Oblique and end views of a vortex pair which has been given initial sinusoidal displacement waves that are out-of-phase ( "1803) on circular arcs as if trailed by an aircraft executing roll oscillations [180]; wavelength"6b, initial wave amplitude"0.23b; b"143.
580
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 82. Wave characteristics as a function of time for various input amplitudes when waves are out-of-phase [180]; "1803. (a) Peak-to-trough amplitude. (b) Rotation of wave planes from initial vertical attitude.
Fig. 83. Wave amplitude ratio, a/a , as a function of time to test G for linearity of the vortex dynamics to input amplitude when input waves are out-of-phase [180]; "1803.
Fig. 84. Photographs from below of vortex wake of L-1011 following roll-oscillation of about 73 amplitude [180]. (From motion pictures of #ight tests conducted by Barber and Tymczyszyn [59]; courtesy of M. R. Barber and R. M. Rhine.) (a) "rst photo; (b) about 1 min later.
attitude while the wave amplitude grows a small amount. Thereafter, the vortices change only a little and do so slowly. As a consequence, the two vortices then appear roughly as a parallel sinusoidal pair which could have been generated by an aircraft executing a series of yaw oscillations. These #ight results con"rm at least the qualitative nature of the dynamics of the vortex wake predicted by the numerical analysis and do much to clarify
the wake dynamics to be expected from various wave inputs. The foregoing results also show that atmospheric disturbances to a vortex pair that are out-of-phase do not result in destructive mutually induced wave growth. The numerical predictions are in agreement with the #ight test results, because it was found that there was no sign of any kind of unlimited wave growth for the out-of-phase
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
581
case similar to that which occurs in the symmetric or in-phase case. It is concluded, therefore, that the antisymmetric or out-of-phase case does not lead to any destructive vortex interactions. The out-of-phase case does produce a vortex con"guration that is stable and therefore much more persistent than even a parallel, non-disturbed wake shape. These results are con"rmed by #ight tests [59] which include observations of the "laments and penetrations vortex wakes. 7.3.5. Vortex pair; intermediate phase angles, 03( (1803 When the waves on the starboard vortex "lament are shifted forward to yield intermediate phase angles, the vortex dynamics is a combination of the in-phase and out-of-phase cases. The mid-phase case of "903, shown in Fig. 85, illustrates the mixture of the two kinds of dynamics such that the waves appear as loops in the end views. As time progresses, the troughs or lower parts of the waves grow in amplitude in very much the same way as the in-phase case. If the numerical simulations were continued, the vortex "laments would probably (in the presence of other disturbances) go into the disconnecting and linking parts of the instability that lead to loop formation and the disruption of the orderliness of the wakes. The curves shown for the amplitude of the input waves as a function of time (Fig. 86) illustrate how phase angle a!ects the growth rate for b"143. It is found that any initial input of that magnitude would eventually go into the rapid wave growth in the wave troughs which is typical of the in-phase dynamics if the phase angle is between 03 and about 1503. Even though the wave amplitude reaches a maximum and then begins to decrease, the vertical extent of the wave continues to grow so that the loop in the end view of the vortex opens up more and more. As time increases further, the troughs of the waves get deeper until the mutual-induction process of disconnecting and linking occurs. It then appears that the in-phase instability comes about for a broad range of phase angles, but a longer time is required for the cases with larger phase-angle di!erences, just as more time is required for the smaller input wave amplitudes. During the early parts of the event, the vortex motions in general resemble more closely those of the case at one end of the range than the other, depending on which is closest. Hence, any out-of-phase disturbances grow more slowly and inconsistently than the in-phase disturbances. 7.3.6. Concluding remarks on the ewect of phase The study of the e!ect of the phase of input waves on the growth of the instability has shown that growth is in#uenced by several parameters in addition to wavelength. First, the phase of the input waves on the port and starboard waves should be the same if rapid growth is expected from the mutually induced instability.
Fig. 85. Oblique and end views of vortex pair which has an initial displacement of sine waves which are midway between in-phase and out-of-phase [180]; "903, wavelength"6b, initial amplitude"0.23b; b"143.
Furthermore, only when the input waves are nearly in phase does the instability proceed to linking and loop formation for disintegration of the wake. That is, wave growth occurs initially if the input waves are out of phase, or nearly so, but the growth stops after the plane of the waves has rotated through 903. Secondly, the growth rate of the waves are more rapid for larger input wave amplitudes than for smaller ones. As illustrated in the tow tank experiments of Liu [80], strong turbulence in the ambient #uid accelerates the decomposition of
582
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 86. Wave amplitude as a function of time for various input phase angles, , of the impressed wave pattern [180]; b"143.
a vortex wake and permits the linking instability to occur at shorter wavelengths. Also, no new destructive mechanisms appear to be initiated by any of the in-between values of the phase angle. It is concluded that any out-of-phase wave components only contribute to the delay of the onset of the rapid growth part of the in-phase instability. That is, the farther that is from 03, the more time is required for the onset of the rapid growth associated with the inphase case. When the port and starboard waves are approximately out-of-phase, destructive wave growth appears to be delayed inde"nitely.
8. Multiple-pair instabilities 8.1. Introduction If the spanwise distance between the vortices in the pair is based on the span of the wing, the amount of time required for the mutually induced instability to go to completion is too long to help with the solution of the capacity problem at airports. If, however, the mutually induced instability can be initiated in multiple vortex wakes, as demonstrated with sawtooth loading in Section 6, which employs multiple vortex pairs, the time required for wake alleviation may be brought into the useful range. That is, the wake interaction is still based on the spanwise distance between vortices, but, in the case of vortex wakes which are composed of multiple pairs, the e!ective vortex span is the #ap length rather than the wing span. Hence, the distance or time required for wake decomposition to become completed can easily be reduced by a factor of 4 or more. Since systematic guidelines have not been developed for the design of vortex
wakes, span loadings, or wing structures that accomplish the desired wake disruptions, any investigation directed towards such a goal is complicated by at least the following factors: (1) the number of parameters available for variation is large; (2) the vortex interactions are a combination of several kinds of dynamics including the inphase and out-of-phase ones; and (3) the analysis method to be used must be capable of treating "nite disturbances, large vortex distortions, and the e!ect of viscosity and turbulence on wave growth. E!orts have been made, therefore, to ensure and to accelerate the onset of the mutually induced instability by manipulating control surfaces [49,74,155,172], or the entire aircraft [59], in order to impress large initial wave amplitudes on the vortex lines as they are generated. The objective, of course, is to reduce the time required to achieve rapid growth in wave amplitude and wake disruption. Large initial wave amplitudes are e!ective in reducing the time for completion of the mutually induced instability but mutiple-#ap vortices proceed more rapidly. Since the mixing achieved with multiple vortex pairs is on a scale of the span of the #ap and not of the wing, they bring about more rapid linking, and the vortex wake appears to be even more unstable, e.g., Section 6. In several of the cases studied [64,69], it was found that two vortex pairs were unstable enough downstream of the wing so that mutually induced, in-phase waves on the vortices grew quickly and then linked across the span to form vortex loops that destroy the coherence of the wake. The short lifetime of the coherent character of vortex wakes comes about primarily, because of the reduced spanwise distance between vortices of opposite sign. For example, the small distance between vortices, as produced by sawtooth loading, makes them more unstable so that wave growth is easy to initiate. Also, the reduced spanwise distance in the vortex pair reduces the time scale for the mutually induced instability, so that the time required for complete disorganization of the wake is reduced by the ratio of the spanwise distance between the vortices to the span of the wing. Since the wakegenerating wing used in the fundamental experiments with sawtooth loading had seven #aps per side, or 14 #aps in all, the reduction in time to wake destruction is 1/14th of that required for the wing with the #aps zero con"guration. In this section, an analysis is presented of the wakes shed by the (303, 03) and the (303, 303) con"gurations of the B-747 with outboard spoilers deployed con"gurations. The objective of the analysis is to show how reduced span between vortex pairs accelerates the demise of lift-generated wakes. It is found, however, that in practice the mutually induced instability is not initiated unless the aircraft is put through rapid roll oscillations to generate large amplitude waves on the vortices shed by the inboard #ap and wingtips [181].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
8.2. Overview of yight tests An illustration of rapidly dispersing wakes that work with landing gear extended and #ight spoilers deployed was obtained inadvertently during the latter part of the #ight test program with the B-747 and L-1011 aircraft by Barber and Tymczyszyn [59] at Dryden Flight Research Center. The primary purpose of the research program at that time was to evaluate the e!ectiveness of turbulence injection by use of spoilers already on each of the aircraft as suggested in wind-tunnel studies [62,63]. The spoiler con"gurations were "rst tested in straight and level #ight to determine how much alleviation of the wake hazard could be achieved. A T-37B aircraft was used to probe the wake to determine the level of hazard posed in comparison with the aircraft in its normal landing con"guration. After the straight and level tests had been completed on both the B-747 and L-1011 aircraft, #ight tests were conducted to determine if the alleviation achieved with #ight spoilers was altered by turning or rolling maneuvers. That is, the #ight tests were conducted in order to answer the question, `do either turning and rolling maneuvers adversely a!ect the hazards posed by the wakes produced by the aircraft with spoilers deployed?a In the #ight experiments, it was found that the wake hazard behind both a B-747 and L-1011 aircraft was signi"cantly altered when the roll-oscillation maneuver was added to their #ight procedure (Table 6). Unfortunately, the roll-oscillation maneuver applied to two different aircraft brought about two very di!erent responses, and neither was anticipated. A theoretical e!ort was then undertaken to "nd an explanation for the #ight results. In summary, the #ight tests showed that, when either the B-747 or the L-1011 aircraft was #own in
583
straight and level #ight, the wake-induced rolling moments with spoilers deployed was about one-half to twothirds of the value when spoilers were not deployed. When the B-747 aircraft was #own with the combination of spoilers deployed and roll oscillations, vortex interactions were generated that reduced the wake-induced rolling moments on a following aircraft to about one-eighth to one-fourth of the value observed for the conventional landing con"guration. That is, the combination of spoilers and roll oscillations with the B-747 reduced the wake overturning moments induced on a T-37B probe aircraft during a direct following encounter to the point where the probe aircraft did not experience an uncontrollable coherent rolling moment at separation distances as small as one and one-half nautical miles behind the wake generator. The pilots reported that the ride during penetration of the wake was like that with a car over a bumpy road, with no coherent rolling moment. In contrast, the vortex wake of the L-1011 aircraft responded in a dramatically di!erent way from the B-747 response, when spoilers were deployed and the aircraft executed roll oscillations. That is, when the roll-oscillation maneuver was added to the landing con"guration with spoilers deployed, the wake hazard did not decrease as with the B-747, but became both more intense and more persistent [59]. As explained in the previous section, the roll-oscillation maneuver of the L-1011 imparts an initial set of wave displacements that are out of phase (i.e., "1803), rather than in phase. Analysis of a set of waves on vortex "laments, suggests that the vortex pair goes from the input shapes to a stable con"guration. The stable con"guration comes about after the wave planes on the two vortices in the pair roll through 903, so that the vortex cores appear in the horizontal plane as
Table 6 Information on #ight tests conducted with roll or pitch oscillations [59] Con"guration Aircraft
Flaps
Spoilers
Maneuver
Results
B-747
303/03
Locked in retracted position
Straight and level #ight
Wake attenuated by about a factor of 2
B-747
303/303
2, 3 & 4 AT 453
Straight and level #ight
Wake attenuated by about a factor of 2
B-747
303/303
2, 3 & 4 AT 453
Roll oscillations at 6 s/cycle
Wake devoid of coherent rotary #ow at 3 n mile
B-747
303/303
Locked in retracted position
Roll oscillations at 6 s/cycle
Wake similar to unattenuated wake shed during straight and level #ight
L-1011
333
2, 3, 4 & 5
Roll oscillations at 4.6 and 9.2 s/cycle
Did not change wake hazard from straight and level #ight character. Very di!erent from B-747 results
L-1011
333
2, 3 & 4
Pitch oscillations at 2.3, 4.6 and 9.2 s/cycle
Excites and changes period of ScorerCrow instability
584
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
snaking railroad tracks (Figs. 81 and 84). The vortices now both lie approximately in the horizontal plane which is a more stable form of the vortices than the one laid out during straight and level #ight, and is therefore more persistent. In other words, the analysis in the previous section explains the #ight results obtained with the L-1011. The analysis to follow provides an explanation for the #ight test results obtained with the B-747 during roll oscillations [181]. Since an immediate explanation for the test observation with the L-1011 aircraft was not available, e!orts were made to determine an explanation for the alleviation achieved. It was even thought that the unexpected and unusually large change in the hazard posed by the vortex wake of the B-747 executing roll oscillations might be a new and possibly important vortex wake instability. An analysis by Holbrook [182] explored the possibility that the sinuous shape of the vortices was large enough that the probe aircraft would have only intermittent encounters with the hazardous portions of the wake. The overturning moments would also then be intermittent. It was thought that the rolling moments perceived by the pilot would then be reduced, even though the peak values had not been changed appreciably. In another study carried out in the Langley Air Tow Facility, Jordan [156] approximated the #ight experiment by activating the same control surface motions, but without allowing the aircraft model to roll. He found that the time-dependent changes in lift across the span caused the vortices generated at the #ap edges to cross the centerline of the aircraft #ight path each time the roll controls were reversed. The observations made in Jordan's experiments did not indicate whether a new kind of wake instability had been
triggered or whether already known vortex mechanisms were responsible for the wake dynamics that were observed. 8.3. Estimate of steady-state span loadings The normalized steady-state span loadings on the B-747 and L-1011 are presented in Fig. 87. The approximate weights of the aircraft (263,000 kg (580,000 lbs) for the B-747 and the 159,000 kg (350,000 lbs) for the L-1011) during the #ights at an altitude of about 10,000 ft above sea level at an indicated velocity of 150 kts were used to determine the lift coe$cients and angles of attack on the aircraft. The span loadings presented in Fig. 87 were then used to determine the strengths and locations of the vortices for both aircraft in their various #ap con"guration (Table 7). Since a reliable method for determining the span loading when spoilers were deployed was not available, the span loadings and the vortex distributions on the aircraft were estimated in those cases by assuming that the lift on the wing where the spoilers are deployed is reduced. For example, the loading on the B-747 with spoilers 2, 3, and 4 deployed is assumed to be approximated by the span loading when the #aps are set at (303, 03). Not approximated is the higher level of turbulence introduced by the spoilers. Similarly, the wake of the L-1011 with its #aps at 333 and spoilers activated is approximated by the vortices listed in Table 7. It should be noted that the strong vortex shed by the inboard edge of the inboard #ap on the B-747 is not present on the L-1011. The di!erences in the #ap design and placement on the wings of the two aircraft probably account for the di!erences in the two wakes in
Fig. 87. Estimated span loadings for test aircraft [181].
!0.061
0.188 #0.046 Q Approximate values
0.185 #0.052 0.060 Q Approximate values !0.063 !0.021 !0.063 0.058 0.225 0.058
#0.110 #0.065 #0.110 #0.0545 !0.020 #0.045 0.219 0.346 0.219 0.225 0.266 0.18 #0.130 #0.064 #0.054 #0.064 #0.0765 #0.103 #0.097 0.381 0.455 0.465 0.455 0.464 0.433 0.41 1.38 1.38 1.38 1.38 1.33 1.33 1.33 03/03 303/03 303/303 303/303 03 333 333 B-747 B-747 B-747 B-747 L-1011 L-1011 L-1011
Stowed Stowed Stowed 2, 3, 4 at 453 Stowed Stowed 2, 3, 4 & 5 deployed
c c c c c >
>
C2 C1 C *
8.4. Two-dimensional simulation of wakes
Flaps
Spoilers
585
the landing con"gurations. Another di!erence which appears to impact the wake-vortex hazard potential, is the somewhat tapered span loading on the B-747 as compared with the more elliptical loading on the L-1011. Experience indicates that alleviation is easier to achieve on tapered loadings than on wings which shed strong wingtip vortices.
Aircraft
Con"guration
Table 7 Locations and strengths of wake vortices trailing from starboard half of wing [181]
>
C3
Vortex
>
C4
>
C5
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Two-dimensional simulations of the wakes of the B-747 and L-1011 are "rst presented as background information, and to show the di!erences in the wakes under steady and level #ight conditions [181]. It is, of course, assumed that the vortex strengths do not vary signi"cantly in the #ight direction. The two-dimensional computations do not include the three-dimensional effects of the mutually induced instability nor the vortex dynamics that goes with it. Comparison of the twodimensional predictions with those computed for the three-dimensional dynamics helps to identify any vortex dynamics instigated by roll- and pitch-oscillation maneuvers. The lines shown in Figs. 88 and 89 depict an end view of the trajectories taken by the vortices from their initial positions listed in Table 7 to their locations 60 spans behind the generating wing. A distance of 60 spans is about two nautical miles behind the B-747 and about 1.53 n mile behind the L-1011. Intermediate distances are not marked on the "gures. The single vortex pair shed by the B-747 with #aps (03, 03) descends unchanged (Fig. 88a). Four of the 5 pairs of vortices shed by the aircraft in its landing con"guration (i.e., #aps (303, 303); Fig. 88b), orbit about one another to form periodic cauli#ower patterns. The "fth and most inboard pair "rst moves downward and inboard until the in#uence of the other vortices has diminished to the point where they can move upward as an isolated pair. In #ight, turbulence from the fuselage, engines and landing gear would cause the inboard vortex pair to coalesce. A contrasting vortex motion develops when the outboard #ap is withdrawn on the B-747 so that only three vortex pairs remain in the wake (Figs. 88c and d). The tip vortices move downward to form an isolated pair but the two #ap vortices execute large circular orbits and then they re-associate to form new pairs of vortices that move o! separately. The e!ect of turbulence, "nite core size, three-dimensional interactions, and changes in vortex strengths from those estimated here can all a!ect the details of the trajectories presented in Figs. 88c and d. However, the presence of the negative inboard vortex pair and its ability to in#uence strongly the other #ap vortices suggests that the large vortex excursions needed to explain the #ight results observed at Dryden Flight Research Center might be produced thereby.
586
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 88. End views of two-dimensional trajectories of vortices in wakes [181] of B-747 from initial locations to positions at ¹"60 (or ¹"100 as noted).
Fig. 89. End views of two-dimensional trajectories of vortices in wakes [181] of L-1011 from initial locations to positions at ¹"60. (a) Roll oscillations of 73 amplitude. (b) Pitch oscillations with same wingtip amplitude as roll oscillations in Fig. 90a.
The wakes shed by the various L-1011 con"gurations consist of either two or three vortex pairs. Since the vortices in the two-pair cases are both of the same sign,
the vortices simply rotate about one another while the entire wake descends (Figs. 89a and c). The presence of a third vortex in the #aps 333 con"guration produces
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
587
Fig. 90. Oblique and end views of wake of B-747 #aps (03, 03) con"guration at three time intervals after beginning of maneuver [181].
a di!erent pattern from the two-pair cases, but the trajectories resemble the pattern in Fig. 88b more than the ones in Figs. 88c and d. The results of the two-dimensional computations indicate that large vortex excursions appear not to be expected for the L-1011 #aps 333 case, because the locations, signs and relative magnitudes of the vortices are not the ones needed for alleviation. 8.5. Three-dimensional simulation of wakes: B-747 The three-dimensional time-dependent dynamics of the wakes shed by the B-747 aircraft during pitch and roll oscillations are now discussed [181]. The dynamics of the vortex wakes were computed by use of the method described in Section 7.2, where the e!ect of phase of the input waves on a vortex pair was studied. Once again the wake was assumed to be generated as a function of time as if the aircraft entered the "eld of view at the left side of the "gure, and exits on the right, moving at one coordinate marker per unit time. As a result, the dimensionless time indicated in each "gure represents the spans of travel of the wake-generating aircraft from the beginning of the event. As done previously, the wakes are displayed on a 303/303/903 oblique graphical view to
yield a three-dimensional perspective of the wake. Only the #exible portions of the wake are displayed. The end views of the wake are again presented at a larger scale (i.e., four times) to show more clearly the size of the waves and their change in shape with time. Also, symbols are placed on the "laments every two spans to assist in the understanding of the vortex shapes. In order to compare the cases more readily and to simulate the #ight experiments, the numerical results presented here assume that one oscillation cycle is completed within six spans of travel by the aircraft, and a roll amplitude of 73. Since the aircraft #ew at 150 knots, or 1.28 spans/s, the theoretical oscillation period is about 4.7 s for the B-747 [59]. As indicated in Fig. 88a, the wake of the B-747 does not undergo any signi"cant changes for 60 spans (or 3 n mile) or more when no #aps or spoilers are deployed, and when no disturbances are imposed on the wake. However, when the same con"guration (i.e., cruise con"guration or #aps (03, 03)) executes a series of roll oscillations, the planes of the disturbance waves rotate through 903 while the wave amplitude grows from about 0.09b to about 0.4b , in roughly 60 time units (Fig. 90a). There after, the wave shape and size appears to stay the same from ¹"60 to 100 and probably until the wake decays
588
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
by di!usion; just as predicted in the previous section in the study of the e!ect of phase. The vortex "laments then simulate a wake trailed by an aircraft executing lateral oscillations, i.e., a snaking motion. It is interesting to note that the initial growth of the waves that was predicted does occur, but the amplitude appears to reach a maximum after the wave planes have rotated in a retrograde manner to an approximately horizontal plane. If only one sinusoidally shaped vortex "lament were present in the #ow "eld, it would rotate almost unchanged. Addition of the second vortex appears to bring about an increase in the wave amplitude by about a factor of four, while the planes of the waves rotate from the vertical to a horizontal attitude, and come to rest. For comparison purposes, the wake of the B-747 #aps (03, 03) con"guration executing pitching oscillations is presented in Fig. 90b. The wave planes of the vortices are noted to rotate slowly in a retrograde motion until they reach an angle of about 453 to the centerplane. The waves then grow in amplitude until the lower part of the vortex waves approach each other closely. By that time, the amplitude of the waves has grown considerably, and is still continuing to grow at a fast rate. In a #ight situation, the vortices would then disconnect and link across the pair to form irregularly shaped loops of vortex "laments. As mentioned previously, the vortex wake of the B-747 when both #aps (303, 303) and spoilers 2, 3, and 4 deployed (Tables 6 and 7) is approximated by the span loading of the (303, 03) con"guration. It is noted that the lift-generated wake then consists of three vortex pairs; that is, a tip vortex and two fairly strong vortices that are shed by the ends of the inboard #ap. The wake dynamics initiated by rolling and pitching #ight maneuvers are presented in Fig. 91. A di!erent response by the vortex wake is noted for the two di!erent initial displacements imposed on the wake. The roll oscillations instigate growth in the waves placed in the two #ap vortices much like those shown in Fig. 90a. As the waves grow, the vortices orbit, and the planes of the waves rotate from nearly vertical to curved diagonal planes. Wave growth "rst occurs while the planes of the two vortices are nearly parallel. During the later stages of the event, a linkingtype interaction appears to be taking control of the vortex motions. The present numerical results therefore suggest that the initial sinusoidal displacements of the vortex "laments brought about by the roll oscillations executed by the B-747 lead to vortex interactions which greatly amplify the vortex displacements at those stations where each wingtip is at its highest position. The numerical results suggest that periodic linking and loop formation may also be starting to occur at about ¹"32. Examination of the motion picture taken of smoke #ow visualizations during the #ight tests of Barber and Tymczyszyn [59] indicates the same kind of vortex motion and thus supports the proposed explanation.
Once again, however, the amplitude appears to be reaching a limit if the linking process does not begin between each set of #ap vortices. It was not possible to discern in the #ight #ow visualizations whether linking actually took place or not, because intense mixing in the #ow "eld was taking place. The ingredient which seems essential for growth of the waves after roll oscillations is the presence of the two vortex pairs that are of opposite sign and of comparable strength. The vortex pair shed at the wingtips does not become involved in the swinging interaction of the #ap vortices, but simply moves inboard and then descends as predicted by two-dimensional theory without the appearance of signi"cant wave growth or instability. These characteristics were also observed in the #ight #ow visualizations. The similarity of the numerical results, and the #ight #ow visualizations, suggests that the span loading and subsequent wake vortex distributions assumed in the numerical work are not too far from the one that occurred in #ight. The results presented in Fig. 91b for pitching motion illustrate an interaction that is a version of the Crow process. The small waves on the vortices appearing on the older parts of the wake (left-hand side of the "gures) are the beginnings of waves that will probably lead to linking. Presence of the third vortex pair does not seem to enhance or hinder the wave growth nor the approach to the linking process. If the aircraft is #own on a straight and level path, the end views of the vortex wakes are about the same as predicted by two-dimensional theory until the vortices undergo the wave growth that leads to linking. The occurrence of this sequence of vortex interactions was con"rmed by #ight test at Rosamond Dry Lake with the B-747 in the (303, 03) con"guration with the gear up and spoilers stowed (Fig. 60). Not so obvious was the "nding that a small amount of turbulence injected into the wake by deployment of any of the landing gear, or by slight yaw, was su$cient to inhibit the growth of the disturbance wave so that linking and loop formation do not occur (Fig. 60). The results obtained from the #ight tests that used roll oscillations suggest that, if an initial displacement of su$cient amplitude is given to the waves on the wake vortices, wave growth does occur to the point where linking and loop formation and the "nal demise of the organized wake results. It is concluded, therefore, that the dynamics observed in the wake of the B-747 following roll oscillations can be attributed to the span loading, which is responsible for the special wake-vortex structure that destroys the wake organization. 8.6. Three-dimensional simulation of wakes: ¸-1011 The three span loadings and vortex wakes presented in Table 7 for the L-1011 were used to carry out numerical simulations of the #ight tests. However, only the #aps (333), spoilers-deployed case is presented, because the two
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
589
Fig. 91. Oblique and end views of wake of B-747 #aps (303, 03) con"guration at three time intervals after start of maneuver [181].
other cases were quite similar, and showed no signi"cant wave ampli"cation that was new. It is to be noted in the three-dimensional computations shown in Fig. 92 that the vortices shed by the L-1011 (with #aps and spoilers deployed) rotate around each other in much the same way as indicated by the two-dimensional theory and shown in Fig. 89. Distortions of the initial shape of the "laments due to roll oscillations of the generating aircraft are again superimposed on the paths. It is di$cult to determine in the end views just what kinds of vortex interactions are taking place. The computations show that, throughout the computational interval, the vortices stay grouped together closely enough that they would probably coalesce into a single pair much the same as they do when the roll-oscillation maneuver is not being used. Subsequent examination of the #ow visualization sequences taken during the #ight test by Barber and Tymczyszyn [59] show that the vortices trailed by the L-1011
coalesce fairly quickly into a single pair at about 0.5 mile or so behind the aircraft. The lack of another vortex pair in the merged wake, which is of comparable strength and of opposite sign, made the wake dynamics observed in #ight appear almost the same as the numerical results displayed in Fig. 90a. That is, the wake of the L-1011 responded to roll oscillations of the generator aircraft as if it were composed of a single pair. Wake alleviation was not sensed by the probe aircraft, because destructive vortex interactions did not occur. In fact, the single vortex pair goes through the dynamics explored previously in the section on the e!ect of wave phase on vortex interactions. As illustrated in Figs. 81 and 84, the planes of the vortices roll through 903 so that the pair forms a sinuous trail in the horizontal plane that is more stable than without the roll-oscillation maneuver. In other words, the wake is more hazardous when a rolloscillation maneuver is executed with the L-1011 than when the aircraft #ies straight and level.
590
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 92. Oblique and end views of wake of L-1011 #aps (333) with spoilers deployed at three time intervals after start of maneuver [181]. (a) Setup in 40;80 ft Wind tunnel. (b) Water tow tank and carriage arrangement at Hydronautics, Inc.
and possibly quantify further the wake ingredients necessary to bring about the di!ering responses of the B-747 and L-1011 wakes to the roll-oscillation maneuver. Based on the results presented in this section and the corresponding #ights tests at Dryden, it is concluded that two ingredients in the vortex wakes of the test aircraft appear to cause the di!erent responses to the roll-oscillation maneuver. First, the B-747 sheds a fairly strong vortex near the fuselage, and the L-1011 does not. Secondly, the L-1011 sheds a vortex near its wingtip that is stronger relative to the #ap vortices than the B-747. These two factors combine to bring about an unstable vortex con"guration behind the B-747 that leads to linking and destruction of the organization of the wake. In contrast, the roll-oscillation maneuver of the L-1011 brings about a stable vortex-wake con"guration that persists. The roll-oscillation maneuver is responsible for both sets of wake dynamics, because it places large initial sinusoidal waves on the "laments that bring about interactions and dynamics that lead to the observed motions. It should also be noted that, even though the present analysis is based on fairly crude estimates of span loadings, and the vortex wakes that they trail, comparison of the numerical results with the #ight motion pictures of smoke visualization shows that the dominant features of the wake dynamics behind the two wake-generating aircraft have been well simulated. It is also concluded that the vortex-wake instability is not of a new type, but just a combination of the symmetric and anti-symmetric mutually induced instabilities that result from multiplevortex interactions.
9. Wake alleviation by wing 5ns 8.7. Concluding remarks on multiple vortex pairs
9.1. Introduction to wing xns
It is concluded that, for multiple-pair vortex wakes, wave ampli"cation requires at least two vortex pairs (four vortices in the wake) of comparable and opposite strength. The separation distances between the vortices must also be large enough spanwise to enable a linkingtype interaction that produces large-scale mixing in the wake. This approach can be tested by adding a vortex pair of opposite sign and of comparable strength near the fuselage of the L-1011. Modi"cation of the inboard #aps on a model of the aircraft to produce such an extra vortex pair leads to two-dimensional trajectories like the ones shown in Figs. 88c and d. Two-dimensional computations carried out during this study, but not presented here, showed that only the stronger fuselage vortex cases show promise. Since the strong tip vortex shed by the L-1011 tends to dominate the wake dynamics, the degree of alleviation to be expected will be less than that achieved with the B-747. Ground-based tests with con"gurations having fuselage vortices would help to clarify
Several con"gurations already described demonstrate that certain vortex interactions are able to bring about large-scale mixing in vortex wakes for substantial reductions in the rolling-moment hazard posed by lift-generated vortices. Since none of the designs discovered so far have negligible penalties, and are therefore currently considered to be unacceptable, a more generalized approach was taken in the search for an ideal wake-alleviation scheme [105,183]. Research was directed at "nding another way to bring about the vortex interactions desired. It was reasoned that not only should the spanwise distribution of wake vorticity be used to control wake dynamics, but a vertical distribution of vorticity should also be used to assist in bringing about the desired rapid disintegration of the wakes. That is, conventional wings shed a vortex sheet that is approximately #at (i.e., in the z"0 plane), and that has a small vertical depth. As a consequence, in conventional wakes the rollup begins at the ends of the vortex sheet near the wingtips, and proceeds
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
inboard. Since the vortex sheet is thin, the sheet winds up in a tight spiral that tends to concentrate the vorticity near the center of the spiral. Whatever vertical depth is present in the initial vortex sheet due to boundary layer on the wing and #aps winds up in the spiral tending to reduce the concentration at the vortex center. It was reasoned, therefore, that addition of vertical lifting surfaces to the largely horizontal wing surface would not only add vertical depth to the vortex wake at the wing trailing edge, but would also impart immediate horizontal motion to some portions of the vortex sheet shed by the wing. The optimum or preferred placement, size, etc. of these vertical surfaces, or wing "ns, and the e!ect that they have on the hazard posed by lift-generated wakes shed, became the subject of several research e!orts in the large wind tunnels at NASA Ames Research Center [105,106,183,184] which are summarized in this section. Although the foregoing reasoning was used to begin the exploration of wing "ns as wake-alleviation devices, the wake-dispersion mechanism appears to be more complicated and, as yet, not amenable to analysis. As a consequence, the study and any optimizations achieved have been carried out experimentally. As more computations were carried out, and when some test results became available from a water tow tank, #ow visualization and wake measurements indicate that the wake is already de-intensi"ed very near the wing trailing edge [93]. It also appears that the wake does not change much thereafter. As a consequence, e!orts so far have provided only a rough concept for the alleviation achieved with wing "ns. Since the results do indicate a great deal of promise
591
for e$cient and rapid wake dispersion, the study carried out so far on wing "ns is described. 9.2. Experimental setup in 40;80 ft Wind Tunnel Since the 40;80 ft Wind Tunnel at NASA Ames was readily available for tests of short duration during the 1970s, several wind tunnel entries were made in order to test the wing-"n concept, and to determine design guidelines experimentally [105,183]. In addition, in cooperation with Langley Research Center, test time was rented in the water tow tank operated by Hydronautics Inc. near Laurel, MD. Diagrams of the experimental setup in the two facilities are presented in Fig. 93. The crosssections of the test sections in both facilities are large enough that wall a!ects on a model with a span of 70.5 in (1.79 m), or 3% scale, are negligible. However, downstream distances available to study the lift-generated wake of a B-747 model are limited in the wind tunnel by the length of the test section and in the tow tank by the depth of the water and the length of the tank. The tow tank is 410 ft (125 m) long, 24 ft (7.6 m) wide, and 12.5 ft (3.8 m) deep. Tests were conducted in the wind tunnel at a free-stream velocity of ; "131 ft/s (40 m/s, q " 20 lb/ft), and at a velocity of 12.5 ft/s (3.8 m/s) in the tow tank. In both facilities, a B-747 wake-generating model (0.03 scale) is mounted from the top of the fuselage by a slender, streamlined strut. In the wind tunnel, the model is mounted near the entrance to the test section, and in the tow tank it is mounted on the forward carriage (Fig. 93b). A plan view of the B-747 model used as the wakegenerating aircraft is presented in Fig. 94. The model had
Fig. 93. Facilities used to obtain data on wing "ns [183].
592
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
its landing gear extended, its leading-edge slants fully deployed, and the wing was designed so that the #aps could be deployed in their stowed, takeo!, or full-landing position. The horizontal tail was set at 03 relative to the fuselage, or aircraft reference plane (i.e., the horizontal tail is at 03 when the aircraft is at 0). A rectangular wing (b "13.1 in (33 cm), AR "5.5, b /b "0.186) was used to represent the following aircraft used in the #ight program (either the Gates Lear Jet or the T-37B). As indicated in Fig. 93, in the wind tunnel, the following model is placed at the downstream end of the test section on a support strut mounted onto a tower which could be raised and lowered and also translated across the airstream. Movement of the following model permits a survey to be made of the energetic part of the vortex wake shed by the wake-generating aircraft, so that the maximum value of the rolling moment can be found, and contours of equal rolling moment determined. The downstream tower could be located at distances as large as 80 ft (24 m or 13.6 generator spans) behind the wakegenerating aircraft, or at any closer distance. Based on the 70.5 in (1.79 m) span of the B-747 model, the 80-ft station corresponds roughly to a 0.5 mile scale distance behind a full-scale aircraft. As explained in Section 6.3, during a typical run, the following model is held "xed at various vertical and lateral positions in the wake for 1 min. The rolling moment at each position #uctuates due to turbulence in the free stream of the wind tunnel which causes motion or meander of the wake as it trails from the wake-generating model [161]. A survey of the wake cross-section is then made wherein the maximum value measured at each location is "rst recorded. The maximum value of all of the measurements taken is then used as the maximum rolling moment in the wake for that con"guration. The distribution of maximums is also used to map out rolling-moment contours. In the wind tunnel, a few con"gurations were tested at a "03, 43, 83, and 123. Most however, were tested only at 43 (C "1.2) to expedite * the investigation of a wider variety of con"gurations. In the water tow tank, the following model is mounted on a second carriage that maintains a "xed distance behind the forward carriage. Since the turbulence level, and consequently the vortex meander, is negligible in the tow tank, the #ow "eld is surveyed for maximum rolling moment by placing the following model at a "xed spanwise station during a run. In order to carry out a vertical survey at the chosen spanwise station, the following model makes a vertical traverse through the wake during a traverse along the channel. In the wind tunnel tests, the devices used to inject vortices on top of and below the vortex wake shed by the wing consisted of vertical surfaces, or "ns, mounted on the wing at a large angle of attack to the free-stream direction (Figs. 94 and 95). A variety of "n shapes were tested in the wind tunnel at the spanwise and chordwise
locations shown as dots in Fig. 94. In the water tow tank, the only "n design tested was the circular-arc planform (Fig. 95e) because it was determined as the best design and limited test time was available. Circular-arc "ns were chosen for the research program because Zimmerman [185] found that wings of circular planform did not stall even at large angles of attack. A study by Moghadam [186] found that planforms of elliptical planform might be even more e!ective as wing "ns, but they have not been tried as yet, because the "n e!ectiveness was found to not increase appreciably when the "n height exceeded a given height. The "n angle of attack was taken as positive when the vortex it sheds had the same direction of rotation as the nearby wingtip vortex. The "rst part of the optimization process explored whether "n performance was best when they were mounted on the upper or lower surfaces of the wing. As expected, a search technique showed that "n locations on top of the wing were much more e!ective than those mounted on the bottom surface of the wing. It is believed that the greater e!ectiveness on top of the wing is attributable to the higher dynamic pressure over the wing as compared with that under the wing. The higher velocity over the top of the wing produces a greater lift on a "n (and consequently a stronger vortex) than if it were mounted under the wing. Therefore, all of the data to be presented for wing locations, angles of attack, etc., were obtained with a "n or "ns mounted on the upper surface of the wing. The search for the optimum location, size, etc., for the various shapes of "ns shown in Fig. 95 was begun with the #at-plate "ns of rectangular planform, and then broadened to include all of the "n shapes shown in Fig. 95.
Fig. 94. Plan view of B-747 wake-generating model [183].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
593
Fig. 95. Fin shapes used in tests [183]. (a) Rectangular and triangular "ns. (b) Rectangular and circular-arc "ns.
9.3. Test results 9.3.1. General comments Wake-hazard data were obtained with a wide variety of "n sizes and shapes to study the e!ect of changes in the angle of attack, location, chord and height on wake hazard. The "rst of the two papers cited in the reference list was restricted primarily to "ns of rectangular planform [105], whereas the second paper considered a wider range of "n designs, and also explored the various "n parameters in more detail [183]. Material contained in both papers is summarized here. As mentioned previously, all of the tests were conducted with the "ns mounted on top of the wing. The test results will be presented for "ns with a planform of rectangular and triangular shapes at the same time, because both were used in the optimization process. 9.3.2. Fin angle of attack The "rst design parameter chosen for study was the angle of attack of the "n. Two sets of data are presented in Fig. 96, and in "gures to follow, so that variations with "n design can be illustrated. Since the "ns were all of low aspect ratio, it was not certain whether or not they would stall at the higher angles of attack. In Fig. 96, the angle of attack was varied from !123 to #363, where the positive sign means that the "n is shedding a vortex of the same sign as the nearby wing tip. According to the data presented in Fig. 96, the "n rapidly decreases the wake hazard as its angle of attack is increased and stall of the
"n, if present, does not appear to a!ect alleviation performance. At "rst it appears that negative angles of attack are ine!ective. However, in tests conducted later in the 80;120 ft Wind Tunnel at NASA Ames [184], negative angles of attack were found to produce similar results. However, the required angle of attack must be larger by about 303 on a swept wing to achieve the same rollingmoment reduction because of the spanwise #ow on the upper surface of the wing due to sweep. The larger negative angles of attack required for the same alleviation carry with them a drag penalty over and above that carried by positive angles. Di!erent "n shapes yield about the same result, and as expected, smaller "ns will produce comparable results if they are placed at higher angles of attack, e.g., circular arc "ns. It is noteworthy that the e!ectiveness of wing "ns for alleviation of vortex wakes is approximately proportional to the angle of attack used. Wing "ns are the only wake alleviation mechanism known to have such a proportional characteristic. 9.3.3. Spanwise location The next parameter studied was the spanwise location of the "n, mounted on the upper surface of the wing (Fig. 97). Various "n sizes were tested at several spanwise locations, and all showed a distinct preference for the location near a point midway between the aircraft centerline and the wingtip. When the results for the circular "n are added to Fig. 97, it is found that smaller "ns have the same characteristics, but that the bucket has
594
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 96. Wake-induced rolling moment on following wing with angle of attack of "ns [183].
Fig. 97. Wake-induced rolling moment on following wing with spanwise location of "n [183]. (a) Rectangular and triangular "ns; h /b "0.085, a "123. (b) Rectangular and circular-arc "ns.
a smaller spanwise extent and smaller bene"t (Fig. 97). As a consequence, more testing is required to be certain that the smaller "ns are in their optimum location. All of the "n con"gurations exhibited the same sensitivity to spanwise location. It was found that the optimum location of a "n was insensitive to the lift on the wing, or to the angle of attack of the "n.
9.3.4. Chord of xn The variation of the wake-induced rolling moment with the chord of the "n for several "n con"gurations is shown in Fig. 98. As the length of the chord of the "ns is increased, the alleviation once again also increases almost linearly up to about c /b "0.08. Above that value an increase in chord appears to be no longer bene"cial. All "n shapes are noted to provide almost linearly increasing alleviation with an increase in chord up to some point where further increases in the "n parameter yield little bene"t.
9.3.5. Height of xn A similar linear trend is found for "n height (Fig. 99), but the bene"t of "n height is limited to values up to around h /b "0.04. This "nding tends to indicate that the original idea for the use of wing "ns to add depth to the vortex wake is not the basis for the success achieved by use of wing "ns. In fact, the decrease in bene"t as h /b increases above 0.08 indicates that the proximity of the vorticity shed by the "n to the wing surface is important in the reduction of the wake-induced rolling moments. Such a variation with "n height is of bene"t, because small heights have less penalty in drag than tall "ns. It is noted in Figs. 98 and 99 that two "ns of a given shape (indicated by a double line) are usually more e!ective than a single "n, but not necessarily superior to a single rectangular "n of the same wetted area. If wing "ns are to be folded down into or onto the wing for cruise, two smaller "ns might be easier to handle than one large "n.
9.3.6. Circular-arc planform As indicated previously, one pair of circular-arc "ns was made with the Clark-Y airfoil section to duplicate the wings studied by Zimmerman [185]. Another pair of wing "ns was also made with the GA(W)-2 section to "nd out if a more recent airfoil design would yield improved performance. A measurable di!erence was not found, but the use of two circular arc "ns at the same time was found to be advantageous. Since preliminary results were promising, these two "n designs were tested more thoroughly in the wind tunnel than other designs, and they were the only ones investigated in the water tow tank. Data from the two test facilities are compared in Figs. 96}100 with the data for other "n shapes. None of the tests indicated that one airfoil shape was to be preferred over the other. Any airfoil shape is believed to be superior to #at-plate cross-sections.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
595
Fig. 98. Wake-induced rolling moment on following wing with chord of "ns [183]; a "43.
Fig. 99. Wake-induced rolling moment on following wing with height of "ns [183]; a "43.
The circular-arc "ns were placed at larger angles of attack than any of the other "ns, because the data of Zimmerman [185] indicated that wings of circular planform do not begin to stall until they reach an angle of attack of 453. Since the #ow angularity over the generator wing is uncertain, the true angle of attack of the "n is unknown. It is known that the local #ow angle over the upper surface of the wing is such that positive "n angles of attack are actually larger than its angle relative to the free-stream direction. The data in Figs. 98}100 show that two "ns with semi-circular planform and Clark Y airfoil sections provide as much or more alleviation than one #at-plate rectangular "n of the same dimensions. Furthermore, two circular-arc "ns, located within about one "n chord of each other, may be easier to install onto #ight hardware than one large "n. The rolling-moment data are presented in Fig. 100 on an expanded scale, so that a comparison can be made of the data from the two facilities. In general, there is little change in the level of the rolling-moment coe$cient, C , J over the range of downstream distances that were tested in the two facilities. Where substantial di!erences do occur, it is believed that the optimum "n position in one
Fig. 100. Comparison of wind tunnel and water tow tank measurements with B-747 model equipped with circular-arc "ns [183]; following wing C 1.
596
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
facility was not the same as in the other, because of the changes in span loading on the wing in the water tow tank due to the nearness of the free-surface of the water. From an overall view, the two sets of data do not di!er appreciably even though the downstream distance to the follower is over three times as large in the tow tank as in the wind tunnel, and the tow-tank model is only 0.4b from the free surface of the water. The experimental optimization process did indicate that the smaller circular-arc "ns provide the needed alleviation with less penalties in lift and drag. This result is consistent with the test results that indicate that those "ns with circular arc planform yield the strongest vortex for the smallest "ns. The best con"guration found for the B-747 in the test time available was a combination of two circular-arc "ns on both the port and starboard wings as shown in the photograph in Fig. 101. The circular-arc "n was found to be the best amongst those tested [185]. If an application is to be tried, it is suggested that "ns of elliptic planform also be tested to "nd out if they do have superior performance when used as vortex injection devices [186]. The lift and drag on the B-747 model is shown in Fig. 102 for the rectangular and circular-arc "ns. Results to be described indicate that properly designed "ns can reduce the associated penalties, and in fact, can increase the lift and reduce the drag of the conventional B-747 landing con"guration. It is felt that the vortices shed by the "ns enhance the velocity "eld over the wing so that any #ow separation on the #ap elements is reduced and
the overall #ow improved. Penalties due to weight and installation costs of a "n still exist, but the results obtained with the smaller "ns indicate that further optimization may lead to con"gurations wherein the wake rolling moments have been reduced to the desired level, and the lift and drag penalties are negligible. The lower drag measured in the water tow tank as compared with wind tunnel measurements is attributed to the lower turbulence and higher Reynolds number in that facility relative to the wind tunnel. The drag data presented in Fig. 102 also calls attention to the fact that contoured airfoils with rounded leading edges achieve leading-edge suction, so that the drag penalty associated with the circular arc "ns is less than the #at plate rectangular "ns. In fact, future tests in the study of the aerodynamics characteristics of wakes shed by aircraft should have been carried out only by use of "ns with airfoil shapes. Fins made of #at metal plate were used however, because they are much less expensive.
9.3.7. Multi-element xns Several "n con"gurations, which had several airfoil sections in close proximity (Figs. 95b and d), were tested in the wind tunnel. Some of these results are listed in the tables presented in Ref. [183], but are not shown graphically, because the alleviation was inferior to simpler "n con"gurations. Although the section lift coef"cients achievable with multi-element airfoils is usually higher, they may lose their advantage at low aspect ratios
Fig. 101. Photograph of model of B-747 mounted upside down on support strut with best "n con"guration (i.e., two circular-arc "ns mounted midway out on each wing) [183].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
597
Fig. 102. Variation of lift and drag with "n height of B-747 model when equipped with rectangular or circular-arc "ns [183]; a "43.
Fig. 103. Variation of wake-induced rolling moment with "n size for various "n con"gurations [183].
or when placed on a re#ection plane like the generator wing which has a boundary layer.
full-landing con"guration was held constant at 43 during the tests, so that the lift coe$cient was approximately, C "1.2, in both test facilities. The data fall in a band * about the rectangular "n data. Of most interest are those that are lowest, namely, the circular-arc and the blown#ap con"gurations. The data point in Fig. 103 for the "n with a blown #ap does not, however, necessarily represent the lowest rolling moment achievable with that "n, because the time needed to optimize its spanwise location, angle of attack, etc., was not available. Since the water tow tank facility was not set up to test blown-#ap con"gurations, those particular tests concentrated on the circular-arc "ns. All of the results indicate that the stronger the vortex shed by the "n, the more alleviation can be achieved. In order to have information on how the wake-induced rolling moment on a small following wing changes with distance across the vortex wake of a "nned con"guration, enough measurements were taken to draw contours of equal rolling moment for a wake shed by both a conventional and a "nned con"guration (Fig. 104). The rollingmoment contours for the "n-modi"ed wake are shaped quite similar to those of the unmodi"ed wakes. A signi"cant di!erence occurs, however, in the magnitudes of the contours in the inner and more hazardous parts of the wake. The "n appears to redistribute the wake vorticity, so that the interior of the vortex has reduced swirl velocities, but the outer parts are hardly changed because the contours for C "0.01 are about the same for both J con"gurations. Even though the contours for C "0.01 J are nearly the same, the rolling moment for the conventional wake is over 0.12 at the center, whereas the "n-modi"ed wake rises to only about 0.04 over a small region near the center. Such a large di!erence in rolling moment for a small change in span loading indicates that alleviation can be accomplished by designing the lift distribution to promote favorable vortex interactions.
9.3.8. Fins with blown yap Since the optimum spanwise location for a "n is in the vicinity of the inboard engine on the B-747 model, it seemed likely that high-pressure air from the engine could be used to enhance the lift or side-force capability of the "ns by chordwise blowing (Fig. 95f ). At the end of the test period, a single blown-#ap con"guration was tested at one location on the wing. The results are presented in the tables in Ref. [183] for two "n angles of attack at the maximum blowing available with the test set up (i.e., a blowing coe$cient based on "n planform of 0.5). The "n at the larger angle of attack did provide signi"cant alleviation, but there was not time available to carry out tests that would have optimized the various "n parameters. These preliminary results do indicate, however, that further consideration should be given to the "n location on the generator wing and to its angle of attack to "nd out if greater alleviation can be achieved with "ns having blown #aps. Also, the use of two or more "ns on each wing should be tried as a method for reducing the size or wetted area of the "n con"guration. 9.4. Discussion of xn conxgurations One means for comparison is to specify that the optimum "n is one that reduces the wake rolling moment a given amount, and that also causes a minimum penalty in lift, drag, weight, etc. (Fig. 103). The measured rolling moment for the devices tested is shown as a function of the ratio of the wetted area of the "ns to that of the wing. A data point as near as possible to the origin is desired, so that both the wake-induced rolling moment and the required "n size are small (a small "n is presumed to impose a smaller penalty than a larger "n). In this comparison, the angle of attack of the B-747 model in its
598
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 104. Contours of equal rolling-moment coe$cient as measured on following wing in wake of B-747 model [183]; a "43.
9.5. Ewect of rectangular xns on span loading It should "rst be noted that wing "ns are the only device discovered so far that produces alleviation in direct proportion to the size, de#ection of the "n and other factors that in#uence the strength of the vortex that it sheds. The alleviation produced by a "n con"guration has also been found to behave in an orderly way without any reversals of performance. The mechanism by which wing "ns achieve alleviation is not clear. It appears that the "ns modify the #ow over the wing so that the vortex wake distribution is modi"ed for rapid dispersal, but the details and concepts behind this process are unknown. As indicated previously, the "ns redistribute the loading on the wing as estimated by vortex-lattice theory (Fig. 105). It is noted that the larger rectangular "n changes the loading substantially over a portion of the span, but the smaller rectangular "n makes only small local changes. The alleviation brought about by the two "n heights is noted in Fig. 100 to be about the same, suggesting that some characteristic other than span loading may be the dominant factor in producing the alleviation achieved by "ns. 9.6. Concluding remarks on wing xns Various theoretical and experimental studies of the performance of aircraft models with "ns mounted on
their wings have not yet identi"ed the #uid-dynamic mechanism responsible for their e!ectiveness nor led to theoretical guidelines for their optimization. It is believed that the wing "ns impart horizontal or spanwise motion of vortex elements to bunch up and to spread out wake vorticity in order to generate interactions to rapidly disorganize and disperse vortex wakes. Several design features of wing "ns for alleviation of the hazard posed by vortex wakes were identi"ed by the test program. First the "n or "ns should be designed to produce the strongest vortex possible while minimizing the penalties associated with the design. The e!ectiveness of a "n design is strongly dependent on its spanwise location on the wake-generating wing. The mechanism of alleviation appears to require vortex placement and strength as well. If the "n is to achieve vortex generation by developing lift in the local airstream around the wing, it develops much more lift when mounted on the upper surface of the wing than on the bottom of the wing. The "ns should be made with an airfoil cross-section (rather than with #at plates) to decrease the drag of the device and increase its e$ciency. Finally, an improved understanding is needed for the details of the mechanism responsible for the rapid modi"cation of the vortex wake to a less hazardous con"guration, so that the design process can be optimized.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
599
Fig. 105. Span loadings as estimated by vortex-lattice theory for wing of B-747 landing con"guration equipped with various "ns con"guration [183]; a "43, c /b "0.085, C +1.18. *
10. Measurements in 80ⴛ120 ft Wind Tunnel 10.1. Introduction In the 1980s, the 40;80 ft Wind Tunnel at NASA Ames Research Center was modi"ed to increase the maximum velocity in the test section from 200 to 300 knots, and to add a large low-speed branch onto its circuit. The added branch has a test section that is 80 ft high, 120 ft across (24.4 m;36.6 m) and about 200 ft (61 m) long with a maximum velocity of 100 knots. The portion of the circuit devoted to the large test section is called the 80;120 ft Wind Tunnel. It is now the largest NASA facility, and consequently, has the greatest downstream test distance, which is the characteristic of interest to the wake-vortex program. A plan view of the wind tunnel (Fig. 106) illustrates the intersection of the test section and constant area di!user with the circuit of the 40;80 ft
Wind Tunnel. The test section alone is long enough that wake measurements can be made at downstream distances that simulate scale distances up to one mile (1.61 km) when models of 0.03 scale are used. Therefore, two tests of about three months duration each were conducted to obtain data on two models of subsonic transport aircraft (i.e., B-747 and DC-10). The purpose of the tests was to expand the database available from wind tunnels on the characteristics of vortex wakes shed by various con"gurations of subsonic transport aircraft [106,184]. As with previous wake vortex tests, the two wind-tunnel entries were designed to evaluate the potential hazard posed by various subsonic transport aircraft in the airport environment, and to develop guidelines for the design of high-lift systems of aircraft, so that their wakes disperse rapidly enough to allow in-trail spacings between aircraft to be safely decreased.
600
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 106. Plan view of test section region of 80;120 ft Wind Tunnel [184].
In both 80;120 ft Wind Tunnel test entries, a 0.03 scale model of the Boeing 747 with a span of 70.5 in (1.79 m) was again used as a wake-generating model. In the second test entry, a 0.03 scale model of the McDonnell Douglas DC-10 with a span of 59.5 in (1.51 m) was also used as a wake-generating model. The test conditions are listed in Table 8. As noted in Table 9, the con"gurations tested include the conventional landing and several modi"cations of it. The purposes of the tests were to provide data for estimating the interaction of following aircraft with the wakes of standard landing con"gurations, and to develop a database on how various wing-design parameters a!ect the wake-vortex structure and its decay with time or distance behind the wake-generating aircraft. In order to assess the characteristics of vortex wakes, the following wings were tested or analyzed that range in size from 0.186 to 1.21 times the span of the wake-generating model (Table 10). Also, a two-component hot-"lm anemometer probe was used to determine the up- and down-wash distributions in the wake at both 81 and 162 ft (24.7 and 49.4 m) downstream measuring stations. An overview of the information obtained during the two test entries, and several applications of the data are presented in this section. 10.2. Experimental setup in 80;120 ft Wind Tunnel The test setup used in the 80;120 ft Wind Tunnel is about the same as, but better equipped than, the one Table 8 Test conditions [184] used in 80;120 ft Wind-Tunnel (24.4;24.4 m) Free stream velocity"131 ft/s Dynamic pressure"20 lb/ft Distances to following models"81 and 162 ft
Table 9 Data on wake-generating models [106,184] B-747 Model Scale of model "0.03 Wing span b "70.5 in Average chord of wing cN "10.1 in Reynolds no. based on cN Re "660,000 Aspect ratio AR "6.96 Wing area S "4.94 ft Horizontal stabilizer angle "03 Landing gear extended Flaps and slats fully deployed
DC-10 Model
"0.03 "59.5 in "7.92 in "518,000 "7.5 "3.56 ft "03
used in the latter part of the 1970s test program in the 40;80 ft Wind Tunnel (Fig. 107). In order to carry out a test, one of the wake-generating models, B-747 or DC-10 (Fig. 108 and Table 9), is mounted through a strain-gage balance to a strut in order to measure the lift, drag and pitching moment exerted on it by the free stream. Instead of locating the experiment on or near the centerline of the wind tunnel, as was done during the 40;80 ft Wind Tunnel tests, the models are now located o! to the side of the 80;120 ft Wind Tunnel centerline (Figs. 106 and 107). The o!-center mounting is used because the 80;120 ft Wind Tunnel merges with the circuit of the 40;80 ft Wind Tunnel along a diagonal junction (Fig. 106). Including the di!user, the constant area region is therefore longer on one side than on the other. Consequently, in order to maximize the downstream distance available for a test, the wake-generating models and following wings are mounted on that side of the test section. In the test sequences, the experimental equipment was con"ned to the test section wherein a 162 ft (49.4 m) separation distance is achieved by
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
601
Table 10 Data on following wings [184] No.
b (in)
C * (in)
C (in)
K *# (deg)
K 2# (deg)
AR
S (ft)
f (Hz)
f (Hz)
1 2 3 4 5
13.12 13.13 6.00 35.97 72.04
2.41 2.84 6.00 7.86 15.67
2.41 0.85 6.00 2.41 4.72
0 30 0 30 30
0 15 0 15 15
5.44 7.14 1.00 7.00 7.06
0.220 0.168 0.250 1.283 5.100
156.0 156.0 190.0 30.5 12.0
13.0 13.0 12.0 11.5 7.3
Fig. 107. Diagram of experimental setup in 80;120 ft Wind Tunnel [184].
locating the wake generator in the forward part of the test section and the survey rig for the follower model at the end of the test section. An 81 ft (24.7 m) separation distance is achieved by locating the generator model just o! to the side of the turn table and not moving the following model and its traversing gear. In this way, the much larger and more cumbersome traverse mechanism that supports the following model need not be moved in order to change the separation distance. An inverted mounting of the generator model is again used to minimize interference of the strut wake with the vortex wake of the generator model (Fig. 107). The model wake then moves upward away from the strut wake, which tends to go straight downstream. The angle of attack of the wake-generating model is set remotely through an actuator and indicator mechanism. The landing con"gurations of the wake-generating models (Fig. 108) include extended landing gear along with fullydeployed leading-edge slats and trailing-edge #aps. As in the past, and as indicated in Table 9, a designation of
#aps (303/303) is used to indicate that the B-747 wakegenerating model is in its full landing con"guration with the leading-edge slats, landing gear, and trailing-edge #aps fully deployed. The other two con"gurations are again part of the study to "nd design guidelines that will make it possible to build e$cient aircraft with acceptably alleviated wakes. In the (303/03), or modi"ed landing con"guration, the inboard landing #aps are fully deployed, and the outboard ones are stowed. The rest of the model is in its full landing con"guration. The third con"guration that was tested, Table 9 and Fig. 108, consists of the conventional landing con"guration with a fairly large "n, like those discussed in Section 9, mounted on the upper surface of each side of the wing to accelerate the dispersion of the vortex wake. The models used as following wings are all made with a NACA 0012 airfoil section and have the planforms shown in Fig. 109 and the characteristics indicated in Table 10. The planforms for the swept wings are based on an average value obtained for the leading- and
602
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 108. Plan view of wake-generating models to illustrate #ap arrangements and locations of wing "ns [184].
Fig. 109. Overhead photograph of following wings used in test program [184].
trailing-edges and taper ratio of a large number of the wings of subsonic transport aircraft now in service. In this way, the following wings used in the tests are representative of subsonic transports, but do not resemble any of them closely. The models are constructed of wood and aluminum, and then covered with "berglass to ensure a smooth, durable "nish along with structural rigidity and adequate frequency response. As a result, the natural frequencies in roll and pitch of the model-balance combinations are several times larger than the lift and rollingmoment frequencies encountered. The trailing model or wing is mounted on a sting (Fig. 107) that can be raised and lowered over a height range of about 8 ft (2.44 m). The vertical traverse mechanism is attached to a tower that can be translated laterally, or spanwise, across the airstream over a range of about 18 ft. The following-wing or wake-encountering model is attached to its sting through a strain-gage balance located inside the centerbody of the wing, so that
the wake-induced lift and rolling moment can be measured. Both a 1 and a 2 in internal-type balance were used in the tests to more adequately cover the wide range of loads that occur when the smallest to the largest following wings encounter a vortex wake. As a result, the natural frequencies in roll and pitch, f and f , of the model-balance combinations (Table 10), are several times larger than the lift and rolling-moment frequencies encountered. As a reference, the natural frequency in roll of the model/balance combination tested during the 1970s was 30 Hz, i.e., when a wing equivalent to model C1 was used. Because the physical distance between the wakegenerating model and the following model is quite large (81 or 162 ft, 24.7 or 49.4 m), a probe to measure the dynamic pressure (i.e., total and static pressure) was attached to the support strut of each model. A correction could then be applied to the coe$cients of the follower if the variations were too large. It was found that the dynamic pressure near the wake-generating model always agreed within measuring accuracy with the test section value, but that the dynamic pressure at the following model was about 1% larger. An analysis of the e!ect of a di!erence in dynamic pressure between the two stations showed that both the lift and rolling-moment coe$cients should be adjusted by a factor that is about the one-fourth power of the ratio of the two dynamic pressures. Since the correction for these test results is then 1.0025, an adjustment in the data was not made. 10.3. Test procedures The procedure used to measure the rolling moment on the following wing consists of several steps. The
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 110. Lift and drag on con"gurations of B-747 wakegenerating model as a function of angle of attack [184].
generator model is "rst set up in its desired con"guration and angle of attack. After the loads on the wake-generating model are recorded (Fig. 110), the following wing is placed at various locations in the vortex wake of the generator model. Since the airstream is not perfectly uniform, the position of the vortex wake moves about with time to cause di!erent amounts of lift and rolling moment to be induced on the following wing. The analog signals from the strain gage balances in the wakegenerating and in the following wings are "ltered with a low-pass "lter at 10 Hz in order to eliminate electronic noise and high-frequency oscillations of the models. (The hot-wire signals were also "ltered in the same way.) Since the "ltered signals also varied with time, the time-varying rolling moment indicated by the strain-gage instrumentation is recorded during a test interval of 1 min. Data samples are then taken of the time-varying "ltered record every 0.1 s, so that 600 data samples are recorded from the 1 min test interval. The permanent or retained record consists of the maximum and the minimum of all of the 0.1 s values that occurred during the 1 min test interval, and also the average or mean value of all 600 samples. A total sample of about 1 min in duration was found to be long enough that two to four peak values of about the same magnitude would occur at the 81 ft test station, but, as will be explained later, is believed to be inadequate at the 162 ft station. If the airstream is perfectly uniform and the vortex wake is steady, di!erent locations of the following wing relative to the wake-generating model cause di!erent amounts of lift and rolling moment to be induced on the following wing. Furthermore, the induced loads would not vary with time. In most wind tunnels however, the induced loads change with time as the wake vortices move about in the wind tunnel in response to the turbu-
603
lent eddies in the airstream. Since these perturbation velocities have a substantial distance (81 or 162 ft), or time, over which to in#uence the vortex positions, movement or meander of the vortex wake may not be negligible at the station where the following model or wing is located. In the 80;120 ft Wind Tunnel where the two tests were conducted, the vortices appear to meander from their time-averaged location up to about 2 in (5 cm or 0.0284b ) at a distance of 81 ft (13.8b ) behind the wake-generating model [162]. At the 162 ft station (27.6b ), the meander distance is twice as large or about 4 in (10 cm or 0.0568b ) from their time-averaged location. Hence, measurements vary considerably with time when made in or near a vortex with a small core radius. For these reasons, data are taken at a sequence of points in a grid as illustrated in Fig. 111 to "nd the location where the rolling moment is a maximum. If the span of the following model is small relative to the span of the generator model, the largest rolling moment is assumed to occur when the centerline of the following model is aligned with the axis of one of the vortices in the wake. These values are then used as the elevations at which spanwise surveys are conducted with various following wings or with a two-component hot-"lm anemometer probe. Since the vortex centers are usually located at di!erent elevations on each side of the centerline (Fig. 111), the survey elevation on each side of the wake is changed at the centerline, so that both surveys pass through the vortex center for their respective sides. The centers of the vortices are indicated as y and
z , because they are identi"ed as the locations where
the rolling moment on a small following wing is a maximum for that side of the centerline. 10.4. Comparison of data from two large wind tunnels Since the 80;120 ft Wind Tunnel had not been used previously for wake-vortex research, and since the
Fig. 111. Illustration of grid pattern used to "nd maximum rolling moment in vortex wakes.
604
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
wake-generating models and the following models, center bodies, strain-gage balances and support hardware were all new, it seemed prudent to "rst compare the new results with those obtained in the 40;80 ft Wind Tunnel. Therefore, the test program was begun by measuring the rolling moment on several con"gurations of the B-747 that had been tested previously. When the data from the two facilities are compared, it was found that they agreed well within the data scatter, or within about $5% [106]. 10.5. Ewect of span ratio on rolling moments As indicated in Fig. 109, the three following wings used in the tests include the swept wings, C2, C4 and C5, that all have the same planform which is a generic average of many of the subsonic transports now in service. Since they all have the same planform but di!erent spans, it is possible to study how the ratio of the span of the follower to the span of the wake generator, b /b a!ects the magnitude of the wake-induced rolling moments. Measurements were taken in the port and starboard portions of the vortex wakes for the three generator con"gurations of the B-747 (Fig. 112). As mentioned previously, the maximum values are believed to be representative of the most hazardous rolling moments in the wake. The data for both the port and starboard sides of the wake are presented as positive values in Fig. 112 so that both sides can be compared more easily. A dashed line at C "0.06 is used to indicate the approximate rollingJ moment capability typical of subsonic transport aircraft. Any points above the C "0.06 line indicate situations J where a following aircraft would have insu$cient rollcontrol capability on board to resist that imposed by the vortex wake of the generator. In fact, an analysis by Rossow and Tinling [104] of results obtained with #ight
Fig. 112. Maximum rolling moments induced on following wings of swept planform in vortex wake of B-747 con"gurations [184]; x "81 ft (24.7 m).
simulators suggests that an encounter with a wake near the ground is probably deemed unsafe by pilots unless the imposed rolling moment is down to about half of the roll authority on board the follower. Such a restraint leaves a reserve of control power available to compensate for the surprise of the encounter and to allow enough roll control by use of ailerons to bring the following aircraft back to a level attitude. As indicated in Fig. 112, when the wake generator is in its conventional landing or (303, 303) con"guration, the rolling-moment coe$cients decrease about linearly as the span ratio, b /b , increases. A similar response does not occur when the wake is shed by a con"guration designed to have a more benign alleviated wake. Since the swirl velocities have been reduced and the vortex core diameters increased, it was at "rst uncertain whether the rolling moments would increase or decrease with span ratio. It is gratifying, therefore, that in the alleviatedwake cases, the wake-induced rolling-moment coe$cients do not change signi"cantly with span ratio. The general trend of the plotted results tends to indicate that if an alleviated wake is safe for small following aircraft it is also likely to be safe for larger aircraft. The approximately constant rolling moment induced on following wings of various sizes by vortex wakes of alleviated con"gurations prompted a study by Rossow [187] of wing e$ciency that will be described in Section 12. Another observation to be noted in the data presented in Fig. 112 is the fact that when the following wing is the same size as the span of the wake generator, the imposed roll is about the same as the typical roll-control available with ailerons. This characteristic of wake encounters has been noted in the past by test pilots #ying in the wakevortex program. When the encounter of the aircraft with a vortex is of short duration or intermittent, a follower of the same size as the generator (or larger) should not experience overpowering rolling moments. A sustained encounter could, however, be judged to be marginally safe or unacceptable during landing or takeo!. The e!ect of the size of the following wing on its susceptibility to a vortex wake is illustrated for both the B-747 and the DC-10 in Fig. 113a as a function of the span ratio, b /b , and in Fig. 113b as a function of inverse span ratio, b /b . The ratio of rolling moment induced on the follower to the lift on the generator tends to deemphsize the e!ect of lift coe$cient on the results. Also, the use of span ratio on the abscissa accounts for the di!erence in relative size of the two wake-generating models. Included in Fig. 113 are two dashed curves that were obtained by use of the up- and down-wash curves at the 81 ft station for the DC-10 wake-generating model as input for a vortex-lattice code. As pointed out in Ref. [184], at some locations in the wake the method overpredicts the maximum rolling moments by up to 10}15% when the following wing is about half the size of the generating wing, and about 30% when the two wings are
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
605
Fig. 113. Comparison of wake-induced rolling moments on swept following wings as a function of span ratio and inverse span ratio [184]; x "81 ft (24.7 m).
about equal. Therefore, the fact that the computed values are above the measured ones is attributable at least partly to the computational method. The use of the inverse span ratio, b /b , permits com parison of the measured data with equations derived in Section 4 which estimate the lift and rolling moment induced by a line vortex (i.e., all circulation concentrated at the center). The closed-form expressions for the maximum values are given by Eqs. (17) in Section 4.2. Since these equations are a linear function of b /b at low aspect ratios, an estimate for the maximum rolling moment induced on a wing by a line vortex is a straight line through the origin in Fig. 113b. Extrapolation of the experimental data to b /b "0 indicates that the closed form expression, Eq. (17b), has the correct form. 10.6. Rolling-moment results: conventional landing conxgurations
model at only 43 angle of attack and with following wing C1. The purpose of the experiment was to determine how much, if any, the vortex wake of the aircraft model was changed due to values of yaw much larger than any possible error in alignment that might have occurred in the setup of the models and struts. Such a question was raised by previous tests which noted a signi"cant di!erence in the port and starboard magnitudes of the rolling moment imposed on following models, even though the model was aligned with the wind tunnel centerline within about $0.13. In order to be sure that the asymmetry in the wake was not due to small errors in yaw placement of the wake-generating model, tests were carried out at yaw angles of b"!23, 03, and #23. A 23 increment was chosen because it far exceeds the accuracy with which the yaw angle of the model can be placed during the setup of the experiment. The results presented in Fig. 114 show
The presentation of the results for the two wakegenerating models is divided into two groups. The "rst group, which will be discussed here, includes the conventional landing con"gurations. The second group, includes those con"gurations wherein modi"cations were applied to the wings of the wake-generating models in an e!ort to reduce the magnitude of the rotary velocities in the wake to alleviate the wake hazard for aircraft which might encounter them. 10.6.1. Ewect of yaw of the wake-generating model Since alignment of the model with the wind tunnel centerline could only be done within 0.13, and since the local airstream may not be exactly aligned with the wind tunnel centerline, a sequence of runs was carried out to examine the e!ects of yaw on the relative strengths of the port and starboard sides of the wake. The sequence of runs was carried out with the B-747 wake-generating
Fig. 114. E!ect of yaw angle on measured rolling moment on following wing C 1 in wake of B-747 model [184]; a "43, x "81 ft (24.7 m).
606
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
that small angles of yaw do not account for the asymmetries in the structure of the lift-generated vortices. It is concluded therefore that di!erences in the vortex wakes on the port and starboard sides are probably due to di!erences in the shapes of the two sides of the wing. 10.6.2. Ewect of angle of attack of the wake-generating model In the past, only a few run sequences were carried out wherein the angle of attack, a , was varied. As indicated in Figs. 115a and b, and as expected, the magnitude of the rolling moments induced on following wing C1 by the wake increase as the lift increases. The results for both the B-747 and the DC-10 at x " 81 ft (24.7 m) and 162 ft (49.4 m) are o!set indicating that some wake decay probably occurred. The larger di!erences at the lower angles of attack are believed to be caused by the turbulence introduced into the wake by the slats and #aps which operate there at signi"cant o!-design conditions. Past experience has shown that introduction of turbulence into the wake of a wind tunnel model can cause the wake-induced rolling moments to decrease by 5}30%. At the upper end of the angle of attack range, the rolling moments are about the same at the two downstream stations, indicating that wake decay is small when the wake-generating wing is operating at near-design conditions. A characteristic not observed in previous tests is a small amount of hysteresis that occurs in the lift on the generator model as the angle of attack is approached from above rather than from below. Once this characteristic was identi"ed, the angle of attack on the generator model was set by approaching the desired angle from above. In this way, the lift at a given angle of attack was the greatest obtained at a given angle of attack. The angle of attack is determined by an indicator fastened to the inside of the wake-generating model in order to eliminate
uncertainty in the angle of attack due to freedom of movement in the drive linkage. If only the intensity of (and not the distribution within) the vortex changes with angle of attack, the maximum rolling moment induced on a following wing would be proportional to the lift on the wake-generating wing. In order to test this possibility, the ratio of rolling moment to lift, "C "/C , is plotted as a function of the angle of J * attack (Fig. 116). Such a linear relationship appears not to exist with either aircraft model. Some of the reason for the non-linearity may be caused by #ow separation on the wake-generating wings at low angles of attack. It is believed however, that the primary cause is attributable to the changes in span loading as the angle of attack changes. The span loading changes with angle of attack, because the inboard parts of wings have large #ap de#ections and the outboard parts near the wingtip do not. A direct comparison of the wake-induced rolling moments produced by the two wake-generating models suggests that, at a given angle of attack, the larger B-747 has a somewhat more intense wake than the DC-10 (Fig. 117a). The more appropriate way in which to compare the results (which removes the sensitivity to C ) is * to plot the ratio, "C "/C as a function of the angle of J * attack (Fig. 117b). The rolling-moment intensity of the two wakes then appears to be comparable. The descent distances of the vortices below the generating wing at the 162 ft station were approximately twice the amounts measured for the 81 ft station becoming about 1.1b at a "103 for both the DC-10 and the B-747. 10.7. Rolling-moment results: alleviated landing conxgurations Another way in which to study the wakes of aircraft is to explore how sensitive or susceptible their lift-generated wakes are to changes in the planform of, or to
Fig. 115. Maximum rolling moment induced on following wing C 1 by wakes of standard landing con"guration of wake-generating models as a function of angle of attack [184].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
607
Fig. 116. Reduced maximum rolling moment, "C "/C , induced on following wing C 1 by wakes of standard landing con"guration of J * wake-generating models as a function of angle of attack [184].
Fig. 117. Comparison of maximum rolling moments induced on following wing C 1 by vortex wakes of the two wake-generating models in their standard landing con"guration [184]; x "81 ft (24.7 m).
devices attached to, their wings. The objective here is to determine whether changes observed in the wake of the B-747 that were found to be successful on the B-747 would also be successful in reducing the intensity of the rotary velocities in the wake of the DC-10 model. 10.7.1. Ewect of span of trailing-edge yaps Early in the wake-vortex research program of the 1970s, it was discovered that the wake intensity of the B-747 could be substantially reduced by changing the standard landing con"guration to the so-called (303, 03) #ap con"guration. The con"guration is achieved by placing the inboard #aps in their standard landing con"guration and the outboard #aps in their stowed position
(a simple form of sawtooth loading). In order to obtain more data on the characteristics of the mechanism produced by the special #ap arrangement, several #ap con"gurations were tested on both the B-747 and the DC-10 models wherein the spanwise extent of the outboard #ap was varied. In this way, the con"gurations tested include, at one limit, the outboard #ap as fully stowed, and at the other limit fully deployed. The intermediate spanwise #ap sizes that were tested include lengths of the outboard deployed #ap that are 25, 50, and 75% of the standard length. Once again, in order to reduce the in#uence of the magnitude of the lift on the rolling-moment data, the data are presented as "C "/C in Fig. 118. The measured J * data obtained with both aircraft models show that the
608
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 118. Variation of wake-induced rolling moments with spanwise size of outboard trail-edge #aps [184]; x "81 ft (24.7 m); a "43 for B-747; a "63 and 83 for DC-10.
induced rolling moment is a minimum when the outboard #ap is completely stowed (e.g., the (303, 03) #ap con"guration of the B-747). The higher value of rolling moment on the port side of the B-747 is consistently observed with this model, and is believed to be caused by the fact that the alleviation mechanism does not go to completion on that side of the centerline within the 81 ft distance from the generator to the following model. The maximum rolling moments are noted to be largest when both #aps are fully deployed. The test results also indicate that intermediate #ap sizes are not to be preferred. It was not possible to determine whether the vortex-linking mechanism attributed to the alleviation on the B-747 (Fig. 60) also applies to the DC-10. 10.7.2. Ewect of wing xns The mechanism by which lift-generated wakes are alleviated when vertical surfaces (wing "ns) are placed on the upper surface of wings is not clearly de"ned. It is, however, the one wake-alleviation scheme that has indicated substantial reductions in the wake-induced rolling moments for the B-747 model when it was tested over a range of wing-"n con"gurations (e.g., Fig. 97). It is of interest to now apply the wing-"n concept to the DC-10 to determine its characteristics and potential level of e!ectiveness on another aircraft with a di!erent high-lift system. The curve in Fig. 119 for the rolling moment as a function of spanwise location of a "n on the B-747 wing indicates that the optimum location for a "n is near the half-way point between the wingtip and centerline [106,183]. A similar result is also found for the DC-10 model (Fig. 119) whether the "n is at a positive or negative angle of attack. A di!erence occurs in the preferred magnitude of the angle of attack of the "n, because
Fig. 119. Variation of wake-induced rolling moment with spanwise location of "ns mounted on upper surface of wings [184]; following wing C 1, x "81 ft.
due to wing sweep, the #ow direction over the upper surface of the wing where the "n is located has a strong inboard component. The optimum spanwise location is about the same on both aircraft models. Any di!erences between the results for the two models may be due to the nature of the two wings, but it is believed to be more likely due to a di!erence in the relative sizes of the two sets of "ns used in the experiment. That is, when the B-747 model was tested, the "n size was 0.0567b ;0.0851b . When the DC-10 model was tested, the "n size was 0.0336b ;0.0672b . The smaller relative "n size was used on the DC-10, because larger sizes degraded the performance a disproportionate amount.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
It is concluded that the mechanism of wake alleviation by wing "ns is probably the same on the two wake-generating models, and that the magnitudes can be made comparable by changes in "n design. The approximately equal e!ectiveness of the "ns on the two models is not surprising. Although the two wing planforms appear to di!er somewhat, both were no doubt designed for minimum weight at a given lift to yield quite similar span-load distributions. If such is the case, the span loadings and the vortex wakes shed by the two models are similar enough that they are about equally susceptible to the in#uence of wing "ns. A number of wing-"n con"gurations were tested on both the B-747 and the DC-10 models at both the x "81 ft and the x "162 ft stations. Fig. 120 presents a summary of the rolling moment data obtained for the wide variety of con"gurations of the two wake-generating models as a function of downstream distance. If the curves were all parallel, the decay rate of the vortices would then have all been about the same. As is evident in Fig. 120, no general pattern appears to exist. The sets of curves for the two models indicate that the vortex intensity sometimes increases and sometimes decreases between the two stations. It is concluded that vortex stretching (and the associated intensi"cation) can account for some of the increase in rolling moment with downstream distance. Decay of the swirling velocities may also have occurred in some cases. The results presented in Fig. 120 will be discussed further in Section 13 to follow along with other information on the decay of vortices. 10.8. Measured spanwise distributions 10.8.1. Overview of data Spanwise surveys through the vortex wakes were made for several reasons. The most important reason was to obtain data on both the wake-induced loads and on the
609
velocity distribution in the wakes to determine the accuracy of the vortex-lattice theory used to calculate wakeinduced loads on encountering aircraft. When the lift and rolling-moment loads induced on following wings are known along with the up- and down-wash distributions at the same locations, the two should be connected by a theory for the loads, as demonstrated in the next section. The precision of the connection will determine the accuracy of the method and of the experimental measurements. If unexplained disagreements occur, #aws in either the theory or the measurements, or both, would need to be found. Another important reason for the measurements is the need for spanwise distributions of both loads and velocity for estimations of the dynamics of aircraft as they encounter vortex wakes. That is, the data will be used in ground-based simulators to study the encounters of aircraft with wake vortices. Other uses for the data include the modelling of vortex wakes as they form, the development of numerical methods for wake dynamics, and to study the characteristics of vortex wakes as they age in the #ow "eld a short distance behind the generating wing (i.e., up to 1 mile). In the surveys taken, each side of the vortex wake was treated separately (Fig. 121) because the vortex center (i.e., the location of the largest rolling moment) is usually at a di!erent elevation on each side of the centerline, i.e., by amounts from zero to 0.06b (Table 11). As described previously, the surveys are carried out by sequentially placing the wing at a number of spanwise locations from the centerline of the generator out to well beyond its wingtip (usually out to about 1.5b ) to establish the upwash in the outer parts of the vortex. Once again, the data taken were the maximum, the minimum, and the mean or time average of the lift and rolling moment imposed by the vortex wake on the following wing at each spanwise location. The same technique was used to measure the up- and down-wash distributions.
Fig. 120. Reduced maximum rolling moment induced on following wing C 1 by wakes of various con"gurations as a function of downstream distance [212].
610
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 121. Illustration of elevation change at wake centerline of path used to carry out spanwise surveys with following models and with hot-"lm anemometer probe [163].
Table 11 Locations of maximum rolling moments and lateral surveys [184] Con"guration of generator
Landing, #aps (303/303)
Modi"ed landing, #aps (303/03)
Landing, #aps (303/303) with "ns, a "183, y /b "0.480
Run no.
Following wing
Port side
Starboard side
>
Z
>
Z
!0.370
!0.471 !0.471 !0.471 !0.471 !0.471
#0.427
!0.342
#0.370 #0.370
!0.342 !0.352
13 28 19A 35 36
1 3 4 5 Hot "lm
15A 17 34 38
1 4 5 Hot "lm
!0.475 !0.475 !0.430
!0.627 !0.627 !0.627 !0.627
#0.501 #0.501 #0.398
!0.426 !0.426 !0.482
23 25 26 33 37
1 3 4 5 Hot "lm
!0.372
!0.512 !0.512 !0.512 !0.512 !0.512
#0.431
!0.400
#0.457 #0.340
!0.400 !0.454 !0.400
!0.342 !0.367
!0.397 !0.313
Spanwise survey taken.
After the locations of the vortex centers were found with following wing C1 as discussed previously (Table 11), spanwise surveys were made with it (Fig. 122) with several of the other following wings and with a hot"lm anemometer probe. Typical data points are shown in Fig. 122 to illustrate their distribution and scatter. In "gures to follow, however, in order to reduce the clutter in the "gures, the symbols are omitted and only a line between the measured points is shown. In the hot-"lm surveys, only the streamwise and vertical velocity components were measured. The two velocity components were
then combined to yield the distribution of up- and down-wash angle, w/u, across the wake. A single spanwise survey was made with Model C3 (the following wing with a 6;6 in planform) in order to "nd out if a wing of small span would produce more accuracy, and a better representation of the vortex wake being surveyed than following wings of larger span. Only one survey was made because the loads were too small to achieve acceptable accuracy with the strain-gage balances chosen for the test. An obvious extension of the smaller-is-better argument is to go to an upwash sensor of the smallest size
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
611
Fig. 122. Typical measured loads on following wing C 1 as it makes a lateral traverse through wake of standard landing con"guration of B-747 model [106]; a "43.
possible; namely, a hot-wire or hot-"lm probe. As a result, lateral surveys of upwash were made with a hot-"lm anemometer probe. After the data had been collected, various adjustments and corrections were applied to the results before they were used in the computations. An increment, *y" 0.028b (i.e., 2 in or 5 cm), was "rst applied to the span wise location to correct for a lateral o!set to align the centerline of the data with the centerline of the wakegenerating model. Various other adjustments were also applied to the data to correct for such items as local #ow angularity in the wind tunnel, any non-zero angle of attack of the following wing or hot-"lm gage relative to horizontal, and possible de#ections of the support sting, traverse tower and rail assembly due to air loads from the free-stream velocity. Although these displacements are each small, the combination appears to be enough to cause an o!set in the measured curves of about C "0.02 and C "0.002. The o!set in the torque dis* J tributions is determined so that the curves for rolling moment far from the centerline have about the same magnitude of rolling moment. Such an adjustment is based on the assumption that a slight twist or lateral asymmetry in the following wings causes a bias in the data [163]. 10.8.2. Up- and down-wash velocity distributions The data taken with a hot-"lm anemometer probe (Fig. 123) provide the up- and down-wash velocity distributions that are used with the vortex-lattice method to
Fig. 123. Up- and down-wash distributions measured with hot"lm probe along a lateral traverse through vortex centers of wakes shed by B-747 model [163]; a "43.
compute the spanwise lift and rolling-moment distributions on the various following models. Table 11 lists the con"gurations of the wake generator, the various following wings or hot-"lm anemometer probe for which a survey was taken, and the locations where the most intense rolling moments occurred on each side of the wake centerline. In the hot-"lm surveys, only streamwise and vertical velocity components were measured. The two velocity components were then combined to yield the distribution of up- and down-wash angle, w/u, across the wake (Figs. 123}126). An obvious feature in Fig. 124 is that the data at x "162 ft is not as smooth as the data at x "81 ft. The increased size of the #uctuations in the velocity distributions at x "162 ft is believed to be caused by the larger meander distances of the vortices at the greater downstream distance. The irregularities in the downwash data indicate a need for longer data-sampling times at downstream distances much greater than 81 ft to determine improved time-averaged and maximum and minimum values for the downwash; e.g., sample lengths of 2}4 min
612
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 124. Downwash distributions in wakes of the two wakegenerating models in standard landing con"guration at two downstream stations [184].
rather than 1 min. The longer sampling period allows more time for the center of the vortex to meander over the entire region for a more complete and consistent time-averaged value of the velocities at the measuring point. A longer sampling period would also help to determine an improved value for the time-averaged location of the vortex center. Even with scatter, the di!erences between the maximum and minimum data curves in Fig. 124 provide an indication of not only the variations in the velocity at a given point in the #ow "eld, but also of the lateral or spanwise displacement of the vortex center as it meanders about. Examination of the maximum and minimum curves in the vortex core region indicates that the vortex meanders sideways about 4 in (i.e., a 2 in radius) at the 81 ft station in both large wind tunnels, and about 8 in (or a 4 in radius) at the 162 ft station in the 80;120 ft Wind Tunnel. Such a variation is expected, because the greater downstream distance allows twice as much time for the turbulent eddies to convect, and to distort the vortices from their time-averaged locations. As long as the velocity of meander is not too rapid, the analog data coming from the hot-"lm anemometer is not signi"cantly altered by the 10 Hz low-pass "lter in the circuit. At 10 Hz, the wavelength of an eddy in the
airstream is about 13 ft (i.e., between 2 and 3 spanlengths). The most surprising feature of the data presented in Fig. 124 is that some of the up- and down-wash velocities in the vortices are noticeably higher at x "162 ft than at x "81 ft. These increases in the swirl velocity with downstream distance indicate that vortex intensi"cation rather than decay occurred. As can be seen in Fig. 120, the maximum measured rolling moments were sometimes less and sometimes greater at the x "162 ft station compared with values at the x "81 ft station, which is an indication that vortex changes with downstream distance are not consistent. Therefore, the rolling moment and the downwash velocity data are consistent with each other, because the instantaneous rolling moments calculated by use of the measured maximum velocity distributions are larger than the measured ones at either the x "162 ft station or at the x "81 ft station. In support of the alleviation e!orts described in the previous paragraph, measurements were also made in the wakes of the B-747 and DC-10 models when con"gured with wing "ns and in the modi"ed landing con"guration (Figs. 123, 125 and 126). In Fig. 123b, data are presented only at the 81 ft station for the B-747 model equipped with rather large wing "ns. In Fig. 123c, the B-747 model had its outboard #ap stowed for the modi"ed landing con"guration. Unfortunately, results were not obtained at the 162 ft station for these two con"gurations. Data were obtained at both stations for several other wing-"n con"gurations of the B-747 and DC-10 models at the 81 ft station (Figs. 125 and 126). The smaller "n sizes in Figs. 125 and 126 were used in an e!ort to "nd more e$cient alleviated con"gurations and to "nd out if the vortex wakes of alleviated con"gurations decay or decompose more rapidly than those of conventional landing con"gurations. It is concluded that, once formed, conventional and alleviated wakes decay at about the same rate unless some sort of three-dimensional instability causes the coherent nature of the wake to break up before the wake decays completely. 10.8.3. Diagnosis of velocity measurements Certain characteristics observed in the data presented in Figs. 123}126 are related to the environment in which the vortex wakes are immersed [162] and to the way that the hot-"lm anemometer data were taken. It is recalled that the time-averaged data presented in Figs. 123}126 represent the measurements taken during a 1-min period at a given point, while the vortex center moves about randomly. In the data-taking process, the 1-min period is divided into intervals of 0.1 s to yield 600 data samples. The maximum and minimum data points are obtained as the two extremities of the 600 samples taken during the 1 min. If the wind tunnel airstream had no turbulence (and therefore no meander), the time-averaged, maximum and minimum data would all be the same
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 125. Downwash distributions at two downstream stations in wakes of two con"gurations of B-747 wake-generating model equipped with small wing "ns [184]; a "43; y /b "0.24, c /b "0.085, h /b "0.014.
Fig. 126. Downwash distributions at two downstream stations in wakes of two con"gurations of DC-10 wake-generating model equipped with small wing "ns [184]; a "83; y /b "0.24, c /b "0.057, h /b "0.017, a "#183.
(Fig. 127a). Since the wind tunnel airstream does contain turbulence, the vortex moves about (meanders), and is stretched and compressed to change the magnitude of the swirl velocities in the vortex; thereby leading to the three curves in each part of Figs. 123}126. In order to understand the e!ect of the meander and of the stretching processes on the relative shapes of the time-averaged, maximum and minimum curves, "rst consider the hypothetical case where the vortex meanders only in the vertical direction. When the vortex moves vertically away from its time-averaged location, the vertical velocity measured along a line across the wake through the time-averaged center of the vortex simply decreases everywhere. The envelope of the absolute value of all such measurements is then the same as if the vortex were stationary (Fig. 127a).
613
If the vortex meandering motion is restricted to the lateral direction only, and does not stretch or compress (i.e., the vortex remains straight, and moves about as a long rod), the velocity curves would all have the same shape, but would be displaced laterally as illustrated in Fig. 127b for the time-averaged, and the two extremities of motion. If a number of instantaneous curves were plotted for all amplitudes of meander, the extremities of the maximum and minimum curves would form an envelope with a #at top and bottom. As the meander distance increases, the #at top and bottom of the envelope would also increase in the lateral direction, but not in magnitude. Next consider the hypothetical case illustrated in Fig. 127c wherein eddies in the airstream combine to bend and stretch the vortex locally, but do not move the vortex center from its time-averaged location at the measuring station. In that case, a lateral or vertical displacement of the center of the velocity curves does not occur. However, the amplitude of the velocity increases in the core region, because vortex stretching reduces the core radius, and by conservation of angular momentum, increases the swirl velocity (Fig. 127c). Since vortex intensi"cation occurs over only the core region, which is usually small, the imposed rolling moment is not changed appreciably, if at all, provided the span of the following wing is more than several core diameters. Small-scale eddies immersed in the vortex would probably cause small instantaneous variations in the pro"le of the swirl velocity (Fig. 127d). It is noted in Fig. 124 that the amplitude of the instantaneous velocity is increased primarily in the core region, and that some broadening of the velocity pro"le also occurs. Since the maximum and minimum curves in Figs. 123}126 are made up of the envelopes of the extremities of the data taken at each survey point, they would include all of the enhanced velocity variations due to vortex motion, stretching, and eddies. The complexity of the interaction of the vortices with the airstream turbulence makes it di$cult to estimate the amount of vortex enhancement to be expected, but it seems that the processes discussed in the foregoing paragraphs, and illustrated in Fig. 127, could account for the larger velocities at the x " 162 ft station. That is, it is conjectured that both meander and vortex stretching occur to form an envelope of the maximum and minimum velocity curves that can have amplitudes and spreading that increases with downstream distance } at least for once. At the 162 ft station, evidence of vortex stretching is believed to be associated with rolling moment measurements found at the periphery of the meander region rather than at the time-averaged location of the vortex center. It is believed that a series of experiments designed to explore the foregoing conjectures is needed to clarify the various characteristics in the data associated with vortex meander and stretching. It should
614
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 127. E!ect of turbulence and vortex dynamics on downwash velocity distributions [212]. (a) (303/303); (b) (303/303) "ns; (c) (303/03).
be remembered that, as aggravating as vortex meander is in the wind tunnel when high-quality measurements are desired, the same or similar phenomenon is often present in the atmosphere [50,122,160]. An improved understanding of how turbulence a!ects the intensity and decay of vortices in the wind tunnel would no doubt enhance the understanding of vortex behavior in the airport environment. A beginning towards a correction or adjustment by which measurements in a turbulent airstream could be converted to velocity distributions for a uniform non-turbulent free stream has been tried with modest success by Baker et al. [89], but was not tried here. Consideration was also given to the possibility that some of the vortex motions at the measuring stations were due to the self-induced ampli"cation of meander, but insu$cient data was available to indicate a connection. Improved and other measurement techniques should be brought to bear on the need for more information on vortex structures [111,188]. 10.8.4. Lift and rolling-moment loads A number of lift and rolling-moment distributions were measured at both downstream stations [106,184]. In order to present the data more compactly, it seemed best to present a shortened version of these distributions at the same time that the data is used to examine the validity of a vortex-lattice method for the computation of the loads on aircraft when they encounter a vortex wake [163]. Therefore, the data and the comparisons are presented in the next section.
11. Validation of vortex-lattice method 11.1. Introduction Throughout the wake-vortex research program, e!ort was, and still is, directed at the development of reliable models and tools for the representation and prediction of the structure and dynamics of vortex wakes, and their interaction with aircraft. As a part of this e!ort, the study reported in this section was carried out in order to obtain an improved understanding of the accuracy of an available computer code to calculate loads on lifting surfaces embedded in the rotary and rotational #ow "elds of vortex wakes [163]. In order to be able to test or validate a computational method for the loads induced on a wing embedded in a vortex wake, the 80;120 ft Wind Tunnel was used to obtain data on the up- and down-wash distributions across the vortex wakes of several con"gurations, as presented in the previous section. The time-averaged velocity distribution data is used as the input #ow "eld for the computer code at the location of the wing in the #ow "eld. The lift and rolling-moment loads on various following wings are also measured at the same locations in the #ow "eld, i.e., along the same line as used to obtain the velocity distributions. Comparison of the measured and predicted loads with each other should then be connected by a single link, i.e., a method for predicting the loads. Not only does such a comparison provide a validation of the computational method, but it also provides a check on
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the "delity of the experimental equipment, and methods used to obtain the data. It was reasoned that the method to be chosen for study must be easy to apply to a large variety of con"gurations, because the number of aircraft con"gurations in the subsonic transport #eet is large. Another reason for simplicity is that the method must not use much computer time (i.e., it should be fast), so that a large number of solutions can be obtained quickly for spatial analyses and for simulation of the dynamics of aircraft-wake encounters. Along with the foregoing requirements, the method should also be accurate enough, so that given a reliable velocity "eld as input, the computed lift and rolling moment fall within the scatter of the values measured in the wind tunnel. A method developed by Hough [139] that ful"ls these requirements is the same vortexlattice method used in various wake-vortex studies [10,60]. 11.2. Applicability of vortex-lattice method A variety of theoretical methods could have been tested as the link between the computed and measured lift and rolling moments. Only the vortex-lattice method is used in the comparisons to be presented, because it is simple to apply, is robust and reliable for many con"gurations, and has the capability to include a variety of wing shapes and vortex structures. Therefore, all approximate methods such as those based on strip theory [10], and those based on global-type arguments [176}178], were discarded as too unreliable for the comparisons being made, even though they can provide insight into vortex/wing interactions. The vortex-lattice method chosen for this study is based on potential #ow theory which assumes that the #ow "eld is steady with time, incompressible, inviscid, and that #ow separation or stall is negligible [139]. Since the velocity "eld that interacts with the following or encountering wing is brought about by a vortex wake, the #ow "eld is solenoidal (or rotational) and not potential. Therefore, if a potential-#ow method, like the vortex-lattice method, is to be used in lift-generated wakes, it must either be modi"ed in some way, or the #ow "eld must be reinterpreted, so that it conforms with potential#ow theory. If the velocity "eld is impressed by a vortex system, the boundary conditions on the various lattices that represent the wing may be speci"ed by (1) assuming that each panel responds to the local #ow angle; or (2) that the wing panels are inclined at an angle to a uniform free stream. The inclination of each lattice panel is assumed to be equal to the angle of attack in the #ow "eld at the control point of the panel. The second interpretation changes a rotational problem into a potential one thereby making the mathematics and #ow "eld consistent. No matter which interpretation is used, the strengths of the vortice-lattice panels are adjusted, so
615
that there is no #ow through the encountering wing at the control points, and the "nal results are the same. In the vortex-lattice method, the lifting panels are constructed by superposition of horseshoe vortices. The cross-stream component of the horseshoe is swept or unswept in order to best "t the planform of the wing, while the other two legs of the horseshoe extend in the downstream direction to in"nity. All three legs of the horseshoe lie in a z"constant plane, which is where the wing camber and the up- and down-wash distribution are applied, i.e., a thin-wing boundary condition. The method employs only one layer of lattices, and does not include a separate lattice or panel system to separately represent the upper and lower surfaces of the wing or tail surfaces being considered. When the geometry of the horseshoe lattice has been established, the strengths of the horseshoe vortices are set in combination by a matrix inversion, so that the boundary conditions on the wing are satis"ed everywhere. When such a potential #ow technique is applied to a wing placed in a rotating and rotational (or solenoidal) #ow "eld, the applicability of the predictions is, at least academically, open to question. That is, since the #ow "eld of the vortices is rotational and not potential, the use of a potential-#ow method is, in principal, not valid even though a reinterpretation is applied. Also, it is reasoned that the oncoming stream may not be considered as a shear #ow composed of a spanwise distribution of vertical velocity. If such an assumption is made, not only is the shear #ow solenoidal and not potential, but the vertical momentum in each vertical shear layer is in"nite rather than "nite, as in a vortex. If however, it is assumed that the #ow "eld and wing are recon"gured, so that the free stream is uniform rather than rotational, and that the wing is twisted to match the angle of attack imposed by the vortex system, the simulated problem is potential. Discussions in the literature justify the assumptions needed to treat the loading on the encountering wing as if the oncoming stream were uniform, rather than rotational, and that the vortex downwash "eld is interpreted as wing twist (or as local angle of attack) [163,189}192]. 11.3. Comparison of predicted and measured loads 11.3.1. Lift The measured time-averaged spanwise distributions of up- and down-wash angle presented in Fig. 123 were used as input into a vortex-lattice code [139] to predict the lift on following wings C1, C4, and C5 (Figs. 128}130) as they encounter the vortex wake shed by one of three con"gurations of the wake-generating model. In each part of the "gures, the computed time-averaged distributions (solid lines) are compared with the measured timeaveraged distributions (data shown as open-circle symbols). It is to be noted that the comparisons have been
616
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
restricted to the time-averaged data, because their use is more straightforward than either the maximum or minimum data sets. In general, the comparisons in Figs. 128}130 indicate that the lift distributions computed by use of the vortexlattice method are in good agreement with the measured values. The agreement of the results in Fig. 128 for following model C1 are very good considering the complexity and unsteady character of the #ow "eld. The comparisons made for the larger following models, C4 and C5, are not as good in the region at and between the vortex centers. A systematic e!ort was made to be sure that the discrepancy between the results was not due to misalignments or adjustments in the data nor to approximations in the mesh size, spacings, etc., in the vortex-lattice code.
Fig. 129. Comparison of measured lift induced on following wing C4 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
Fig. 128. Comparison of measured lift induced on following wing C1 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
Examination of the comparisons for following model C1 indicate that the predictions follow the measured data well within experimental accuracy. The larger than usual discrepancy for following model C1 in the port vortex behind the (303/03) con"guration is not unexpected, because the alleviation mechanism for that wake did not go to completion for that side of the wake. As a result, two vortices are in close proximity causing the wake to be very unsteady, and the rolling moments to be somewhat higher. The generally good agreement in Fig. 128 for following model C1 indicates that the assumptions made in order to apply the potential-#ow vortex-lattice method to the rotational #ow "eld of vortex wakes are valid approximations for small span ratios, b /b . Furthermore, since following model C1 is the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
617
Fig. 130. Comparison of measured lift induced on following wing C5 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
smallest of the three following wings, it is the one expected to su!er most from #ow separation or stall whenever the vortex #ow "eld impresses a large angle of attack on the following wing. Since no such deviation is noted for following model C1, #ow separation probably is not the cause of the discrepancies that appear for following models C4 and C5 in Figs. 129 and 130. It is concluded therefore, that the di!erences between the computed and measured data are due to some characteristic of the #ow "eld that is not included in the vortex-lattice method or in the application of the boundary conditions. Since the agreement of the predicted and measured data for following wing C1 is very good, it is also concluded that the experimental and data reduction techniques are adequate and produce reliable data. 11.3.2. Rolling moment The sequence used for the comparisons presented in Figs. 131}133 for rolling moment parallel those presented previously for lift. Once again the rolling-moment distributions computed for following model C1 (Fig. 131) are in very good agreement with the measured data. The values computed for following model C4 (Fig. 132) are also in quite good agreement in most regions except near the vortex centers, where the magni-
Fig. 131. Comparison of measured rolling moment induced on following wing C1 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
tude of the predictions are again too large. The same comments can be made for the comparisons presented for following model C5 (Fig. 133) but the magnitude of the discrepancy has increased over that observed for the two smaller encountering wings. Once again, the discrepancies are believed to be due not to #ow separation, nor to lack of accuracy of the application of the vortex-lattice method, but, as discussed in the next section, due to one or more #ow-"eld characteristics not included in the method. 11.4. Assessment of assumptions As mentioned previously, a systematic e!ort was made to be sure that the discrepancy between the results was
618
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 133. Comparison of measured rolling moment induced on following wing C5 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
Fig. 132. Comparison of measured rolling moment induced on following wing C4 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
not due to misalignments or adjustments in the data nor to approximations in the mesh size, spacings, etc., in the vortex-lattice code. It was found that the computed values usually changed less than 1% at any place along the span due to any of the items tried. After the foregoing possibilities had been tested and eliminated as being responsible for the discrepancy between computed and measured distributions, the assumption made in the application of the vortex-lattice method regarding the streamwise downwash distribution was investigated. That is, when the vertical velocity at each control point is set, it is assumed that the value is constant for all control points at the same spanwise station; i.e., the downwash is assumed to be the same for
each column of streamwise panels or lattices, and an allowance for distortion of the oncoming vorticity distribution is not made. If so, changes in the solenoidal character of the oncoming stream by the encountering wing are ignored by the theory used to compute the loads. It is believed that this approximation is the most logical reason for the discrepancy between the computed and measured lift and rolling-moment distributions. In support of this conjecture, it is again noted that the vortex-lattice method is quite accurate when the following wing is small, and that the error increases as the following wing increases in size. Similarly, the trend in predictive accuracy follows the fact that small following wings (i.e., small values of b /b ) cause small or negligible distortions to a vortex wake, whereas larger wings (i.e., large values of b /b ) cause larger distortions in the structure of the vortex wake. Since little distortion is expected when the following wing is small, like following wing C1, the vortex-lattice method would be expected to be reliable with only small or negligible error. However, when the following wing is large, like C4 and C5, the distortion of the vorticity "eld, and the resulting downwash distribution is expected to be larger, and perhaps even quite signi"cant.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
It remains to con"rm that the discrepancies between computed and measured data are caused by vortex-wake distortions brought about by the in#uence of the penetrating wing. The "rst requirement is that it can be shown that wake distortion is able to bring about the changes in magnitude and distribution observed between the predicted and measured quantities for the larger wings. It would then be desirable to develop an e!ective method to properly analyze the wing/vortex}wake interaction, and apply it to the test con"gurations studied here. The distortion of the oncoming vortex wake by the presence of the following wing is not taken into consideration by the vortex-lattice method. That is, an assumption is made that the oncoming stream is potential, and not solenoidal. An estimate of the distortion that can be brought about by a wing/vortex}wake interaction is relatively simple to obtain by use of a Tre!tz-plane type of analysis [163]. The computations in Fig. 134 were carried out by analyzing the motion of two-dimensional point vortices arranged in a circular distribution, and with a strength distribution designed to approximate the vorticity distribution typical of lift-generated vortices. The boundary conditions on the motion of the vortices are applied so that, prior to the x/b "0 station, the vortices move as if in two-dimensional free space. Downstream of x/b "0, the vortices above z/b "0 move as if they are over an in"nite #at plate, and those below z/b "0 move as if they are under an in"nite #at plate. Both of these two
619
motions are simulated in the Tre!tz plane by use of images. At each of the x/b stations speci"ed in Fig. 134, the in"nite plate is assumed to end. The downwash distribution is then calculated for the position of the vortices at that station as if the plate (and the images) were not there. The various parts of Fig. 134 represent the amount of interaction for following wings of di!erent sizes as indicated by the x/b values noted in each part of Fig. 134. That is, the upper "gure for x/b "0 represents the downwash induced in the free stream by the undisturbed vortex wake. Each "gure that follows illustrates the distortion in the wake caused by a following wing of larger size, and the downwash induced by the new wake shape. The example presented in Fig. 134 assumed that the leading edge of the #at plate was sharp and thin enough to divide the vortex in half as it encounters the wing, without otherwise distorting the impinging vortex structure. Therefore, the calculations presented in Fig. 134 do not simulate the bluntness of the leading edge of the following wings. Since the small following wings are thin compared to the depth of the wake, a zero thickness is a valid approximation. However, when the following wing is large, the bluntness of the leading edge and the thickness of the wing might be enough to cause the high-speed vortex core to stay intact and to pass either above or below the wing rather than being split in half as assumed in Fig. 134. If this occurs, sample computations indicate that the resulting downwash distributions are as
Fig. 134. Distortion of vorticity distribution in a vortex wake as it encounters a #at plate of various downstream sizes [163].
620
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
a whole about the same as the thin-wing results, but the distributions di!er in detail. It is noted in Fig. 134 that those point vortices on top of the #at plate or wing move outboard with time, and those under the #at plate move inboard with time, just as anticipated intuitively. This movement redistributes the vorticity in the wake so that the downwash in the spanwise region between the two vortex centers is reduced, just as observed with the lift for the larger following wings. Furthermore, the outboard distributions of downwash are slow to be altered, just as observed with the lift comparisons. Also, it is noted that the total change in downwash velocity across the vortex centers is slow to be altered, so that the rolling moment on an encountering wing would also be slow to be changed by wake distortion. Computations were also carried out for vortex distributions that approximate solid-body rotation, and the results were about the same but took longer to come about.
12. Wake energy, span e7ciency and span loading 12.1. Introduction The characteristic of non-hazardous wakes to be discussed here is their e$ciency, or lack thereof, and possible techniques to remedy the problem. The discussion uses the relationship between e$ciency of the lifting surfaces, and the kinetic energy in the wake that the wing sheds. If a non-hazardous wake con"guration is to be found, it must have a wake that has much less energy than conventional designs for two reasons. First, a nonhazardous wake must have low velocities and therefore low energy. Secondly, an e$cient wing sheds a lowenergy wake. From basic aerodynamics, the wake energy, span e$ciency and span loading, are all connected. Therefore, this section considers lifting wings that are designed so that the desired lift is generated with a low level of wake energy, and a corresponding high span e$ciency [187]. A goal of the study was to "nd optimum con"gurations. However, a procedure for optimization was not found, because a relationship between span loading, vortex wake structure and energy was not available. Such a relationship becomes very complex and nonlinear, because it must include vortex interactions and viscous forces which reform the multiple vortex wake at the wing trailing edge into a single vortex pair. The study began with the observation that alleviatedwake con"gurations often shed vortex wakes that induce about the same rolling-moment coe$cient on following wings of all sizes [187]. As shown in Fig. 112, the windtunnel data indicates that, when a wing is embedded in an alleviated wake, the maximum vortex-induced rolling moment on a wing is very nearly constant with span ratio for several di!erent alleviation mechanisms. Computa-
tions carried out by use of vortex-lattice theory, and the downwash data in Fig. 123, con"rm that the spanwise vertical velocity distributions also re#ect the low and nearly constant value of wake-induced rolling moments for the alleviated con"gurations over a wide range of span ratios, b /b , and for di!erent wing planforms. In order to investigate the possibility as to whether the span loadings had special characteristics that would lead to new wing designs, a study was made of the vortex wakes at the downstream station where the measurements were made, i.e., at 81 ft or 0.5 mile scale distance behind the wake-generating model [187]. In order to determine the span loadings that correspond to these downstream vortex wakes, the analysis "rst "nds the vortex structures that make up the measured downwash distributions. An inverse Betz method described in Section 5 is then used to derive the corresponding span loadings. Analysis of these span loadings, and consideration of the induced drag and the energy in various wakes, yields information on some of the characteristics and penalties associated with the design of wings for less hazardous wakes. It is recommended that tools be developed for an optimization process that includes drag, wing-root bending moment, weight, complexity, etc., and the design of vertical and horizontal lifting surfaces for vortex wakes that have an acceptable hazard. The discussion to follow considers the energy in idealized wing designs, their e$ciency, criteria that should be used to determine e$ciency, and what factors need to be considered in the design of a wing with low or negligible hazard due to its vortex wake. 12.2. Estimated span loadings In order to provide an estimate for the structure of the vortex wakes being studied, the span loadings on the various wake-generating con"gurations, were calculated by means of vortex-lattice theory for the wing of the wake-generating model at 43 angle of attack (Fig. 135). Since the two alleviated wakes to be analyzed in this study (Fig. 123b and 123c) have gone through strong two- and/or three-dimensional vortex interactions after they were generated, and before the measurements were taken, the relationship of the "nal vortex wake to the original span loading on the wake-generating model has become obscure. That is, because of the vortex interactions, the vortex wake far downstream behind the wing has taken on an alleviated form. If the "nal vortex wake had been generated directly from a monotonic span loading, the span loading would no doubt be quite di!erent from the one that actually generated the wake. A question to be answered in this section is whether the "nal vortex wakes that are benign can be interpreted by use of inverse rollup theory for span loadings that have the same lift but less penalties than the original alleviated wing design.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 135. Comparison of parabolic span loading with those estimated for the wings of the con"gurations of B-747 model tested in wind tunnel [187]; a "43.
12.3. Analysis of downwash data 12.3.1. Vortex structures The procedure used to "nd the time-averaged structure of the vortices that make up a wake consists of several steps. First, a determination is made as to how many vortices are present in the wake, and roughly where their centers are located. In the cases being analyzed here, only two vortices, or a single pair, are present in the wake when it arrives at the measuring station located at x "81 ft. One possible exception is the port side (nega tive y values) of the modi"ed landing or (303, 03) con"guration (Fig. 123c). Such a possibility was observed during the data-taking process when the measurements indicated two peaks in rolling moment that were both higher than measured for the starboard side of the wake. Therefore, for the modi"ed landing case, the velocity survey, and the analysis presented here were carried out as if only one vortex was present on each side of the centerline. Since the lateral velocities are negligible on a path through the vortex centers, only the vertical and streamwise velocity components were measured. Since a vortex pair induces a downward velocity on itself, the next step in the analysis is to remove the proper amount of downwash at each spanwise station from the measured distributions in Fig. 123. The velocity "eld of each vortex is then evaluated as if it was isolated from the opposite vortex in the pair. The procedure used assumes that, near the vortex center, the #uid motion is nearly axisymmetric after the downward velocity of the pair has been removed. If the #ow "eld is symmetrical about each vortex center, the data inboard and outboard of the
621
vortex center should yield the same swirl velocity. However, since a vortex pair is present in the #ow "eld, two processes in#uence the location and shape of the streamlines (Fig. 30). The "rst process to be considered is caused by the opposite vortex in the pair. Its presence changes the concentric streamlines for an isolated vortex to be shifted outboard to form a series of circular streamlines whose centers are shifted outboard by increasing amounts as the streamline radius increases (Fig. 30b). If such a streamline pattern is to be preserved, the vortices must be held in place by force, which does not occur in a vortex wake. The second process which causes the streamlines to be di!erent from the concentric circles for an isolated vortex is brought about by the downward motion of the pair when they are released (Fig. 30c). A steady-state streamline system is achieved by superimposing a uniform upward free-stream velocity on the #ow "eld, so that the #ow around the vortex pair has an internal part inside the oval that is usually rotational (i.e., contains circulation) and an external part that is irrotational when the #ow is approximately inviscid. The streamlines of interest in the present analysis are those inside the vortex oval (Fig. 30c). Fortunately, the lateral displacement of the streamlines due to the opposite vortex, and the compression of the rotational part of the #ow "eld into the interior of the oval by the downward motion of the vortex pair, combine to produce nearly concentric streamlines as assumed for isolated vortices (Fig. 30c). The radial (or lateral) location of a particular element of circulation from the wing as deposited in the vortex oval con"guration is probably not the same as if the vortex being analyzed were really isolated. In the analysis to follow, the vortices are treated as if they are symmetrical inboard and outboard of their centers, which appears to be a good approximation for the vortex oval. As will be seen in the results of the analysis, symmetry does exist at smaller distances from the vortex center but not for the outer parts of the vortex structure. Since the hot-"lm anemometer probe is "xed relative to the wind tunnel, the velocities measured include the self-induced downward motion of the vortex pair, and the velocity "eld of the opposite vortex. For this reason, an iterative procedure is used to adjust the data for the downward motion of the vortices, and to determine the structure of isolated vortices that make up the downwash distributions (Fig. 123). Since the downwash adjustments needed are not known at the outset, they must be found iteratively. The process begins by assuming a location for the vortex center and an estimated value for the in#uence of the opposite vortex. The swirl velocities on the two sides of the vortex center are then compared. If they are not about the same in the vicinity of the vortex center, a change in the overall upwash increment is made. The computations are then iterated upon until they agree within experimental accuracy. After each revised upwash
622
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
distribution has been found, a new vortex center is located by interpolating along the up- and downwash curve through the core region of the vortex to "nd the spanwise location where the downwash velocity passes through zero. The entire process converges in about "ve iterations. The foregoing procedure was used to determine the time-averaged vortex structures for the three con"gurations of the B-747 model for which wake-surveys were taken. As mentioned in the previous paragraph, the downwash data in Fig. 123 was "rst divided into port and starboard structures. Each of those data sets were again divided at the center of the vortex into two groups (Fig. 136). One group includes the data located between the vortex center and the centerline of the wake, and the other group includes all of the data outboard of the vortex center. Therefore, Figs. 137, 138, and 139 present curves for both the port and starboard sides of the wake and for both the inboard (dashed curves) and the outboard data (solid curves) sets. The inboard and outboard data sets are in quite good agreement near the vortex centers, but at larger radii the two sometimes di!er considerably. The alleviated wake shed by the (303, 303) with-"ns con"guration is noted to have smaller swirl velocities and a smaller swirl velocity gradient through the core regions (Fig. 138) than the wake vortices shed by the standard landing con"guration (Fig. 137). The modi"ed landing con"guration has smaller swirl velocities, but the gradient through the core is still quite steep (Fig. 139). 12.3.2. Span-load distributions from isolated vortex structures The simple method introduced by Betz and described in Section 5, relates the span loading on a wing, or the vortex sheet that it sheds, to the rolled-up vortex far downstream. The inverse-Betz method, also described in Section 5, relates the structure of the fully de-
Fig. 136. Division of measured upwash distributions at center of vortex and at centerplane of wake for calculation of isolated vortex structures.
veloped vortex to a span loading that could have generated the vortex. That is, from Section 5, the bound circulation in the wing at the spanwise station, y, is related to the circulation in the "nal vortex by Eq. (45). The isolated-vortex structures, presented in Figs. 137}139, were inserted into the foregoing equations for the inverse Betz method to retrieve the span loadings from the measured data (Figs. 140}142). The retrieved span-load distributions have been made dimensionless by dividing the circulation bound in the wing by the circulation in a pair of vortices that is required for rectangular or uniform span loading when the lift on the wing and the distance between the vortex centers are the measured ones, i.e., a reference circulation, C . That is, C /b ; "C /(2AR (*y/b )), (54) *
Fig. 137. Vortex structures derived from the time-averaged downwash data in Fig. 123a for the standard landing con"guration [187]; #aps (303, 303).
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
623
Fig. 138. Vortex structures derived from the time-averaged downwash data in Fig. 123b for the standard landing con"guration with "ns mounted on top of wing [187] at y /b "0.254; h /b "0.057, c /b "0.083, a "183; #aps (303, 303).
Fig. 139. Vortex structures derived from the time-averaged downwash data in Fig. 123c for the modi"ed landing con"guration [187]; #aps (303, 03).
where *y/b is the spanwise distance measured between the port and starboard vortex centers. It is noted that the ratios of circulations, C(y)/C , all reach or exceed 1.0, which indicates that the vortices do contain the circulation needed to account for the lift on the wakegenerating wing. The spanwise locations where C(y)/C +1.0 are displaced spanwise from the wing centerline because the cross-plane streamlines are o!set due to the presence of the opposite vortex and compressed by the downward motion of the vortex pair (Fig. 30). Since the streamlines are o!set, the circulation they contain is also o!set causing the ratio C(y)/C to become about one at spanwise locations other than the centerline. 12.3.3. Discussion of retrieved span loadings It is "rst noted that the span loadings retrieved from the measured wakes (Figs. 140}142) do not resemble very closely the ones calculated for the wing con"gurations (Fig. 135). The most apparent di!erence is the disappearance of the humps and valleys predicted by vortex-lattice theory due to the lift on the #aps and wing "ns. Such a result is expected, because the vortices shed at the ends of the #aps are often close to each other, and since they are of opposite sign, they interact destructively to smooth out the original variations in the strength of the vortex sheet being shed. Furthermore, the swirl of separate vor-
tices of the same sign in the wake near the trailing edge of the wing interact to smear or smooth out the vorticity concentrations in the wake. Also suppressed in the rollup process is the abrupt fallo! in lift at the wingtip, because the low-energy boundary layer on the wing and #aps migrates to the core regions of the vortices [146]. For the foregoing reasons, the retrieved span loadings taper monotonically from a maximum near the wing centerline to zero at the wingtip. Any characteristic in the original vortex sheet caused by the #ap ends or the wing "ns appears to have been obliterated. This result ful"lls one purpose of the study which was to "nd out how much complex vortex sheets shed by wings change as they roll up into a vortex wake in the far "eld. Comparison of the results presented in Fig. 135 with those in Figs. 140}142 indicates that the changes can sometimes be large. In spite of uncertainties in the data and in the methods used to compute the retrieved span loadings, they still appear to have de"nable characteristics. In the case of the standard landing or (303, 303) con"guration (Fig. 140), the retrieved loadings closely resemble the one shown for parabolic loading in Fig. 135. It is also noteworthy that the loadings are quite similar to the one derived by Jones [152] through an optimization process based on lift and wing-root bending moment for a wing span 1.15 times that of an elliptically loaded wing.
624
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 140. Span loadings derived from vortex structures in Fig. 137 for the standard landing con"guration [187]; #aps (303, 303).
Fig. 141. Span loadings derived from vortex structures in Fig. 138 for the standard landing con"guration with "ns mounted on top of wing [187]; y /b "0.254, h /b "0.057, c /b "0.083, a "183; #aps (303, 303).
Fig. 142. Span loadings derived from vortex structures in Fig. 139 for the modi"ed landing con"guration [187]; #aps (303, 03).
In the case of the wake of the (303, 303) con"guration with wing "ns, the retrieved span loadings (Fig. 141) also resemble the one that was designed by Jones [152] as optimized to have minimum drag for a given span and a given wing-root bending moment, i.e., his design for a wing span that is 1.3 times as large as the one for elliptic
loading. When such an optimization is carried out, the corresponding vortex sheet at the wing trailing edge has an initial downwash velocity distribution wherein the outboard parts of the vortex sheet rotate as a solid body. The speci"cation of solid-body rotation by the vortex sheet was also suggested as a means for preventing the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
vortex sheet from rolling up into a concentrated vortex with an intense core, i.e., a span loading tailored for a benign wake. In the inverse Betz method, it is assumed that a vortex sheet tailored in this way would roll up from the wingtip inboard. In reality, it rolls up from the center of the sheet to form a somewhat more intense but still benign vortex. The third con"guration studied was the modi"ed landing or (303, 03) con"guration of the B-747 model, produced by withdrawing the outboard #ap to its stowed position on the standard landing con"guration. The span loading predicted for such a wing at 43 angle of attack (Fig. 135) has only the one hump at the spanwise station where the inboard #ap is fully deployed. The corresponding retrieved span loading (Fig. 142) appears to be approximated by a parabolic pro"le [144,145] much like the retrieved span loadings for the (303, 303) con"guration (Fig. 140). The two cases di!er in that the (303, 303) wake is much more hazardous than the (303, 03) wake. As pointed out previously, the vortex sheet shed by such a span loading does roll up from the wingtip as assumed by the Betz' method. It is believed that the addition of the low-energy wakes produced by the landing gear and yaw of the aircraft migrates to the centers of the vortices, so that their core diameters increase in size. The increased core diameters make the vortices more rigid, so that the mutually induced instability that leads to threedimensional linking between vortices does not occur (e.g., Fig. 60). 12.4. Wake hazard and induced-drag As stated in the introduction to this section, the primary objective of the research being reported is to "nd new ways to design wings that are e$cient, and that shed non-hazardous vortex wakes. Since the energy in the vortex wake of a wing is well known to be proportional to the drag due to lift, or the induced drag, one way to
625
investigate the e$ciency of a wing is to study the distribution of kinetic energy in its vortex wake. In this analysis, it is assumed that the velocity in the free-stream direction is roughly constant, so that the kinetic energy of the wake vortices is contained only in the across-stream velocity components. The relationships to be derived will be applied to components typical of vortex wakes; namely, a vortex pair composed of two equal and opposite vortices with cores that rotate as a solid body (Rankine vortices), and a pair with vortex cores that have constant swirl velocity (Fig. 143). A vortex pair is used to model the wake, because the energy content for a single vortex goes to in"nity as the outer limit of integration becomes large, whereas, the energy integral remains "nite for a pair of equal and opposite vortices. An expression for the kinetic energy content for vortex wakes in general is di$cult to derive, but the case for a single pair of Rankine vortices has been evaluated by Spreiter and Sacks [193]. In their analysis, the #ow "eld is divided into an irrotational or outer part, and a rotational or inner part that contains the circulation of the vortices (Fig. 144). The integral for the energy in the irrotational part of the #ow "eld is then given by [193]
o E " 2
(v#w) dy dz.
(55)
1
Since the outer part of the #ow "eld is irrotational, it can be expressed by a potential function, u, and the integration over the surface, S, can be changed into the contour integration, C, as shown in Fig. 144: o E " 2
!
u
Ru ds. Rn
(56)
The quantity s is the distance along the contour, and n is in the direction perpendicular to the contour surface. In order to simplify the contour integration, the circulation is assumed to be contained within the circles whose
Fig. 143. Idealized vortex structures for study of energy distributions in vortex wakes [187].
626
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
drag of a wing as
Fig. 144. Idealized vortex pair and contour, C, used to integrate for kinetic energy in irrotational part of #ow "eld [193].
centers are o!set from the b spanwise spacing, so that they correspond to the streamlines induced by a pair of point vortices (located a distance b apart) (Fig. 144). The kinetic energy of the #uid in the irrotational part of the #ow "eld was found by Spreiter and Sacks [193] as
oC b !2r #(b #4r . E " ln 2p b #2r !(b #4r
(57)
The energy inside the vortical region of the vortices is calculated by use of the integral [193] as
o P E " 2prv dr. 2 F
(58)
When the vortex core rotates as a solid body, as it does for a Rankine vortex, v ) "rC/2pr, the kinetic energy F in the core is given by oC E ) " . 8p
(59)
Similarly, when the vortex core rotates with a constant swirl velocity, v ) "C/2pr , the energy in the rotational F part of the #ow "eld is oC E ) " . 4p
(60)
The total kinetic energy in the vortex wake is then given by the sum for the two regions as E"E #E .
(61)
The last relationship needed is that between the energy in the wake, and the induced drag which is found from the expressions for lift and for the induced
4AR b C C " , (62) "G ep b b; where e is the span e$ciency. Since the induced drag and the kinetic energy are both proportional to the square of the circulation in the vortices, they are proportional to each other and can be used interchangeably when various con"gurations are being compared. It is "rst noted that the energy in the &Rankine' and &constant-swirl-velocity' vortex cores, Eqs. (57) and (58), are both proportional to C and independent of the core radius, r . Hence, in both of these cases, if C is the same for two core sizes, the large vortex core has the same energy as the small core. The induced drag is then also proportional to the square of the circulation shed by the wing, but the vortex-induced rolling moments are proportional to the "rst power of the circulation, and how it is distributed. Since the energy in both a large and a small core are the same (i.e., for the same circulation but not necessarily the same lift), the di!erence in the total energy for a concentrated vortex (i.e., a small core radius) and for a dispersed (i.e., a large) vortex core is given by the energy in the #ow "eld between the two core radii, as if the #ow were potential, or
b !2r #(b #4r oC *E " ln 2p b #2r !(b #4r
b #2r !(b #4r , (63) b !2r #(b #4r where r and r are respectively the radius of the small and of the large cores. Another interesting feature of the energy relationships for large and small core sizes is that it takes a larger increment in energy to enlarge a small vortex core a small radial amount than it does to enlarge a large core by the same radial amount. Furthermore, a non-hazardous or large-core vortex contains less energy, and consequently corresponds to a smaller induced drag than a vortex with a small core. In other words, if a lift-generated wake can be designed to shed vortices with large cores, for the same centerline circulation as with elliptic loading, its induced drag would be less, as demonstrated by Jones [152] when he designed span loadings based on wing-root bending rather than on "xed span. Before discussing span loadings for alleviated wakes further, induced drags computed for several candidate types of span loadings are compared in the upper part of Table 12 on the basis of a "xed span without any other restraints placed on the design. Such a comparison is based on the fact that, if the span of the wake-generating wing is held constant, the optimum span loading is elliptic with the span e$ciency e equal to 1. The induced drag for each span loading listed in Table 12 is proportional to ;
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the inverse of the span e$ciency, or the quantity p"1/e, where e"1 for elliptic loading as shown in the table. If, for example, the span loading is designed to produce a vortex wake with a reduced intensity in its core, the centerline circulation needs to be increased to o!set the triangular character of the loading and thereby produce the same lift as an elliptically loaded wing of the same span. Therefore, the span e$ciency decreases, and the drag for a given lift is p times the induced drag for elliptic loading. Therefore, the induced drag is larger for triangular loading (Table 12). In addition, the increased total circulation in the vortex also increases the swirl velocities and the energy in the vortex wake, so that the desired alleviation is not achieved, i.e., if the design is optimized only on the basis of span and induced drag. If, however, the drag of alleviated con"gurations is based on a minimization based on wing-root bending moment instead of span as suggested by the optimization studies carried out on the span loadings for planar wings by Jones [152], the results are quite di!erent. In Jones' paper, a series of designs are derived that optimize the span loading for minimum induced drag while holding the lift and the wing-root bending moment constant, i.e., the span of the wing is allowed to change. As a result, one of the solutions found increases the wing span by 15% over that for elliptic loading, and thereby achieves 15% less induced drag while holding the lift and the wing-root bending moment constant; lower part of Table 12. If the span of the wake-generating wing is increased by 30%, or to 1.3 times that for an elliptically loaded wing, the induced drag is again about 15% less than for an elliptically loaded wing, and the lift and the wing-root bending moment are the same (Table 12). As mentioned earlier, this span loading is very similar to the span loading retrieved for the "nned-wing con"guration (Fig. 140). The foregoing results point out that an appearance of being ine$cient by one set of design criteria may turn out to be more e$cient by another set of criteria. This suggests that an optimization for alleviated wings should utilize a more complete set of parameters. Such a process may provide wing span loadings for benign wakes that have acceptable or greater e$ciency than wing designs in current use. In addition, the results found here point out that the optimization process should include not only horizontal lifting surfaces, but vertical surfaces that lift sideways as well. At this time, it is not clear what parameters should be used in such an optimization scheme nor exactly how the structure of the vortex wake is related to wing geometry. The results presented in Figs. 135 and 140}142 illustrate the complexities that can occur between vortex wake structures at the wing trailing edge, and at the station where the vortices are fully developed. Most of the discussion in this paper has been directed at the wake hazard rather than at alleviation. The two
627
Table 12 E$ciency factors for various span loadings [187] Loading type
Span e!., e
Ezciency based on span Elliptic 1.00 Parabolic 0.91 Triangular 0.73 Min. root bend. 0.66 Solid-body rot. 0.38
p"1/e
Span
1.000 1.101 1.366 1.524 2.612
1.00 1.00 1.00 1.00 1.00
Ezciency based on wing-root bending moment Min. root bend. 1.18 0.85 Min. root bend. 1.18 0.85
1.15 1.30
terms di!er in that wake hazard refers to the vortex wake directly, whereas alleviation assumes that a given loading on the wing has had something added to it, taken from it, or done with it, to reduce the hazard posed, i.e., it has been alleviated. Most current conventional wing designs probably shed a hazardous wake-vortex pair that contains a larger amount of energy (i.e., rotational kinetic energy) than does a benign vortex wake with the same circulation per vortex. However, an aircraft with an alleviated wake may have more drag (i.e., kinetic and heat energy in its wake). Such is the case, because the span loading on the wing "rst generates an energetic vortex wake. Work or energy must then be expended to modify the vortices, so that they become non-hazardous. This is usually accomplished by removing or dispersing the kinetic rotational energy to alleviate the hazard posed. When such a wake has been alleviated to reduce the swirl velocities, some of the original energy in the wake plus the energy expended in making the conversion has been turned from kinetic energy into heat energy thereby making the remaining swirl velocities less hazardous. A good illustration of such a process is the use of drag-type devices to inject turbulence into the vortices to di!use their cores [62,63,67]. Such an observation again points out the need for procedures that design the wing lifting surfaces directly for all of its desired factors, such as the lift, e$ciency, minimum weight, and an acceptable wake-vortex hazard.
13. Vortex decay 13.1. Introduction The term vortex decay implies a steady monotonic decrease with time in the magnitude of the swirl velocity distribution in the vortex. As indicated in the foregoing text, the #ow "eld of a vortex pair is non-linear, and especially in the presence of atmospheric turbulence, can
628
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
undergo a wide variety of dynamic motions that usually accelerates the demise of the #ow "eld. The measurements by Ci!one and Orlo! [91,92] of vortex decay in a water tow tank with very little ambient turbulence (Fig. 2) found that the maximum swirl velocity in a vortex "rst tends to remain constant before beginning a prolonged decay process roughly as t\ . The development of a second-order closure tubulence model by Donaldson [32,141}143] led to numerical simulation of the decay of isolated vortices that predicted the same type of decay pattern. The numerical studies carried out on the decay of vortex pairs found that the decay of vortex wakes was best predicted when the turbulence in their numerical codes was turned o!. It was concluded that the "nite grid sizes used in the numerical procedures introduced a redistribution of vorticity that simulates viscous and turbulent forces. Although the transfer of energy by the numerical procedures used in the computations is small, it is large enough to yield decay rates comparable with or greater than the observed ones. Computational procedures for vortex wakes that have been developed since that time appear to have now either suppressed or avoided the di!usion of vorticity associated with numerical procedures used in the earlier codes [35,72,75,76,86,97,173,175,194}196]. In each of these studies, the e!ect of turbulence on the #ow "eld is modelled by techniques that consider the in#uence of swirl and rotary shear on the magnitude of transfer of momentum. Laboratory measurements of the turbulent structure of vortices provide a means for testing the various theories being developed [79,80,89,154,168, 197,198]. The development of improved sensors are dealt in papers [100,111,188,199]. The in#uence of swirl and shear on turbulence are treated in detail by Zeman [200] in a study of the decay of isolated vortices. In his study, the ability of vortex #ow "elds to smear and damp out turbulence is identi"ed and analyzed. He describes the process as one wherein the self-generated turbulence within a vortex exists, but the radial transfer of momentum is so e!ectively damped by the swirl velocities and their gradients that vortex decay is dominated by viscous stress rather than by turbulent transfer of momentum. It is believed that it is for these reasons that vortex #ow "elds behind even large aircraft appear to be of a laminar rather than turbulent type when substances are injected into the #ow "eld to visualize the streamlines. It also explains why vortices persist as if the #ow "eld were laminar rather than turbulent, and why vortex instabilities usually break up the coherent #ow "eld of the vortices well before viscous and turbulent decay processes cause their demise. The swirling shear velocities tend to damp out turbulent eddies thereby bringing about a laminar character to the vortex #ow "eld. The laminar character of the inner part of vortices, even when embedded in a turbulent environment, is frequently observed by means of #ow visualization.
Fig. 145. Diagram of distortion caused in turbulence eddies by swirling shear #ow "elds of vortices [61].
When smoke or marker #uids are injected into the vortices, they are observed to not disperse for long periods of time, but continue to mark the cylindrical patterns of #uid motion up until the vortex #ow "elds break down due to instabilities or atmospheric disturbances. Observations of this kind indicate that the slow decay of swirl velocities and dispersion of vorticity must be associated with shear forces that are more nearly laminar than turbulent. A possible mechanism by which the e!ectiveness of turbulent eddies is made vanishingly small is illustrated in Fig. 145. Just as the laminar sublayer of the boundary layer on a #at plate damps out eddies near the surface, the swirling and shearing #ow of a vortex causes a circular eddy to be distorted into a #at, high aspect ratio ellipse, which is readily damped to ine!ectiveness. Therefore, existing small-scale turbulence introduced into the vortex by the viscous wake of the aircraft wing of the vortices causes nearly circular eddies to become distorted into long narrow slits that are ine!ective in transferring momentum radially, and that are damped quickly. If however, the eddies introduced into the vortical #ow "eld have a scale that, like atmospheric turbulence, is large compared with the part of the vortex that has a laminar character, the vortices are convected into sinuous shapes that grow with time and bring about breakdown of the vortex structure at the sharp bends in the vortices as illustrated very nicely in Fig. 37 of Garodz and Clauson [50]. The decay of lift-generated wakes is discussed in the text to follow along with methods which may be used to study the nature of the decay process. A discussion will also be presented in Section 16 on attempts to use of the injection of turbulence into vortex wakes as a means to accelerate their demise by destroying the organized structure of the swirling motions.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
629
13.2. Natural decay
assumed that the swirl velocity in a turbulent vortex may be written as an extension of Lamb's model as
13.2.1. Simple models for decaying vortices One of the oldest and simplest equations for the decay of an isolated vortex is the Oseen/Lamb formulation [9] given by
!r C , v " 1!exp F 2pr 4t(l#e)
C !r v " 1!exp . F 2pr 4lt
(64)
Eq. (64) was found by Lamb through an adaptation of a solution presented by Oseen for the di!usion of an isolated two-dimensional line source with time. Eq. (64) is commonly referred to as the Lamb vortex structure. An isolated vortex is chosen for study, because the problem is a two-dimensional one which involves only time and the radial variation of velocity on streamlines which are concentric circles. Since the radius at which the maximum swirl velocity occurs changes as the vortex ages, a relationship is now found for the radius at which the slope of the velocity function in Eq. (64) is zero. The radius at which the swirl velocity is maximum is usually de"ned as the core radius of the vortex. Di!erentiation of Eq. (64) to "nd the radius at which the velocity is a maximum yields r "1.25643121 4lt
(65a)
or r "2.24181(lt. The maximum swirl velocity may then be written as C v "0.71533 . (65b) F 2pr Eq. (65a) predicts the t\ decay rate indicated by data taken in #ight and in water tow tanks [90}92,101]. The plateau region vanishes for this formulation, because all vortices are assumed to have their circulation concentrated at r"0 when the vortex begins its decay process. Since vortices generated by lifting wings, water jets, etc., in the laboratory or in #ight, have zero swirl velocities at their centers, the function of the plateau region in Fig. 2 appears then to be an adjustment region which brings the curve for the decay of the maximum swirl velocity with downstream distance out into the vicinity of the t\ curve. Although such an interpretation is intuitively correct, its application has many variations that depend on the nature of the vortex-generating wing and on the environment in which the vortices are embedded. In the 1950s, Squire [201] extended Lamb's result to include vortices whose turbulence could be characterized by the circulation content of the vortex, because as he states, `the simplest formula is usually as good as any othera. He meant, of course, that such a model is useful as a "rst approximation, and when better information is not available. In order to obtain a simple result, Squire
(66)
where C is the entire circulation content of the line vortex. In Squire's model, the turbulence does not vary with radius. In simpli"ed terms, Squire substitutes the quantity (l#e) for the laminar value of the kinematic viscosity, l, where e is de"ned as an eddy viscosity which is taken as e"aC , (67) where a is a constant. The decay process predicted by both Eqs. (65a) and (66) has the t\ character. A more realistic approach to the turbulent structure of vortices is to conduct an analysis that includes the selfgenerated turbulence in the vortex and the turbulence in the ambient #uid. Several such analyses include a global type formulation by Greene [176] which predicts the demise of vortex pairs in various types of atmospheres. A more rigorous approach by Kuzmin [202] derives equations for the interaction of self-generated and ambient turbulence with the vortex structure for an evaluation of the decay rate of vortices for various wind conditions. In one of the earliest and simplest analysis of vortex decay, a simple formulation was derived by Ho!man and Joubert [51] for the structure of a turbulent vortex. In their analysis, an expression for the Reynolds stress is derived by use of the conservation of the moment of momentum of the concentrically circular #ow "eld of the vortex. As an outcome of their analysis, a relationship for the variation of the circulation with radius is derived in the form C(r)/b ; "A ln(r/b ), (68) where A is a constant. If a linear variation of the circulation with the logarithm of the radius is found in the data for a measured vortex, it is assumed that the turbulence model used by Ho!man and Joubert to derive Eq. (68) applies to the vortex structure. In what may be labeled as a fourth method, is the development of simple analytical relationships for the distribution of swirl velocity in an isolated vortex. The functions developed simply approximate measured distributions, and usually do not have a physical basis that permits estimates to be made of the decay process [203}205]. The functions derived often apply to vortices shed by either rotors or wings. One such function with considerable latitude is given by r/r C v" , (69) F 2p [1#(r/r )L]K where n and m are arbitrary and r is the core radius of the vortex. If m"1/n, the maximum swirl velocity occurs
630
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
at r and decays as 1/r in keeping with conventional vortex structure [205]. Although some of the equations used in the "t to measured data are interesting, and provide an equation that approximates measured vortex structures, their use in the interpretation of data, and their use for the determination of a decay rate for the vortex is not clear. 13.2.2. Numerical simulations Even though this overview is not intended to include numerical simulations, the large amount of e!ort devoted to the subject suggests that mention must be made of research in this area. The large amount of e!ort directed at the development of computer codes is an attempt to satisfy the need for an accurate representation of the development of the vortex wake as it leaves the liftgenerating surfaces of the aircraft, and proceeds through decay and decomposition to a harmless state. If a code were available that could simulate with a high con"dence level any portion of the wake history accurately, the experimental measurements could be guided much more judicially, and solutions to various aspects of the wakevortex problem could be found more readily. Most of the simulations appear to solve special or idealized problems to provide some guidance and intuition. Since wakevortex dynamics is non-linear, and can on occasion respond to viscous and turbulent features of the #ow "eld in a seemingly erratic way, numerical simulations are very di$cult to accomplish accurately for the general case. Nevertheless, development of computer codes to do so should be attempted with short term goals that ful"ll less ambitious objectives. One of the "rst attempts at the development of a computer code for the simulation of the entire wake history of lift-generated wakes was carried out by Teske et al. [206] as an extension of the work of Donaldson and Bilanin. The code followed the development of the lift-generated wake from the trailing edge of the wing into the far "eld where the mutually induced instability of Crow sets in and pinches o!, and the wake decays. As time progressed, the computer codes began to use "nite-di!erence methods to better simulate the dynamics and internal processes of the vortices and their interactions. For the interested reader, some of the research e!orts on the development of numerical simulations for vortex wakes are presented in some of the references listed [32,34,51,72,73,75,76,78,79,86,89,97,141,142,175, 188,194,196,197,200,207}210]. Some of the articles treat not only the convective, viscous and turbulent processes within lift-generated wakes, but they also include e!ect of convective and turbulent processes in the ambient #uid on the wake dynamics. Several of the papers include comparisons with experimental measurements. A numerical simulation was carried out by DaclesMariani et al. [196] of the vortex wake shed by the
standard landing con"guration of the B-747. The intent of the simulation was to "nd out how well a newly developed computational method [195] could simulate the changes observed in the vortex wake structure measured in the wind tunnel. The downwash data measured in the wake of the standard landing con"guration of the B-747 model at 81 ft (Fig. 124a) was used as input. Two versions of a computer code were then used to predict the structure of the wake at the 162 ft station (Fig. 146). The "rst version of the code uses the full Navier}Stokes formulation to predict the downstream #ow "eld. The second version, Model II in Fig. 146, is also based on the Navier}Stokes equations, but some simplifying assumptions, suitable for vortical #ows, are made in its formulation to make the code run more quickly. The results from the computations made by use of the full Navier}Stokes formulations are included to show that the more approximate and faster method, Model II, yields about the same result. The computer code assumed that the free stream was uniform and contained no turbulence. The numerical results presented in Fig. 146 indicate that the two numerical results only di!er slightly from each other, and both predict only a small change in the downwash distribution across the wake between the 81 and the 162 ft stations. When the computed distributions are compared with the time-averaged measured distribution, the agreement is quite good on the starboard side, but not so good over much of the port side of the wake. Two explanations for the di!erences between the computed and measured results seem to apply. First, the experimental downwash was a!ected by the turbulence in the wind-tunnel airstream which was not simulated in the computations. Second, the measurements were not made correctly. Since the computations and the measurements are in
Fig. 146. Comparison of upwash distributions as computed by use of Navier-Stokes simulation with time-averaged distribution as measured in 80;120 ft Wind Tunnel at x "162 ft. Input data for computation from x "81 ft (24.7 m) (From Dacles Mariani et al. [196]).
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
good agreement on the starboard side of the wake, and over a portion of the port side, it is believed that improvements need to be made in the measurement techniques at downstream distances larger than 81 ft. Improved techniques were used on the starboard side, which probably explains the good agreement there. It is also possible that segments of the two pro"les on the starboard side of the wake are in quite good agreement, because the survey was made through the center of the meander region, whereas the port side survey was made through the point of maximum rolling moment. Since the computed result and the experimental measurements are in good agreement over much of the starboard side and a portion of the port side, it is concluded that improvements in the measurement techniques and procedures would probably bring the wind tunnel data into better agreement with the calculated pro"les over the entire wake. 13.3. Observations of decay 13.3.1. Swirl velocity The information presented here is intended to draw together information presented previously in this overview in order to assist the reader in an overview of the decay of swirl velocity with time or distance behind the wake-generating wing. First recall that the changes in the maximum swirl velocity with downstream distance as measured in a water tow tank (Figs. 2 and 3) indicated that the maximum swirl velocity is "rst nearly unchanged and then decays roughly as the inverse of the square root of time, or 1/t . Since the background or ambient turbulence is vanishingly small, the decay process follows the process expected according to the Lamb}Oseen relationship, Eq. (65a), (65b). As the turbulence level in the ambient #uid increases, the wake vortices change from having nearly straight to highly sinuous axes. As pointed out by Crow and Bate [74], Liu [80,98,99], and others, the background turbulence has the capability to initiate natural instabilities in vortex wakes, and thereby hasten the destruction of the coherent nature of the vortices. Not only does the ambient turbulence initiate instabilities in the wake, but it also helps to disperse the vorticity in the wake. Therefore, whenever attempts are made to make measurements in vortex wakes, the lateral motions of the #ow "eld make it di$cult to separate the decay process from vortex changes with time. It is to be remembered that the in-trail wake-vortex separation problem in the airport environment is usually one that involves vortices embedded in some sort of ambient turbulence. Since the interaction of vortex wakes with the ambient turbulence is complex, simple rules for conversion of vortex results obtained in a turbulent environment to a non-turbulent one, and vice versa, are not available, so that numerical simulation is necessary [72,75,208,209].
631
Since the NASA 40;80 ft and 80;120 ft Wind Tunnels have a free-stream turbulence level of about 0.5%, the vortices take on a sinuous shape which causes the #ow "eld of a vortex to meander about at a given downstream distance [161,162]. As discussed in Section 10, the meandering motion, and the in#uence of the ambient turbulence on the vortices was such that it was not possible to discern a clear downstream trend in the swirl velocity (Fig. 120). For example, the downwash data at the two separation or downstream distances, x "81 and 162 ft, presented in terms of #ow-"eld angularity, w/u, in Figs. 122}126, is that the data at x "162 ft is not as smooth as the data at x "81 ft. The increased size of the #uctuations in the velocity distributions at x "162 ft are believed to be caused by the larger meander distances of the vortices at the greater downstream distance. It is believed that some of the irregularities in the downwash data can be suppressed by longer data-sampling times. The most surprising feature in the data presented in Fig. 124 is that some of the up- and downwash velocities in the vortices are noticeably higher at x "162 ft than at x "81 ft. These increases in the swirl velocity with downstream distance indicate that vortex intensi"cation rather than decay occurred, which is opposite to intuition. It would be hoped that the vortex wakes measured in the wind tunnel could be compared with data from other sources. In the search for data on the same or similar con"gurations it was noted that several pro"les measured in water tow tanks are quite similar to those in Fig. 124 even though the wake-generator was a #at wing of rectangular planform (e.g., Fig. 2 of Baker et al. [89] and Fig. 4 of Jacob et al. [174]) and not similar to the wings shown in Fig. 108. Even though the lifting surfaces di!er considerably, the downwash "elds appear very similar to one another. The data developed for helicopter rotors by Leishman and Bagai [41], and McAlister [42] for isolated wingtips also appears to be similar to the vortex structures shed by aircraft, but appears to decay much faster. A simple way to evaluate vortex intensity is to compare the vortices on the basis of maximum swirl velocity as done previously [91,92,101]. For example, measurements on the landing con"gurations tested in the 80;120 ft Wind Tunnel can be compared with those available from #ight experiments [15,17,122]. Measurements made in #ight behind a B-747 in its landing con"guration indicate a maximum swirl velocity [15,17] of about v "0.5; as compared with values around F 0.2; or less in the wind tunnel (Figs. 122}126). Other tower-#yby experiments obtained values in excess of 1.2; for the B-727, B-757 and the B-767 in their landing con"gurations [50]. Lidar measurements were taken by Hallock and Burnham [122] at 24 s (1 mile) after the passage of a B-747 in its conventional and in an alleviated con"guration (#ight spoilers deployed). They
632
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
measured maximum swirl velocities of 0.2; and 0.1; , respectively. Those values are close to those measured in the wind tunnel. At 24 s the following distance is about 1 mile, or about the same scale distance as in the 162 ft station in the wind tunnel. For the conventional landing con"guration, the lidar data presented by Hallock and Burnham [122] appears to indicate a larger core size followed by a constant swirl velocity out to about r/b "0.09 which is not observed in the wind-tunnel data. At larger radii the swirl velocity falls o! at about the same rate as measured in the wind tunnel. In other analyses of full-scale data obtained in #ight, Abramson and Burnham [110], and Sarpkaya [211] present information on a variety of con"gurations. Some of the wide variations in maximum swirl velocity can probably be attributed to Reynolds number and scale di!erences between the models and #ight hardware. The small scale of the wind tunnel models probably results in #ow separation on the wing and on the #ap elements, which is probably much greater than that which occurs on the full-scale aircraft. Even small amounts of #ow separation are known to cause the core size of the shed vortex to be larger than without #ow separation, which in turn reduces the swirl velocity. However, it is questionable whether the large di!erences noted here can be entirely attributed to di!erences in #ow separation that came about in the various tests. 13.3.2. Vortex-induced rolling moment As mentioned in Section 10, a number of con"gurations of the B-747 and the DC-10 models were tested for rolling-moment hazard in the 80;120 ft Wind Tunnel at both the x "81 and the x "162 ft stations. Fig. 120 presents a summary of the rolling moment data obtained for the wide variety of con"gurations of the two wakegenerating models as function of downstream distance. Since the curves do not all even slope the same way, the changes with downstream distance appear to include both decay and ampli"cation. It is concluded that vortex stretching (and the associated intensi"cation) can account for at least some of the increase in rolling moment with downstream distance. Decay and restructuring of the swirling velocities may also have occurred in some cases. It is not surprising then that similar occurrences are present in the #ight data. Since the #ight data has very large scatter due to the di$culty with penetration paths not always being along the path of most intense encounter, the "nal curves were usually drawn through only the highest data points obtained. Quite often the data did indicate a decrease with distance behind the wake-generating aircraft. However, on some occasions the probe aircraft would encounter a vortex at large downstream distances, and "nd that the encounter was even more intense than experienced at stations nearer the generating aircraft. Since pilot input can make the response of the aircraft appear to be caused by a vortex
more intense than expected, and the penetration path is uncertain, the higher rolling moment responses were "rst dismissed as a bad data point. However, when several cases of excessive rolling moment had been experienced, some of the data points were included in the reporting [55]. These results suggest that some of the inconveniences of ambient turbulence in the free stream of groundbased facilities are o!set by the fact that they do simulate experience in #ight tests. Since it is easier to repeat tests and to perform diagnostic tests in ground-based facilities, the ability to chase down the causes of unexpected data is increased.
14. Tests for similitude in vortex structures 14.1. Introduction The data obtained in the 80;120 ft Wind Tunnel at the two downstream stations where velocity surveys were taken are now used to "nd out if the vortex structures have approached or have made the transition from their rolled-up structure to a similarity pro"le [212]. The objective of the investigation is to "nd out if any features associated with vortex decay can be identi"ed in the wind-tunnel data. In particular, the theoretical vortex models used are those of Lamb/Squire [9,201] or the Ho!man}Joubert [51] to "nd out if a particular pattern or universal characteristic is evident in the vortices that make up the measured downwash distributions reported in [106,184]. First of all, it is not obvious, nor is it required, that vortex structures (which are very di!erent from each other when "rst rolled up) should all go to a self-similar type of structure and stay in such a relationship throughout the decay process. The problem is even more complicated by the fact that the wind tunnel, and the atmosphere, have turbulence in the ambient #uid which causes the vortices to become sinuous and to have increased radial transport of angular momentum; especially at the periphery of the vortex structures. If similitude exist, it may be easier to identify and quantify the changes with downstream distance between the 81 and the 162 ft stations in the wind tunnel. Not only are the changes with distances slow, but the changes due to decay are hard to separate from those that occur due to the sinuous motion of the vortices which causes stretching and compression of the vortex cores. The velocity pro"les for the isolated vortex structures (Figs. 137}139) are now analyzed to determine if similitude exists according to one of two models. Only the data from one side of the wake (i.e., the side with the most data points and with the smoothest distribution) are reported to reduce the number of "gures to be presented. Results from the other side of the wake produced about the same results. The objective is to determine whether the pro"les
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
of swirl velocity correspond to or can be approximately represented by either the Lamb/Squire [9,201] or the Ho!man}Joubert [51] model for a universal structure of turbulent vortices. If the data "t either criterion, the information may be of use in the generation of a selfsimilar representation for vortex structure and decay. Research similar to that to be reported here has also been carried by Eisenhuth et al. [118] and Owen [213]. The likelihood of the occurrence of similitude by means of a summation of a number of exponential parameter like the Lamb/Squire model for a turbulent vortex was studied by Iversen [214]. Based on the turbulence model assumed to exist in the vortices analyzed, his results indicate that the early structure of vortices shed by wings of various shapes and span loadings lose their distinctive character and all structures eventually tend towards a universal pro"le like the Lamb/Squire vortex structure. Such an assumption is supported by the results presented in Section 12. Since the downstream distance available in the large wind tunnels is limited to about 162 ft, some viscous and convective restructuring of the vortices will probably have occurred, but it seems doubtful that viscosity and turbulent forces would have had enough time to bring the vortex structures close to a universal character. Nevertheless, the data presented in "gures to follow indicate that some sort of representation may exist. Since the data quality is questionable in some cases, and the downstream distances available are not large enough, it is not certain whether the vortices are on the way to a universal structure or whether the close agreement is fortuitous. In a somewhat related study, Rossow [215] attempted to "nd the vortex structure from measured rolling moments by approximating the vortex structures with a series of Lamb vortices. Thereby, a measured rolling-moment distribution across a wake could be interpreted for the corresponding up- and down-wash distribution that generated the rolling moments. It was found that the process was feasible, but lacked accuracy in the retrieved velocity distribution because it was not close to those estimated for the wakes by Betz' method. It was concluded that whenever possible direct measurement of the velocity "eld with a hot wire is much more accurate and e$cient. The Lamb vortex representation also was not useful in the determination of viscous e!ects. 14.2. Oseen/Lamb/Squire structure As presented in Section 13 on vortex decay, a solution presented by Lamb [9] for the di!usion of an isolated two-dimensional line vortex over time was extended by Squire [201] to include vortices whose turbulence could be characterized by the circulation content of the vortex. Based on Squire's analysis, the swirl velocity in a turbulent vortex may be written as an extension of
633
Lamb's model as Eq. (66) in Section 13.2.1 as v "(C /2pr)[1!exp(!r/4t(l#e))], where C is the F entire circulation content of the line vortex. In simpli"ed terms, Squire justi"es the substitution of (l#e) for the laminar value of the kinematic viscosity, l, where e is de"ned as an eddy viscosity which is given by Eq. (67) in Section 13.2.1 as e"aC where a is a constant. Since the laminar solution and Squire's turbulent solution have the same form, a test to "nd out whether a vortex resembles a univeral self-similar pro"le or not can be made by rewriting Eq. (66) as
1 C G(r/b )"(r/b ) ln " , 4tb(l#e) C !C(r)
(70)
where C(r) is given by C(r)"2prv . F
(71)
In the analysis of the data available, a variety of exponents on the parameter (r/b ) were tried. Since most of the results corresponded best with either the "rst or second powers of (r/b ), only the results for those two exponents are presented here. Therefore, the equations used to "nd out if a vortex pro"le resembles one that is universal and of the form of the so-called Lamb vortex (or Squire's version of it) are plotted as a function of radius when written as
G(r/b ) 1 C " ln , (r/b ) (r/b ) C !C(r)
(72a)
G(r/b ) 1 C " ln . (r/b ) (r/b ) C !C(r)
(72b)
14.3. Howman}Joubert structure A second method by which an organized structure of a turbulent vortex can be represented was derived by Ho!man and Joubert [51] and shown to be applicable to the vortex wakes shed by a wide variety of aircraft [118,213]. As mentioned previously, an expression for the Reynolds stress is derived by use of the conservation of the moment of momentum of the concentrically circular #ow "eld of the vortex. As an outcome of their analysis, a relationship for the variation of the circulation with radius is derived which has the form given by Eq. (68) presented in Section 13.2.1 as C(r)"A ln(r/b ), where A is a constant. In order to obtain the most straightforward test, the axes for the graph should be chosen to provide for a straight-line character in the data. A formulation for the constant A will not be done, because the analysis becomes too uncertain. Therefore, in "gures to follow, the circulation will simply be plotted as a function of ln(r/b ) with the constant A set equal to one.
634
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
14.4. Sample results from similitude tests Vortex data formulated to test the two similitude parameters are presented in Figs. 147}150. The structure of
the isolated vortex derived from the measured downwash distributions are presented in Figs. 137}139. The tests for similitude (or for a universal character) according to the Lamb/Squire model with an exponent of one or two are
Fig. 147. Tests for similitude on data taken in starboard side of wake of B-747 model in standard landing con"guration [212].
Fig. 148. Tests for similitude on data taken in starboard side of wake of DC-10 model in standard landing con"guration [212].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
635
Fig. 149. Tests for similitude on data taken in starboard side of wake of B-747 model in standard landing con"guration with large "ns [212]; x "81 ft (24.7 m).
Fig. 150. Tests for similitude on data taken in port side of wake of B-747 model in modi"ed landing con"guration [212]; x "81 ft (24.7 m).
636
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
presented in the upper parts of the "gures as indicated, and the tests for the Ho!man}Joubert model are presented in the lower parts of the "gures, also as indicated in each. A great deal of credence should not be placed on data taken near the vortex centers, because the data are not as reliable as those at larger radii. It is reasoned that small errors in the lateral location of the data points can cause a large percentage change in the determination of the circulation. It is "rst noted in the tests carried out for the Lamb/Squire model that more of the vortex data have a more nearly linear relationship with the parameter de"ned in Eq. (72a) than with the quadratic de"ned by Eq. (72b), even though the quadratic is the theoretically preferred quantity. That is, the curves are more nearly constant in the upper part of Figs. 147}150 than they are in the lower part of the "gures. The conclusion to be drawn from those "gures is that neither the Lamb nor the Squire vortex model provides a realistic approximation to the data. It therefore seems unlikely that the shear forces between radial layers of #uid can be represented by a constant value of laminar viscosity or turbulence like the one proposed by Squire [201]. In only the one case (Fig. 149) does the quadratic variation hold, and then only approximately. Even then, it is not possible to determine an apparent eddy viscosity, e, because the time t"0 (at which the vortex could be considered a line vortex) to establish a virtual or apparent beginning point for the vortex history is not known. Also, a determination of e by use of corresponding vortex pro"les for the 81 and the 162 ft stations could not be found, because the data are not reliable enough to carry out an evaluation. The tests for the straight-line character of the graphs for the Ho!man}Joubert test are presented in the lower parts of Figs. 147}150. It appears that almost all of the data studied (including some not presented here) have a straight-line character over a portion of their pro"les. These results suggest that a turbulence structure along the lines assumed by the Ho!man} Joubert analysis is probably present in the cases tested. It is also noted that the straight-line similitude characteristic occurred for a wide variety of con"gurations and span loadings. The radial extent over which the straightline characteristic persists does not seem to be much larger for the data taken at the 162 ft station than at the 81 ft station. Such a result probably re#ects the fact that vortex decay, and vortex change, with downstream distance are very slow once the vortex has rolled up behind the wake-generating wing. The foregoing tests for similitude indicate that the turbulent shear forces between streamlines in a vortex are large enough that they need to be included in the decay of vortices. Furthermore, the data suggests that the tubulence formulation should have the character of the model proposed by Ho!man and Joubert [51].
15. Vortex instabilities 15.1. Introduction Some of the decay processes discussed in the previous section assumed that the ambient #uid is so quiescent that the vortices decay by gradually spinning down without any other type of motion being instigated or imparted to the vortex. When a vortex, or a pair of vortices, is embedded in a real environment, like the atmosphere, random motions of the air cause the vortex axis to become sinuous in shape. Also, small-scale eddies in#uence the vortex by convecting rotary momentum from one radial location in the vortex to another to enhance the di!usion process. Of interest in this section are the instabilities in a vortex that can be initiated by disturbances from within the vortex wake or from the ambient #uid. Vortex instabilities are studied, because they have the potential to grow to a large enough amplitude to quickly destroy the coherent structure of an isolated vortex or the entire vortex wake. A good example of a vortex-wake instability that brings about large-scale mixing is the mutually induced instability in a single vortex pair analyzed by Crow [49] which has been discussed in Sections 7 and 8. Since the mutually induced, or Crow, instability has already been discussed at length, it is mentioned here as an example of the mixing that can be brought about in vortex wakes to destroy the initially coherent structure of the wake. The study of the stability of vortex wakes is continuing in the hope of "nding other wake instabilities that proceed more rapidly, more reliably, and more destructively than presently known instabilities for lift-generated wakes. An example of instabilities that are usually not e!ective in alleviating vortex wakes, is the phenomenon known as vortex breakdown or bursting wherein the radius of the vortex core is suddenly enlarged by several fold. Vortex core bursting usually occurs in response to a persistent pressure gradient along the vortex axis. Such an instability is most applicable to the vortices that form over highly swept wings at high angles of attack, and the corresponding loss of lift associated with vortex breakdown or bursting. It appears that the destruction of the vortex is con"ned to regions near its axis, and that the angular momentum in the #uid is preserved, so that wake-induced rolling moments are not dramatically decreased [216]. Since catastrophic breakdown or bursting has not been observed in vortex pairs that trail from transport aircraft, and computations indicate that bursting lowers the wake-induced rolling moment by only a small amount, vortex bursting does not compete with the mutually induced instability for rapid and thorough destruction of vortex wakes. A wide variety of instabilities can a!ect vortex structure, e.g., photographs of instabilities on vortex structures in Van Dyke's book [38]. The "rst example presented on
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
his p. 59 consists of small-scale distortions on the hollow core of a buoyancy-driven vortex. The spiral variations in the core diameter are inertial waves that propagate along the vortex core at about the stream velocity, and do not appear to initiate distortions of the core that grow to large enough amplitude to eventually destroy the coherent structure of the vortex. Another photograph on p. 67 of Van Dyke's book, illustrates how small-scale waves form on the core region of ring vortices and grow rapidly with time. In a short period of time, the periodic distortions grow large enough to destroy the entire #ow "eld of the ring vortex. First identi"ed by Widnall [36], the instability has rightfully become associated with her name [38]. The mutually induced instability of Crow mentioned previously, which is frequently observed in vortex pairs that trail from aircraft in cruise con"guration at high altitude, is illustrated in Fig. 71 (from Crow [49] and Van Dyke [38]) and in Figs. 72}74 (from Liu [80,98,99]). It is noted that the vortex cores marked by condensed water vapor in engine exhaust, or by dye, remain nearly intact throughout the growth stage of the instability. The core of the vortices only disappears near the end of the event where the vortices become signi"cantly stretched and bent. The instability has the virtue that it involves both vortices in the pair and promotes vigorous mixing throughout the wake by means of the sinuous shapes of the vortices and the irregularly shaped loops that form. 15.2. Small-scale vortex instabilities As the foregoing discussion indicates, the name smallscale instability implies that the vortex #ow "eld promotes the growth of small disturbances, usually in the region of the vortex core or near the center or axis of a vortex. If the instability is predicted theoretically, it is usually necessary to determine the ultimate growth of the distortions experimentally, because the resulting dynamics is usually so complicated that it must be followed numerically or experimentally. If the "nal sizes of the disturbances are restricted to the core region of the vortex, the swirling #ow "eld does not lose much of its hazard potential [216]. If however, the distortions grow large enough to be comparable with the size of the wing span, the hazard posed by the wake may be reduced to an acceptable level. One of the "rst analyses carried out on possible smallscale instabilities in the core region of vortices was carried out by Lessen et al. [217], Lessen and Paillet [218], and Zalay et al. [219]. Experiments conducted to test the instability used both the rotor blade of a helicopter, and a "xed wing to generate the vortex. The disturbance to the vortex core was produced by a jet of air directed into the vortex near its axis. It was found that any smoke or #uid markers introduced to follow the #uid motions were
637
rapidly di!used by the blowing, and that the maximum swirl velocities in the vortex were reduced substantially. However, the rolling moment induced by the resulting vortex on a following wing was almost unchanged [220]. It is concluded that either the turbulence generated by the jet of air along the vortex axis, or the resulting instability, produced chaos only in the core region of the vortex. In either case, the rest of the vortex was left nearly intact, so that its hazard potential remained. In a related study, the e!ect of engine exhaust and landing gear extension on vortex dispersion was examined by use of measurements of the vortex-induced rolling moment on a following wing both in #ight and in ground-based experiments [58,61,66,220]. Even though there was some scatter in the data, the results indicated that the vortex-induced rolling moment on a following wing or aircraft is attenuated by engine thrust by up to 10}20%. The alleviation was, however, found to be inadequate for a decrease in the in-trail spacing between aircraft for arrival and departure at airports. Similar results were found for disturbances introduced into the wake by drag devices [58,62,63,87,88]. It is believed that the reductions in wake intensity observed when disturbances (i.e., turbulence) were injected into vortex wakes are caused by the enhanced di!usion of the circulation in the wake vortices, and not by any catastrophic vortex instability. Such a result is not surprising, because as mentioned in Section 12 on wing e$ciency, a great deal of energy is required to change the diameter of an energetic vortex core. Before vortex instabilities are discussed further, two forms of vortex dynamics observed in condensation trails will be described. Both were noted in the #ight tests conducted with the B-747 at Dryden Flight Research Center in the 1970s. The "rst, appearded to be an orderly modi"cation of the core region of vortices shed by the B-747 and illustrated in Fig. 151. It was observed only twice and then only for short periods of time, i.e., about 5}10 s. To the author's knowledge, a photograph of the event has not been taken. As illustrated in Fig. 151, the vortex contorts itself much like a rubber band being wound ever tighter. That is, instead of winding up or spinning within the same tubular space, the vortex core appeared to wrap around itself by jumping out into a tight spiral around its original location. The new core con"guration then has a radius which is larger by about
Fig. 151. Diagram of small-scale distortion on vortex core in wake of B-747 that appears similar to knots which form on rubber band as it is wound ever tighter.
638
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
a factor of two or three and that appears to have a central core and a tight spiral wrapping over it that is on the outside of the original tubular core. The outer vortex **windingsa appeared to wrap sequentially and progressively in one direction along the original vortex on the outside of the original tube. The wrappings proceeded along the core only a short distance until the core region, and the newly wrapped core region, lost their identity and became turbulent. This process caused only the core region of the vortex to become incoherent and left the outer part of the vortex intact until some other process in the wake caused the organization in the wake to be destroyed. A second form of vortex dynamics observed in the #ight tests involved not only the core but also the outer parts of the vortex. The event is a common one that might be called a form of core breakdown, and was observed in almost every wake. Britton [167] describes the event as another type of instability in which vortex burst occurs in the outer part of the vortex leaving a core behind, i.e., the burst does not entirely destroy the vortex. As sketched in Fig. 152 from observations of the wakes trailed by the NASA B-747 in over#ights at NASA/ DFRC, the event consists of a swirling type of radial #ow that appears to come from the core region of the vortex. It also appears that the #ow inside the core is toward the breakdown point from both directions along the core. The disk-shape region lies in a plane perpendicular to the vortex axis. The #ow visualization provided by vaporized mineral oil indicated that the air in the core region of the vortex #owed along the core from both directions to the location of the event. The axial #ow occurring along the core then turns from an axial direction to one in a radial direction, where the air #ows away from the vortex axis in spiral fashion. The radial #ow at the sharp bend appeared to interupt the vortex at that station, so that breakdown of the #ow "eld of the vortex was initiated. When the mutually induced instability did not lead to linking of the vortex pair, and when the vortices became sinuous because of atmospheric eddies or self-induced motions, such a disk-type breakdown mechanism at sharp bends in the vortex axes was the "rst part of a general mixing whereby vortex wakes break up. In fact, in the airport environment where aircraft are con"gured in their landing con"guration (as was the case in the Dryden tests), the vortex wakes are most often dispersed by the action of atmospheric eddies that caused the vortices to become more and more sinuous with time until the disk-type of breakdown (Fig. 152) occurs. Photographs of the event are presented for several events in a water tow tank by Liu [80] in Figs. 72}74, and in #ight by Britton [167], Crow [49] and in Fig. 3 of MacCready [221], and in a tow tank by Olsen [158]. On occasion, the breakdown event consists of a single diskshaped region where the swirling radial #ow is obvious, but more often it consists of a number of events adjacent
Fig. 152. Diagram of #ow from vortex core when it is bent sharply thereby causing the #ow "eld of the core region to decompose. Compare with Figs. 72}74.
to each other along the vortex core so that the region appears as an old fuzzy bottle brush with bristles of irregularly length as indicated in the "gures just mentioned. 15.3. Large-scale vortex instabilities Consideration is given here to vortex instabilities that, when initiated, bring about mixing in vortex wakes on a scale the size of the wing span of the wake-generating aircraft or larger. The instabilities must then have a scale or wavelength much larger than the core size. In addition to providing a large amount of mixing in the wake, the wing con"guration required to implement the instability should either maintain or increase the e$ciency of the aircraft. A vigorous search for those kinds of vortex mechanisms has been in progress for over 25 years with some success, but without one or more clearly de"ned solutions. The following subsections describe some of the e!orts that have been made. Most of the instabilities to be described rely on turbulence in the ambient #uid, or in the wind-tunnel airstream, to initiate the instability. The turbulence in ground-based facilities is consistent and reliable, but turbulence in the atmosphere is quite variable and unreliable. Therefore, ground-based tests are good developmental screening tools, but "nal proof-ofconcept must be made with #ight tests under a wide variety of operational situations. 15.3.1. Stability of single vortex pair As pointed out in Sections 7 and 8, one of the "rst mechanisms observed to bring about the complete disintegration and dispersion of a single pair of wake vortices is the mutually induced instability identi"ed by Scorer [165,120] and correctly explained by Crow [49]. As pointed out in Sections 7 and 8, the alleviation process is e!ective, but the time required to accomplish the needed wake spreading of the sinuous vortex "laments is unacceptably long for the airport environment. Therefore,
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
e!orts have been made to ensure, and to accelerate the onset of the Crow or mutually induced instability by manipulating control surfaces [155,172] or the entire aircraft [59,158]. The objective was to impress waves of large amplitude on the vortex lines as they are generated in order to reduce the time required to achieve rapid growth in wave amplitude and wake disruption. It was found that the process occurs most readily when the generating aircraft is in an aerodynamically clean con"guration, so that the vortex cores are small and the rotary velocities high. When the vortex cores are large due to the entrainment of low-energy #uid that trails in the wakes of landing gear and #aps, the growth rate of the instability waves is slow, or may not occur at all. A theoretical and experimental study was carried out by Leweke and Williamson [222] on the instability of a single pair of counter-rotating vortices. Their study extends the analysis of Crow by including disturbances that are of shorter wavelength, which are on the order of the vortex core diameter rather than the spanwise spacing between the vortices. The paper is especially interesting, because it provides the theory for the instabilities, and then also demonstrates the modes experimentally. In the "gures presented, Leweke and Williamson point out that the vertical and spanwise displacements of the vortices are in phase and not in re#ectional symmetry. The "gures presented show that the long wavelength instability of Crow is in progress, and has not yet progressed to the point of vortex linking. It is interesting to note that the instability is illustrated in the pictures of vortex "laments taken of the vortex loops formed shortly after linking, and the subsequent formation of waves of short wavelength (e.g., Fig. 71 from Crow [49], Figs. 1 and 2 in MacCready [221], and Fig. 13 in Scorer and Davenport [120]) are close to re#ectionally symmetric. This behavior in condensation trails at high altitude appears to be fairly consistent, and is frequently observed. It is believed that the paper of Leweke and Williamson contributes substantially by calling attention to the short wavelength counterpart of the long-wavelength version of the mutually induced instability. The #uid dynamics associated with the short wavelength instability does not appear to be related to either of the #uid motions illustrated in Figs. 151 or 152. It is also not clear whether the short wavelength instability leads to mixing that is restricted to the region near the core of the vortex, or whether the outer part of the vortex #ow "eld experiences mixing with regions beyond the wingtip region. 15.3.2. Stability of multiple vortex pairs In order to expand the knowledge on the instabilities and mixing that occurs in wakes like those shed by a wing with sawtooth loading (e.g., Fig. 43), Hackett and Evans [170] conducted a numerical study of the wake dynamics expected for several con"gurations. The analysis method was directed at prospective mutually induced
639
instabilities that might occur in wakes composed of multiple vortex pairs. Their more comprehensive analysis con"rmed the results predicted by the Tre!tz-plane type of analysis carried out earlier, and gave insight into the dynamics expected in more complex liftgenerated wakes. In a recent paper, Crouch [223] extends the analysis carried out by Crow [49] for one vortex pair to liftgenerated wakes composed of two vortex pairs. For these muliple-vortex con"gurations, Crouch identi"es a variety of mutually induced instabilities between the various vortices. The distortions in the axes of the vortices include both symmetric and antisymmetric modes which are of shorter wavelength than those that occur on a single vortex pair. It is found that the growth rates of the instabilities are greater for two pairs than for a single pair. Since the spanwise distance between vortices is much less in the cases analyzed by Crouch than usually found for a single vortex pair, the wavelengths of the instabilities are much shorter, and the time required for the dynamics of the wave instability to proceed through linking and dispersion is much shorter than in the single pair case. The vortex shapes presented in Fig. 11 of Crouch's paper are very similar to the #ight photographs shown in Fig. 60 of the wake shed by the (303, 03) con"guration of the B-747 which sheds three vortex pairs. When the vortex dynamics does proceed to completion, the alleviated wake was described by the pilots of penetrating aircraft as one that induced a bumpy ride, but also one that appeared to have little or no coherent rotary motion [59]. These #ight experiments support Crouch's predictions of very high growth rates, and demonstrate that the mutually induced instability in multiple vortex wakes is able to bring about a nearly complete loss of coherence in the wake within a short time behind the wake-generating aircraft. Crouch's analysis was not, however, able to predict the sensitivity of the instability to deployment of any of the landing gear nor to yaw of the aircraft, which were found in #ight to reduce the e!ectiveness of the instability by a considerable amount (e.g., Fig. 60). In a series of numerical simulations of two vortex pairs, Rennich and Lele [69] obtained wake dynamics which appears to be in agreement with Crouch's results. Both analyses point out the possibilities for large-scale mixing that are generated by sawtooth-type loadings [151]. These results coupled with the #ight test results obtained with the (303, 03) con"guration of the B-747 (Sections 7 and 8) indicate that under certain circumstances it is possible to design a lift-generated wake that disperses rapidly enough that wake-vortex spacings at airports can be reduced [58,59,181]. Further support for the concept, and for some of the limitations of the concept, are provided by the experimental results obtained in the 40;80 ft Wind Tunnel and in a water tow tank with a wing equipped with seven pairs of #aps [10,91]. The
640
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
#aps enabled the wing to shed eight vortex pairs that interacted quickly to produce chaos in the wake. However, the mixing mechanism became subdued as the lift on the wing was increased enough to make the #ap vortices subordinate to the pair shed by the wingtips. The advantages gained when large input disturbance waves are imposed on a vortex wake is illustrated by an example described in Section 8. Some of that information is repeated here to again indicate the uniqueness and di$culty with the concept. As pointed out previously, the event occurred near the end of the #ight test program at Dryden. As a last-minute check on the resilience of vortices that had been alleviated by means of turbulence injection by use of spoilers, several #ights were made where the wake-generating aircraft executed a series of roll-oscillation maneuvers. The roll oscillations were used to simulate the curving structure of vortices that might occur as the aircraft rolls and turns when a wave o! is given during landing. To everyone's surprise, the alleviation achieved with spoilers deployed during roll oscillations was far greater than that achieved with the spoilers deployed during straight and level #ight. It was found that the larger input disturbance waves were able to initiate a mutually induced instability in the two vortices shed by the inboard #ap, so that the wake structure became incoherent, according to numerical simulation of the #ight experiments with vortex "laments. In the numerical results, the wake was simulated with vortex "laments based on the assumption that deployment of the spoilers modi"ed the span loading, so that it could be approximated by the (303/03) con"guration. The vortex strengths were therefore based on computed span loadings, and showed that the large initial "nite displacements of the "laments by the roll oscillations activates a mutually induced instability that leads to rapid decomposition of the entire vortex wake [181]. The wake alleviation achieved with the B-747 by use of spoiler deployment and roll oscillations was not achievable with any other con"guration of the B-747 or the L-1011 [59]. The example just described is interesting from a research point of view. It is not, however, applicable to subsonic transport aircraft, because the required rapid rolling maneuvers causes passenger comfort and safety to be compromised, and because the dynamic loads imposed on the generating aircraft produce unacceptable structural fatigue. 15.4. Vortex injection by use of wing xns The wing-"n concept for wake alleviation has already been treated in Section 9, and so is only mentioned here because the mechanism that brings about the reduction in swirl velocity is not yet known. It is believed that it is some form of mutually induced instability, but how the instability proceeds to achieve large reductions in wake
intensity that are roughly proportional to the "n angle of attack is unknown.
16. Turbulence injection 16.1. Introduction The introduction or addition of turbulence into a liftgenerated wake in order to more rapidly di!use the intense swirling velocities, or to initiate an instability, was tried with much e!ort during the early part of the wake-alleviation program in the 1970s. The topic was left until near the end of the paper not only because the technique was not very successful, but also because the information in previous sections was needed to put the investigations into perspective. For example, when the wake-vortex program of the 1970s began, several well-known aerodynamicists believed and expressed their strong opinions that nothing signi"cant could be done to make a lift-generated wake non-hazardous. Their reasoning was that the wing had to produce lift to enable the aircraft to #y, and the production of lift by a wing of "nite span requires that appreciable downward momentum is imparted to the air. Since the downward moving air has side edges, vortices result. As described in a previous section, part of the statement is wrong, because the hazard posed by wakes of conventional wings has been signi"cantly reduced by more than just one method. The problem with the alleviation successes found so far is that the e$ciency of the wake-generating aircraft is degraded by an unacceptable amount, or the alleviation was unreliable. In order to illustrate the types of concepts that were tried, an overview of several experimental programs will be described. Work began on turbulence injection devices soon after the initial series of #ight tests being used to determine spacing distances between aircraft at airports were being completed by the FAA and NASA. The #ight data indicated that, without some sort of modi"cation to vortex wakes, the decay rate is too slow in the airport environment for e$cient use of runways. Research e!orts were then started to "nd ways to bring about a more rapid decomposition of the vortices, so that aircraft could be safely spaced more closely for landing and takeo!. Since #ow visualization of vortices behind aircraft indicated that the vortices had what appeared to be a laminar structure throughout much of its swirling motion, it seemed logical to introduce turbulence into the swirling regions to increase substantially the turbulence in the #ow "eld. It was reasoned that the increased turbulence would break down the laminar #ow making it turbulent, and thereby increase the rate of decay and dispersion of the vortices. Such a concept was supported by the observation that laboratory vortices were di$cult to generate, and to maintain if the ambient air was not
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
nearly quiescent, i.e., even small amounts of turbulence would disrupt the vortex structure. At the time when this research began (i.e., about 1970), the idea was primarily directed at the utilization of turbulence to more rapidly di!use the highly energetic parts of the vortices near their centers. An e!ort to trigger speci"c instabilities was not intended, but any instabilities that would have been initiated by the injected turbulence would have been gladly accepted. Research with turbulence injection devices covers a broad range of devices including spoilers, splines, wingtip jets and fans, and engine thrust. Results from investigations on these devices are presented in various papers included in conference proceedings [25,27}30,224]. Studies have also been conducted on the e!ect of various turbulent environments on vortex wakes [72,78,154,213,214]. In general, it was found that many of the devices tried were e!ective in reducing the rotary velocities in wake vortices, so that the maximum velocity in the plateau region of decay is reduced. Unfortunately, as exhibited by the curves in Fig. 2, a reduction in the initial value of the circumferential velocity generally leads to an increase in the downstream extent of the plateau region, so that the net decay of the vortex far downstream is not greatly in#uenced. A further disadvantage of turbu-
641
lence injection is that a reduction in the rotary velocities near the axis of the vortex does not greatly reduce the rolling moment imposed on following aircraft whose wing spans are substantially larger than the diameter of the vortex core; which includes most aircraft. Three devices tried in the NASA wake-vortex program of the 1970s are now discussed. Alleviation achieved with engine thrust has already been discussed in Sections 1 and 2. 16.2. Wingtip spoiler One of the "rst, if not the "rst, device tried was a spoiler mounted on the wingtip of a Convair 990 operated by NASA. A wind tunnel study by Corsiglia et al. [94] indicated that a relatively small wing tip spoiler was capable of reducing the maximum rotational velocity in the shed vortex by a factor of about three. When a full-scale version of the device was tested in #ight on one wingtip of a Convair 990 (Fig. 153), the pilot of the Lear Jet aircraft used to penetrate the wake could not distinguish the di!erence between the vortices shed by the treated and the untreated wingtips [94]. Instruments onboard the Lear Jet penetrating aircraft did show however, that the roll acceleration imposed on the probe aircraft by the vortex was lowered from 4.4 to 2.4 rad/s
Fig. 153. Convair 990 aircraft operated by NASA Ames Research Center with vortex dissipater mounted on left wingtip to disperse vortex wake; Corsiglia et al. [94].
642
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
as it moved from the untreated to the treated trailing vortex. Some of the di!erences between the two observations behind the two wingtips may have been due to a di!erence in the path of penetration by the probe aircraft. Since roughly the same result occurred on several penetrations, it is more likely that the results of the roll acceleration instrumentation do represent the alleviation achieved. It is believed that the correct explanation lies in the fact that both the alleviated and the nonalleviated vortex roll accelerations experienced by the pilot far exceeded the aileron-induced roll capability of the Lear Jet (1.15 rad/s). Under those circumstances, the pilot perceived that he was experiencing overpowering rolling moments from both the treated and untreated vortices, and the di!erence indicated by the instrumentation was not apparent to him. The foregoing experiment again points out the fact that e!ective alleviation must bring the wake-vortex induced rolling moments down to the point where the vortex-induced rolling moment is less than about onehalf of the roll authority on board the aircraft. Anything less will still be perceived as hazardous. The small change in rolling moment indicated by the #ight tests, even though the maximum swirl velocity in the vortex may have been reduced by a factor of three (as in the windtunnel experiment) is to be expected. The di!erence in results arises, because a reduction in swirl velocity only in the core region of the vortex does not achieve much change in the overall rolling moment induced on aircraft when the wing span is much larger than the vortex core diameter. 16.3. Wingtip spline In a second example of turbulence injection, the size of the device used to inject turbulence into the wake was increased in size relative to the aircraft in order to achieve an acceptable level of alleviation [67]. The con"guration consisted of a spline or umbrella-type apparatus that trailed just behind the wingtip of a four-engine propeller-driven transport (Figs. 154 and 155). When the modi"ed and unmodi"ed aircraft were tested in #ight, the wake-induced rolling moment on a small propellerdriven aircraft was found to be reduced by about 72%. As expected, #ight in the modi"ed vortex wake by the probe aircraft was found to be a controllable situation at separation distances of less than 2 n mile. The disadvantage of the spline device was that it increased the landing drag of the C-54 by about a factor of two. It is informative to examine the wake history of the con"guration, because as illustrated in Fig. 155, the reduction occurs almost immediately behind the C-54. As is typical of a plateau region, little or no decay occurs during the next 8 km. At that point, natural decay appears to have reduced the vortex intensity behind the unmodi"ed aircraft to the point where the two wakes have roughly equiva-
Fig. 154. Unmodi"ed C-54 wake-generating aircraft and wingtip spline assembly used to test vortex attenuation concept; Patterson et al. [67].
lent rolling-moment hazards. This result appears to again support the contention that turbulence injection a!ects the plateau region of vortex decay but not the far-"eld decay. Later in the wake-alleviation program, Patterson [68] proposed that a large propeller be placed behind the wingtip in place of the spline to remove energy from the vortex. Such a device could then extract rotational energy from the airstream with either a low drag penalty or by providing thrust. In a similar study, Snyder [71]
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
643
devices are of a size that is probably less than one-tenth of the span of the generating aircraft, which is too small to demolish the structure of the vortex wake. Furthermore, injection of turbulence increases the drag of the aircraft and may create unwanted dynamic loads on the aircraft structure which may cause premature fatigue failures. 16.5. Atmospheric turbulence
Fig. 155. Measured vortex-induced rolling moments induced on single engine probe aircraft to test vortex attenuation concept with splines in wind tunnel and in #ight; Patterson et al. [67].
studied the e!ect that a wingtip propeller and its direction of rotation would have on the vortex location and on the span loading. Since e$cient wing designs for jet transport aircraft shed a large part of their vorticity inboard of the wingtip, devices that work in the wingtip region fell out of favor.
The atmosphere is the best turbulence injection apparatus currently available. Not only does it provide large-scale turbulence in the lower atmosphere that has a scale and energy level capable of rapidly dispersing vortex wakes, but it is available at no cost [8,48,74,80,83,86,110,112,122]. Unfortunately, dispersion of vortex wakes as provided by the atmosphere is intermittent and does not always occur when needed. Since wake dispersion by the atmosphere is very e!ective, studies have been undertaken on how to best implement reduced aircraft separation distances during windy periods, and to use conventional spacings during calm periods.
17. Wake-vortex avoidance schemes 17.1. Introduction
16.4. Flight spoilers already on aircraft Both wind-tunnel and #ight tests were used to "nd out if spoilers already on board most large transport aircraft might serve as turbulence generators capable of reducing the hazard in vortex wakes to an acceptable level [62,63]. If any of the concepts was acceptable, the cost of implementation should be quite reasonable. The e!ect of the thrust of jet engines as turbulence injecting devices was also studied [66]. However, the alleviation achieved with spoilers, engine thrust, and other turbulence injection devices was found to consist primarily of a reduction in the rotary velocities near the core of the vortices, and did not seem to accelerate the decay of vortices in the far "eld enough to provide the needed alleviation. A number of other devices that rely on turbulence injection were also tested experimentally [25,220]. It was concluded, therefore, that in only one of the many con"gurations tested was enough alleviation produced to satisfy the requirement for 2 or 3 n mile spacings, but the spline device had unacceptably high penalties [67]. As far as future prospects are concerned, further improvements in wake-vortex alleviation by use of turbulence injection are not likely. The experiments carried out so far indicate that the concept is unacceptable, because the size of the mixing eddies needed to signi"cantly reduce the hazard posed by wake vortices at a 2}3 n mile goal needs to be on the order of the wing span. In contrast, eddies produced by on-board turbulence
Since lift-generated wakes of aircraft persist long enough to pose a hazard to following aircraft during approach and takeo!, the most obvious solution is to avoid the wake vortices of previous aircraft. If avoidance is to be accomplished on a consistent basis, and since vortices are not usually visible, a reliable method must be developed to be sure that the #ight corridors are free of hazardous vortices when an aircraft enters the airspace. The "rst e!ort at the development of an avoidance scheme began in the late 1960s with the #ight program by the FAA. On the basis of the information obtained by Garodz et al. [12}21] from the #ight program, and information from NASA and other sources, the separation guidelines were determined as listed in Table 1. Shortly thereafter, it was found that the separation guidelines were e!ective, because they allowed enough time for the vortices from one aircraft to move out of and away from the #ight corridor to be used by following aircraft. The foregoing decisions bene"ted from the fact that they were made at a time when the exhaust from jet engines of most transport aircraft contained noticeable amounts of soot particles. The soot particles served as #uid #ow markers that, quite often, made it possible for pilots of following aircraft to clearly see the core regions of vortices shed by preceding aircraft, and thereby avoid them. In the early 1970s, it was mandated that the turbulence in the burner cans be increased, so that the soot
644
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
output from the engines became negligible. As a consequence, lift-generated vortices are now seldom visible behind jet aircraft in the vicinity of airports. E!orts to "nd a way to visualize or detect in some way the presence and location of vortices have not yet produced a successful operational system [24,28,199]. A good review of work by the FAA on the development of vortex sensors for detection and measurement of vortices is presented by Abramson and Burnham [110] and Burnham [111,112]. A good overview of a number of detection systems under study at the time by a variety of other groups is available in the 1991 FAA Conference edited by Hallock [28]. At a 1997 wake-vortex meeting [225] held at Ottawa, Canada, presentations described a number of wakevortex avoidance systems now under development by France, Germany, Russia, United Kingdom, and the United States. Also described at the meeting were programs for the development of record-keeping systems for wake-vortex encounters. The purpose of the recordkeeping systems is to assemble data so that the weather conditions and circumstances under which vortex encounters occur can be identi"ed, and corrective measures taken. An overview is presented in this section on wakevortex avoidance systems. More information is provided in the 1997 conference proceedings [225] where abstracts, slides, and some discussions on the presentations are included. Since the various avoidance systems have some common components, but di!er in the details, and because the study of avoidance schemes is a side-issue for this paper, an overview will be presented of only two study programs, namely, the Vortex Advisory System (VAS), which was developed and tried in the late 1970s, and the Aircraft Vortex Spacing System (AVOSS), because it is a very broad based theoretical and experimental program. The Aircraft Vortex Spacing System (AVOSS) is now being designed and developed by NASA Langley Research Center for and in cooperation with the FAA. The reason for choosing this system for discussion is that it has been underway for probably the longest time, is the most comprehensive, and is developing the largest database of any of the programs [2,24,50,121, 123,124,211,226]. A discussion is then presented on various features of avoidance systems that appear to either simplify the task, or make it more di$cult. 17.2. Vortex Advisory System (VAS) In an e!ort to safely reduce all of the separation distances listed in Table 1 to a uniform 2 or 3 n mile during approach and depart of aircraft at airports, a vortex advisory system was developed in the 1970s by use of measurements made on vortices shed by aircraft as they arrive and depart at airports [30,227]. The measurements used in the determination included measurements
Fig. 156. Wind ellipse on which Vortex Advisory System (VAS) was based. Shaded region is safety region to allow for a transition from adequate wind to one of inadequate wind and vice versa; Wood [30].
with: an array of anemometers of over 50,000 landings (100,000 vortices) and 5000 tako!s; a monostatic acoustic vortex system of 15,000 landings and 2000 takeo!s; and a laser-doppler velocimeter of over 5000 landings. The measurements were made at Chicago O'Hare, New York JFK, London Heathrow and Denver airports. The data showed that after about one minute only 16% of the vortices were still in the vicinity of the #ight corridor. Further analysis showed that after 80 s (i.e., 3 n mile at a landing speed of 135 knots) the residual vortices all fell inside of the wind ellipse reproduced in Fig. 156 [30]. That is, after 80 s, the vortices were either blown out and away from the #ight corridor, or they were dissipated by ground turbulence when the local wind vector was outside of the ellipse shown in Fig. 156. The data made it possible to draw elliptic contours of wind velocity and direction outside of which an approach or departure #ight corridor becomes free of any detectable vortex. A second ellipse, with a shaded region between the two, was used to allow for a transition region between a hazardous and a non-hazardous situation. Designated the `Vortex Advisory Systema (VAS), the system was tried at O'Hare Airport near Chicago. The decision to test VAS at O'Hare was based on the fact that
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the airport was near capacity, had a mixture of tra$c that included a large percentage of aircraft in the heavy category, and the area was often windy. Unfortunately, at the stage of development of the interfaces between VAS and the #ight control system already in place at O'Hare, the decision-making processes had not been developed thoroughly enough to be incorporated smoothly into the #ight-control procedures. As a consequence, airport capacity was decreased rather than increased. In retrospect, the implementation of the VAS concept should "rst have been applied at a relatively non-busy airport where it could have been re"ned into a complete smoothly-working system. Once re"ned, implementation at an extremely busy airport, like Chicago O'Hare, would have a much better chance for success. Since the concept failed on its "rst application, the VAS concept has been dismissed as unworkable, which was probably a big mistake for a number of reasons. First, it could have served as a pilot program for the various systems now under study, and could have provided information as to which should be rejected and which should be considered for implementation. Secondly, since the VAS concept is sound, further testing and development at a sequence of airports would no doubt have provided increased capacity at most airports until an improved replacement would become available. It might still be advisable to carry out practice implementation of a simple system like VAS to gain experience with vortex avoidance systems, because the more complex systems now being considered will no doubt have even more unexpected problems than encountered by VAS. 17.3. Aircraft Vortex Spacing System (AVOSS) After the VAS concept was dropped in the late 1970s, e!orts to make measurements on wake vortices at airports, and to "nd satisfactory alleviation methods for lift-generated wakes were signi"cantly scaled back by NASA and the FAA. In the early 1990s, a number of programs to develop wake-vortex avoidance systems were again started. Most concepts include the e!ects of the atmosphere on vortex persistence and location, and have as their goal a precision which permits a safe separation distance between aircraft under all weather conditions of about 3 n mile. As mentioned previously, probably the most ambitious of all of the programs is the Aircraft Vortex Spacing System concept being developed by NASA Langley Research Center. The research underway has the goal of enabling safe improvements in the capacity of the nation's air transportation system by bringing about a reduction in the in-trail spacing of airplanes. At the time that the program began, and to a large extent at the present time, the scienti"c basis does not exist to quantify the wake transport and decay properties of lift-generated vortices, nor the aircraft}vortex interaction dynamics, with su$cient accuracy to put into
645
use weather-dependent aircraft separations, that are signi"cantly di!erent from current standards. The major goal of the research at Langley is to provide the technology base and systems to permit the same airport capacity levels during instrument operations that are presently experienced during visual airport operations. In support of that goal, Hinton [2,123,124] presents a description of the components that make up the AVOSS. When completed, AVOSS will provide a system concept that uses available knowledge of aircraft wake generation, atmospheric modi"cation of those wakes, wakeencounter dynamics, and operational factors to provide dynamic wake-vortex spacing criteria for use at airports by Air Tra$c Control. In 1997, a decision was made to reduce the emphasis on wake-encounter dynamics and concentrate more on vortex avoidance. Several guidelines were placed on the characteristics of AVOSS. As described by Hinton [124] they are: (1) The "nal system must be such that it can be approved for operational use, including a large degree of robustness, reliability and cost realism. (2) The safety provided must be equal to or greater than the current system. (3) AVOSS will not require an increment in pilot skill level or training. (4) No aircraft structural or system modi"cation will be required. (5) AVOSS will not alter current pilot functions nor change airborne/ground responsibilities. (6) It is permissible to require special air tra$c control (ATC) or #ight procedures that are compatible with current skill levels. Within these constraints, the new system must increase airport capacity as much as possible. The AVOSS System Concept is illustrated schematically in Fig. 157 and the Predictor Subsystem in Fig. 158 to indicate the complexity of the problem. One of the most apparent uncertainties is the weather state at the airport when an aircraft arrives. Since aircraft spacing at the arrival airport must be known before the aircraft departs its originating airport, an ability to predict the weather state in advance by hours is required. Even the measurement of the weather and atmospheric state along the #ight corridor as a function of time is di$cult, whereas comparable accuracy for the same data several hours in advance seems impossible. As a consequence, an intense theoretical and experimental program of prediction and measurement of the atmosphere and of the dynamics of lift-generated vortices embedded in them has been underway for about "ve years. Measurements have been made at various airports in the vicinity of the #ight corridor for approach and departure and e!orts have been made to predict the motion and structure of the vortices [24,72,86,97,121,198,208,211,225,226]. The analyses and measurements will hopefully yield reliable solutions for the time-dependent weather at a given airport and for the weather several hours in advance. In addition, it must be possible to place error bounds on the various parameters that govern vortex transport and decay. The
646
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 157. AVOSS System Concept; Hinton [124].
Fig. 158. AVOSS Predictor Subsystem; Hinton [124].
di$culty of the task is awesome, and it seems that it may be necessary to bring other factors into the planned system to simplify the problem to one that can be solved satisfactorily in the near future.
18. Simpli5cation of vortex-avoidance systems 18.1. Overview A number of speci"cations are usually placed on vortex wake advisory or avoidance systems in order to insure that it "ts smoothly into the rest of the air transport system when it is implemented. It should be kept in mind that even a small change in some of the speci"cations can sometimes signi"cantly reduce the complexities of a wake-vortex avoidance system, and also improve safety. If, for example, the guidelines placed on the development of an avoidance system make it necessary to accommodate the entire conically shaped ILS region like the one illustrated in Fig. 159, unnecessary e!ort is required, as will be illustrated. The cross-section of the
Fig. 159. Illustration of conically-shaped #ight corridor used for Instrument Landing System (ILS) for approach.
approach corridor is small at runway threshhold, but becomes quite large at approach distances beyond the middle marker (5 n mi). For example, at 5 n mi the crosssection of the ILS conical corridor has a diameter of over 1500 ft. Since aircraft are permitted to locate themselves anywhere in the approach corridor, the wake-vortex
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
avoidance system must have the capability to guarantee to pilots of following aircraft that they will not encounter a wake vortex with enough strength to signi"cantly disrupt their approach path and touchdown throughout the entire conical region. Such a requirement is very di$cult to ful"ll and to still decrease spacing between aircraft on a regular basis. It seems logical then to design the approach and departure corridors so that the requirements on the wake vortex advisory system be eased. The text to follow describes a study of several design features of the air tra$c system that would simplify considerably the problems associated with the development of vortex avoidance systems [228]. A feature to be avoided is also described. 18.2. Flight corridor of small cross-section 18.2.1. Accuracy of global positioning system (GPS) Obviously, it is much easier for vortex wakes to move a small distance to vacate a #ight corridor than to move a large distance. This fact suggests that aircraft on approach to or departure from airports should be restricted to #ight corridors that are as small as practical in crosssection [228]. The size of the #ight corridor depends, of course, directly on the navigation systems on board subsonic transport aircraft to maintain accurate control of their #ight paths. A strong supporting reason for making a transition to #ight corridors of small crosssection is that the technology needed for implementation is currently available from the Global Positioning System (GPS) that operates by use of satellites orbiting earth. Although not its original purpose, GPS technology is ideally suited for the location and guidance of transport aircraft, and is in current use on many aircraft. Furthermore, research is underway to upgrade the accuracy of GPS so that aircraft will be able to execute zero visibility landings safely under all weather conditions. Consideration has therefore been given to the possible simpli"cations that can be derived by making the approach #ight corridors at airports as small as guidance technology for aircraft will permit [228]. The present aircraft guidance system used at airports is the Instrument Landing System (ILS). The ILS currently provides approach corridors which have a conical shape wherein the point of the cone is at runway threshhold, and the open end is at the beginning of the approach path for aircraft (Fig. 159). At touchdown the #ight corridor is quite small, but at the middle marker and beyond, the 33 conical #ight corridor becomes 1500 ft and larger in diameter. Since the #ight corridor has a large cross-section, it takes vortex wakes a long time to move out of it. If, however, the corridor were reduced in a size just within the capability of present aircraft guidance systems, like GPS, the wake vortices would have only a short distance to move before they were out of the #ight corridor.
647
Optimally, the cross-section of the #ight corridor should also be constant in size, rather than conical. The GPS currently in service is based on a satellite system that transmits location information at two frequencies. The "rst frequency is currently being used by non-military users, and the second is selectively available. It has recently been announced that the United States has the intention to remove selective availability on the second frequency by 2005 and to add a third frequency to the system (Aviation Week and Space Technology, April 6, 1998, p. 60). It is estimated that the availability of three frequencies should improve the precision of location, so that maximum errors decrease from 100 to 3}10 m. Prior to this decision, the FAA planned to use "xed reference stations along with the current satellite system to increase the accuracy of location near airports to achieve errors less than $33.5 m ($110 ft) in the horizontal direction, $9.5 m ($31 ft) in the vertical direction, and less than 1 m at the runway threshold [229]. Additional accuracy (down to several cm.) is also currently achievable by use of pseudo-satellites, or pseudolites, to essentially calibrate the GPS receivers near airports so that accuracies are based on fractions of a wavelength rather than on several wavelengths [230}232]. When these accuracies of location are coupled with some of the more accurate autopilot systems, it appears that it is possible to hold an aircraft on an approach path accurately enough to permit zero visibility landings. Since accurate location and guidance of aircraft will be available in several years for another purpose (zero visibility landings), it seems obvious to inquire how such a capability can be used to simplify the avoidance of lift-generated vortices at airports. A study conducted by Rossow [228] concludes that GPS should be utilized to design approach corridors that are long, slender and constant in cross-section, rather than conical. The small cross-sections of the #ight corridors should extend out from the runway threshold at the conventional approach angle used by aircraft (3.53 to the horizontal at the present time) as far as needed to bring aircraft safely into and along approximately the same #ight path. Since safety is assured once inside the #ight corridor, the distance from runway threshold at which the controlled corridor should end will probably be governed by the requirement that the altitude at that point must be high enough for aircraft to safely recover from a vortex encounter if one should occur. Some additional rationale behind the design of #ight corridors is described in subsections to follow. 18.2.2. Vortex transit times If GPS #ight corridors of small size are adopted for wake-vortex avoidance at the same time that they are adopted for zero visibility landings, the volume of atmosphere throughout which a vortex advisory system must keep track of lift-generated vortices is considerably
648
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 160. Contours of constant rolling-moment coe$cient for vortex wake to indicate boundary of hazardous region [228]; b "200 ft (61 m), C "1.5, b /b "0.29. J
reduced. The example used in illustrative computations by Rossow [228] was assumed to be 80 ft wide and 80 ft high (i.e., 24.4;24.4 m) but could be even smaller. The bene"t received from a #ight corridor of small crosssectional size is that, for a given situation, the time required for a vortex wake to vacate the corridor by the wind or by self-induced velocities is correspondingly small. An estimate of the self-induced downward velocity of a vortex pair shed by aircraft indicates a spread from several ft/s for small transports to about 10 ft/s for larger transports. However, the transit time involves not only the motion of the vortex centers, but also the hazardous region around the vortex pair, because the hazard associated with the vortex wakes is the item that must move out and away from the #ight corridor. The cross-sectional size of the hazardous region of a vortex pair was estimated by calculating the wakeinduced rolling moment on a following wing in the vicinity of a vortex wake over a range of locations. Points that have the same rolling moment are then connected to produce lines of constant rolling-moment coe$cient for the wake as shown in Fig. 160. The wake is assumed to be symmetrical above and below the vortex centers (located at y/b "0.4, z/b "0.0), and anti-symmetrical port and starboard. The center of the wake, and not the center of the wake-generating aircraft, is located at the origin. The contours presented in Fig. 160 are taken as representative of the wake structure from about seven spanlengths, or 1/4 mile, to about 80 spanlengths, or 3 mile behind the wake-generating aircraft. The computations are presented for C "1.5, and a ratio of the span of the following * wing to that of the generating wing of b /b "0.29, e.g., a wake-generating aircraft with a wing span of about
200 ft (61 m) and a following aircraft with a wing span of about 60 ft (18.3 m). The example presented is typical of a small aircraft behind a heavy aircraft and is not directly applicable to any two particular aircraft. Contours for aircraft more nearly equal in size to the heavy leading aircraft are similar to the example in Fig. 160 but have smaller induced rolling moments near the vortex centers [104]. By use of the information in Fig. 160, it is possible to de"ne a boundary outside of which the lift-generated wake does not pose a rolling-moment hazard. Identi"cation of the hazardous boundary begins with the observation that the maximum aileron-induced rolling moment is typically "C "+0.06 for subsonic transports [104]. JB The inner cross-hatched regions around the vortex centers and inside the "C ""0.06 contours then denote J those regions where the wake-induced rolling moments exceed the maximum aileron-induced rolling-moment of the encountering aircraft. Outside of these regions, the wake-induced rolling moment on the following aircraft is always less than 0.03, i.e., "C "40.03. Under those cirJ cumstances, it is estimated that the encountering aircraft has enough roll control power for the ailerons to cope with and recover from any vortex-induced roll excursion [104]. In order to be conservative, the hazardous region is taken as extending one span in the vertical and two in the horizontal direction in order to be well outside of the "C ""0.01 contours where an encounter would be barely J perceptible. Next, assume that the #ight corridor is small relative to the size of an aircraft of 200 ft span (61 m), and is centered on the corridor (Fig. 161). The hazardous region is then much larger than the #ight corridor, so that the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
649
Fig. 161. Superposition of hazardous region of large transport aircraft and 80;80 ft (24.4;24.4 m) #ight corridor with centerlines aligned [228].
hazardous contours extend out well beyond the sides of the corridor, even when the wake-generating aircraft is centered on the corridor. If an approach or departure is to be safe from a vortex encounter, enough time must be allowed for the wake to move the maximum distances possible, either vertically or sideways to separate the two regions. The worst situation for lateral or vertical transfer is for the aircraft to be at the opposite side of the #ight corridor from the direction of travel of the wake. In equation form, the maximum horizontal and vertical travel distances are then given by [228] *y "B #B /2,
(73a)
*z "D #D /2,
(73b)
where B and D are the breadth and depth dimensions of the #ight corridor, i.e., for most subsonic transports, B "2b and D "b . Eqs. (73) point out the import ance of the size of the #ight corridors, because they can be changed but the size of the hazardous region cannot. Obviously, the minimum amount of time for the #ight corridor to become safe occurs when the #ight corridor is of zero size, that is, when the #ight of all aircraft are constrained to #y along a given line so that B "D +0. Any increase in the size of the #ight corridor to allow for deviations from a small corridor adds linearly onto the time for the hazardous region of the vortices to move out of the #ight corridor. In equation form, the time required for the hazardous region to vacate the #ight corridor is given by [228] *t "[B #B /2]/v , W
(74a)
*t "[D #D /2]/w , X
(74b)
where v is the velocity component of the wind across the #ight corridor, and w is the self-induced downward velocity of the vortex pair. For convenience, and to be conservative, the span of the largest aircraft in the current #eet (b +200 ft) is used for the reference hazardous re gion. If the #ight corridor is taken as 80 ft;80 ft, and the wind is not blowing, the hazardous region needs to move downward by (80 ft#100 ft) to vacate the #ight corridor. If the descent velocity of the vortex pair is taken as w "5 ft/s, 36 s are required for the wake to vacate the #ight corridor. A 1 min (or 3 n mile) spacing would then provide safe separation distances for aircraft [228]. When smaller wake-generating aircraft are considered, the self-induced velocity of the vortex pair is sometimes smaller. Some or all of their reduced downward speed is o!set by the smaller distance, B /2 or D /2, that the vortices have to travel in order to clear the #ight corridor and become avoidable. It is noted that the centerline (i.e., not necessarily the entire aircraft) of the following aircraft is constrained to the #ight corridor. Certain parts of the aircraft will usually protrude outside of the #ight corridor. It is not necessary, however, to allow extra time or space for the two regions to become separated, because the rollingmoment computations are based on the relative locations of the centerline of the wake, and the centerline of the following aircraft. Thus, the computations already take into account the entire velocity "eld of the vortex wake and the entire wing of the following aircraft. 18.3. Straight or curved yight corridors Consideration is given here to the preferred shape for the #ight corridor (i.e., straight versus curved). The desire
650
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 162. Plan view of curved approach path in horizontal plane [228]. (a) Positive curvature. (b) Negative curvature.
for simplicity in any avoidance procedure almost dictates that straight-line #ight corridors be used, because any curvature of the #ight corridor complicates the programming for approach and departure operations. It seems prudent however, to at least consider curved corridors in case a particular shape has a decided advantage over the straight-line #ight path. The question to be answered then is whether curved #ight corridors lead to conditions that signi"cantly decrease the likelihood of a vortex encounter, and thereby merit the extra e!ort needed to execute them. Curved paths in the discussions to follow can mean a path with continuous curvature, or a path that has two or more straight-line segments that approximate a curve. When the curvature is only in the horizontal plane as the aircraft descends for landing or ascends after takeo!, the vortex hazardous region descends in still air as it would if the #ight path were straight. However, if a wind is blowing parallel to any part of the curved trajectory (Fig. 162), the downward motion of the vortex wake is in#uenced by a head- or tail-wind e!ect. The apparent descent of the vortex wake may then be enhanced or reduced depending on the wind direction and magnitude, and whether the aircraft is landing or taking o!. It is therefore concluded that a curved, or segmented turn in the horizontal plane while on approach or departure is more complex to monitor and has a higher risk for wake encounters than a straight-line #ight corridor. Finally, no
di!erence appears to exist between curvature due to a turn to the port or to the starboard. Consider next both positive and negative #ight path curvatures in the vertical plane (Fig. 163). Note that the angles of the #ight paths relative to the ground are much larger than actual ones to better illustrate possible hazardous situations. If all aircraft follow the same #ight corridor, and the vortex wakes descend in still air according to their self-induced velocity, the risk of an encounter with the hazardous-wake region is not increased for either type of #ight path. However, if a head- or tail-wind is blowing, the steeper parts of the #ight paths are more susceptible for the wake moving into the path of a following aircraft. It is therefore important to maintain a minimum slope along #ight corridors, which is provided by a straight-line #ight path from a given altitude to touchdown. Hence, once again a straight-line #ight path is less susceptible to wind-caused unacceptable motion on the part of the vortex wake than any curved path. Furthermore, if aircraft are allowed to follow either a straightline or one of the curved #ight paths shown in Fig. 163, the mixed trajectories cause the aircraft carrying out a straight-line #ight to cross the vortex wake of the preceding aircraft. In a study of a proposed two-segment approach, it was found that the mixture of straight-line and two-segment approaches were particularly hazardous; Kurkowski, Barber and Garodz [119]. Without going into other possibilities, it is apparent that #ightpath curvature in the vertical plane can also be more hazardous than a straight one, is more complex to operate, and certainly does not present an advantage over #ight corridors that are straight. 18.4. Relocation of yight corridors Consider here the case wherein the #ight paths of the wake-generating and following aircraft can each be controlled separately and precisely. A reduction in wakevortex spacing distances would then seem possible, because the system would be able to guide the following aircraft along an adjustable path where the vortices shed by the preceding aircraft will not be encountered, no
Fig. 163. Side view of curved approach path in vertical plane [228].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
651
Fig. 164. Side view of relocation of #ight corridors along runway to illustrate large amount of space required [228].
matter how closely they follow one another [228]. For example, the #ight path of one aircraft would be laid out, so that it would land at or near the beginning of the runway. Since the vortex wake of the leading aircraft will descend when there is no wind, the next or following aircraft would be directed along a #ight path that is directly above the one used previously (Fig. 164). Such a procedure is one that has been used in the past during conditions when visual #ight rules can be followed. Similarly, if the wind is blowing, the following aircraft can avoid a vortex encounter by moving its #ight path to port or starboard, up or down, by an amount that depends on the magnitude and direction of the wind. The basic idea is to place the relative locations of succeeding #ight paths, so that the wind and the self-induced velocities do not allow vortices to move into the #ight path of following aircraft. The amount of relocation of each #ight corridor depends on the size of the crosssection of the #ight corridor and of the wake-vortex hazardous region, and magnitude in the wind and its uncertainties. In that way, each succeeding aircraft has its own #ight corridor located so as to avoid all other corridors and vortex wakes of other aircraft. Furthermore, the corridors should all be straight and parallel so that #ight paths do not cross the wakes of preceding aircraft. In principal, the foregoing process is the way that relocation of #ight corridors should work. However, relocation of the #ight corridors cannot be continued inde"nitely, because airports are of "nite size so that previous corridors must eventually be recycled. If a #ight corridor is to be reused, su$cient time must be allowed after relocation for the vortices to decay to a harmless level, or to move far enough away that they do not pose a hazard when a corridor is recycled. In addition, the time required for an aircraft to transit its entire approach or departure #ight path is usually longer than the time interval between aircraft. Several #ight path corridors will therefore need to be active at a given time for both landing and takeo!, which introduces more complications.
Before proceeding further, the most serious drawback is that succeeding #ight corridors must be shifted so that overlap with previous #ight corridors does not occur, and the amount to be shifted is not small. From Fig. 164, the intersection of a #ight corridor on approach with the runway surface is given by *x "D /tan h ,
(75a)
where D is the depth of the #ight corridor, which is taken as the vertical uncertainty in the location of the aircraft. If the size of the hazardous region is the determining factor, *x "D /sin h ,
(75b)
where D is the depth of the hazardous region perpen dicular to the #ight path, and not the vertical extent. The impossibility of the situation becomes apparent when, for example, the size of the intersection of an 80 ft;80 ft corridor with the runway is considered (Fig. 164). For approach angles of h "3 and 53, the footprint of the corridor intersection with the runway, is found by Eq. (75a), to be 1526 and 914 ft, respectively. If the corridor depth is based on the depth of the hazardous region for a large aircraft, its imprint along the runway is even larger. Similarly, the impracticality of the corridor relocation method is also apparent when lateral relocations are considered. In those cases, the relocation distance needs to be based on the width of the hazardous region, B , which is 2b in width, or about 400 ft (122 m) for a large aircraft. For comparison, commercial runways vary from 150 to 300 ft (46}91 m) in width and from 8000 to 12,000 ft long (2438}3658 m). The two runways at Mo!ett Field, CA, that are used by NASA Ames Research Center are both 200 ft (61 m) wide and are 8100 and 9200 ft (2469 and 2804 m) in length. Since a vortex is shed any time that an aircraft carries lift, the termination of the #ight corridor at the runway surface should include a region where the landing aircraft "rst touches down, loses it lift, and begins its rollout. Since a vortex hazard still exists in that region, the depth of the #ight
652
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
corridors should be increased to accommodate the added hazardous region. For the foregoing reasons, it is concluded that relocation of #ight-path corridors to avoid vortex wakes is impractical as a wake-vortex avoidance method. Similar conclusions are drawn when it is realized that aircraft landing while visual #ight rules are in e!ect often use a visual estimate to determine whether or not they are above the #ight path of the preceding aircraft. Since such a relative location is di$cult to judge without GPS determined #ight paths, it is easily possible that a pilot believes his aircraft to be above the #ight path of previous aircraft, when in reality it is below. 18.5. Atmospheric data monitoring All proposed wake-vortex avoidance systems require regular monitoring of atmospheric motions along the approach and departure corridors to determine the locations of vortex wakes, and the status of the atmosphere. Only with information on the magnitude and direction of the winds present in and around the #ight corridors can vortex avoidance be assured. The task is easier if the #ight corridors are small in cross-section, but data on local wind velocities are still advisable, if not required. The needed information on the atmosphere can be obtained from the aircraft in the corridors by use of equipment on board the aircraft. That is, the three components of the speed of the aircraft relative to the ground are determined by use of GPS equipment. The three components of the velocity of aircraft through the air can be measured with onboard aerodynamic instrumentation. The di!erence between the two measurements yields the wind velocity. When the two sets of measurements are transmitted to an airport ground station, the data can be processed for determination of atmospheric motions. It is therefore recommended that each aircraft in the corridor transmit the information on its location, orientation, and on its velocity relative to the air (and to the ground) to a monitoring station at the airport. The monitoring station checks the data for inconsistencies and accuracy, and then determines the velocity components of the winds along the #ight corridor. The wind data is then used to predict the locations of the vortex wakes ahead of each aircraft to be certain that a vortex encounter does not occur. If an unsafe condition is predicted, the aircraft that would be involved are noti"ed to make a go-around or to use another runway. If the computations predict that the #ight corridor is free of all vortex in#uences ahead of the aircraft, no messages are sent and aircraft are free to continue their approach and landing. All of the GPS systems mentioned previously are capable of yielding accurate values for the velocity of aircraft relative to the ground. It remains however to determine whether the aerodynamic instrumentation
currently on board subsonic transports provides the required accuracy or not. If current instrumentation is found to be insu$cient, improvements will need to be made.
19. Remarks on status of research The foregoing text indicates that one or more wakemodi"cation methods have been identi"ed that provide adequate alleviation of the hazard posed by vortex wakes. Of these, the wing-"n concept appears to o!er the most reliable and #exible approach to solutions that are acceptable to airframe manufacturers. In order to accomplish this goal, research is needed to develop design guidelines for e$cient lifting systems that shed benign wake}vortex systems. Experiences with the research conducted on the wakevortex problem indicates that progress is most rapid when theoretical tools are used to guide and interpret experimental results. Not obvious from the foregoing results is that preliminary results on ideas to be tried, and the veri"cation of theoretical models, are best carried out in ground-based facilities rather than in #ight. Groundbased facilities have the advantage that they can provide information in less time, and with less expense than #ight experiments. Also, ground-based experiments can be carried out on idealized con"gurations that are too hazardous to test in #ight. Lastly, any #ight experiments, even though not necessarily expensive, have high visibility to the scienti"c community. High visibility limits greatly the number of trials and errors, and high risk failures, that are tolerated by funding sources. Which prospects should be pursued in order to "nd a solution to the lift-generated vortex problem? Before a supposedly new prospective idea is proposed for study, it is very important to "rst become familiar with past e!orts, and to then follow the literature closely, so that wasted e!ort is avoided. In the past, the research areas have usually been divided into three categories. (1) How hazardous is the lift-generated wake shed by a given aircraft? (2) How can the wake be modi"ed to make it non-hazardous to following aircraft while still retaining the e$ciency of the generating aircraft? (3) How can vortex wakes be e!ectively and e$ciently avoided? A great deal of e!ort has gone into all three of these items. Item number one needs to be improved upon so that the hazard posed by any new aircraft design can be predicted before the design leaves the drafting board, or computer. This is not yet possible within satisfactory accuracy by use of current technology. As mentioned in the "rst paragraph of this section, more work is needed on item number (2), which relates to the development of guidelines for the design of aircraft so that they shed benign wakes. Admittedly, a satisfactory solution has not yet been found, but the research to date indicates that
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
a solution is possible. At this time, funding is being applied primarily to the development of wake-avoidance systems for airports, without much being devoted to the development of alleviation concepts. It is hoped that a more balanced program will come about in the near future. If support for research on wake-alleviation concepts becomes available again, it is suggested that the study of all concepts be enlarged to include a new variety of optimization parameters as indicated in Section 12 of this paper. In this way, designs for aircraft lifting systems will be found that simultaneously increase the e$ciency of aircraft, and make their vortex-wake benign. Most of the wake-vortex avoidance systems under study at this time do not include the use of the GlobalPositioning System to control the #ight of aircraft into and out of airports along narrow #ight corridors. It is believed that failure to include these features in the wave-vortex avoidance systems being developed is a big mistake. Indications are that such a technique must be employed to reduce the work load required to insure that vortex wakes are not in the #ight corridors being used by following aircraft. Preliminary study also indicates that a workable wake-vortex avoidance system can become available in the near future if the Global-Positioning System is used to bring about su$ciently accurate guidance of aircraft to make narrow #ight corridors practical. At this time, all of the problems associated with the use of GPS for guidance along #ight corridors of small crosssections have not been solved, but, since it is a relatively new and rapidly expanding technology, the remaining problems may be solved in the near future. In summary, the purpose of this paragraph is to point out that #ight corridors of small cross-sections are required if the design of a practical wake-vortex avoidance system is to be achieved. That is, one that safely increases the capacity of airports. Lastly, there is always room for improvement in the methods used to take data in experiments. Throughout this paper reference has been made to areas where the test techniques and procedures used in a test could be improved upon, or were inadequate. First and foremost, methods for data taking should begin to address in a more complete fashion the e!ect of turbulence in #ight, and in the wind tunnel, on the dynamics and persistence of vortex wakes. Some of the improvements will require a great deal of e!ort and innovation, and others will be easy to implement. One such technique that needs much improvement is an ability to better follow the development of vortex instabilities (like those of Crouch [223], Crow [49], and Leweke and Williamson [222]). Obviously, methods are needed to help identify and better diagnose the three-dimensional, timedependent wave motions on vortex "laments as they trail behind lift-generating wings in wind tunnels and water tow tanks. In addition, progress in the development of
653
new ideas and concepts like those suggested by various authors and described in this overview will be expedited greatly if ground-based facilities are readily available for use in the needed experimental parts of the investigations.
References [1] McGowan WA. Calculated normal load factors on light airplanes traversing the trailing vortices of heavy transport airplanes. NASA TN D-829, May 1961. [2] Hinton DA. Aircraft vortex spacing system (AVOSS) concept and development. In: Credeur L, Perry RB, editors. Proceedings of the NASA First Wake Vortex Dynamic Spacing Workshop, Langley Research Center, Hampton, VA, NASA/CP-97-206235, May 13}15, 1997, p. 11}22. [3] Bleviss ZO. Theoretical analysis of light plane landing and take-o! accidents due to encountering the wakes of large airplanes. Report SM-18647, Douglas Aircraft Co., Inc., Santa Monica, CA, 1954. [4] Kraft Jr CC. Flight measurements of the velocity distribution and persistence of the trailing vortices of an airplane. NACA TN 3377, March 1955. [5] Rose R, Dee FW. Aircraft vortex wakes and their e!ects on aircraft. Tech. Note No. Aero. 2934, British Royal Aircraft Establishment, December 1963. [6] Robinson GH, Larson RR. A #ight evaluation of methods for predicting vortex wake e!ects on trailing aircraft. NASA TN D-6904, November 1972. [7] Wetmore JW, Reeder JP. Aircraft vortex wakes in relation to terminal operations. NASA TN D-1777, April 1963. [8] Zwieback EL. Trailing vortices of jet transport aircraft during takeo! and landing. AIAA J Aircraft 1964;1(5):308}10. [9] Lamb, Sir Horace. Hydrodynamics, 6th ed. New York: Dover, 1945. [10] Rossow VJ, Corsiglia VR, Schwind RG, Frick JKD, Lemmer OJ. Velocity and rolling-moment measurements in the wake of a swept-wing model in the 40- by 80-foot Wind Tunnel. NASA TM X-62,414, April 1975. [11] Jacobsen RA, Drinkwater III FJ. Exploratory #ight investigation of aircraft response to the wing vortex wake generated by the augmentor wing jet STOL research aircraft. NASA TM X-62, 387, May 1975. [12] Garodz LJ, Schutz CM. Analysis of low atmospheric density wake turbulence characteristics for jet transport category aircraft, FAA Data Report, Project 177-621-04X, February 1968, NAFEC, Alantic City, New Jersey. [13] Garodz LJ. Measurements of the vortex wake characteristics of the Boeing 747, Lockheed C5A and other aircraft. FAA Data Report Project 177-621-03X, April 1970, NAFEC, Atlantic City, New Jersey. [14] Garodz LJ. Investigation of the relatively long timehistory characteristics of the CV-880 airplane in terminal area-type #ight operations. FAA Data Report Project 504-303-03X, November 1970, NAFEC, Atlantic City, New Jersey.
654
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[15] Garodz LJ. Measurements of Boeing 747, Lockheed C5A and other aircraft vortex wake characteristics by tower #y-by techniques. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st ed. New York: Plenum Press, 1971, p. 265}285. [16] Garodz LJ. Federal aviation administration full-scale aircraft vortex wake turbulence #ight test investigations: past, present, future, AIAA Paper 71-97, New York, 1971. [17] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the Boeing 747 trailing vortex system using the tower #y-by technique. FAA-RD-73-156. NAFEC, Atlantic City, NJ, June 1974. [18] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the Boeing 727 trailing vortex system using the tower #y-by technique. FAA-RD-74-90, NAFEC, Atlantic City, NJ, August 1974. [19] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the McDonnell-Douglas DC-9 trailing vortex system using the tower #y-by Technique, FAA-RD-74-173, NAFEC, Atlantic City, NJ, November 1974. [20] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the Boeing 707 trailing vortex system using the tower #y-by technique, FAA-RD-75-15, NAFEC, Atlantic City, NJ, March 1975. [21] Garodz LJ, Lawrence DM, Miller NJ. Measurement of the trailing vortex systems of large transport aircraft using tower #y-by and #ow visualization (summary, comparison and application). FAA-RD-75-127, NAFEC, Atlantic City, NJ, May 1975. [22] Kuechemann D, editor. Progress in Aeronautical Sciences, vol. 7. London, England: Pergamon Press Ltd., 1966. [23] Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, New York: Plenum Press, 1971. [24] Credeur L, Perry RB, editors. Proceedings of the NASA First Wake Vortex Dynamic Spacing Workshop. Langley Research Center, Hampton, VA, NASA/CP-97206235, May 13}15, 1997. [25] Gessow A, editor. NASA Symposium on Wake Vortex Minimization. NASA SP-409, 1976. [26] Hall MG. Vortex breakdown. Ann Rev Fluid Mech 1972;4:195}218. [27] Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977. [28] Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } vol. 1 and 2, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, October 29}31, 1991. [29] Meier GEA. Chairman, AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. [30] Wood WD, editor. FAA/NASA Proceedings Workshop on Wake Vortex Alleviation and Avoidance, Report No. FAA-RD-79-105, U.S. Dept. of Transportation, November 28}29, 1978. p. 1-1 to 1-42. [31] Delery JM. Physics of vortical #ows. AIAA J Aircraft 1992;29(5):856}76.
[32] Donaldson CduP, Bilanin AJ. Vortex wakes of conventional aircraft, AGARDograph No. 204, May 1975. [33] El-Ramly Z. Aircraft trailing vortices } a survey of the problem. Technical Rept. ME/A72-1, Carlton University, Ottawa, Canada, November 1972. [34] Sa!man PG. Vortex interactions. Ann Rev Fluid Mech 1979;11:95}122. [35] Spalart PR. Airplane trailing vortices. Ann Rev Fluid Mech (Palo Alto, CA) 1998;30:107}38. [36] Widnall SE. The structure and dynamics of vortex "laments. Ann Rev Fluid Mech (Palo Alto, CA) 1975;7:141}65. [37] Vyshinsky VV (Project Mgr). Investigation of vortex wake evolution and #ight safety problems } collection of papers. Trudy TsAGI, vol. 2627, Publishing Dept. of TsAGI, Moscow, Russia, 1997. [38] Van Dyke M. An album of #uid motion. Stanford, CA: The Parabolic Press, 1982. [39] Hallock JN. Aircraft wake vortices } an annotated bibliography (1923}1975). Report FAA-RD-76-43, U.S. Dept. of Transportation, January 1976. [40] Hallock JN. Aircraft wake vortices: an annotated bibliography (1923}1990), Report DOT-FAA-RD-90-30, DOT-VNTSC-FAA-90-7, U.S. Dept. of Transportation, John A. Volpe National Transportation Systems Center, Cambridge, MA, January 1991. [41] Leishman JG, Bagai A. Challenges in understanding the vortex dynamics of helicopter rotor wakes. AIAA J 1998;36(7):1130}40. [42] McAlister KW. Measurements in the near wake of a hovering rotor. AIAA Paper 96-1958, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [43] McCroskey WJ. Vortex wakes of rotorcraft. AIAA Paper 95-0530, AIAA 33rd Aero Sciences Meeting and Exhibit, Reno, NV, January 9}12, 1995. [44] Andrews WH, Robinson GH, Larson RR. Aircraft Response to the Wing Trailing Vortices Generated by Large Jet Transports. NASA Aircraft Safety and Operating Problems, vol. I, NASA SP-270, May 1971, p. 115}26. [45] Andrews WH. Flight evaluation of the wing vortex wake generated by large jet transports. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed. New York: Plenum Press, 1971, p. 287}8. [46] Andrews WH, Robinson GH, Larson RH. Exploratory #ight investigation of aircraft response to the wing vortex wake generated by jet transport aircraft. NASA TN D6655, March 1972. [47] Bisgood PL, Maltby RL, Dee FW. Some work on the behaviour of vortex wakes at the royal aircraft establishment, Royal Aircraft Establishment Tech Memo 1244, August 1970. [48] Bisgood PL. In-#ight studies of vortex wakes, 1970}73. Establishment Tech Memo 1554, November 1973. [49] Crow SC. Stability theory for a pair of trailing vortices. AIAA J 1970;8(12):2172}9. [50] Garodz LJ, Clawson KL. Vortex wake characteristics of B-757-200 and B-767-200 aircraft using the tower #y-by technique; vols. 1 and 2. NOAA Technical Memorandum ERL ARL-199, NOAA Environmental Research Laboratories, Air Resources Laboratory, Silver Spring, MD, January 1993.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 [51] Ho!man ER, Joubert PN. Turbulent line vortices. J Fluid Mech. 1963;16 (Part 3):395}411. [52] McCormick BW, Tangler JL, Sherrieb HE. Structure of trailing vortices. AIAA J Aircraft 1968;5(3):260}7. [53] McWilliams IG. Hazard extent about aircraft trailing wake vortices-analytic approach. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference, Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 23}30. [54] Sammonds RI, Stinnett Jr GW, Larsen WE. Wake vortex encounter hazard criteria for two aircraft classes. NASA TM X-73,113, June 1976. (Also FAA-RD-75-206.) [55] Smith HJ. A #ight test investigation of the rolling moments induced on a T-37B airplane in the wake of a B-747 airplane. NASA TM-56031, April 1975. [56] Singh B, Kutty TM, Wentz Jr WH. Preliminary investigation of rolling moments induced by trailing vortices for several wing-tip modi"cations. Wichita State University Aeronautical Report 72-1, 1972. [57] Wentz Jr. WH. Evaluation of several vortex dissipators by wind tunnel measurements of vortex-induced upset loads. Wichita State University Aeronautical Report 72-3, 1972. [58] Barber MR, Hastings Jr. EC, Champine RA, Tymczyszyn JJ. Vortex attenuation #ight experiments. In: Gessow A, Editor, NASA Symposium on Wake Vortex Minimization, NASA SP-409, Feburary 25}26, 1976, p. 369}403. [59] Barber MR, Tymczyszyn JJ. Wake vortex attenuation #ight tests: a status report, NASA CP-2170, 1980, p. 387}408. [60] Corsiglia VR, Rossow VJ, Ci!one DL. Experimental study of the e!ect of span loading on aircraft wakes. AIAA J Aircraft 1976;13(12):968}73. [61] Corsiglia VR, Dunham RE. Aircraft wake-vortex minimization by use of #aps. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976, p. 305}38. [62] Croom DR. Low-speed wind-tunnel investigation of various segments of #ight spoilers as trailing-vortex-alleviation devices on a transport aircraft model. NASA TN D-8162, March 1976. [63] Croom DR. Low-speed wind-tunnel parametric investigation of #ight spoilers as trailing-vortex-alleviation devices on a transport aircraft model, NASA TP-1419, 1979. [64] Nikolic VR, Jumper EJ. Attenuation of airplane wake vortices by excitation of far-"eld instability. AIAA 93-3511, 11th AIAA Applied Aerodynamics Conference, August 9}11, 1993, Monterey, CA. [65] Nikolic VR, Jumper EJ, Nelson RC. Modi"ed, discretevortex method for studying wing-loading e!ects on wake dynamics. AIAA J Aircraft 1996;33(1). [66] Patterson JC, Jordan Jr FL. Thrust-augmented vortex attenuation. In: Gessow A, editor. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976. p. 251}70. [67] Patterson JC, Hastings EC, Jordan FL. Ground development and #ight correlation of the vortex attentuating spline device. In: Gessow A, editor. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976. p. 271}303.
655
[68] Patterson Jr JC. Exploratory wind-tunnel investigation of a wingtip-mounted vortex turbine for vortex energy recovery. NASA TP-2468, 1985. [69] Rennich SC, Lele SK. Method for accelerating the destruction of aircraft wake vortices. AIAA J Aircraft 1999;36(2):398}404. [70] Rossow VJ. Prospects for alleviation of hazard posed by lift-generated wakes. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } vol. 1, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD-92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, October 29}31, 1991. p. 22-1 to 22-40. [71] Snyder Jr MH. E!ects of a wingtip-mounted propeller on wing lift, induced drag, and shed vortex pattern. Ph.D. thesis, Oklahoma State University, Stillwater, OK, May 1967. [72] Ash RL, Zheng ZC. Numerical simulations of commercial aircraft wakes subjected to airport surface weather conditions. AIAA J Aircraft 1998;35(1):18}26. [73] Cantwell B, Rott N. The decay of a viscous vortex pair. The Phys of Fluids 1988;31(11):3213}24. [74] Crow SC, Bate Jr. ER. Lifespan of trailing vortices in a turbulent atmosphere. AIAA J Aircraft 1976; 13(7):476}82. [75] Devenport WJ, Zsoldos JS, Vogel CM. The structure and development of a counter-rotating wing-tip vortex pair. J Fluid Mech 1997;332:71}104. [76] Eaton JA, O'Flaherty MP. Flow"eld prediction of threedimensional wing trailing vortices using advanced turbulence models, AGARD 78th Fluid Dynamics, Conference Proceedings 584, Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Trondheim, Norway, Conference Proceedings 584, 20}23 May 1996. Paper No. 7, p. 7-1 to 7-7. [77] Follin GJ, Devenport WJ. E!ects on the turbulent structure of a counter-rotating vortex pair, AIAA Paper 96-1959, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [78] Kandil OA, Adam I, Wong TC. Far-"eld turbulent vortex-wake/exhaust plume interaction for subsonic and HSCT airplanes. Paper No. AIAA 96-1962, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [79] Graham JAH. Reynolds-stress measurements in a turbulent trailing vortex. J Fluid Mech 1984;147:353}71. [80] Liu H-T. E!ects of ambient turbulence on the decay of a trailing vortex wake. AIAA J Aircraft 1992; 29(2):255}63. [81] Miranda JA, Devenport WJ. Turbulent structure in the spiral wake shed by a lifting wing. AIAA J 1998; 36(4):658}60. [82] Moore DW, Sa!man PG. Axial #ow in laminar trailing vortices. Proc Roy Soc London Ser A 1973;333:491}508. [83] Rudis RP, Burnham DC, Janota P. Wake vortex decay near the ground under conditions of strong strati"cation and wind shear. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 11, p. 11-1 to 11-10.
656
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[84] Sarpkaya T, Daly JJ. E!ect of ambient turbulence on trailing vortices. AIAA J Aircraft 1987;24(6):399}404. [85] Vaughan JM, Brown DW, Constant G, Eacock JR, Foord R. Structure, trajectory and strength of B-747 aircraft wake vortices measured by laser. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 10, p. 10-1 to 10-10. [86] Zheng ZC. The e!ects of atmospheric turbulence on aircraft wake vortices. AIAA Paper No. 96-1954, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [87] Corsiglia VR, Schwind RG, Chigier NA. Rapid scanning, three-dimensional hot-wire anemometer surveys of wingtip vortices. AIAA J Aircraft 1973;10(12):752}7. [88] Corsiglia VR, Rossow VJ. Wind-tunnel investigation of the e!ect of porous spoilers on the wake of a subsonic transport model. NASA TM X-73,091, January 1976. [89] Baker GR, Barker SJ, Bofah KK, Sa!man PG. Laser anemometer measurements of trailing vortices in water. J Fluid Mech 1974;65(Part 2):325}36. [90] Ci!one DL. Correlation for estimating vortex rotational velocity downstream dependence. AIAA J Aircraft 1974;11(11):716}7. [91] Ci!one DL, Orlo! KL. Far-"eld wake-vortex characteristics of wings. AIAA J Aircraft 1975;12(5):464}70. [92] Ci!one DL, Orlo! KL. Application of laser velocimetry to aircraft wake-vortex measurements. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976, p. 157}92. [93] Ci!one DL. Vortex interactions in multiple vortex wakes behind Aircraft. AIAA J Aircraft 1977;14(5):440}6. [94] Corsiglia VR, Jacobsen RA, Chigier N. An experimental investigation of trailing vortices behind a wing with a vortex dissipator. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, Plenum Press, 1971, p. 229}42. [95] Corsiglia VR, Orlo! KL. Scanning laser-velocimeter surveys and analysis of multiple vortex wakes of an aircraft. Proceedings of the Aircraft Wake Vortices Conference, March 15}17. Report FAA-RD-77-68, U.S. Dept. of Transportation, Transportation Systems Center, Cambridge, MA, 1977, p. 114}23. [96] Corsiglia VR, Iversen JD, Orlo! KL. Laser-velocimeter surveys of merging vortices in a wind tunnel. AIAA J Aircraft 1978;15(11):762}8. [97] Delisi DP, Greene GC, Robins RE, Singh R. Recent laboratory and numerical trailing vortex studies, AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 34, pp. 34-1 to 34-10. [98] Liu H-T, Srnsky RA. Tow tank simulation of vortex wake dynamics. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } vol. 1 and 2, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD-92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, October 29}31, 1991. p. 32-1-26.
[99] Liu H-T, Hwang PA, Srnsky RA. Physical modeling of ground e!ects on vortex wakes. AIAA J Aircraft 1992;29(6):1027}34. [100] Reinath MS. Doppler global velocimeter development for the large wind tunnels at Ames Research Center. NASA TM 112210, September 1997. [101] Iversen JD. Correlation of turbulent trailing vortex decay data. AIAA J Aircraft 1976;13(5):338}42. [102] Kirkman KL, Brown CE, Goodman A. Evaluation of e!ectiveness of various devices for attenuation of trailing vortices based on model tests in a large towing basin. NASA Contractor Report NASA CR-2202, December 1973. [103] Smith WG, Lazzeroni FA. Experimental and theoretical study of a rectangular wing in a vortical wake at low speed. NASA TN D-339, October 1960. [104] Rossow VJ, Tinling BE. Research on aircraft/vortexwake interactions to determine acceptable level of wake intensity. AIAA J Aircraft 1988;25(4):481}92. [105] Rossow VJ. E!ect of wing "ns on lift-generated wakes. AIAA J Aircraft 1978;15(3):160}7. [106] Rossow VJ, Sacco JN, Askins PA, Bisbee LS, Smith SM. Measurements in 80- by 120-foot wind tunnel of hazard posed by lift-generated wakes. AIAA J Aircraft 1995;32(2):278}84. [107] Iversen JD, Bernstein S. Trailing vortex e!ects on following aircraft. AIAA J Aircraft 1974;11(1):60}1. [108] Nelson RC. The dynamic response of aircraft encountering aircraft wake turbulence. Tech Report AFFDL-TR74-29, Air Force Flight Dynamics Laboratory, WrightPatterson Air Force Base, OH, June 1974. [109] Nelson RC. Dynamic behavior of an aircraft encountering aircraft wake turbulence. AIAA J Aircraft 1976;13(9):704}8. [110] Abramson S, Burnham DC. Ground-based measurements of wake vortices from landing aircraft at Airports. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Trondheim, Norway, Conference Proceedings 584, 20}23 May 1996. Paper No. 13, p. 13-1 to 13-7. [111] Burnham DC. Review of vortex sensor development since 1970. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 47}66. [112] Burnham DC. B-747 vortex alleviation #ight tests: ground-based sensor measurements. Report DOT-FAARD-81-99, U.S. Dept. of Transportation, February 1982. [113] Burnham DC. Wake vortex alleviation system requirements. Report DOT-TSC-FA427-PM-84-19, U.S. Dept. of Transportation, May 1984. [114] Burnham DC. Wake vortex avoidance systems: requirements analysis. Report DOT-TSC-FA527PM-84-46, U.S. Dept. of Transportation, November 1984. [115] Burnham DC. TSC hazard model for wake vortex encounters. Report DOT-TSC-FA627-PM-86, U.S. Dept. of Transportation, November 1985.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 [116] Burnham DC, Hallock J. Wake vortex separation standards: analysis methods. Report DOT-VNTSC-FAA97-4, U. S. Dept. of Transportation, Federal Aviation Administration, May 1997. [117] Condit PM, Tracy PW. Results of the Boeing company wake turbulence test program. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed. New York: Plenum Press, 1971, p. 473}508. [118] Eisenhuth JJ, McCormick BW, Nelson RC. Analysis of experimental measurements of trailing vortex systems of large jet transport aicraft. Proceedings of the National Aerospace Electronics Conference, Dayton, OH, May 17}19, 1971, p. 28}35. [119] Kurkowski RL, Barber MR, Garodz LJ. Characteristics of wake vortex generated by a Boeing 727 jet transport during two-segment and normal ILS approach paths. NASA TN D-8222, April 1976. [120] Scorer RS, Davenport LJ. Contrails and aircraft downwash. J Fluid Mech 1970;43(Part 3):451}64. [121] Vicroy DD, Bowles RL, Brandon JM, Greene GC, Jordan Jr. FL, Rivers RA, Stewart EC, Stough III HP, Stuever RA. NASA wake vortex research. ICAS-946.2.2, 19th Congress of the International Council of the Aeronautical Sciences, September 19}23, 1994, Anaheim, CA. [122] Hallock JN, Burnham DC. Decay characteristics of wake vortices from jet transport aircraft. Paper No. AIAA 97-0060, 35th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6}10, 1997. [123] Hinton DA. Aircraft vortex spacing system (AVOSS) conceptual design. NASA TM 110184, Hampton, VA, August 1995. [124] Hinton DA. An aircraft vortex spacing system (AVOSS) for dynamical wake vortex spacing criteria. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. p. 23-1}23-12. [125] Hallock JN, Burnham DC, Tombach IH, Brashears MR, Zalay AD, Barber MR. Ground-based measurements of the wake vortex characteristics of a B-747 aircraft in various con"gurations. AIAA Paper 77-9, January 1977. [126] Hastings Jr EC, Keyser Jr GL. Simulated vortex encounters by a twin-engine commercial transport aircraft during "nal approach. SAE Technical Paper 800775, May 1980 (also NASA TM-81782). [127] Johnson WA, Rediess HA. Study of control system e!ectiveness in alleviating vortex wake upsets. Paper No. 141, Systems Technology, Inc, Hawthorne, CA, August 1973. [128] Johnson WA, Teper GL, Rediess HA. Study of control system e!ectiveness in alleviating vortex wake upsets. AIAA J Aircraft 1974;11(3):148}54. [129] Sammonds RI, Stinnett Jr GW. Hazard criteria for wake vortex encounters. NASA TM X-62,473, August 1975. [130] Tinling BE. Estimation of vortex-induced roll excursions based on #ight and simulation results. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference, Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977. p. 11}22.
657
[131] Tinling BE. Estimates of the e!ectiveness of automatic control in alleviating wake vortex induced roll excursions. NASA TM-73,267, August 1977. [132] Tinling BE. Estimation of the e!ect of the delayed #ap approach on the wake vortex hazard. NASA TM-73,179, September 1977. [133] Streeter VL. Fluid dynamics. New York: McGraw-Hill, 1948. [134] Talay TA. Introduction to the aerodynamics of #ight, NASA SP-367, 1975. [135] Rossow VJ. Estimate of loads during wing-vortex interactions by Munk's transverse-#ow method. AIAA J Aircraft 1990;27(1):66}74. [136] Munk MM. Fundamentals of #uid dynamics for aircraft designers, New York: The Ronald Press Co., 1929. [137] Jones RT, Cohen D. Aerodynamics of wings at high speeds. vol. VII. In: Donovan AF, Lawrence HR. editors. High speed aerodynamics and jet propulsion}aerodynamic components of aircraft at high speeds. Princeton University, NJ: Princeton University Press, 1957. [138] Maskew B. Numerical lifting surface methods for calculating the potential #ow about wings and wing-bodies of arbitrary geometry. Ph.D. Thesis, Loughborough Univ. of Tech., England, October 1972. [139] Hough G. Remarks on vortex-lattice methods. AIAA J Aircraft 1973;10(5):314}7. [140] Betz A. Verhalten von Wirbelsystem, ZAMM 1932; Bd. XII (3): 164}74. (Also available as NACA TM 713.) [141] Donaldson CduP, Sullivan RD. Decay of an isolated vortex. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed. New York: Plenum Press, 1971, p. 389}411. [142] Donaldson CduP, Snedeker RS, Sullivan Roger D. Calculation of aircraft wake velocity pro"les and comparison with experimental measurements. AIAA J Aircraft 1974;11(9):547}55. [143] Bilanin AJ, Teske ME, Donaldson CduP, Snedeker RS. Viscous e!ects in aircraft trailing vortices. In: Gessow A, editor, NASA Symposium on Wake Vortex Minimization, NASA SP-409, February 25}26, 1976, p. 61}128. [144] Brown CE. Aerodynamics of wake vortices. AIAA J 1973;11(4):531}6. [145] Rossow VJ. On the inviscid rolled-up structure of liftgenerated vortices. AIAA J Aircraft 1973;10(11):647}50. [146] Rossow VJ. Prediction of span loading from measured wake-vortex structure } an inverse Betz method. AIAA J Aircraft 1975;12(7):626}8. [147] Rossow VJ. On extended-Betz methods for rollup of vortex sheets. AIAA J Aircraft 1997;34(5):592}9. [148] Rosenhead L. The formation of vortices from a surface of discontinuity. Proc Roy Soc London A 1931;134: 170}92. [149] Westwater FL. The rolling up of the surface of discontinuity behind an aerofoil of "nite span. Aeronautical Research Council, London, Repts. and Memo. 1692, 1935. p. 116}31. [150] Rule JA, Bliss DB. Prediction of viscous trailing vortex structure from basic loading parameters. AIAA J 1998;36(2):208}18. [151] Rossow VJ. Theoretical study of lift-generated vortex wakes designed to avoid rollup. AIAA J 1975; 13(4):476}84.
658
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[152] Jones RT. The spanwise distribution of lift for minimum induced drag of wings having a given lift and a given bending moment. NACA Technical Note 2249, December 1950; see also, Collected works of Robert T. Jones. NASA TM X-3334, February 1976, p. 539}54. [153] Iversen JD, Brandt SA, Raj P. Merging distance criteria for co-rotating vortices. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 161}72. [154] Iversen JD, Park S, Backhus DR, Brickman RA. Hotwire, laser anemometer, and force balance measurements in cross-sectional planes of single and interacting trailing vortices. AIAA Paper No. 78-1194, 11th Fluid and Plasmadynamics Conference, Seattle, WA, July 10}12, 1978. [155] Bilanin AJ, Widnall SE. Aircraft wake dissipation by sinusoidal instability and vortex breakdown, AIAA Paper 73-107, 1973. [156] Jordan Jr FL. Flow visualization of the wake of a transport aircraft model with lateral-control oscillations. NASA TM 84623, June 1983. [157] McMillan OJ, Nielsen JN, Schwind RG, Dillenius MFE. Rolling moments in a trailing-vortex #ow "eld. AIAA J Aircraft 1978;15(5):280}6. [158] Olsen JH. Results of trailing vortex studies in a towing tank. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st ed. New York: Plenum Press, 1971. p. 455}72. [159] Jacobsen RA, Short BJ. A #ight investigation of the wake turbulence alleviation resulting from a #ap con"guration change on a B-747 aircraft. NASA TM-73, 263, July 1977. [160] Jacobsen RA, Barber MR. Flight test techniques for wake vortex minimization studies. In: Gessow A, editor. NASA Symposium on Wake Vortex Minimization, NASA SP409, February 25}26, 1976, p. 193}220. [161] Zell PT, Flack K. Performance and test section #ow characteristics of the National Full-Scale Aerodynamics Complex 40- by 80-foot Wind Tunnel. NASA TM 101065, February 1989. [162] Zell PT. Performance and test section #ow characteristics of the National Full-Scale Aerodynamics Complex 80- by 120-foot Wind Tunnel. NASA TM 103920, January 1993. [163] Rossow VJ. Validation of vortex-lattice method for loads on wings in lift-generated wakes. AIAA J Aircraft 1995;32(6):1254}62. [164] Stickle JW, Kelly MW. Ground-based facilities for evaluating vortex minimization concepts, NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976. p. 129}55. [165] Scorer RS. Natural aerodynamics. New York: Pergamon Press, 1958. [166] Bofah KK. Some remarks on aircraft wake vortex analysis. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 31}46. [167] Britton JW. Some remarks on en-route vortex encounters. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68,
[168]
[169] [170]
[171]
[172]
[173]
[174]
[175]
[176] [177]
[178] [179]
[180]
[181]
[182]
[183]
[184]
[185]
U.S. Dept. of Transportation, March 15}17, 1977, p. 243}6. Eliason BG, Gartshore IS, Parkinson GV. Wind tunnel investigation of Crow instability. AIAA J Aircraft 1975;12(12):985}8. Tombach IH. Observations of atmospheric e!ects on vortex wake behavior. AIAA J Aircraft 1973;10(11):641}7. Hackett JE, Evans PF. Numerical studies of three-dimensional breakdown in trailing vortex wakes. AIAA J Aircraft 1977;14. Widnall SE, Bliss D, Zalay A. Theoretical and experimental study of the stability of a vortex pair. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed., New York: Plenum Press, 1971. p. 305}38. Bliss DB. E!ect of unsteady forcing on the sinusoidal instability of vortex wakes. AIAA J Aircraft 1982; 19:713}21. Gerz T, Ehret T. Wake dynamics and exhaust distribution behind cruising aircraft. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 35, p. 35-1 to 35-12. Jacob J, Savas O, Liepmann D. Trailing vortex wake growth characteristics of a high aspect ratio rectangular airfoil. AIAA J 1997;35(2):275}80. Spalart PR, Wray AA. Initiation of the Crow instability by atmospheric turbulence. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 18, p. 18-1 to 18-8. Greene GC. An approximate model of vortex decay in the atmosphere. AIAA J Aircraft 1986;23(7):566}73. Kantha LH. Empirical model of transport and decay of wake vortices between parallel runways. AIAA J Aircraft 1996;33(4):752}60. Kantha LH. Empirical model of transport and decay of wake vortices. AIAA J Aircraft 1998;35(4):649}53. Rossow VJ. Spur-type instability observed on numerically simulated vortices. AIAA J Aircraft 1988; 25(9):835}41. Rossow VJ. Prospects for destructive self-induced interactions in a vortex pair. AIAA J Aircraft 1987; 24(7):433}40. Rossow VJ. Wake hazard alleviation associated with roll oscillations of wake-generating aircraft. AIAA J Aircraft 1986;23(6):484}91. Holbrook GT. Vortex wake hazard analysis including the e!ect of the encountering wing on the vortex. M.S. Thesis, George Washington Univ., Washington, DC, August 1985. Rossow VJ. Experimental investigation of wing "n con"gurations for alleviation of vortex wakes of aircraft. NASA TM 78520, November 1978. Rossow VJ, Fong RK, Wright MS, Bisbee LS. Vortex wakes of two transports measured in 80- by 120-foot Wind Tunnel. AIAA J Aircraft 1996;33(2):399}406. Zimmerman CH. Characteristics of Clark-Y airfoils of small aspect ratios. NACA TR 431, 1932.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 [186] Moghadam MM. Experimental investigation of vortices shed by various wing "n con"gurations. M.S. thesis (J. D. Iversen advisor), Iowa State University, August 1979. [187] Rossow VJ. Vortex structures and span loadings from alleviated-wake measurements. AIAA Paper 97-2262, 15th AIAA Applied Aerodynamics Conference, Atlanta, GA, June 23}25, 1997. [188] Desabrais KJ, Johari H. Direct circulation measurement of a wing tip vortex using ultrasound. Paper AIAA 980609, AIAA 36th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 12}15, 1998. [189] Barrows TM. Simpli"ed methods of predicting aircraft rolling moments due to vortex encounters. AIAA J Aircraft 1977;14(5):434}9. [190] Filotas LT. Vortex induced wing loads. AIAA J 1972;10(7):971. [191] Flax AH. Comment on &&Simpli"ed methods of predicting aircraft rolling moments due to vortex encounters''. AIAA J Aircraft 1977;14(11):1151}2. [192] Jones WP. Vortex-elliptic wing interaction. AIAA J 1972;10(2):225}7. [193] Spreiter JR, Sacks AH. The rolling up of the trailing vortex sheet and its e!ect on the downwash behind wings. Institute of the Aeronautical Sciences, Inc., J Aeronaut Sci 1951;18(1):21}32,72. [194] Bandyopadhyay PR, Stead DJ, Ash RL. Organized nature of a turbulent trailing vortex. AIAA J 1991;29(10):1627}33. [195] Dacles-Mariani J, Zilliac GG, Chow JS, Bradshaw P. Numerical/experimental study of a wingtip vortex in the near "eld. AIAA J 1995;33(9):1561}8. [196] Dacles-Mariani J, Hafez H, Kwak D. Prediction of wakevortex #ow in the near- and intermediate-"elds behind wings. Paper AIAA 97-0040, AIAA 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6}10, 1997. [197] Han YO, Leishman JG, Coyne AJ. Measurements of the velocity and turbulence structure of a rotor tip vortex. AIAA J 1997;35(3):477}85. [198] Ramaprian BR, Zheng Y. Measurements in rollup region of the tip vortex from a rectangular wing. AIAA J 1997;35(12):1837}43. [199] Back LH. Optical and physical requirements for #uid particles marking trailing vortices from aircraft. AIAA J Aircraft 1976;13(7):483}9. [200] Zeman O. Persistence of trailing vortices: a modeling study. Phys Fluids 1995;7(1):135}43. [201] Squire HB. The growth of a vortex in turbulent #ow. Aeronaut Quart 1965;XVI(Part 3):302}6. [202] Kuzmin VP. Estimation of wake-vortex separation distances for approaching aircraft. In: Vyshinsky VV (Project Mgr), Investigation of vortex wake evolution and #ight safety problems } collection of papers. Trudy TsAGI, vol. 2627, Publishing Dept. of TsAGI, Moscow, Russia, 1997, p. 209}24. [203] Vatistas GH, Lin S, Kwok CK. Theoretical and experimental studies on vortex chamber #ows. AIAA J 1986;24(4):635}42. [204] Vatistas GH, Lin S, Li PM. A similar pro"le for the tangential velocity in vortex chambers. Exp Fluids 1988;6(2):135}7.
659
[205] Vatistas GH, Kozel V, Mih WC. A simpler model for concentrated vortices. Exp Fluids 1991;11:73}6. [206] Teske ME, Quackenbush TR, Bilanin AJ, Wachspress DA. Vortex roll-up, merging and decay with the uniwake computer program. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } Vol. 1 and 2, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD-92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, Oct. 29}31, 1991. p. 33-1-20. [207] Phillips WRC. The turbulent trailing vortex during rollup. J Fluid Mech 1981;105:451}67. [208] Proctor FH. Numerical simulation of wake vortices measured during the Idaho Falls and Memphis "eld programs. AIAA Paper No. 96-2496, 14th AIAA Applied Aerodynamics Conference, New Orleans, LA, June 17}20, 1996. [209] Risso F, Corjon A. Direct numerical simulations of wake vortices in intense homogeneous turbulence. AIAA J 1997;35(6):1030}40. [210] Sa!man PG. Structure of turbulent line vortices. Phys. Fluids 1973;16(8):1181}8. [211] Sarpkaya T. Decay of wake vortices of large aircraft. AIAA J 1998;36(9):1671}9. [212] Rossow VJ. Measured changes in vortex wakes with downstream distance. AIAA Paper No. 98-2524, 16th AIAA Applied Aerodynamics Conference, Albuquerque, NM, June 15}18, 1998. [213] Owen PR. The decay of a turbulent trailing vortex. The Aeronaut Quart, 1970;XXI (Part 1):69}78. [214] Iversen JD. Inviscid to turbulent transition of trailing vortices. AIAA Paper No. 75-883, Hanford, CT, 1975 (also Iowa State University Report ISU-ERI-Ames 74241, November 1974). [215] Rossow VJ. Wake-vortex structure from lift and torque induced on a following wing. AIAA Paper No. 93-3013, 24th AIAA Fluid Dynamics Conference, Orlando, FL, July 6}9, 1993. [216] Bilanin AJ, Teske ME, Hirsh JE. Deintensi"cation as a consequence of vortex breakdown. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference, Report FAA-RD-77-68, U. S. Dept. of Transportation, March 15}17, 1977, p. 283}96. [217] Lessen M, Singh P, Paillet F. The stability of a trailing line vortex, Part I: inviscid theory. J Fluid Mech 1974;63(Pt. 4):753}63. [218] Lessen M, Paillet F. The stability of a trailing line vortex, Part II: viscous theory. J Fluid Mech 1974;65(Pt. 4):769}79. [219] Zalay AD, White RPW, Balcerak JC. Investigation of viscous line vortices with and without the injection of core turbulence, RASA Rept. 74-01, February 1974, Rochester Applied Science Associates, Rochester, NY. [220] Dunham Jr. RE. Unsuccessful concepts for aircraft wake vortex minimization. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976, p. 221}50. [221] MacCready PB. An assessment of dominant mechanisms in vortex-wake decay. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st ed. Plenum Press, 1971, p. 289}304. [222] Leweke T, Williamson CHK. Cooperative elliptic instability of a vortex pair. J Fluid Mech 1998;360: 85}119.
660
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[223] Crouch JD. Instability and transient growth for two trailing-vortex pairs. J Fluid Mech 1997;350:311}30. [224] Stickle JW. Wake vortex alleviation } the NASA program. In: Wood WD, editor. FAA/NASA Proceedings Workshop on Wake Vortex Alleviation and Avoidance. Report No. FAA-RD-79-105, U.S. Dept. of Transportation, November 28}29, 1978, p. 2-1-56. [225] Posluns H, editor. Proceedings of the International Wake Vortex Meeting. Ottawa, Ontario, Canada, 2}4 December 1997. [226] Stough III HP, Greene GC, Stewart EC, Stuever RA, Jordan Jr. FL, Rivers RA, Vicroy DD. NASA wake vortex research. AIAA Design, Systems and Operations Meeting, August 11}13, 1993, Monterey, CA, AIAA Paper 93-4004. [227] Spitzer EA, Hallock JN, Wood WD. Status of the Vortex Advisory System. Proceedings of the Aircraft Wake Vortices Conference, edited by Hallock JN, Report No. FAARD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 326}34. [228] Rossow VJ. Wake-vortex separation distances when #ight-path corridors are constrained. AIAA J Aircraft 1996;33(3):539}46.
[229] Loh R, Shively C, Swider R. Overview of the FAA's di!erential GPS CAT III technical feasibility demonstration program. AIAA Guidance, Navigation and Control Conference, August 9}11, 1993, Monterey, CA, AIAA Paper 93-3836-CP. [230] Cobb HS. GPS pseudolites: theory, design, and applications. SUDAAR Report 707, Stanford University, Dept. of Aeronautics and Astronautics, Palo Alto, CA, September 1996. [231] Lawrence DG. Aircraft landing using GPS: development and evaluation of a real time system for kinematic positioning using the Global Positioning System. Stanford University Dept. of Aeronautics and Astronautics, Palo Alto, CA, SUDAAR Report 690, September 1996. [232] Pervan BS. Navigation integrity for aircraft precision landing using the Global Positioning System. Stanford University Dept. of Aeronautics and Astronautics, Palo Alto, CA, SUDAAR Report 677, March 1996.
Lift-generated vortex wakes of subsonic transport aircraft Vernon J. Rossow* NASA Ames Research Center, Mail Stop N247-2, Mowett Field, CA 94035-1000, USA
Contents 1. Introduction 1.1. Justi"cation 1.2. Background 1.2.1. Literature 1.2.2. Modi"cation of vortex wakes 1.2.3. Ground-based experiments 1.3. Scope of the paper 2. In-trail spacing of aircraft at airports 2.1. Flight experiments 2.2. Experiments with #ight simulators 2.3. Possibilities for wake-vortex accommodation 3. Lift and circulation 4. Simple estimate for vortex-induced loads 4.1. Description of #ow "eld 4.2. Analysis 4.3. Comparison with other methods 4.4. Applications 5. Span loading and vortex structure 5.1. Introduction 5.2. Description of Betz' analysis 5.3. Invariants for motion of vortices 5.4. Rollup equations 5.5. Vortex-wake examples 5.6. Vortex wakes with multiple pairs 5.7. Extended-Betz methods 5.8. Inverse-Betz method 5.9. Region of applicability 6. Design of non-hazardous vortex wakes 6.1. Introduction 6.2. Hypothetical non-hazardous wake con"gurations 6.2.1. Tailored loading 6.2.2. Sawtooth loading 6.3. Experimental veri"cation 6.3.1. Ground-based experiments 6.3.2. Swirl velocity 6.3.3. Span loading 6.3.4. Measured rolling moment 6.3.5. Predicted rolling moment
509 509 511 511 512 513 515 516 516 519 523 523 526 526 528 530 533 536 536 536 538 539 540 540 543 544 546 546 546 546 546 549 550 550 550 553 555 557
* Tel.: #1-650-604-4570; fax.: #1-650-604-3489. E-mail address: [email protected] (V.J. Rossow) 0376-0421/99/$ - see front matter. Published by Elsevier Science Ltd. PII: S 0 3 7 6 - 0 4 2 1 ( 9 9 ) 0 0 0 0 6 - 8
7.
8.
9.
10.
6.4. Application of sawtooth loading to aircraft 6.4.1. Ground-based tests 6.4.2. Flight tests Mutually induced instabilities in single pair 7.1. Introduction 7.2. Numerical method 7.3. Vortex-pair instability 7.3.1. Introduction 7.3.2. Isolated vortex 7.3.3. Vortex pair; waves in phase, "03 7.3.4. Vortex pair; waves out-of-phase, "1803 7.3.5. Vortex pair; intermediate phase angles, 03( (1803 7.3.6. Concluding remarks on the e!ect of phase Multiple pair instabilities 8.1. Introduction 8.2. Overview of #ight tests 8.3. Estimate of steady-state span loadings 8.4. Two-dimensional simulation of wakes 8.5. Three-dimensional simulation of wakes: B-747 8.6. Three-dimensional simulation of wakes: L-1011 8.7. Concluding remarks on multiple vortex pairs Wake alleviation by wing "ns 9.1. Introduction to wing "ns 9.2. Experimental setup in 40;80 ft Wind Tunnel 9.3. Test results 9.3.1. General comments 9.3.2. Fin angle of attack 9.3.3. Spanwise location 9.3.4. Chord of "n 9.3.5. Height of "n 9.3.6. Circular-arc planform 9.3.7. Multi-element "ns 9.3.8. Fins with blown #ap 9.4. Discussion of "n con"gurations 9.5. E!ect of rectangular "ns on span loading 9.6. Concluding remarks on wing "ns Measurements in 80;120 ft Wind Tunnel 10.1. Introduction
559 559 563 571 571 575 576 576 576 576 578 581 581 582 582 583 584 585 587 588 590 590 590 591 593 593 593 593 594 594 594 596 597 597 598 598 599 599
508
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
10.2. Experimental setup in 80;120 ft Wind Tunnel 10.3. Test procedures 10.4. Comparison of data from two large wind tunnels 10.5. E!ect of span ratio on rolling moments 10.6. Rolling-moment results: conventional landing con"gurations 10.6.1. E!ect of yaw of the wake-generating model 10.6.2. E!ect of angle of attack of the wake-generating model 10.7. Rolling-moment results: alleviated landing con"gurations 10.7.1. E!ect of span of trailing-edge #aps 10.7.2. E!ect of wing "ns 10.8. Measured spanwise distributions 10.8.1. Overview of data 10.8.2. Up- and down-wash velocity distributions 10.8.3. Diagnosis of velocity measurements 10.8.4. Lift and rolling-moment loads 11. Validation of vortex-lattice method 11.1. Introduction 11.2. Applicability of vortex-lattice method 11.3. Comparison of predicted and measured loads 11.3.1. Lift 11.3.2. Rolling moment 11.4. Assessment of assumptions 12. Wake energy, span e$ciency and span loading 12.1. Introduction 12.2. Estimated span loadings 12.3. Analysis of downwash data 12.3.1. Vortex structures 12.3.2. Span-load distributions from isolated vortex structures 12.3.3. Discussion of retrieved span loadings 12.4. Wake hazard and induced-drag 13. Vortex decay 13.1. Introduction 13.2. Natural decay
600 602 603 604 605 605 606 606 607 608 609 609 611 612 614 614 614 615 615 615 617 617 620 620 620 621 621 622 623 625 627 627 629
13.2.1. Simple models for decaying vortices 13.2.2. Numerical simulations 13.3. Observations of decay 13.3.1. Swirl velocity 13.3.2. Vortex-induced rolling moment 14. Tests for similitude in vortex structures 14.1. Introduction 14.2. Oseen/Lamb/Squire structure 14.3. Ho!man}Joubert structure 14.4. Sample results from similitude tests 15. Vortex instabilities 15.1. Introduction 15.2. Small-scale vortex instabilities 15.3. Large-scale vortex instabilities 15.3.1. Stability of single vortex pair 15.3.2. Stability of multiple vortex pairs 15.4. Vortex injection by use of wing "ns 16. Turbulence injection 16.1. Introduction 16.2. Wingtip spoiler 16.3. Wingtip spline 16.4. Flight spoilers already on aircraft 16.5. Atmospheric turbulence 17. Wake-vortex avoidance schemes 17.1. Introduction 17.2. Vortex Advisory System (VAS) 17.3. Aircraft Vortex Spacing System (AVOSS) 18. Simpli"cation of vortex-avoidance systems 18.1. Overview 18.2. Flight corridor of small cross-section 18.2.1. Accuracy of global positioning system (GPS) 18.2.2. Vortex transit times 18.3. Straight or curved #ight corridors 18.4. Relocation of #ight corridors 18.5. Atmospheric data monitoring 19. Remarks on status of research References
629 630 631 631 632 632 632 633 633 634 636 636 637 638 638 639 640 640 640 641 642 643 643 643 643 644 645 646 646 647 647 647 649 650 652 652 653
Abstract The #ow "elds of vortices, whether buoyancy-driven or lift-generated, are fascinating #uid-dynamic phenomena which often possess intense swirl velocities and complex time-dependent behavior. As part of the on-going study of vortex behavior, this paper presents a historical overview of research conducted on the structure and modi"cation of the vortices generated by the lifting surfaces of subsonic transport aircraft. Although primarily presented from an experimental point of view, the derivation and use of relatively compact theoretical formulations and concepts are included. Experience with lift-generated wakes has shown that they are so complex that progress requires application of a combined theoretical and experimental research program, because either alone often leads to incorrect conclusions. The primary purpose of the research to be described is to "nd a way to reduce the hazard potential of lift-generated vortices shed by subsonic transport aircraft in the vicinity of airports during landing and takeo! operations. The information presented points out that the characteristics of lift-generated vortices are related to the aerodynamic shapes that produce them and that various arrangements of surfaces can be used to produce quite di!erent vortex structures. It is concluded that a satisfactory aerodynamic solution to the wake-vortex problem at airports has not yet been found, but a reduction in the impact of the wake-vortex hazard on airport capacity may soon become available through wake-vortex avoidance concepts currently under study. Published by Elsevier Science Ltd.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
509
Nomenclature AR b c C * C J e G(r/b ) ¸ M p PQ
aspect ratio wing span wing chord lift coe$cient ("¸/qS) rolling-moment coe$cient ("M/qSb) span e$ciency circulation parameter, Eq. (70) lift rolling moment acceleration in roll ratio of roll accelerations ("p /p , B "C /C B ) J J q dynamic pressure ("o; /2) r radius S wing planform area t time ; free-stream velocity u, v, w velocity components in x, y, z directions = Kirchho!}Routh path function x distance in #ight direction y distance in spanwise direction z distance in vertical direction X, >, Z (x/b, y/b, z/b)
1. Introduction 1.1. Justixcation The capacity of an airport is governed by such factors as the number and arrangement of runways available, the landing and takeo! distances required for arriving and departing aircraft, and the hourly distribution of those activities. Capacity is also limited by the fact that the spacing between aircraft must be large enough to insure that safety is not compromised on the ground nor in the air. While aircraft are in the air during approach and departure, the in-trail spacings are now larger than needed for other factors because it is based on the hazard posed by the lift-generated wakes of aircraft that have previously used the airspace (Fig. 1). The hazard posed is an aerodynamic one wherein the swirl velocities in wake vortices are strong enough to cause an encountering aircraft to roll uncontrollably. The problem comes about because vortices decay or decompose so slowly that the hazard they pose now governs airport capacity. The impact of the hazard posed by vortex wakes is most apparent near airports where aircraft numbers and density are concentrated for landing and takeo!. Furthermore, aircraft are constrained to certain #ight corridors for their approach to the airport and for landing on
a c C d
angle of attack point vortex circulation bound circulation aileron angle of de#ection
Subscripts av averaged over time at a given point cl centerline value cs constant-swirl velocity in core f following wing or probe g wake-generating model ir irrotational part max maximum on one side of centerline mi minimum at a given point mx maximum at a given point o centerline value r rectangular loading ro rotational part s vortex sheet sb solid-body rotation in core v vortex w wing
a runway. On departure from an airport, aircraft also take o! from a given runway so that vortices shed by aircraft during and after rotation, and during climb, can pose a hazard to following aircraft. In such situations, if an encounter occurs, the wake penetration is again nearly aligned with a vortex axis rather oriented in an acrossaxis path (Fig. 1). For the foregoing reasons, the Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) have supported the study of vortex wakes for over 30 years. In this program, research e!orts have been devoted to the study of the fundamental physics of lift-generated vortices, to the magnitude of the hazard they pose to aircraft, to possible means for avoiding them, and to methods for making vortex wakes decompose more quickly. The hazard posed by vortex wakes appears in di!erent forms depending on how following aircraft encounter them. As shown in Fig. 1, an aircraft #ying across the vortices experiences strong and rapid changes in up- and down-loads that may damage the aircraft or cause it to lose control. Analyses of across-trail and in-trail penetrations were made by McGowan [1] in the early part of the wake program, and it was found that the in-trail encounter was the hazard that had the most signi"cant impact on airport capacity. McGowan also studied across-wake
510
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 1. Possible encounters with lift-generated wake by a following aircraft [228]. (a) wing of rectangular planform at several angles of attack; (b) wings with various planforms; a "53.
encounters and found that they could also pose a vertical-load hazard. However, across-wake encounters are not likely to occur on approach or departure. As a consequence, almost all of the research e!orts have been directed at wake penetrations nearly parallel to the vortex axes. As illustrated in Fig. 1, when following aircraft penetrate a vortex wake at a location not near vortex centers, the aircraft experiences up- or down-loads depending on which part of the wake is encountered. These disturbances are usually modest in amplitude and, even though they are of a sustained nature, most aircraft can accommodate the up- or down-draft that the vortices generate. If, however, the following aircraft penetrates the vortex wake near the centerline of a vortex shed by a preceding aircraft that is larger, the follower experiences an overpowering rolling moment due to the swirling #ow "eld of the vortex. If the encounter occurs near the ground, or the subsequent loss of control is catastrophic, the following aircraft may impact the ground. As a consequence, the study of vortex wakes has focussed on the hazard posed by the rolling-moment intensity of vortex wakes. Since vortex wakes of aircraft are persistent and can be hazardous, following aircraft must delay their arrival until the vortex wakes shed by previous aircraft have either descended below or been blown out of the #ight corridor by the wind, or decayed to a harmless level. For these reasons, current minimum separation distances (Table 1) were set for circumstances when instrument #ight rules (IFR) apply. Under visual #ight rules (VFR), the #ight crew receives advisory information on tra$c and wake vortices, and is then free to choose their own spacing, which is usually close to that speci"ed in Table 1. The minimum IFR distances listed in Table 1 for the various weight classes of transport aircraft are based primarily on observations of the lifetime and motion of
wake vortices at airports. The distances listed indicate the amount of time needed for the vortices to decay to a harmless level in ground e!ect or to move downward and/or sideways so that they are well outside of the #ight corridor of any following aircraft. It is to be noted that larger separation distances are speci"ed for small aircraft (including business types) following larger aircraft to insure a comparable margin of safety for the smaller aircraft, which are more susceptible to over-powering vortex-induced rolling moments. The added distance allows more time for the vortices to move farther out of and away from the #ight corridor, and to decay. Since the separation guidelines must allow for worst-case conditions, they tend to be conservative. The spacings listed in Table 1 were modi"ed in 1996 to provide weight categories that better re#ect the weights of aircraft that currently use airports in the United States; Table 2 [2]. Also, the B-757 aircraft was placed in a category by itself that lies between that of heavy and large
Table 1 Terminal Radar Minimum Separation Distances; Gessow [25] Type of following aircraft (km) Small2 Large2 Heavy2
Generator Large Heavy Separation (n mile) (km) (n mile) (km) (n mile)
Small
5 5 5
3 3 3
7 5 5
4 3 3
11 9 5
Less than or equal to 5.67 Mg (12,500 lb). 5.67}140 Mg (12,500}300,000 lb). Greater than or equal to 140 Mg (300,000 lb).
6 5 4
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 Table 2 U.S. Separation Standards; Hinton [2] After July 1996 Reduced ROT Documented. (Distances in n mile) Following aircraft
Heavy
Leading aircraft B-757 Large
Small
Heavy Large Small
4 5 5, 6T
4 4 5
2.5 2.5 2.5
2.5 2.5 3, 4T
Table 3 Approximate Separation time intervals; Hinton [2] Based on standard separation, constant airspeed of 120 knots (Small), 140 knots (757/Large) & 160 knots (Heavy). Following Aircraft
Heavy
Leading aircraft B-757 Large
Small
Heavy
90 90
106 90
72 56
94 56
Large
129 145
103 103
64 64
86 64
Small
150 188
150 171
90 120
75 75
leading aircraft. Since air tra$c controllers can more accurately control the time rather than distance between aircraft, Table 3 lists spacing in seconds between aircraft at the outer marker (upper number) and at threshold (lower number). Two sets of numbers are required, because aircraft travel at di!erent velocities in the approach corridor for a runway. As more information and as conditions change, the values listed in Tables 2 and 3 will probably change again. Other countries have also changed the data in Table 1, and some now use spacing criteria di!erent from that listed in Tables 2 and 3. Based on factors such as runway occupancy time after touchdown, and before lift-o!, the minimum safe separation distance between aircraft in the airport environment, and especially while in the #ight corridors during landing and takeo!, is estimated to be about 2 n mile
511
(nautical miles). One goal of wake-vortex research is to "nd a way to reduce or avoid the wake-vortex hazard so that all landings and takeo!s can be carried out with an in-trail spacing of 3 n mile. If such a reduction were put into practice without an e!ective avoidance scheme, the likelihood of a vortex-wake encounter would increase unacceptably, because less time is allowed for the wake to move out of the way and to decay. Since most aircraft cannot now safely enter the newly formed wakes of larger aircraft, methods must be developed for either reducing wake velocities to a safe level, or to avoid vortex wakes. The con"gurations of generating and following aircraft that need to be treated are those used for landing or takeo! wherein their #aps are deployed and landing gear are extended. Furthermore, since the penetrating aircraft is either landing or taking o!, the nearness of the ground will limit the acceptable unexpected coherent rolling motion caused by a vortex encounter. Lastly, since the #ight velocities of aircraft in the approach and departure corridors are between 130 and 200 knots, analysis of the #uid dynamics of the vortices and the #ow "elds surrounding the aircraft can assume the air to be incompressible. 1.2. Background 1.2.1. Literature The literature on the hazard posed by lift-generated vortices is quite limited up through the early 1960s. One of the "rst papers written about the possible hazard posed by the wakes of large aircraft appeared when the DC-6 was put into service in about 1950. Bleviss [3] estimated the decay rates of the various wake components, and concluded that the so-called propeller wash spread quickly enough that it could be considered nonhazardous to other aircraft #ying more than several spans behind the generating aircraft. He noted, however, that the lift-generated vortices in the wake decay so slowly that they persist for some distance behind the generating wing, and could pose a hazard to following aircraft. The study of lift-generated vortices as a hazard to following aircraft intensi"ed during the 1960s and early 1970s, because the size di!erences between large and small aircraft landing at airports was becoming larger rapidly, and more wake-vortex-induced accidents began to occur. Several investigations by Kraft [4], McGowan [1], Rose and Dee [5], Robinson and Larson [6], Wetmore and Reeder [7], and Zwieback [8] were carried out from 1960 to 1964 to de"ne the vortex-wake structure and to estimate the loads imposed on a penetrating aircraft as it enters the wake from di!erent directions. The results showed that the loads imposed by a wake may overpower the control capability, and may exceed the structural limits of the penetrating aircraft. Based on #ight test results, and on estimates of vortex decay by use of Lamb's vortex model [9], the time
512
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
required for the wake to decay to a safe level was estimated to be far in excess of 3 min (i.e., 6}9 n mile at landing velocity). In order to better understand the structure and slow rate of decay of lift-generated vortices, measurements of the wake velocities were made in #ight by Kraft [4] in 1955 with a P-51 (= "8800 lb) as the wake-generating aircraft, and with two larger aircraft as the probe aircraft (= "13,480 and 16,400 lb). In addition to obtaining some of the "rst in-#ight measurements of vortex structure, it was found that the strength of the vortices did not decrease appreciably for about 35 s behind the generating aircraft, and that the propeller wake is not detectable at distances in excess of about 1000 ft behind the aircraft. The apparently rather slow decay of the vortices seemed to depend on the atmospheric structure present at the time of the #ight tests. The data-reduction techniques developed for these experiments are similar to those used in other ground-based [10] and #ight [11] investigations of wake vortices. When several axial penetrations were made into the wake, the pilot found that it was di$cult to maintain a precise course, and that the vortices caused disturbances similar to severe atmospheric turbulence. No mention was made of overpowering vortex-induced roll excursions, probably because the penetrating aircraft was about twice as large as the generating aircraft. Breakup of the wake began about 60 s after the vortex lines became very sinuous from motions brought about by atmospheric eddies. It was also noted that the sinuous shape of the vortices made it di$cult for the pilot to "nd and stay in the vortices for prolonged measurements. During the 1960s, the FAA began an extensive #ight program to study the nature of, and hazard posed by, wake vortices shed by subsonic transport aircraft in service at the time [12}21]. One of the objectives of the #ight program was to obtain direct measurements of the vortex structures shed by a wide variety of aircraft. Data on the structure of the vortices were obtained by #ying various subsonic transport aircraft well o! to the side of an instrumented tower so that the wind would blow the shed vortices across the instrumented tower for a measurement of their velocity and pressure. Intentional penetrations by following aircraft of vortex wakes shed by a lead aircraft were also carried out at a safe altitude to determine when overpowering rolling moments occurred, and to obtain estimates for the separation distances listed in Table 1. About the time that the #ight tests were being carried out by Garodz et al. [12}21], interest in the characteristics of wake vortices shed by transport aircraft was increasing rapidly and various workshops and summary articles appeared in the literature. Although not devoted directly to the rolling-moment hazard posed by liftgenerated vortices, an excellent background summary of the #uid dynamics of vortices appeared in Vol. 7 of the Progress in Aeronautical Sciences as edited by
Kuechemann [22]. In order to stimulate interest in, and to summarize the current status of, research on the subject of lift-generated vortices, a symposium was held in 1970 that resulted in the publication of proceedings that provides an excellent background survey and introduction into the wake-vortex hazard problem at airports [23]. Also, during the 1970s, the Federal Aviation Administration (FAA) and National Aeronautical and Space Administration (NASA) began intensive groundbased and #ight-research programs into the nature of and solution to the wake-vortex hazard problem. As a consequence of the large increase in the study of vortices, a number of conferences have been held since the late 1960s that produced very informative proceedings [23}30]. Furthermore, a number of summary articles have appeared in various publications [16,31}36]. A good status report of the work on wake-vortex research in Russia at TsAGI is provided by Vyshinsky [37]. The photographs of various #ow phenomena, including some good ones of vortices, in a book by Van Dyke [38] is recommended for intuitive guidance. In addition, two bibliographies by Hallock [39,40] provide a complete listing of titles, authors, and abstracts available at the time of publication. Rather than put out a new ever larger book of abstracts, an internet address has now been established by Hallock that includes all of the listings in an on-line bibliography which is updated regularly; i.e., 1www.volpe.dot.gov/wv2. Although research on rotorcraft technology provides some valuable information that also applies to the vortices shed by aircraft in linear #ight (e.g., [41}43]), the large volume of other articles on the aerodynamics, noise, etc., of the vortices shed by helicopter rotor blades along a circular path will not be discussed. 1.2.2. Modixcation of vortex wakes Since the objective of the research on wake vortices is either to modify them so that they are harmless, or to avoid them, the types of equipment to be used to achieve these objectives is not straightforward. If the objective is to change vortex wakes, the existing structure of vortex wakes should "rst be determined before steps directed at changing the vortices can be undertaken. As will be seen in the survey literature listed in the foregoing paragraph, the magnitude and the nature of the hazard posed by wake vortices were "rst studied by use of #ow visualization, by analysis, and in #ight [5,8,12}21,37,44}55]. Even though the structure of lift-generated vortices had not been fully de"ned, and the hazard completely evaluated, research e!orts intensi"ed greatly toward the development of methods for producing benign vortices or that would promote more rapid decomposition of vortex wakes than achieved through natural decay [25,56,57]. Addition of turbulence to the vortex wakes of aircraft was the "rst option considered because excess turbulence
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
in the ambient #uid was known to disrupt or prevent the formation of laboratory vortices. Therefore, when the FAA/NASA wake vortex program was started in the early 1970s, turbulence injection (or addition of turbulence to the wake by means of various devices) was the "rst method tried. An overview will be given in Section 16 of the e!orts made to promote the rapid disintegration of vortex wakes by use of turbulence-producing devices on the generating aircraft. At about the same time, the mutually induced instability of a vortex pair was analyzed by Crow [49] which called attention to a mechanism that brings about closed loops in the vortex pair. After formation, the vortex loops gyrate about to produce mixing in the wake on a scale equal to or larger than the wingspan of the wake-generating aircraft. Many variations on the general approach to turbulence injection and to mutually induced instabilities were postulated and tried. Some that appeared to be e!ective at reducing the wake hazard continue to be studied [58}71]. Various wake-vortex dispersion mechanisms are listed below in approximately the chronological order in which they were tried. The listing is somewhat arbitrary and is not intended to include all of the concepts investigated. 1. 2. 3. 4. 5. 6. 7.
Spoiler and spline devices. Wingtip blowing. Forward or reverse thrust of the engines. Flight spoilers already on aircraft. Wingtip turbine. Span loading. Wing "ns.
Results from investigations on some of these devices are presented in various conference proceedings [25,27}30]. If any of the con"gurations tried under item 4 had been successful, it might not have been necessary to signi"cantly modify the aircraft, i.e., if the required #ightspoiler equipment already on board the aircraft proved to be adequate. Application of some of the other concepts listed could require extensive modi"cation of the wakegenerating aircraft, which would reduce the attractiveness of the alleviation concept. The use of span loading on the wake-generating wing and of wing "ns to deintensify the vortices are discussed in sections to follow. Not included in the foregoing list is the decay due to self-generated turbulence in the #ow "eld of the wake itself, and the ambient turbulence present in the #ow "eld ahead of the aircraft through which it #ies (i.e., atmospheric turbulence). A number of papers on the characteristics and structure of unmodi"ed decaying wakes were also written [72}86]. The early research work de"ned the nature of the hazard posed by vortex wakes when an aircraft makes an in-trail encounter with a vortex wake. The primary con-
513
cern soon became one of the magnitude and the persistence of the rolling-moment hazard. Therefore, analytical and ground-based studies concentrated on the decay of vortices, and the #ight measurements concentrated on #ow visualization and on intentional penetration of the vortices by a following aircraft. It was found that the cross-sectional region of the wake that is hazardous to a following aircraft is small, and di$cult or impossible to "nd without some sort of #ow visualization to indicate where the vortex centers are located [12}21,50,58,59]. The primary reason for deliberate penetrations into a vortex core by an aircraft was to determine whether or not enough control was available on board the penetrator aircraft for it to proceed through to a safe landing at an airport. It was found that the measurements in #ight tended to be qualitative and to have a large amount of scatter among the results, because the vortices to be penetrated were sinuous in shape and the response of the aircraft to the vortex #ow "eld was often an intensely dynamic one. It was then realized that an understanding of the vortex structure, its decay, and potential hazard require improved measurements of vortex wakes as a function of time or distance behind the wake-generating aircraft. It was also concluded that this kind of data could best be obtained in ground-based experiments, where the test conditions could be better controlled at a more modest cost. This paper presents an overview of experiments directed at the understanding, evaluation, and possible modi"cation of vortex wakes. The introduction of various theoretical tools will be made to illustrate their use as a guide for the experiments, and to the interpretation of the results obtained. Reference to #ight test results will be made for comparison with ground-based results, and to show how they helped to guide the ground-based experiments. 1.2.3. Ground-based experiments The distribution of the swirling velocity in vortex wakes is the characteristic of most importance for a determination of the in-trail hazardous nature of the wake. When research e!orts were expanded in ground-based facilities, a signi"cant portion of the e!ort was devoted to the development of improved methods for measuring the velocity distribution in the #ow "eld of the wake [25,27]. It was found that wake vortices tended to meander rapidly enough that it was di$cult to obtain measurements of the velocity distribution with enough accuracy to test various theories. One solution to the problem was to mount a hot-"lm anemometer on the end of a rotating arm for a rapid survey of vortex wakes, and thereby eliminate the problem with vortex meander (e.g., [10,87,88]). Di$culties with the test equipment and with data reduction prompted the search for other simpler and less-intrusive test techniques. The subsequent
514
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
development of laser-velocimetry provided a good technique for obtaining test data in both wind tunnels and in water tow tanks (e.g., [60,61,80,87}100]). Measurements made with laser velocimeters made pioneering discoveries in the decay characteristics of vortex wake (e.g., [90}93]). Of particular signi"cance at the time was the "nding that the maximum swirl velocity in a vortex changed negligibly at "rst, and then decayed roughly as the inverse of the square root of time (i.e., as t\ , Fig. 2). It was assumed that the behavior of the entire vortex would be about the same as the maximum swirl velocity. The #at or nearly zero decay region of the vortices in Fig. 2 is referred to as the plateau region. The similarity of the decay rates of vortices shed by various wings prompted Iversen [101] to study a wide variety of measurements of wake vortices. Scaling parameters were then derived to collapse the data into a narrow band (Fig. 3). The small "gure on the upper right-hand side of Fig. 3 presents the functional dependence used in the horizontal scale. In summary, the measurements in water tow tanks con"rmed that the self-generated decay of lift-generated vortices is far too slow to be of use for the reduction of the in-trail spacings currently being used between aircraft in the vicinity of airports. For example, based on the data in Fig. 2, the vortex wake of a heavy aircraft like the B-747 would not even begin to decay until the desired spacing of 3 n mile has been reached or exceeded. The di$culties with accurately measuring velocity distributions, and then translating them into rolling moments, led to the development of the following-wing technique [102]. The simplicity of the method and the approximately good agreement with rolling moments determined by use of measured velocity distributions [10] was soon adopted as not only satisfactory, but the preferred instrument for the determination of the rolling-moment hazard posed by a vortex wake. The follow-
ing-wing technique has the virtue that it integrates the swirl velocity distribution over a portion of the #ow "eld to yield an indication of the net rolling moment. The entire vortex wake can then be surveyed for the nature of the rolling-moment hazard without the need for an elaborate measurement technique and data reduction process for the determination of the rolling moment. Research showed that for most wings of interest the rolling moment depends primarily on the span of the follower, and is relatively independent of taper and sweep. When measurements from ground-based facilities are compared with those in #ight, the agreement is generally quite good. The precision of the comparisons are compromised however, because the #ight measurements are taken during a dynamic encounter, whereas the wind tunnel or water tow tank results are measured with "xed following wings [55,103]. It was decided thereafter that the best way to test the rolling moment intensity in a vortex wake during a #ight experiment is to approach the vortex center from below, so that the pilot had good visual contact with the vortex location, and so that he can then guide the aircraft upward quickly through a region at or near the vortex center. The penetrating aircraft then experiences imposed roll accelerations of short duration without much change in velocity or intended trajectory [104]. Data reduction is thereby simpli"ed greatly, and the test results improved. Measurements made in wind tunnels and in air or water tow tanks also improved with time as various techniques were re"ned. It was "rst found to be essential that the wake-generating model be mounted on a slender aerodynamically clean strut fastened to the top rather than to the bottom of the fuselage or centerbody. The vortex wake of the wake-generating model then moves away from the wake of the support strut to minimize the interference of the strut with the vortex wake being
Fig. 2. Water tow-tank results for the maximum swirl velocity as a function of downstream distance; ; "6.8 ft/s (2.07 m/s) Ci!one and Orlo! [91].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
515
Fig. 3. Correlation of maximum swirl velocity in lift-generated vortices as a function of downstream distance; Iversen [101].
studied [10,105,106]. Also, it was found earlier that the complications caused by the motion of the vortex centers (brought about by non-uniformities in the airstream) cause the wake to have a time-dependent character that depends on the facility being used. Special techniques must be used, therefore, if reliable results are to be obtained. One technique used with some success is to measure the maximum, minimum and time-averaged quantities of the parameters of interest during a certain measurement interval [106]. 1.3. Scope of the paper An overview is presented on the theoretical models used to guide the tests on vortex wakes with various items of equipment and facilities used to obtain data. Reference to equipment and test techniques are given only as needed to help explain the nature of the results. The paper attempts to summarize work carried out from about 1970 to the present time. Much of the work to be
described was sponsored by the FAA/NASA wakevortex program. Along with the experimental results to be described, various theoretical methods are presented to show how they have guided the test programs, and have helped to interpret the data obtained. Applicable theoretical models provide a guide for the experimentation, so that tests can be carried out in a systematic way rather that by random testing. Analysis of the data obtained is then also expedited, and the dynamics of vortex wakes better understood. It is also shown how the theoretical relationships between measured parameters can be used to not only test the theory, but also to determine the "delity of the test equipment and techniques used. Experimental results from water and air tow facilities, wind tunnels, #ight and #ight simulators are included. The overall theme of the results to be described is the evaluation, reduction and avoidance of the rolling-moment hazard posed by the vortex wakes of subsonic transport aircraft which are generally con"gured in their landing con"guration with #aps and slats deployed, and landing gear extended.
516
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
The objective of the theoretical and experimental research to be discussed is to diagnose vortex wakes, so that the dynamics of their generation, persistence, modi"cation, and demise are understood and predictable by use of analytical relationships or by numerical analysis. In such a process, experiments need to be conducted to "nd when and how simpli"ed models of vortex wakes break down or fail to apply, and how to develop improved models for the #ow "eld. Experiments are most e!ective and useful when they are used to test particular theoretical models or analyses as part of an e!ort to improve the models or to develop new ones. In this way, it should become possible to modify or tailor the structure of vortex wakes to achieve the characteristics desired.
2. In-trail spacing of aircraft at airports 2.1. Flight experiments The scienti"c study of lift-generated vortices began with the introduction of vortex-lift concepts by Lanchester and Prandtl in the early 1900s. As mentioned previously, the possible hazard posed to small aircraft by the vortex wakes of much larger aircraft was "rst analyzed by Bleviss [3] when the DC-6 was put into service in the early 1950s. Somewhat later, several theoretical studies were made of the consequences that could occur if aircraft inadvertently encountered a vortex wake [1,5,107}109]. These papers and other unpublished estimates of the hazard posed by lift-generated vortices prompted increased e!ort on the subject. In the late 1960s, e!orts were started on the development of guidelines that would recommend in-trail separation distances between aircraft on approach and departure at airports. Probably, the primary reason for the increased e!ort was the increasing size di!erences between large and small transport aircraft that were being put into service. Since very few results were available from groundbased facilities or theoretical tools, and because the safety requirements dictated a maximum reliability of the results at the earliest possible time, it was decided to determine the information by conducting #ight tests. The objective was to produce a table (e.g., Tables 1}3) that would indicate to aircraft operators the minimum spacing between aircraft that would insure against hazardous encounters with vortex wakes on approach and departure from airports. The e!orts are described in a number of papers [4,6,8,12}21,44}48,50,53,55,66,67,110}122]. The material presented here provides a brief description of the process and some results, but does not go into the many interesting discoveries made during this early study of purposeful encounters made by aircraft with vortex wakes. The intent of this presentation, which is taken largely from Andrews et al. [44}46], Condit and Tracy [117] and Hallock and Burnham [122], is to indicate
how the "rst separation guidelines in Table 1 were obtained, and how they have changed in the United States (Tables 2 and 3). The test program of the 1960s included a wide variety of aircraft that included large military and a variety of subsonic transport aircraft along with small aircraft such as a Lear Jet and a Cessna-210. A graphical presentation of the aircraft used in the study reported by Andrews et al. [44] illustrates the variety of aircraft pairs, and the separation distances at which vortex encounters were tested (Fig. 4). All penetrations were made possible by injecting some type of smoke, vaporized oil, or powder from the wake-generating aircraft into the vortices, so that they were visible to following aircraft. Without some sort of #ow visualization, the trailing vortices were almost impossible to "nd. As illustrated in Fig. 5, the penetrations were made from directly aft of the wakegenerating aircraft to minimize the induced structural loads, and to best simulate the kinds of in-trail encounters to be expected on approach and departure from an airport. During the encounter, the pilot of the following aircraft tried to position his aircraft in the center of a vortex (made visible by #ow visualization) and to hold it there. Hence, only the core region of the vortices were speci"cally probed for hazard. For aircraft smaller than the semi-span of the wake-generator, a penetration of one vortex probably covers the most hazardous region in the wake. If, however, the penetrating aircraft is on the order of the same size as the wake-generating airplane, the most hazardous location in the wake is theoretically not at the center of a vortex. Observations of the #ight path of probe aircraft as they encounter a vortex wake made it
Fig. 4. Summary of aircraft used in wake vortex #ight program; Andrews et al. [44].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 5. Procedure used to probe the vortex wake of a generator aircraft; Andrews et al. [44].
apparent that a large part of the entire wake region is probed by test aircraft as it attempts to "nd and stay in the center of a vortex, and to recover from a vortex upset. The procedures used to determine the hazard posed by the vortex wake of one aircraft when another aircraft penetrates it were of two types. The initial test procedure was to position the aircraft at the maximum separation distance at which the vortex trail was visible, and then proceed to #y in or near the center of the vortices until a speci"ed minimum separation distance was reached (Fig. 5). The second method was to position the probe aircraft at a pre-arranged separation distance, and to then evaluate the response characteristics for a period of approximately 2 min. In both cases, the task of the pilot was to maintain the wings of the aircraft level, and to return to the center of the vortex as soon as possible
517
following an upset. In order to expedite the program and to provide a margin of safety for potential upset recovery, the tests were conducted at 2591 and 3810 m (8500 and 12,500 ft) altitudes. The wake-generating aircraft were #own at speeds from 130 to 170 knots, which is considered normal for terminal-area operations. The speed of the probe aircraft was generally comparable with that of the generator. The tests were observed and recorded on video tape, and the relative locations of the aircraft pairs were recorded on a digital system. As stated by Andrews et al. [44], the primary objective of the foregoing vortex-encounter program is to determine a ratio of the maximum vortex-induced roll-acceleration response of the probe airplane to the maximum roll-control power of the probe airplane as a function of separation distance. The rationale for separation distance assumes that when the maximum control power of the probe aircraft is equal to the induced rolling moment from the vortex wake of the generating aircraft, the separation from the generating aircraft is considered to be a safe minimum (Fig. 6). The straight lines in Fig. 6, and in "gures to follow, represent the upper envelope of data for the maximum roll accelerations experienced during all encounters. The quantity p with the subscript &measured' in Fig. 6 represents the roll acceleration of the penetrating aircraft. When the subscript is d , the
quantity represents the roll-acceleration capability of the penetrating aircraft when full-aileron de#ections are used. A safe encounter then assumes that aileron de#ections are applied instantly as needed when a vortex-wake encounter occurs. Results from Andrews et al. [44] for other aircraft are presented in Figs. 7 and 8. As explained in the foregoing paragraphs, the #ightdetermined separations are based on deliberate encounters with the most intense regions of a vortex wake. It is
Fig. 6. Method used to determine aircraft separation distances: C-5A as wake-generating aircraft, DC-9 as probe aircraft, landing con"guration; Andrews et al. [44].
518
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 7. Proposed aircraft separation distances when in landing con"guration; Andrews et al. [44].
Fig. 8. Summary of separation criteria; Andrews et al. [44].
noted that the separation guidelines listed in Table 1 are sometimes smaller than the safe encounter distances found in the various references. Since su$cient time or distance is allowed between aircraft during landing or takeo!, a vortex is usually not encountered, because they have moved downward and/or sideways too far from the #ight corridors to be a hazard. Experience with the recommended spacings during instrument #ight conditions indicates that the spacings listed are indeed adequate for most purposes. Somewhat later, and as indicated by Hinton [2,123,124], for an unknown reason vortex encounters behind some aircraft were more fre-
quent than most of the rest of the #eet, e.g., the B-757. For this reason, and because the aircraft was close to the 300,000 lb division between large and heavy aircraft, a special category was assigned to the B-757, and other changes were made as well (Table 2). It should be noted in Table 2 that the weight limits on the various aircraft categories have also been changed. An added complication are the two numbers, and the letter ¹, listed in the leading-aircraft blocks for heavy and large categories when the following aircraft is small. The "rst of the two numbers indicates the recommended minimum spacing between aircraft at the outer marker (about 7}10 n mile
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
from the end of the runway), and the second number with the letter ¹ attached is the recommended minimum spacing between aircraft at runway threshhold. Hinton [2] presents Table 3 in order to call attention to the fact that separation distances should be based on time rather than on distance, because vortices move and decay as a function of time. Therefore, when leading and following aircraft approach airports at di!erent velocities, the spacings (in time and distance) between aircraft often changes between the outer marker and touchdown on the runway. Although it was well known that vortex wakes descend behind the wake-generating aircraft, uncertainty existed as to how quickly and how far down the wakes would descend. It was found in various #ight tests that wakes would frequently descend below the wake-generating aircraft by at least 500 ft, and often as much as 1000}1500 ft while they were visible. Analysis of both the motion of vortex wakes and the hazardous region around them by Burnham and Hallock [27,28,39,40,112}116,122,125], indicates that the speci"ed spacings provide safe passage under most conditions. They also determined that the roll control available by use of aileron de#ection on board a penetrating aircraft should be at least twice the vortex-induced rolling moment posed by the wake of a leading aircraft. The factor of two provides enough control to not only overcome the vortex-induced rolling moment, but allows enough spare control so that the aircraft can be returned to its normal attitude when its intended #ight path has been disturbed. If such a criterion were imposed on the #ight data shown in Figs. 6 and 7, the horizontal lines used for acceptable separation distances would be drawn at p /p "0.5
B rather than at 1.0, as shown in the "gures. 2.2. Experiments with yight simulators Further information on what is considered by pilots as a safe or acceptable level of hazard was determined by use of #ight simulators. The information summarized here was developed in #ight simulators at NASA Ames and Langley Research Centers and by analysis of that data. The tests in the simulators were carried out to obtain safely, and at modest cost, more information on the levels of acceptable vortex-induced motions, and to obtain repeatable data on excursions caused by wakevortex encounters. Tests were conducted with piloted ground-based simulators [54,104,108,109,126}132] which included not only the dynamics of vortex encounters, but also the e!ects of atmospheric turbulence on the perception of hazard by the pilots while occupied with the usual piloting duties associated with the airport environment. Also, the experiments were planned so that the wake-vortex encounters were unexpected rather than deliberate. The forces and moments on the probe aircraft were computed at each increment of time by use of
519
a strip-theory type of analysis that was fast enough to provide data on a real-time basis for the six degrees of freedom of motion. The piloting task was to #y a 33 glide slope towards a landing with an abort capability if desired. The pilots who had previous #ight experience with wake-vortex encounters reported that the simulations were quite realistic and a good representation [54,129]. Also, the simulations were judged to be a useful and valid method for establishing hazard criteria. After a number of simulated encounters had been #own under both visual #ight conditions (VFR) and instrument #ight conditions (IFR), the separation of occurrences into hazardous and non-hazardous categories correlated best with maximum roll or bank angle [54,129,130,132]. The data used to infer boundaries between hazardous and non-hazardous conditions is reproduced in Fig. 9 for a range of altitudes and bank angles. The boundaries are summarized in Fig. 10 for both IFR and VFR. It was concluded from the simulations that under IFR conditions, a roll angle of more than 5}73 is perceived as hazardous at altitudes of 200 ft or less. The primary reason given by the pilots for rating an encounter as hazardous was proximity of the ground, and subsequent altitude loss caused by the encounter. Two more values can be inferred from the data of Sammonds and Stinnett [129] when they divide their roll acceleration data (reproduced in Fig. 11) into two groups. In the "rst (Fig. 11a), the entry angle into the vortex is held constant while the vortex strength is varied. In the second (Fig. 11b), the data for a given vortex strength are plotted as a function of maximum bank angle while the entry angle into the vortex is varied. Even though some sort of relationship appears to exist in the data, extrapolation to low values of bank angle can only be done in an approximate fashion. Therefore, lines drawn through the center of the data points, or along the upper or lower edges of the data scatter, provide an estimate of the roll acceleration not to be exceeded if the encountering aircraft is to roll no more than 53 or so. If such a connection and the extrapolation are valid, the values estimated for maximum acceptable roll acceleration due to a vortex encounter appear to range from about 0.8 rad/s to about 1.6 rad/s. In order to be conservative, the 0.8 rad/s value is chosen as representative of maximum tolerable values for p . A value for the roll-control ratio PQ can be calculated for aircraft by using the appropriate value for p . From Tinling [130], typical values B (Table 4) for the roll control acceleration range from about 0.6 rad/s for large aircraft to 1.8 rad/s for small aircraft [104]. Since the Lear Jet characteristics were used for the following aircraft in the ground-based simulations, the appropriate value (Table 4) for p is B 1.15 rad/s. The corresponding value for the roll control ratio, PQ , is then (0.8/1.15) or about 0.7 for the Lear Jet, which is not signi"cantly greater than the value of 0.5
520
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 9. Data for maximum bank angle from simulated encounters for all entry conditions tested-VFR; Sammonds et al. [129].
Fig. 10. Summary of data from simulated encounters indicating the boundaries between hazardous and non-hazardous conditions for all entry conditions tested with a Lear Jet and a B-707/720 aircraft; Sammonds et al. [54].
recommended by Burnham [113,115] and by Rossow and Tinling [104]. A similarly well-de"ned boundary between hazardous and non-hazardous conditions was not found for either roll rate or roll acceleration, e.g., Fig. 12. It may be that since the vortex intensity was for larger aircraft (C"92.9}185.8 m/s (1000}2000 ft/s)), the roll velocities and accelerations that occurred in the simulations did
not go to low enough values to completely de"ne a boundary. In the absence of enough data at the lower values of roll acceleration to de"ne a sharp boundary between hazardous and non-hazardous roll accelerations, the available encounters are extrapolated to the low altitudes of interest for separation guidelines. When such an extrapolation is made (Fig. 12), the maximum tolerable roll acceleration is estimated to be about
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
521
Fig. 11. Data for maximum roll acceleration from simulated encounters for all entry conditions tested under VFR conditions; Sammonds et al. [129]. (a) Data for constant vortex strength (C"92.9 m/s (1000 ft/s)), variable entry angle into vortex. (b) Data for constant encounter angle (W"$103, h"!103), variable vortex strength.
1.6 rad/s, which exceeds the value of 1.15 rad/s capability of the Lear Jet used in the simulation. Since the acceptable value exceeds the capability of the aircraft, either the extrapolation in Fig. 12 is invalid or roll acceleration is an insensitive indicator of hazard. A value for PQ between 0.5 and 1.0 appears to be of about the correct magnitude, because Smith [55] reported that pilots of the T-37B probe aircraft placed the safe separation distance behind a B-747 alleviated con"guration at about 5.5 n mile. At that distance, the max-
imum measured rolling moment was about 0.6 of the aileron capability of the T-37B probe. A similar "gure for the non-alleviated wake of the B-747 is a more uncertain, because the data do not go beyond the 13 n mile distance that was judged by the pilot to be safe. However, data at the 10}11 n mile distance scatters from about PQ "0.4}0.8. Since these #ight tests were all VFR and at altitude, it is not clear how they are related to the more delicate situation that exists with IFR conditions and low altitude [104]. The foregoing results are in agreement
522
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Table 4 Aircraft roll-control characteristics [104] Aircraft
Wing span (ft)
Available roll control, c B J
Roll-control power, p B (rad/s)
Cessna 210 T-37B Lear Jet PA-30 DC-9 B-737 B-727 Convair 990 B-707 B-747
36.6 33.8 34.0 36.0 89.4 93.0 108.0 118.0 145.8 195.7
0.056 0.060 0.047 * 0.067 0.097 0.092 0.059 0.080 0.068
* * 1.15 1.87 0.97 * 0.62 * * *
with the value of 0.5 estimated for PQ by Burnham [113] while carrying out a study of wake-alleviation requirements. The "nding that a vortex encounter is considered non-hazardous if the maximum roll excursion is below a certain value prompted studies by Johnson and Rediess [127], Johnson et al. [128], Tinling [130}132] of the feasibility and e!ectiveness of an automatic control system on maximum roll angle. It was observed that since the simulator experiments were designed to make the vortex encounter unexpected, the pilot response during a typical encounter "rst consisted of a time delay of
about 0.4 s. During this time delay, the aircraft undergoes the initial accelerations induced by the velocity "eld of the vortex. The pilot then applies roll control in proportion to the perceived roll rate. Based on the pilot response, it was reasoned that a considerable reduction in roll excursion could be achieved if an automatic system was used to command immediate aileron action. A numerical analysis was then carried out by Tinling [131] which showed that when the full amount of roll control is used with an automatic system, and when the parameter PQ is less than one, the angle of roll can be kept within acceptable limits. An illustration of the e!ectiveness of an automatic control system is presented in Fig. 13 for a range of roll accelerations. It is apparent that the on-board capability of the following aircraft can increase the value of the roll-control ratio PQ , which is required to qualify a wake as non-hazardous, or acceptably alleviated. If the on-board response is minimal, the value of PQ that is required could be as low as the 0.4 value estimated on one of the #ight tests. If the on-board capability is maximized, the acceptable value for PQ could approach 1.0. In summary, the foregoing estimates for PQ , which include the response time of the pilots, range from 0.4 to 0.8. Hence, a single approximate value for PQ that is recommended as a general rule for all aircraft is that PQ 40.5 for a manageable wake encounter. When this value is combined with typical values for the maximum aileron-control capability contained in Table 4, it appears that the vortex-induced rolling-moment coe$cients should not exceed about C "0.03. J
Fig. 12. Data from simulated encounters illustrating variation of maximum bank angle with maximum roll acceleration due to the vortex; Sammonds et al. [129].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 13. Estimate of maximum bank angle due to vortex encounters for several levels of roll-control authority for automatic system based on numerical analysis; Tinling [131]. (a) without circulation; (b) circulatory #ow only; (c) with correct circulation for Kutta}Joukowsky condition.
2.3. Possibilities for wake-vortex accommodation Consideration is given here to the currently available possibilities for achieving the reduction in wake-vortex hazard potential needed to satisfy the requirement that C 40.03 for all following aircraft. The magnitude of the J problem is illustrated by noting that the wake vortices trailing from a B-747 can induce a rolling moment on a Lear Jet type following aircraft about equal to C "0.12 at 1}2 n mile behind the generating aircraft J [60,61]. Hence, an accommodation of some sort by a factor of about 4 must be made. If 2 n mile separation distances are to be achieved, following aircraft must either: (1) avoid wake encounters; or (2) increase its rollcontrol power to the point where an acceptable attitude can be maintained throughout any wake that might be in the #ight corridor. If the wake-generating aircraft is to solve the wake-spacing problem, design of its lifting surfaces must be carried out so that the intensity of the swirling velocities in the wakes are so benign that current control capabilities are su$cient. Each of these possibilities has its own set of di$culties. For example, wake avoidance at the 2}3 n mile separation requires special restraints on the #ight paths of wake-generating and following aircraft so that, as they use the same #ight corridor, the vortex wakes move quickly away, so that approach and departure can be made safely. Several prospective avoidance systems are described in the last part of this paper. None has been
523
developed to the degree needed for application at this time. The second possibility mentioned above is to increase the roll-control power on board the penetrating aircraft in order to maintain attitude control throughout any vortex wake encounter. Such a change appears impractical, because it would require large changes in the characteristics of the aircraft. Since transport aircraft are designed for e$ciency in cruise, they cannot be readily adapted to special requirements (which may degrade cruise performance) to cope with occasional situations during landing and takeo!. For example, an increase in the roll control power of an aircraft by a factor of 4 would require major changes in the wing and aileron design. Since the aileron rolling-moment capability typical of current transport aircraft is about C B "0.06, an upJ grade to over 0.2 would be a major undertaking, and would probably be found to be an impractical solution. Not only are large changes required in the wing structure, but the mechanisms must also apply such large roll-control forces rapidly enough to maintain control the instant a vortex is encountered. The combination of large control surfaces and rapid de#ection for a variety of #ight circumstances poses di$cult design problems for a large #eet of transport aircraft and does not appear to be a satisfactory approach to a solution. When the FAA/NASA wake-vortex research program was started in the early 1970s, the most attractive solution at that time was to alleviate the rotary velocities in the lift-generated wakes to the degree where the rollingmoment coe$cients induced on any following aircraft would be negligible compared with the roll-control capability on board the aircraft. As mentioned previously, this requires roughly a four-fold reduction in the rotary velocities of the wake. This goal has been found to be very di$cult to achieve, even when other considerations such as e$ciency and cost of implementation are not included. Also, any penalties imposed by the alleviation scheme on e$ciency and costs of implementation should be small in comparison with the savings generated by higher airport capacities, which are estimated at from 20 to 40% for busy airports with a large percentage of aircraft tra$c concentrated in the heavy category. Nevertheless, research results found so far indicate that the foregoing goal is reachable. Further research may present solutions that ful"ll all of the characteristics needed for a satisfactory wing design. Information in the following sections provides a history of the work carried out so far on the alleviation of the hazard posed by vortex wakes.
3. Lift and circulation In order to discuss the structure and modi"cation of lift-generated vortices, a brief overview of the concepts behind lift on, and the vortices shed by, a wing of "nite
524
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
span, along with some de"nitions for certain terms will be given in this section. The theory of lift began with the visualization of the #ow "eld around wings. These observations led Lanchester and Prandtl to the vortex theory of lift wherein the strength of the vortex is called its circulation, C. Wing theory begins with the circulation around an airfoil (usually considered a two-dimensional #ow "eld) which is brought about by designing the airfoil with a sharp trailing edge to insure a clean departure of the streamlines over the top and along the bottom of the airfoil, and thereby bring about circulation and lift. Without circulation, the streamlines around the airfoil would tend to #ow around the sharp trailing edge (Fig. 14a). If the #ow "eld associated with circulation (Fig. 14b) is added to the #ow "eld in Fig. 14a, the #uid #ows smoothly o! of the top and bottom of the airfoil past the sharp trailing edge (Fig. 14c). In practice, circulation is produced by the sharp trailing edge on the airfoil. Since the air is not able to make the sharp turn at the trailing edge, the #ow separates from the upper and lower surfaces of the airfoil smoothly rather than making the sharp turn (Fig. 14c). The modi"cation of the #ow "eld from Fig. 14a to 14c is theoretically and mathematically equivalent to adding circulation to the #ow "eld around the airfoil (the Joukowsky hypothesis [133]). The circulation required is the amount which is just su$cient to cause the streamlines that wet the airfoil to depart the airfoil at its sharp trailing edge as shown in Fig. 14c [134]. Di!erent amounts of lift are produced by changing the angle of attack of the airfoil relative to the free-stream velocity. An increase in lift is obtained, because more circulation is required on the airfoil to bring about a smooth departure of the streamlines at the sharp trailing edge of the airfoil. The #ow "eld of a wing is produced by placing airfoil sections side by side to form a three-dimensional lifting
surface of "nite size. If all of the airfoil sections are of the same size, a wing of rectangular planform is produced (Fig. 15). Trailing vortices could then be considered to begin at the wing surface. It is more convenient, however, to have the circulation symbolically continue through the wing from wingtip to wingtip (Fig. 15). At the wingtips, the vortices enter the air and are swept downstream behind the wing to form the trailing vortices. Similarly, the vortices far behind the wing are considered to be joined by a segment of the vortex passing across the wake between the two downstream ends of the trailing vortices that were generated when the aircraft lifted o! the runway (Fig. 15). In the same way, the two ends of the vortices are also joined by an across-stream vortex as the aircraft lands and reduces its wing lift to zero. After the vortices are generated, and as time passes, all of the vortex lines associated with the entire #ight of an aircraft mix with the surrounding air and di!use so that, after several minutes, air motions due to the vortices are usually indistinguishable from local winds and the turbulence they generate. As mentioned previously, one purpose of the wake-vortex research program is to "nd out how fast the vortices lose their identity, and how to accelerate the process. In Fig. 15 it is assumed that the lift on each airfoil section across the span of the wing is the same so that all of the circulation bound in the wing trails downstream from each wingtip. A constant lift across the span of the wing is, however, not possible. Since the span of the wing is "nite, the ends of the wing allow the high-pressure air on the bottom of the wing to #ow around the wingtips to the low-pressure region on the top (Fig. 16). As a consequence, the circulation bound to each airfoil section decreases from the centerline of the wing to the wingtips, where the lift vanishes. Rather than all of the circulation being trailed or shed only from the wingtips as shown
Fig. 14. Flow "eld around airfoil; Talay [134].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
525
or by Stokes' theorem [133]
C" (v dy#w dz), !
Fig. 15. Vortex pattern shed by wing with rectangular loading; Talay [134].
in Fig. 15, circulation is now shed all along the trailing edge of the wing. Also, the total lift on the wing is then a summation of the circulation bound to each of the airfoil sections. The lift may be written as an integration of the circulation bound in the wing along its span as
>@ C(y) dy. (1) \@ Since the lift varies across the span of the wing, and the bound circulation is shed all along the trailing edge of the wing, a vortex sheet is formed that begins at the wing trailing edge and extends downstream behind the wing. The local strength of the vortex sheet, c(y), is given by the gradient of the bound circulation as Lift"o;
dC(y) . c(y)" dy
(2)
As the distance behind the wing increases, the vortex sheet rolls up from the wingtips drawing more and more of the vortex sheet at inboard stations into the rolled-up vortex to form a pair of oppositely rotating trailing vortices. Since the circulation is shed in a sheet that extends over the span of the wing, it is then also distributed or spread over the cross-section of each trailing vortex. Circulation shed throughout a cross-section of the wake, rather than as a thin sheet at the trailing edge of the wing, is referred to as vorticity. The amount of vorticity, X, at a given point in the #uid is de"ned by the gradients in the velocity components at the point [9,133] de"ned by
(3)
where C is the path along which the integration is carried out, and that encloses the area A. The circulation, C, determined by Eq. (3) represents the total strength of all the vortex "laments that pass within the contour C. If the contour is made large enough to include the vortex sheets shed by both sides of the wing, the total circulation within the contour is zero, because equal amounts of positive and negative vorticity are included. The port and starboard vortex sheets are connected by across-stream vortices bound in the wing which produced lift. The circulation and the vorticity in a vortex are given a direction by use of the rule wherein the "ngers of the right hand are placed around the vortex, so that the "ngers point in the direction of swirl. The thumb then indicates the direction of the vorticity or circulation. In twodimensional or planar #ow, counter-clockwise (i.e., increasing meridian angle) swirl is denoted as positive circulation, and clockwise swirl as negative circulation. The foregoing illustrations become complex when the wakes of subsonic transports are considered. First, as stated previously, the lift on the wing is not constant between the wingtips, but varies continuously from a maximum near the centerline of the wing to zero at the wingtips (Fig. 16). Secondly, the wing con"guration during landing and takeo! is not necessarily simple in shape, but usually consists of a system of #aps, slats and ailerons (Fig. 17). The #aps are used to produce large values of lift at low angles of attack during low approach and departure velocities, and the slats to prevent #ow separation at the leading edge of the wing. Hence, circulation is shed or trailed in several sheets that are not necessarily adjacent, and that extend from the wing trailing edge downstream. Multiple vortex sheets form because the wing is not a #at continuous trailing edge, but rather one with partialspan #aps, that leave spanwise gaps for openings through which engine exhaust passes rearward for undisturbed
X";U where U is the local velocity vector. The circulation is found by integrating the vorticity over a chosen area, A, which is usually placed at a cross-section of a stream tube. Since the streamwise component of the vorticity and circulation are of most interest in the study of vortex wakes, the expression for the x-component is written as
C"
Rw Rv ! dy dz Ry Rx
Fig. 16. E!ect of "nite span on loading of wing; Talay [134].
526
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 17. Typical #ap and aileron assembly on wing; Talay [134].
thrust, i.e., exhaust gates (Fig. 17). When the wing has such a complex shape, #ow visualization (e.g., by use of smoke) makes the wake "rst appear to be composed of one or more continuous sheets that vary in strength, and contort to "t the wing trailing edge. A small distance behind the wing, the vortex sheet appears to be composed of several pairs of separate vortices (Fig. 18a). At larger distances behind the wing, the vortices usually blend or merge into a single vortex pair, and to stay that way (Fig. 18a and b). As the vorticity leaves the wing trailing edge, the swirling motion in the vortices smears and scrubs the distribution of vorticity, so that discontinuities in the shape of the vortex sheet, and in vortex strength across the span of the wing, are smoothed out into the "nal vortex structure. As the vortices age, the originally straight lines become distorted by low-velocity aircurrents to produce a sinuous shape in the vortices (Fig. 18). The experiments and analyses to be described use a coordinate system that places the uniform free stream in the positive #x direction, the horizontal direction across the airstream in the #y direction, and #z in the vertical direction. The wing is assumed to be centered on the x-axis and to be lifting in the #z direction. In general, the #uid in which the vortices are embedded is assumed to be incompressible.
4. Simple estimate for vortex-induced loads From the outset of the wake-vortex research program, a desire was often expressed for a relationship that would de"ne the maximum or worst-case value for the rolling moment induced on a following wing by a vortex of a given strength, i.e., circulation. The "rst part of that problem is simple, because the most hazardous vortex is one that has all of its circulation concentrated at its
center, i.e., a point vortex. All other vortex structures have smaller swirl velocities over some portion of their radius, which makes them less hazardous. A worst-case situation also requires that the encountering wing captures the most intense part of the vortex #ow "eld. This occurs when the vortex center and wing centerline are aligned. It remains then to derive an estimate for the worst-case rolling moment. Such a relationship has been found in closed form for the encounter of a #at wing of "nite span with a line vortex when the wing is moving in a direction parallel to the axis of the line vortex [135]. A line vortex is de"ned as a vortex structure wherein all of the circulation in the vortex is concentrated at its axis. In a two-dimensional #ow "eld, the cross-section of the vortex #ow "eld would then appear as a point vortex wherein the swirl velocity is given by v "C/2pr. The F solutions found are shown to yield realistic results for all types of interactions and to provide simple closed-form expressions for the various #ow "eld parameters. After the #ow "eld and its idealizations are described, the steps used to obtain a solution are presented along with several applications of the results. 4.1. Description of yow xeld The problem being considered here (Fig. 19) assumes that the axis of the vortex is aligned with the #ight direction of the encountering wing [135]. The vortex is assumed to have a circulation of C , and to be positive when it has counter-clockwise rotation from a pilot's viewpoint. The vortex is located at a distance r from the centerline of the wing at an elevation angle of h relative to the spanwise direction of the wing, where the subscript sv is used to denote quantities related to the vortex in the slit plane where the wing and its vortex wake appear as a slit looking upstream (Fig. 20). The surface that encounters the vortex is shown in Fig. 19 as a #at
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
527
Fig. 18. Photograph of oil vapor mist used to visualize rollup of vortex wake from wing of B-747 aircraft when landing #aps are deployed and landing gear stowed; Corsiglia et al. [61]. (a) First photo. (b) 20 s later.
rectangular wing for simplicity, but the analysis treats the wing as a lifting line and does not specify its shape. In the computation, it is assumed that the wake trailing from the lifting line remains as a #at sheet. The procedure used to obtain the solutions presented here is patterned after the transverse-#ow method described in Chapter V of Munk [136], wherein the #ow about the wake is con-
sidered as two-dimensional in order to determine the vorticity distribution in the wake. Munk used this method to derive elliptic loading as the most e$cient for a given span, and to analyze other lifting systems of "nite span. The shape of the wing needed to achieve the #ow"eld boundary conditions is not included in the analysis (e.g., Chapter II of Munk [136]).
528
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
these expressions when the signs of multiple-valued square roots had to be chosen. A very satisfactory scheme was then found by "rst squaring both Eqs. (5a) and (5b) and then combining the results in such a way as to eliminate the dependence on h . As a result, a quadratic equation was generated for the quantity, (r#a/r), as (r#a/r)!r(r#a/r)!2a(2a!y#z)"0. (6)
Fig. 19. Diagram of #ow "eld for encounter of wing with a nearby vortex [135].
Fig. 20. Mapping of slit in physical plane into a circle [135].
4.2. Analysis Since the wake shed by the encountering wing is assumed to remain as a #at sheet, the #ow "eld far downstream of the wing in a plane transverse to the #ight direction can be treated as two-dimensional. If the vortex wake is taken to be a slit of vanishingly small separation between the upper and lower surfaces (Fig. 20), it can be mapped from a circle into a slit by the function f "f #a/f
(4)
or y "y (1#a/r),
(5a)
z "z (1!a/r),
(5b)
where y "r cos h , z "r sin h , and r"y#z. Eqs. (5a) and (5b) are simple to apply when the mapping process goes from the circle to the slit plane. In the other direction, which happens to be the one necessary for the present analysis, the procedure is more complex. Several attempts were "rst made to invert Eqs. (4) and (5) directly, but they all resulted in unmanageable expressions which also became ambiguous when the mapping did not involve the "rst quadrant. Further di$culty also arose in
Solution of Eq. (6) for the quantity inside the parantheses yields another quadratic equation in terms of r which is again easily solved. The quantity r is then found by taking the square root obtained from the solution of the second quadratic equation. In each of these steps, the positive sign is chosen for the square root to be sure that r remains positive. After r has been found, h is found by use of Eqs. (5a) and (5b). In the computations for the mapping, a point on or just outside of the circle or slit is always taken slightly in excess of the circle radius (i.e., above or below the slit that represents the wake) to be certain that the point in question is mapped into the #ow "eld and not into the inside of the circle or slit. Since the #ow "eld is linear, the contributions of any number of vortices can be superimposed. For the present, however, consider a single vortex passing somewhere near a wing and its wake (Figs. 19 and 20). If the circle in the mapped plane is to be a boundary, an image vortex must be placed inside the circle at the same angle, h , as the impinging vortex and at the radius, r "a/r , from the center of the circle. An additional vortex of the same strength as the impinging vortex must be placed at the center of the circle, so that the net circulation inside the circle vanishes. Since both a positive and negative vortex are added to the #ow "eld inside the circle, the net circulation upstream and far downstream of the wing are both equal to the magnitude of the circulation in the impinging vortex. If a vortex had not been added at the center of the circle, the net or total circulation in the transverse #ow "eld far downstream of the wing would be zero. The complex potential for the cross-stream #ow "eld is then given by U"(iC/2p)ln[f (f !f )/(f !a/fM )], (7) where no tangency or Kutta condition is speci"ed at the edges of the wake. The solution given by Eq. (7) yields the potential and stream function when separated into real and imaginary parts. The velocity components are found by taking the complex derivative of Eq. (7). The velocity on the surface of the slit is then found from the circumferential velocity on the surface of the circle as v "(v sin h !w cos h )/2 sin h . The vorticity in the wake is found from
(8)
c (y )"v ) !v ) .
(9)
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Substitution of the various derived quantities into Eq. (9) yields the vorticity distribution for the wake in terms of the wing span, b , or the radius of the circle, a"b /4, and the location of the impinging vortex in the circle plane as
C c(y )" 4pa sin h
r !a 2! r #a!2ar cos(h !h ) r !a ! , (10) r #a!2ar cos(h #h ) where a position on the slit is related to a corresponding one on the circle by
y "2a cos h . (11) The span loading on the encountering or following wing is obtained by integration of the intensity of the vortex wake, c (y ), for the bound circulation, C(y ), or W C(y )"! c(y) dy \@ to yield
C C(y )"! p
(r #a) h !tan\ tan[(h !h )/2] (r !a) (r #a) !tan\ tan[(h #h )/2] . (12) (r !a) When Eq. (12) is used to compute the span loading, the arc tangents sometimes switch quadrants at improper values of the arguments. If the arc tangents do not make a smooth transition between quadrants, unwanted discontinuities and errors occur in the loading. This di$culty can be eliminated by combining the two arc tangent functions through the use of trignometric identities so that Eq. (12) becomes
C C(y )"! p
(r #a) sin h ; h !tan\ . (r #a)cos h !2ar cos h (13) Now that the circulation bound in the wing is known, the lift and torque induced on the wing by the vortex can also be found by integration of the equations,
¸"!o;
@
\@ @
C(y ) dy ,
(14a)
y C(y ) dy . (14b) \@ The integrations are carried out by "rst transforming them to the circle plane. Integration by parts is then used to conform the integrals to "t those listed in standard integral tables. By this technique, the coe$cients of lift M"!o;
529
and rolling moment induced on the following or encountering wing by a vortex are found as [135] C "!AR (C /b ; )(b /b )(a/r )cos h , (15) * C "(b /b )(a/r )cos 2h , (16) J where a positive value of lift is taken as upward. The rolling-moment coe$cient is taken as positive when the torque is in the same direction as the rotation direction of the impinging vortex. An equation for the drag due to lift that corresponds to Eqs. (15) and (16) was not derived, because the integrations were not obvious and an evaluation of drag is not needed as much as lift or rolling moment. Eqs. (15) and (16) are of value, because they indicate the dependence of the induced lift and rolling moment on the signi"cant parameters for an encounter; namely, the span ratio, aspect ratio, vortex strength, and the location of the vortex relative to the wing centerline. It should be noted that Eqs. (7)}(16) are given in terms of the location of the vortex in the circle plane even though the quantities represented apply to the slit or physical plane. Transformation back and forth between the two planes is relatively easy by use of Eqs. (5) and (6). The maximum values predicted by the transverse-#ow method for lift and rolling moment are given by setting r equal to a, the radius of the circle, and h equal to zero for the maximum lift, and equal to 903 for maximum rolling moment [135]: C ) "[AR ](C /b ; )(b /b ), (17a) * C ) "[AR /8](C /b ; )(b /b ). (17b) J The magnitude of the two maximums in Eqs. (17) are noted to be the same except for a factor of eight. The two formulas are quite accurate for small aspect ratios (i.e., less than one), but quickly become less accurate as aspect ratio increases above one. It has been pointed out by Jones [137] that the lift-curve slope for a wing of small aspect ratio is given by dC /da"pAR/2, and that, at * larger aspect ratios, more accuracy is obtained with another relationship given by dC /da"2pAR/(pAR#2), (18) * where the quantity AR is the aspect ratio of the wing, p is the ratio of the semi-perimeter of the wing to its span, and dC /da is the lift-curve slope of the encountering wing * (e.g., p. 95 of Jones [137]). It is therefore recommended that the quantity, 2dC /da/p be substituted for AR in* side the square brackets in both Eqs. (17a) and (17b). In Eq. (17a) for the lift, the functions in Eq. (18) are based on the full span of the following wing. However, in Eq. (17b) for the rolling-moment coe$cient, the functions in Eq. (18) should be based on half of the span of the following wing [135]. It is reasoned that the entire wing is in either an upwash or downwash for maximum lift, but when the
530
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
maximum rolling moment occurs, only half of the wing is in an upwash and half is in a downwash. The change in vertical velocity at the wing centerline is simulated in Eq. (18) by use of half of the following wing for evaluation of the various parameters it contains. 4.3. Comparison with other methods The solutions derived by use of Munk's transverse#ow method are now applied to several problems to illustrate the accuracy of the predictions by comparing them with the vortex-induced loads predicted by a vortex-lattice method on a #at wing of rectangular planform [135]. Since the shape of the wing is not speci"ed by the theory, there is some question as to how the results presented here should be tested. If the wing is cambered and/or twisted to redirect the rotary #ow of the impinging vortex, the results could be made to agree exactly, because the assumptions would be the same. However, a di!erent wing shape must then be used for each vortex strength and location. It seems best then to compare the present predictions on the basis of a #at wing of rectangular planform which does not "t any particular aircraft, but is representative of many wing shapes in use. The methods available to be used in the comparison range from quite simple strip-theory type analyses to fairly involved "nite-di!erence methods. Of these, the two methods to be used here are a modi"ed strip theory which incorporates features suggested by Munk [136], Jones [137] and Maskew [138], and a vortex-lattice method developed by Hough [139]. Both methods assume that the wake is not changing with time, and that the penetrating wing is "xed at some point in the wake so that the #ow "eld can be treated as steady state. The di!erences between these two prediction schemes for the maximum torque on a following wing were found to be small compared with the uncertainties usually experienced in obtaining test data. Since the span-load distribution predicted by strip theory is directly proportional to the local upwash without any redistribution of vorticity, it is not useful for comparison with the load or vorticity distributions. Hence, the modi"ed strip theory will be used only to derive equations for the lift and torque induced on the wing when the vortex is at its most e!ective or intense location for each quantity. The vortex-lattice method will be used to make more detailed comparisons. The "rst of the two quantities to be derived with the modi"ed strip theory is the lift induced on an encountering wing when the vortex impinges on the wing at a distance y from the wing centerline. Since the impinging vortex is a potential vortex, and has no core, the velocity distribution is given by v "C /2pr. F
(19)
Integration of the lift distribution when the vortex is in the z"0 plane yields C ) "[1/(1#3/AR )](C /b ; )(b /b ) * ;ln[(y !b /2)/(y #b /2)], (20) where the aspect ratio function inside the "rst set of brackets arises from the empirical correction for strip theory as suggested by Jones [137]. Similarly, the rolling moment induced by the vortex on the encountering wing is found by integration of the torque to yield C ) "[1/(1#6/AR )](C /b ; )(b /b ) J ;+1#0.5 ln[(y !b /2)/(y #b /2)],. (21a) The empirical aspect-ratio function derived by Jones, Eq. (18), di!ers slightly from quantities inside the brackets in Eqs. (20) and (21a), (21b) re#ecting the fact that the maximum torque location for the vortex puts half of the wing in an upwash and half in a downwash #ow "eld, making the e!ective aspect ratio half as large as when the vortex impinges at the wingtip [136]. Note that both Eqs. (20) and (21a) become in"nite when the vortex impinges on either wingtip, i.e., y "$b /2. This characteristic makes it di$cult to use these equations for #ow "elds that contain point or line vortices, because the answer may depend on the proximity of a vortex to a control point. Vortex-lattice methods present a similar di$culty whenever a point vortex falls on or too near a control point, and therefore are also not useful for #ow "elds that contain point vortices. When the vortex impinges on the wing centerline, the lift vanishes and the rolling-moment coe$cient takes on the "nite value [135] C ) "[1/(1#6/AR )](C /b ; )(b /b ). (21b) J It is to be noted that the strip-theory result, Eq. (21b), has the same form as predicted by the transverse-#ow theory, Eqs. (17a) and (17b), except for the aspect ratio function. It is for this reason that in each of these equations, the dependency on AR is indicated by square brackets to emphasize where the functional di!erence between various theories appears to be concentrated. Since the strip theory result for maximum rolling moment and vortexlattice theory have been found to be in good agreement with experiments [10], the results obtained with the transverse-#ow method need to be examined in more detail to "nd out how well they compare with the loads on #at wings of rectangular planform. The vortex-lattice method of Hough [139] makes possible an evaluation of the accuracy of the transverse-#ow predictions for the vortex-induced span loadings and the integrated parameters. Since the vortex-lattice method is a numerical procedure, the velocity distribution of the vortex must not contain in"nite values in case a control point inadvertently falls on or near the center of a vortex.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
531
Fig. 21. Variation of lift and rolling moment coe$cients with spanwise distance along a line just above the vortex center [135].
In order to cover such a possibility and still have a vortex structure that approximates a potential vortex, the vortex used in the comparisons was a Rankine vortex [9] with a small but "nite core of radius, r "0.001b (Fig. 21a). Even though a small core is speci"ed for the vortex, the vortex-lattice solution responds as if the core were as large as the distance to the control point nearest the center of the vortex. Such an approximation does not always a!ect the results signi"cantly, but may be responsible for some of the di!erences between the two predictions. The wing used for the vortex-lattice computation has a rectangular planform and has no twist or camber. As expected, all of the expressions derived for the wing}vortex interaction indicate a linear relationship with the dimensionless vortex strength. Such a relationship is expected in the absence of #ow separation or other #ow anomalies that lead to nonlinear characteristics. Such a well-behaved linear characteristic for the other parameters like the span ratio, b /b , and the aspect ratio of the following wing, AR , is not necessarily expected. Hence, these variations will now be investigated. The lift and rolling moment predicted by the transverse-#ow method, and the vortex-lattice method, are "rst compared in Fig. 21 as the wing is given locations along a line just above the horizontal axis of the vortex. As mentioned previously, the vortex used in the vortexlattice computation was given a core of radius, r "0.001b (Fig. 21a). Even with this precaution, un realistically large positive and negative values of lift and rolling moment occurred at locations along the y-axis
whenever the vortex center was too near a control point of a wing panel or lattice. For this reason, a dashed curve for the vortex-lattice prediction is not presented in Fig. 21 for y/b values between !0.05 and #0.05. Outside of this region, no portion of the wing is near the vortex center, so the vortex-lattice method does not have di$culty, and the two predictions are in good agreement. Of course, the closed-form expressions derived here have no di$culty with nearness to the center of a point vortex. The span ratio parameter, b /b , was chosen as the next part of Eqs. (15) and (16) to be studied, because all of the equations predict a linear dependence of lift and torque on it. The comparison in Fig. 22a indicates that the relationship is indeed not only linear, but the rolling moments are in very good agreement when the vortex center and the wing centerline are aligned. However, when the vortex impinges on the wingtip (Fig. 22b), the agreement is not as good even though the transverse-#ow and vortex-lattice methods both predict a linear relationship with b /b . The reason for the lack of agreement is not obvious, but as mentioned previously, may be caused by the dependence of the vortex-lattice method on the nearness of the control points to the vortex center. The "nite mesh size of the vortex-lattice method may also contribute to the di!erence but probably not signi"cantly. Next, the e!ect of aspect ratio on the lift and rolling moment predicted by the two methods are compared in Fig. 23. Once again, the quantities are evaluated at the
532
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 22. Variation of lift and rolling-moment coe$cients with the inverse of the span ratio as predicted by transverse-#ow and vortex-lattice methods [135]; C /b ; "0.1.
vortex locations that yield maximum values for each. As observed in Fig. 21, the lift has a maximum whenever a wingtip is at the vortex center. The magnitude of the rolling moment maximum predicted by the transverse#ow method is the same at the wingtips as at the wing centerline (Eq. (16)). The comparisons in Fig. 23 show that the linear relationship predicted by the transverse#ow method is not con"rmed by the vortex-lattice results. As anticipated by the assumptions made in the transverse-#ow theory, the two predictions are in agreement with one another at low values of AR . As AR increases however, the transverse-#ow method increas-
Fig. 23. Variation of lift and rolling-moment coe$cients with aspect ratio of following wing as predicted by transverse-#ow and vortex-lattice methods [135]; C /b ; , b /b "0.2.
ingly overpredicts the loading. Such a result points out that the encountering wing needs a large chord if, as assumed in the theory, the wing is to turn the rotary #ow "eld of the vortex so that it does not penetrate the wake. Hence, even though the theory of the transverse-#ow method did not specify the planform of the wing nor its twist and camber, it did require that the wing should be of a size and shape that would de#ect the rotating airstream around the wing. As indicated in Fig. 23, one possible design that accomplishes the #ow diversion is a wing with a large chord or small aspect ratio. According to the results of the comparison, the required amount
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
of turning is apparently provided by the #at rectangular wing used in the vortex-lattice examples when its aspect ratio is below about one. The transverse-#ow result can be corrected by the simple aspect-ratio function, Eq. (18), derived by Jones [137], but the results are not exact. Trial-and-error attempts were then used to develop a function of AR that would bring the two predictions into more precise agreement. A function that corrects for lift when the vortex is aligned with a wingtip is given by F (AR )"[1#0.5AR ] tan(0.6AR ). (22a) * A function that corrects the rolling moment prediction when the vortex is aligned with the wing centerline is given by F (AR )"[1#1.6AR ] tan(0.4AR ). (22b) J If Eqs. (22a) and (22b) are used instead of the simple AR parameter in Eqs. (17) and (18), the straight lines presented in Fig. 22 for the transverse-#ow method are converted into curved lines that lie within a line width of the vortex-lattice results. However, when Eqs. (22a) and (22b) were applied to other locations of the vortex relative to the wing to obtain the span loading, lift, and rolling moment, the agreement with vortex-lattice theory was not nearly as good. Some of the discrepancies may be due to failures of the vortex-lattice method to represent some aspects of the aerodynamic interaction process. When both predictive methods are applied in circumstances where their respective assumptions are not violated, the two results agree. In the cases considered, they agree well only when the aspect ratio is small. In order to further illustrate the character of the transverse-#ow results, the span loadings are compared with vortex-lattice results in Fig. 24 for AR "1.0 when the
533
vortex is aligned with the wing centerline and with the wingtip. Once again the vortex center is not near enough to a vortex-lattice control point to yield unrealistic results, but the loading may also not be accurately represented. Note that the agreement is quite good except for the lift magnitude when the vortex impinges on the wingtip. Such a di!erence is expected when the comparisons in Fig. 23 are examined at low values of AR . In general, it is recommended that the proper aspect ratio be used in the lift-curve slope function given by Eq. (18), and the discussion that follows it. 4.4. Applications Several examples of problems that can be treated by use of the results of the transverse-#ow method (Eqs. (15) and (16)) are now presented to illustrate applications. The author's primary interest was to have available a simple, quick means for the calculation of the contours of constant lift and torque for any system of point vortices; e.g., one that represents a lift-generated wake. In order to illustrate such a capability, the contours for a single or isolated vortex are "rst presented in Fig. 25. Such a computation is relatively simple, because they are known in closed form from Eqs. (15) and (16). In the case of two or more vortices, a predictor/corrector method is used to generate the contours. The contours for a pair of point vortices are presented in Fig. 26 for both lift and rolling moment in order to illustrate application to the simplest of lift-generated wakes. Obviously, the results in Figs. 25 and 26 are easily extended by superposition to any number and arrangement of point vortices, thereby providing the tools sought at the beginning of the investigation. In order to illustrate the technique and to check the accuracy of the
Fig. 24. Comparison of spanwise loading as predicted by the transverse-#ow and vortex-lattice methods [135]; C /b ; "0.1, b /b "0.5, AR "1.
534
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 25. Predictions by transverse-#ow method of the contours of equal lift and rolling-moment coe$cients as induced on a following wing by a point vortex [135].
Fig. 26. Predictions by transverse-#ow method of the contours of equal lift and rolling-moment coe$cients as induced on a following wing by a pair of point vortices [135]; b /b "1.
approximation of vortex structure by any number of point vortices, the structure of a Rankine vortex core is simulated with 19 point vortices (Fig. 27). Comparison is then made with the vortex-lattice method by assuming a continuous distribution of velocity in the vortex, so that the computation does not have di$culty. In order to indicate the accuracy of the point-vortex approximation, and of Eqs. (15) and (16), the two predictions are compared in Fig. 27 along a line through the center of the vortical region. Since the agreement is quite good, the example illustrates the e!ectiveness with which a system of point vortices can be used to represent a continuous distribution of vorticity. The wiggles in the transverse#ow prediction are small-scale versions of the #uctuations shown in Fig. 21 for a single vortex. As the number
of vortices used to simulate a given vortex structure increases, the amplitude and length of the wiggles decreases. Another example which illustrates the use of Eqs. (15) and (16) for estimating lift and torque throughout a vortex wake is presented in Fig. 28. A system of 40 point vortices is used to represent the lift-generated wake of an elliptically loaded wing. The contours of constant torque are presented at several time intervals or distances downstream of the wing trailing edge as noted in the "gure. The technique developed to produce Fig. 28 makes it possible to evaluate the wake hazard as a function of time for a wide variety of lifting con"gurations. In the cases studied so far, it was found that the maximum rolling moment induced on a following wing by a vortex system
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
535
Fig. 27. Lift and rolling moment on a wing as it traverses through a vortex with a core of radius r "b . Transverse-#ow method uses a system of point vortices to simulate the continuous distribution of vorticity in the Rankine vortex used in the vortex-lattice method [135]; C /b ; "0.1, b /b "0.5, AR "1.0.
Fig. 28. Contours of equal rolling-moment coe$cient at various instants of time as the wake shed by an elliptically-loaded wing rolls up [135]; C /b ; "0.1, b /b "0.5, AR "1.0.
536
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
does not change appreciably during the time history of the wake even though the contours change somewhat. This result is not expected to be true for all wakes, because the maximum value of the gradient in vertical velocity is not an invariant of vortex systems. It should also be noted that the maximum torque predicted is larger than any of those measured in wind tunnels for two reasons. First, viscous e!ects di!use the high energy concentrated in the vortex cores. Secondly, most of the wakes measured were shed by wings with slats and #aps that shed some turbulence which tends to di!use the cores of vortices and reduce the induced torque. In all of these examples, note that even though wiggles occur in the contours due to the "nite number of point vortices used in the simulation, the predicted torque always provides realistic values when the vortex impinges on any part of the encountering wing. This attribute makes the foregoing results usable in a wide variety of circumstances not possible with strip or vortex-lattice theories, unless special precautions are taken to avoid the proximity of vortex centers to control points. If the aspect ratio of the following wing is to be much greater than one, an empirical adjustment, such as Eq. (18), should be made to the results predicted by the transverse-#ow method to improve the quantitative accuracy of the method for aspect ratios much above one. These comparisons also add con"dence in the ability of vortex-lattice methods to properly represent rearrangement of the velocity and vorticity in the #ow "elds produced by the interaction of a wing with a vortex. The comparisons also demonstrate that the closed-form expressions derived by Munk's transverse #ow-"eld method are quantitatively very good at small aspect ratios. At higher aspect ratios, a correction factor like the one in Eq. (18) needs to be applied to the lift-curve slope for the shape and aspect ratio of the encountering wing to improve the accuracy of the predictions.
5. Span loading and vortex structure 5.1. Introduction A relationship between the span loading on the wakegenerating wing, and the structure of the vortices it sheds was "rst derived by Betz [140]. Although not utilized after its introduction until around 1970, it is one of the most signi"cant theoretical tools available for the understanding of wake-vortex generation, and for the design of experiments conducted in support of wake-vortex research programs. The importance and applicability of Betz' formulation was identi"ed and called to the attention of researchers by Donaldson and his associates as a part of the interpretation of #ight data, and of e!orts
to analytically and numerically treat the dynamics and decay of lift-generated vortex wakes [32,141,142]. Before the derivation of Betz' method is presented, the assumptions made and the process used to derive the equations are discussed. The vortex invariants for the time-dependent motion of two-dimensional (or point) vortex systems [9] are presented, because the invariants are needed in the derivation, and because they are useful for a wide variety of purposes that relate to the study of vortex systems. An overview will then be presented of extensions to the basic Betz method that have been made, and experiments conducted to determine the reliability of the method. Section 6 will describe how the simple Betz relationships can be used to design vortex wakes that are less hazardous. 5.2. Description of Betz' analysis Betz' method [140] relates the two-dimensional inviscid structure of the lift-generated vortex sheet shed at the trailing edge of a wing to the structure of the fully developed vortices far behind the wing. As such, the method does not concern itself with the time-dependent motion of the initially nearly #at vortex sheet shed at the trailing edge of a lifting wing as it rolls up into the fully developed axially symmetric vortices located far behind the wake-generating wing (Fig. 29). The analysis is treated as a two-dimensional one between an initial time and a "nal time. The assumption of axial-symmetry for the rolled-up vortices is approximately valid when the portion of the wing wake being analyzed is far enough in the spanwise direction from the opposite vortex, so that the "nal Tre!tz-plane streamlines do not deviate far from circular (Fig. 30a). The invariants for two-dimensional timedependent vortex systems are used to relate the radius at which a portion of the circulation in the vortex sheet at the trailing-edge of the wing is deposited in the fully developed vortex. In the strictest sense, the invariants require that all of the vortices or vorticity in the #ow "eld be included in its evaluation. The Betz method [140], however, and the analyses to follow, apply the invariants to only certain portions of the vortex system at a time. Justi"cation for such an assumption at the station far downstream from the wing is made by noting that the swirl velocity in an axially symmetric vortex depends only on the circulation contained within the radius where the velocity is being determined. Since the streamlines are then concentric circles, circulation outside of the radius does not in#uence the velocity which is given by v "C(r)/2pr, F
(23)
where C(r) is the circulation inside the circular streamline. As mentioned in the previous paragraph, much of the simplicity of the basic-Betz method results from the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
537
Fig. 29. Conceptual process used by Betz' method to derive equations for rollup of vortex sheet [147].
Fig. 30. Streamlines for the #ow"eld of point vortices designated by "lled symbols.
assumptions made in the analysis. First, the span loading at the wingtip being analyzed is assumed to be far from the vorticity being shed by the opposite side of the wing, so that the streamlines in the rolled-up vortex can be approximated by concentric circles (Fig. 30a). If the circulation and rolled-up vortex on the opposite side are included in the analysis, the streamlines would be o!set laterally as illustrated for two point vortices in Fig. 30b. The second equal and opposite vortex in the #ow "eld also causes the vortex pair to move downward due to the mutual induction of the velocity "eld of the two vortices. If this downward motion is included in the analysis,
the streamlines associated with the vortex pair, and the circulation distribution, are con"ned to a vortex oval (Fig. 30c) [9]. In Fig. 30b and c, the spanwise distance between the vortices is kept the same to illustrate the di!erences in the streamline arrangements. When the vortex pair moves downward, the streamlines are no longer perfect circles. Also, the approximate centers of rotation are o!set laterally, only a small amount and not by nearly the amount that takes place when the vortices are held in place (Fig. 30b). It is believed that a great deal of the success of the Betz method comes about because the
538
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
streamlines, although not perfect circles, are nearly circular and much more concentric in Fig. 30c than they are in Fig. 30b. Therefore, when a vortex sheet is rolled up, circulation associated with each streamline is distributed throughout a region of the #ow "eld enclosed by the oval. These complications are all assumed to be negligible in Betz' method, but should be kept in mind when applications are made to situations where unusual results occur. Since the in#uence of the opposite vortex fades linearly with the distance between the vortex centers, some sort of in#uence is present throughout the rollup. The in#uence is probably truly negligible only near the center of a vortex where high rotational velocities dominate. Another restrictive assumption in the basic Betz' method is that the vortex sheet shed by the wing rolls up in an orderly fashion from the wingtip inboard. In such a process, successive layers of the vortex sheet are wrapped around the center and previous wrappings of the vortex (Fig. 29). It is found from the study of experimental and idealized hypothetical span loadings that the vortex sheet shed by a wing usually does roll up from the wingtip inboard in an orderly fashion. If such an orderly rollup is to occur, not only must the span loading increase monotonically from the wingtip inboard, but the strength of the vortex sheet that it sheds must also have its maximum intensity at the wingtip and then decrease monotonically from the wingtip inboard [32,142}147]. Extensions to the basic Betz method that provide an approximate remedy for span loadings that violate this criterion will be discussed in a section to follow. 5.3. Invariants for motion of vortices The invariants for the time-dependent motion of twodimensional vortex systems relate a given function or state at a given time (i.e., at the wing trailing edge), to the state of the system at another time (i.e., at a station far behind the wing) [9]. In order to facilitate the analysis to follow, the invariants presented in various texts are now written for vortex sheets that are approximated by N point vortices whose strengths are given by, c , and locations by (y , z ). The equations are written as G G G [147]. Conservation of circulation: , C "C " c "constant. G G
(24)
Conservation of "rst moment of circulation: , y C " c y "constant, , G G G
(25a)
, z C " c z "constant. , G G G
(25b)
Conservation of second moment of circulation: , J " c [(y !y )#(z !z )]"constant. G G , G , G Conservation of angular moment of circulation: , M " c [(y !y )w !(z !z )v ] G G , G G , G G ,\ , c c " G H"constant. 2p G HG> Conservation of energy:
(26)
(27)
o ,\ , = "! c c ln[(y !y )#(z !z )] G H G H G H 4p G HG> "constant. (28) In Eqs. (24)}(28), and those to follow, the subscript s is used to denote quantities in the across-stream (or Tre!tz) plane located at the trailing edge of the wake-generating wing where the vortex sheet begins, and the circulation is spread out as a thin sheet. The subscript v is used to denote quantities at the Tre!tz plane located far downstream from the wing where the vortices in the wake are assumed to be fully rolled up into an axially symmetric vortex (Fig. 29). The subscript w is used to refer to the wing, and to quantities associated with the span loading. Eqs. (26) and (27) are written so that the centroid of circulation (y , z ) is used as the reference location on , , which the second moment and angular moment are computed in order to put the equations in the forms needed for the rollup analysis. The equations are still applicable even if another reference location is used. The spanwise and vertical velocity components in Eq. (27) for the ith vortex are given by 1 , v "! [c (z !z )]/[(y !y )#(z !z )], G G H G H G H G 2p H (29a) 1 , w "# [c (y !y )]/[(y !y )#(z !z )]. G G G H G H G H 2p H (29b) The function = for the energy in Eq. (28), which is often referred to as the Kirchho!}Routh path function, is sometimes written with a positive sign. The negative sign is correct, however, because it represents the variable portion of the kinetic-energy content (usually designated by ¹) of the #ow "eld. When the integration over the #ow "eld is carried out to determine the energy, the positive part is found to be a constant. The positive part is also found to become in"nitely large when the area of integration is expanded to include the core region of the point vortices and the region at very large radius.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Since the in"nite parts are constant with time, they are usually left out of any analysis of time-dependent vortex motions. Since an equation for the energy of a system of concentric vortex rings in the rolled-up vortex plane is not available, it is derived by integration of the equation for the kinetic energy of the #uid between the rings [147]. Since the fully developed vortex is assumed to be axially symmetric, the energy, ¹ , is given by o ¹" v2pr dr, (30) 2 F where the swirl velocity for (r (r(r ) is given by L\ L L\ c G. v " (31) FL 2pr G The integration for the energy in the #ow "eld goes from the radius of one vortex ring to the next (Fig. 31). Since the circulation from a given point vortex is spread over an annulus of zero thickness, no energy is contributed by the ring itself. Furthermore, it appears that no energy is expended by the process which distributes the circulation contained in the point vortex around the annulus. Since the "rst point vortex is deposited at the center of the rolled-up vortex at zero radius, the "rst integral in Eq. (30) is given by
o P c o dr" c[ln(r )!ln(r) ]. ¹ " (32) L 2 2pr P 4p In Eq. (32), the contribution to the energy by the term that goes to in"nity as rP0 is constant with time, and is therefore ignored. Similarly, the contribution to the
539
energy by the #uid outside of the radius of the outermost ring also goes to in"nity at the upper limit of integration. Once again, it is constant with time and is ignored. The symbol = (rather that ¹ ) is used to denote the time-invariant portion of the kinetic energy in the #ow "eld of the vortex sheet, because it does not contain the in"nite contributions to the invariant for energy. Similarly, the parameter = is used to denote the "nite quantities for the energy in the #ow "eld of the rolled-up vortex. The "nite and variable parts of the energy of the rolled-up vortex where the point vortices are deposited are then
o cln(r )#(c #c )ln(r /r ) = " 4p #(c #c #c )ln(r /r )#2 L\ L # c ln(r /r )! c ln(r ) . (33) G L L\ G L G G Eq. (33) is the axially symmetric version of the energy equation, Eq. (28), which is needed in discussions to follow for the development of rollup equations for vortex wakes. The foregoing equations apply to the invariants of the time-dependent motion of two-dimensional point vortices in an inviscid, incompressible #uid. The corresponding integral forms of the equations for vortex sheets are obtained by substituting
dC(s) c" ds, G ds
(34)
where s is the distance along the vortex sheet. The summation over the point vortices is then changed into an integration along the vortex sheet. 5.4. Rollup equations
Fig. 31. Idealized #ow "eld with point vortices spread over concentric annuluses to illustrate computation of energy in rolled-up plane [147].
In this section, the basic-Betz rollup method is derived by use of the "rst three invariants (i.e., Eqs. (24)}(26)) written in integral form as suggested by Eq. (34). The distance s along the vortex sheet is taken as y , because the vortex sheet is initially approximately #at so that its variation in height, z , is ignored. It is emphasized here that the vortex invariants strictly apply only when all of the circulation in the #ow "eld is included in the various summations. If such a requirement is strictly enforced, and the vortex invariants are applied to the vortex system as a whole, very little information is obtained, because Eqs. (24) and (26) vanish, and because the "ve summations usually contain a much larger number of unknowns than the "ve equations are able to ful"ll. Therefore, Betz' method achieves a solution for the rollup problem by specifying that the invariants be applied progressively to portions of the #ow "eld, so that the number of unknowns does not exceed the number of equations
540
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
available as each vortex-sheet element is incorporated into the rolled up vortex for a solution. For this purpose, the summation is made over only a portion, n (beginning with n"1) of the vortices (or segments of vortex sheets) in the #ow "eld rather than all of the segments as given by N. It is found that the results achieved by Betz' method are in good agreement with experiment, even though the invariants are applied to only certain portions of the vortex system at a time. Good results are achieved because the assumptions made, and the guidelines given by Betz [140], are approximately valid for the way that the invariants are applied. When the vortex invariants are applied to portions of the vortex system, it is noted in Eq. (24) that the portion of the vortex sheet that has been incorporated into the vortex by Betz' method is also equal to the circulation bound in the wing at that spanwise station (i.e., C (y )"C (y )), so that the two can be used interchange L L ably. The center of the rolled-up vortex is located at the centroid of circulation (y , z ). The conservation of circuL L lation as it is transferred from its location at y in the G vortex sheet behind the wing into the fully developed vortex far behind the wing is now written as
W dC(y ) G dy (35) G dy @ G where the integration begins at the wingtip and then proceeds inwardly to the point y successively, until the L centerline of the span loading is reached. The radius, r , G that encloses the circulation in the vortex is related to the corresponding spanwise station on the wing, y , by the G second moment of circulation written for the spanwise station on the wing as C (r)"C (y)"
W dc(y ) G [(y !y )#(z !z )] dy G G G G G dy @ G and at the rolled-up vortex as J(y)"
(36a)
W dc(r ) G r dr . (36b) dr G G @ G At each stage of the rollup, the second moment of circulation is conserved as each segment of vortex sheet is transferred to the rolled-up vortex which requires that J (r )"J (y ). If the second moments of circulation in the G G two planes are the same at each point on the span, the di!erence between two successive segments is also the same. As the number of vortex sheet segments or elements are added to the summation by stepwise increases in n, the incremental increase in the second moment becomes J(r)"
*J "J !J "c r L L L\ LL and,
(37a)
*J "J !J . L L L\
(37b)
Therefore, when increments in the second moment of circulation for the two planes are equated, *J "*J , L L the radius at which the circulation, c , from the nth vortex L is deposited is given by
1 r" , (38) (J !J ) L L L\ c L where the circulation contained in the nth vortex is spread over an annulus or ring of zero thickness at the radius r . The relationship between r and y that corresL L L ponds to Eq. (38) is then [145,147] r ""y (y )!y " L L L Eq. (39) may also be written as
(39)
(40)
v "C (r )/2pr . F L L
(41)
1 WL r "! C (y) dy. L C (y ) L @ The swirl velocity in the vortex is given by
5.5. Vortex-wake examples In order to gain an understanding of how the structure of the rolled-up vortex changes with variations in span-load distribution, a series of cases were calculated by use of Eqs. (39)}(41) [145]. The function used for the various span-load distributions on the wake-generating wing is C (>)/C "(1!>,)+, (42) where >"2y/b . The z"0 plane is de"ned as the hori zontal plane through the vortex sheet at the trailing edge of the wing, and/or center of the fully developed vortex. Fig. 32 presents the spanwise loading, circulation, and vertical velocity for the rolled-up vortex for several values of N and M, assuming that rollup begins at the wingtip as postulated in the original Betz theory. Instead of plotting C (r)/C and v as a function of R"2r/b , the F results are presented at their position on the >"2y/b axis to better illustrate their relative location spanwise to other vortices that may be in the wake. The curves for the velocity in these "gures and in those to follow, terminate at the edges of the region where vorticity is located so that the velocity distributions in the irrotational parts of the #ow "eld are not presented. 5.6. Vortex wakes with multiple pairs Before discussing extended-Betz methods, several simple examples are presented to indicate the complications that can arise when the vortex wakes of aircraft with #aps deployed are analyzed. The examples presented in Figs. 33}35 for three di!erent span loadings were chosen to illustrate the e!ect of span loading, or the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
541
Fig. 32. Examples of fully developed vortices that form behind various span loadings [145] represented by C (y)/C "[1!(2y/b ),]+, by assuming that vortices roll up from the wingtip. (a) N"2.0, M"0.5. (b) N"2.0, M"1.0. (c) N"1.0, M"1.0. (d) N"2.0, M"2.0. (e) N"0.5, M"1.0. (f) N"1.0, M"2.0.
vortex sheet strength, on sheet division and rolled-up structure of the "nal vortex wake. The method used to simulate the time-dependent motion of the vortex wake was introduced and demonstrated by Rosenhead [148] and Westwater [149]. (For more background information on the use of two-dimensional point vortices to represent vortex wakes, see the appendix of Ref. [148].) The method uses point vortices in the Tre!tz plane to represent the segments of the vortex sheet across the span. The velocity components of the various vortices are determined by the velocities induced by the other vortices in the #ow "eld. The displacement of each vortex is calculated by use of the average velocity between time steps, and then iterating for the "nal locations. The point vortices were not given a "nite core size as is often done to limit the motion of the vortices when they are close together [65]. The dimensionless
label with each of the plots for the three cases correspond roughly to 0, 5, and 10 spanlengths behind the wakegenerating wing. The axes have been shifted downward in all cases, so that the vortex locations remain in the "eld of view. Elliptic loading (C(y)/C "[1!(2y/b)] ) is chosen "rst to demonstrate how the vortex sheet rolls up from the wingtip inboard without sheet division (Fig. 33). In contrast, a vortex sheet of constant strength (as shed by an isolated triangularly loaded wingtip, (C(y)/C " 1!(2y/b)), rolls up from each end so that the vortex sheet is divided in half to form two vortices of equal strength, and structure (Fig. 34). (The port side of the wake is left blank to emphasize the one-sided character of the example.) It is to be noted in Fig. 34 that four point vortices in the center of the vortex sheet are represented by open rather than "lled symbols. From the movement
542
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 33. Time-dependent rollup of vortex sheet shed by elliptic loading; 26 point vortices on each side used in simulation [147].
of these four vortices, it becomes clear that, as expected, a single vortex sheet of constant strength divides at its center to form two equal vortices. If however, the vortex sheet is shed by an entire wing that is triangularly loaded, the inboard ends of the vortex sheets from the port and starboard sides of the wake are now adjacent and opposite in sign. The two sheets of constant and opposite strength now in#uence the division process, so that the two rolled-up vortices are not of equal magnitude or structure (Fig. 35). Rather, the in#uence of the vorticity on the opposite side of the centerline causes the division point of the two vortex sheets to be o!set, so that all four of the point vortices at the center of each sheet are incorporated into the outboard vortices, to form two vortex pairs of unequal strength. One guideline sometimes used for sheet division suggests that sheet division be chosen at those spanwise
Fig. 34. Time-dependent rollup of vortex sheet shed by isolated wingtip with triangular loading, i.e., vortex sheet of constant strength; 26 point vortices used in simulation [147].
locations where the up- or down-wash velocities vanish. Such a criteria is also inadequate, because such a guideline indicates that three rather than four point vortices join the outboard vortex, which is not what occurs. The results in Figs. 34 and 35 demonstrate that the rollup process does depend (sometimes weakly) on all of the vorticity in the #ow "eld. Approximate vortex structures can still be derived, however, if vortices outside of the rollup region do not signi"cantly in#uence the dynamics of the sheet motion, and certainly do not dominate it. The examples in Figs. 33}35 have a far simpler rollup process than the vortex sheets shed by wings with #aps deployed, and with wing mounted engines (e.g., Figs. 17 and 18). If the drag of the wing and its high-lift elements, and the thrust of the engines, are added to the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
543
vortices approach one other closely because the velocity is singular at the center of a point vortex. Nevertheless, point-vortex representations can provide useful insights and quantitative estimates if used properly. 5.7. Extended-Betz methods
Fig. 35. Time-dependent rollup of vortex sheet shed by triangular loading, i.e., two adjacent vortex sheets of constant and opposite strength; 26 point vortices on each side used in simulation [147].
self-induced convection of the circulation in the wake, the formation of the "nal con"guration of vortices is even more complicated, thereby requiring more extensions of the basic-Betz method than discussed here. It is also important to note that the use of point-vortex calculations to simulate the dynamics of vortex wakes is simple, convenient and representative of a number of characteristics of vortex wakes. However, the method does have faults. Firstly, the accumulation of vorticity or circulation into discreet locations prevents simulation of the stretching and spreading of the circulation in a vortex sheet over the spiral shape during the rollup process. It also does not include the slow asymptotic assimilation of the remote weak segments of the sheet into the "nal vortex structure. The point-vortex representation also sometimes yields unrealistic motions when two or more
The double-valued curve in Fig. 32e is a consequence of choosing the circulation shed at the wingtip as the rollup center. If Betz's method is modi"ed, or extended, so that rollup centers are based on the details of the span-load distribution (rather than always "xing it at the wingtip), more realistic vortex structures are found for more general span loadings. An attempt was made to "nd exact relationships for the locations of the starting points for the vortex centers, and for the points in the vortex sheets where circulation divides between two adjacent vortices, but the desired relationships were not found [147]. It was found that none of the vortex invariants, including the one for energy, produce any kind of indication as to when a rollup process is proceeding correct physically or not. It then becomes necessary to assume a roll-up sequence, as Betz did, or to determine the proper sequence by introduction of other mathematical techniques. It is possible, however, to identify some simple, approximate guidelines for these parameters that usually produce realistic vortex structures for complex vortex wakes [10,95,142,146]. The extensions applied by Donaldson et al. [142] and by Rossow [145,147] to the basic formulation of Betz [140] treat two aspects of the rollup procedure that were not considered in the original analysis. The "rst relates to the division of vortex sheets for rollup into multiple vortices on each side of the centerline. Once the vortex sheet has been properly divided, the second aspect concerns how, and in what sequence, the vorticity in the vortex sheet should be layered around the center of each rolled-up vortex in the wake. Guidelines presented in the foregoing references recommend that the vortex sheet be divided for separate vortices at locations where the initial vortex sheet ends, passes through zero (or has minimum strength), and/or where the self-induced vertical velocity passes through zero. The centers, about which each vortex begins its wrapping sequence of vorticity, are chosen at those locations where the vortex sheet ends, and/or where the sheet has a maximum strength. When the vortex center is located at the ends of a sheet segment, it forms a single spiral as it progresses from its originally nearly #at structure to the "nal axially symmetric fully developed vortex. When a vortex center is located somewhere in the middle of a vortex sheet segment, and not at an end, vorticity is incorporated into the rolled-up vortex from both sides of the chosen center; that is, the sheet rolls up as a double-layered spiral. For example, dc (y)/dy is in"nite at the wingtip for elliptic loading and c (y) is also in"nite there. For the
544
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
triangularly loaded case, the derivative dc (y)/dy is in" nite at both wingtips and at midspan, because c (y) is discontinuous there. In Figs. 32e and f, the strength of the inboard or wing root portion of the vortex sheet is a maximum and the vortex strength would, in fact, be discontinuous across the junction of the left and right wings, so that rollup is estimated to begin at center span rather than at the wingtip in both of those cases. The parabolic and contoured loadings shown in Figs. 32b and d have their maximum values of c (y), respectively, at the tip and about halfway out to the wingtip. As already mentioned for parabolic loading, the wingtip is chosen as the rollup site, because c (y) is discontinuous there, being "nite for y4b/2 and zero for y5b/2. If two or more vortices are produced on each side of the wing, the vortex sheet is divided into rollup segments at those places where c (y), or its derivative, is zero. For example, in triangular loading, the sheet is divided at y"b/4, so that the two vortices are of equal strength. The computations presented in Figs. 33}35 show that such an estimate is not exact. In order to perform the calculations for vortices originating at several places along the semispan, Eq. (40) is rewritten so that rollup begins at the estimated rollup site, y"y , as
1 WL r" [C (y)!C (y )]dy . L C (y )!C (y ) L W
(43)
If the rollup site occurs at the midpoint of the sheet, Eq. (43) is applied to the two segments of the sheet separately, and the two resulting curves for C (r ) are added. That is, L it is assumed that the two parts of the sheet roll up within
one another without interacting. The "nal variation of C (r )"[C (r )" !C (r )" ] is then used in Eq. (41) L L L for the determination of the swirl velocity in the vortices. The center of the vortex is, of course, located at the centroid of the segment. Fig. 36 shows the application of these techniques to the four cases that do not have the entire rollup beginning at the wingtip. An interesting and convincing application of the rollup rules for the extended-Betz method was made by Corsiglia and Orlo! [95] by use of a scanning laser velocimeter to survey the wake 1.5 spans behind a 0.03 scale model of a B-747 in a wind tunnel. The comparisons made in Figs. 37 and 38 indicate quite good agreement of the predicted vortex strengths with those measured in the wind tunnel. The modi"ed or adjusted span loadings were made as an approximation to the loss of lift to be expected, due to #ow separation on the various lifting elements, and to account for the fact that the vortexlattice calculation did not account for the presence of the fuselage on the aircraft model. The adjustments made to the vortex-lattice solution and to the span loadings indicate that judgements are required if the simple technique introduced by Betz is to be used successfully [95]. It must also be recognized that the vortex cores identi"ed by Corsiglia and Orlo! a short distance behind the wakegenerating model will merge with one another as the wake ages to form a single vortex pair.
5.8. Inverse-Betz method As experimental data began to accummulate for the velocity distributions in vortex wakes, a need arose for
Fig. 36. Examples of fully developed vortices for the same span loadings presented in Fig. 32c}f, but with rollup beginning points determined by rules for multiple vortex wakes [145]. (a) N"1.0, M"1.0. (b) N"2.0, M"2.0. (c) N"0.5, M"1.0. (d) N"1.0, M"2.0.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
545
a theoretical relationship that would make it possible to go from the measured velocities back to the span loading that generated the wake. One need for such a relationship is the desirability to go backwards to "nd out how turbulent and viscous e!ects modi"y vortices as they age, and also to "nd out how vortex mixing modi"es vortices in the near term of their history. Such a reverse or inverse method adapted from the original Betz method has been labeled the inverse-Betz method [146]. Naturally, the inverse method is based on the same assumptions as the direct- or basic-Betz method. The derivation begins with the expression that relates the radius, r , in the L vortex to the spanwise station on the wing, y , where the L increment in circulation is "rst deposited in the vortex sheet shed by the wing. From Eq. (40), the relationship between r and y for the starboard or right wing may be L L written as
Fig. 37. Comparison of maximum vortex circulation from vortex-lattice theory and the axisymmetric model for the measured velocities; B-747 (303, 03) con"guration with gear stowed; Corsiglia et al. [95].
1 WL r "! C (y) dy. L C (y ) L @ Since the circulation in the vortex, C (r ) contained L within the radius r is equal to that shed by the wing L between its tip at b/2 and the element of circulation at y being transferred, the conservation of circulation L yields C (r )"C (y ). Eq. (21a), (21b) can then be L L written as
d WL d [r C (r )]" C (y) dy dr L L dr L L @ dy "!C (y ) L L dr L so that dy r dC (r ) L. ! L"1# L dr C (r ) dr L L L On integration from the wingtip inboard, one form of the inverse-Betz relationship between y and r is given L L by
PL r dC (r) b dr. !y "r # L L C (r) dr 2
(44)
A simpler form of Eq. (44) is obtained by writing the circulation as C (r )"2pr v , so that, in terms of L L F measured quantities,
Fig. 38. Comparison of maximum vortex circulation from vortex-lattice theory and the axisymmetric model for the measured velocities; B-747 (303, 303) con"guration with gear stowed; Corsiglia et al. [95].
b PL d(rv ) F. !y "r # L L 2 v F
(45)
Application of both the basic- and inverse-Betz methods will be presented in a section to follow on experimental veri"cation.
546
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
5.9. Region of applicability The simplicity of both the direct- and the inverserollup methods results from the assumptions that the vortex is completely rolled up, and that the rollup process is inviscid and orderly. These two assumptions then limit the downstream interval over which the theories apply. The upstream end of the region of applicability begins where the rollup of the vortex sheet is largely completed, and can be estimated by use of inviscid, timedependent rollup calculations. Results such as those presented in Figs. 18 and 33 for the numerical estimates of the time required for a major part of the rollup process to be completed indicate that a major part of the rollup process behind many wings can be considered as practically complete within three to "ve span lengths behind the generating wing. The e!ect of viscosity and turbulence on the core of the vortex has recently been added as another extension of the Betz method [150]. Their method appears to be able to account for some of the di!erences between the basic Betz method and experiment in the core region of the vortices. The downstream end of the region of applicability is the distance at which viscous and turbulent decay of the vortex has modi"ed its structure to the extent that the inviscid theory no longer approximates it. An estimate for this limit can be obtained from the data of Ci!one and Orlo! [91] wherein a so-called plateau region is identi"ed (Fig. 2). Within this plateau region, they found that the vortex maximum swirl velocity decays very little, but is followed by a region where the vortex decays roughly as t\ . Based on these considerations, the region of applicability of the Betz method lies between about three span lengths and the downstream end of the plateau region for simple span-load distributions. If the span loading is complicated enough that multiple vortex pairs are shed, and that persist into the far "eld, the Betz methods do not, of course, apply with a great deal of accuracy.
6. Design of non-hazardous vortex wakes 6.1. Introduction It was reasoned that, since Betz' method [140] made a direct theoretical relationship between the span loading on the wake and the vortex wake that it sheds, it may be possible to design the span loading, so that the vortex wake of the wing is non-hazardous. In such an endeavor, it is assumed that a span loading will produce a vortex con"guration that is non-hazardous, and that is stable to three-dimensional disturbances even though it is derived by use of a two-dimensional/Tre!tz-plane method. A di$culty then arises in that the de"nition of a nonhazardous wake is not a straight-forward process.
Since clearly de"ned guidelines were not available nor identi"ed, it was assumed that the span loading should be such that the vortex wake that it sheds should simply not roll up, but maintain its shape until some outside disturbance causes the wake organization to be disrupted and possibly to decompose and decay quickly [151]. 6.2. Hypothetical non-hazardous wake conxgurations Two wake con"gurations were designed by use of the non-rollup criterion [151]. The "rst vortex wake design was produced by specifying that the initial vortex system shed by each wingtip should rotate as a solid body or sheet (Fig. 39a). The resulting span loading is very similar to those designed by Jones [152] to have a minimum induced drag for a given span and wing-root bending moment. In fact, Jones' designs initially rotate more closely to a solid sheet than the design selected here, but both rotational motions break down rather quickly due to in#uence of the rest of the wake, and due to the plane of the rotating sheets moving out of the original design plane. Since the span loading was tailored to produce a vortex wake with certain characteristics, any span loading of this type is referred as `tailored loadinga. The second hypothetical wake-vortex con"guration [151], designed by the foregoing method, assumed that all of the vortex elements would translate downward at the same velocity (Fig. 39b). At "rst, it seemed that the resulting span loading should be elliptic. Further consideration indicated that the vortex sheet shed by elliptic loading does move downward at the same velocity everywhere except for the two wingtip vortices, which move upward to start the rollup process. Therefore, another solution is found for the case where all vortices (including the ones at the wingtips) translate downward at the same velocity. When the matrix for the vortex strengths is inverted, it is found that the wake consists of vortices whose strengths alternate in sign, and whose magnitudes oscillate about elliptic loading (Fig. 39b). The span loading that sheds a vortex wake that translates downward as a unit then consists of a square-shaped sawtooth superimposed on top of an elliptically-shaped loading (Fig. 39b). If a large number of point vortices is used to represent the wake, the oscillations in magnitude are smaller than if a small number of vortices is used, but the oscillations appear to persist inde"nitely. Any span loading with large spanwise oscillations in its loading is referred to as `sawtooth loadinga. 6.2.1. Tailored loading The time-dependent characteristics of the foregoing two wakes were "rst studied by approximating the three-dimensional dynamic problem with the two-dimensional time-dependent motion of point-vortices in the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
547
Fig. 39. Two span-load distributions designed so that their vortex wakes do not roll up in the conventional sense but stay in approximately the same shape as when shed [151]. (a) Tailored loading. (b) Sawtooth loading.
Tre!tz plane [133]. It is assumed that the wake is initially a #at sheet as it leaves the trailing edge of the wing. The time-dependent motions of the vortices are then assumed to move as if they are in a two-dimensional system where small-scale three-dimensional distortions in the vortex con"gurations are suppressed. In order to provide an illustration of the method with a familiar span loading, the technique is presented in Fig. 40 for elliptic span loading, which may be considered an extension of the
results presented in Fig. 33. The shapes of the vortex lines are determined by connecting the locations of the vortices at each time step wherein time and distance behind the wake-generating wing are assumed to be equivalent, as the Tre!tz plane moves downstream with the free-stream velocity. It is noted in Fig. 40 that the wake rolls up from the wingtips inboard to form a pair of counter-rotating vortices typical of most wings that have conventional span loadings.
Fig. 40. Point-vortex simulation in Tre!tz plane of wake structure by elliptically loaded wing [151]. (a) Span load and vortex velocity distributions. (b) Wake structure.
548
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Since the strengths of the point vortices used to represent the rotating array are all of the same sign, a span loading for a wing is designed by use of an array for each wingtip (Fig. 41a). The space allowed between the two arrays is arbitrary and allows a uniform loading over the center part of the wing where the fuselage is located. The ratio of the parts of the wing designed to rotate to the total span of the wing is considered as the amount tailored. For example, the span loading Fig. 41a is tailored over 0.9 or 90% of its span, thereby making it approximately triangular. Since the arrays were designed to rotate when they were isolated from the rest of the wing, the calculations were carried out to obtain a more realistic estimate for the wake dynamics that might occur in an experiment. The initial downward velocity of the vortex arrays that represent the vortex wake are also shown in Fig. 41a. As shown in Fig. 41b, the rotation of the two vortex sheets persists in its idealized form for a rotation of about 903 before the sheets break up into parts that rollup separately. If the initial conditions for pure rotation are disturbed by displacing a point vortex in the vertical direction, the orderly part of the rotation is a!ected sooner, but the wake structure at later times does not appear qualitatively to be much di!erent from that shown in Fig. 41b. If the gap between the two rotating arrays is increased from 10% of the span to a larger value, the arrays rotate more independently; however, the vorticity is then spread over a smaller part of the span, resulting in a concentration of shed vorticity and a more intense wake. Note in Fig. 41a that the centerline circulation of tailored loadings must be increased above that required for an elliptically loaded wing of the same span in order to have the two wings carry the same lift. Any such increase adds to the hazard posed by the wake
which must also be overcome by any alleviation developed by the tailored design. If the number of point vortices used to represent the rotating array is allowed to increase inde"nitely, the circulation distribution in the wake becomes continuous and is given by dC(y) 4C c(y)"! "$ [1!(2y/b)] , dy pb
(46a)
where C is the centerline circulation required for a given lift. The bound circulation in the wing is then C C(y)"C(!b/2)#$ (2y/b)[1!(2y/b)] p ;sin\(2y/b)#p/2].
(46b)
By use of the extended-Betz method, the radius in the vortex where a sheet segment is deposited is given by 2r/b">!2C [(1!>) !1]/[3p[C(>)!C(0)]], (46c) where >"4[y]/b¹ , and ¹ is the fraction of the wing that is tailored. The circulation C (r) contained in the vortex at radius r is then C (r)"2C (y) (46d) because the vortex sheet rolls up about its center rather than from an end [151]. The center of a vortex on each side of the wing is located at the centroid of the circulation in the tailored loading on the wing which is at the center of each rotating sheet. The circumferential velocity in the vortices is again given by v "C (r)/2pr. F
Fig. 41. Span loading tailored so that vortex wake shed by each wingtip rotates as a rigid sheet [151]; corresponds to span loading for minimum wing-root bending moments [152]. (a) Span load and vortex velocity distributions. (b) Wake structure.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
In an e!ort to obtain an estimate for how accurately Betz's extended method predicts the rollup of the wake, a comparison is made of the circulation distributions in various vortices. For reference, the Betz distributions for rectangular and elliptic loadings are presented as dashed lines in Fig. 42. The circulation distribution in the rolledup vortex for 90% tailored loading as predicted by the extended-Betz method is shown as a solid line (Eqs. (46a)}(46d)). The stepped curve for the radial distribution of circulation as predicted by the Tre!tz-plane simulation at the dimensionless time equal to 3, was determined from the numerical data by increasing the circulation from zero at the centroid as each point vortex is passed while the radius increases. The radial distance of each point vortex from the centroid of circulation is used as the abscissa at which the circulation takes a stepwise increase. The Tre!tz-plane and extended-Betz methods are noted to be in good agreement; no doubt, somewhat because the span loading is not complicated. 6.2.2. Sawtooth loading The point vortices in a vortex wake that has been designed to translate downward as a unit, alternate in sign across the span (Fig. 43). If the circulation in the vortices across the span are added together, they sum to zero circulation. A single array can therefore be used to represent the entire wake of a lifting wing. When the vortex distribution is integrated across the span to determine the bound circulation (or span loading) on the wing, the discontinuous or stepped curve shown in Fig. 43a is obtained. Such a loading could be interpreted as an approximation to the loading achieved by de#ecting
549
Fig. 42. Radial distribution of circulation in wake vortices shed by 90% tailored loading as predicted by time-depending Tre!tz-plane method and by extended-Betz rollup theory [151].
a large number of #aps upward and downward across the span of the wing. As expected, the speci"ed downward motion of the vortices in the array is achieved when the time-dependent calculations are carried out, i.e., the "rst part of Fig. 43b. If, however, the initial condition of one or more of the vortices is disturbed (e.g., by displacing the "fth vortex vertically a small amount), the speci"ed motion breaks down quickly into the chaotic motion shown in the latter part of Fig. 43b. The unequal strengths of the vortices cause the various pairs of vortices in the wake to orbit in a seemingly random motion to promote mixing in the
Fig. 43. Span loading designed so that vortex wake shed by each wingtip initially moves downward as a rigid sheet [151]. (a) Span load and vortex velocity distributions. (b) Wake structure.
550
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
wake on a large scale. Mixing of this kind suggests rapid dispersion of the circulation throughout the wake so that the entire wake would tend to be neutralized quickly in a real #uid. It was also found that smaller amounts of sawtooth loading could be added to conventional loadings to also theoretically induce large mixing motions of vortices in the wake. The foregoing idealized concepts served as a basis for the experimental program by suggesting span loadings for vortex wakes that were either less hazardous at the outset or that would become less hazardous more quickly than conventional designs. The next section will discuss some experimental results designed to test some of the conceptual relationships identi"ed between span loading on the wing and the vortex wake that it sheds. 6.3. Experimental verixcation In 1972, the wake-vortex research program began conducting wake-vortex experiments in wind tunnels [10,60}63,87,88,95,96,153,154], in water tow tanks [61,89}93,96,102,155}158] and in #ight [4,11}21,44}48, 50,55,58,59,119,159,160]. The material to be presented in this section is devoted to experiments designed to investigate tailored and sawtooth type span loadings [58}61,90}93,95,112,125,159,160] to determine their effectiveness for the reduction of the hazard posed by vortex wakes. 6.3.1. Ground-based experiments Wind tunnel tests in the 40;80 ft (12.2 m;24.4 m) Wind Tunnel at NASA Ames were carried out to study the characteristics of vortex wakes shed by lifting wings of conventional and of special design [10]. The test setups used to measure the velocity distribution in the vortex, and to measure the rolling moment on a following wing are illustrated in Figs. 44a and b. Both experimental setups generated the vortex wake to be studied by use of a swept wing whose planform was typical of those used on subsonic transports and that had seven #aps on each side of the centerline which could be adjusted in 53 increments (Fig. 45). The large number of #aps allowed the span loading on the wing to be changed from a cruise condition, when all of the #aps are in a stowed, or non-de#ected, position, to those typical of landing, parabolic, and the two unconventional ones described previously and labeled tailored and sawtooth loadings; see table in Fig. 45. The span loadings estimated by means of vortex-lattice theory [139] for the various wing con"gurations at an angle of attack of 83 are presented in Fig. 46. The symbols denote points calculated by the vortex-lattice method. At a distance of 80 ft (24.4 m) downstream of the wakegenerating wing, either a hot-"lm apparatus (Fig. 44a, inset) or a following wing (Fig. 44b, inset) was mounted on a tower that could be positioned horizontally over
a 14 ft (4.27 m) range. In addition, the follower wing could be positioned vertically over a 10 ft (3 m) range. The only encounter direction studied with the setup shown in Fig. 44b was an axial penetration by the following wing set at zero incidence. Most of the tests were conducted at a free-stream velocity of ; "131 ft/s (40 m/s), (q "20.1 lb/ft) corresponding to a Reynolds number of 843,000 based on average wing chord. Several di!erent values of free-stream velocity were used during the rolling-moment tests to obtain moments of a magnitude such that the optimum sensitivity of the balance could be used. 6.3.2. Swirl velocity As shown in Fig. 44a, the hot-wire probe is mounted at the end of a rotating arm of about 7.34 ft (2.24 m) that rotated at 120 rpm, which was rapid enough, so that, in the wind tunnel, the circumferential velocity of the probe dominated the meander velocity of the vortex. Vortex meander comes about because the free-stream velocity in the wind tunnel is not perfectly uniform, since it contains turbulent eddies of di!erent sizes [161,162]. In the 40;80 ft Wind Tunnel, the vortex meanders over a circle of about 2 in (5 cm) radius at a distance of 80 ft (24.4 m) behind the wake-generating wing (Fig. 47). As a consequence, local lateral velocities in the eddies convect the wake vortices sideways and vertically thereby generating a sinuous shape to the centerline of each of the vortices. Therefore, as the vortex lines are swept downstream by the free-stream velocity, the location of the vortices at a given downstream station meanders randomly about its time-averaged location (Fig. 47). If a stationary probe is located near the center of the meander region, the instantaneous measurement changes from a maximum to zero swirl velocity in a fraction of a second due to the meander of the vortex. An air jet used to calibrate the hot-wire probe is located at the bottom of the arc of the rotating arm, so that a calibration signal is generated on each revolution. It was found that the instrumentation was di$cult to keep properly tuned and the measurements required extensive data reduction techniques [10]. It was concluded that the rotating-arm technique is an e!ective but clumsy method for measuring the instantaneous structure of vortex wakes. The test procedure consisted of moving the tower that supports the rotor arm assembly across the wind tunnel until, as noted on a paper-chart recorder, a maximum occurred in the number of times that the hot-wire probe had encounters with the vortex per unit time. A permanent record of 5 min duration was then made on magnetic tape and paper chart. The data runs for analysis were taken from the magnetic tape, so that the record could be ampli"ed enough to obtain 3}4 signi"cant "gures of accuracy. Five records out of the large number taken during the 5 min were then chosen for analysis on the basis of how close to a vortex
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
551
Fig. 44. Experimental setups in 40;80 ft Wind Tunnel used to make measurements in vortex wake of swept wing model [10]. (a) Three components of velocity. (b) Rolling moment.
center that the hot-wire probe had passed. After the three components of velocity had been determined for the various runs, the motion of the hot-wire probe and the velocity of the vortex center relative to the wind tunnel coordinate system were removed from the hot-wire measurements in order to arrive at a
corrected measurement of the structure of the vortex wake. Since both processes could only be done approximately, the accuracy of the measurements was limited. In order to develop a vortex structure usable for analysis in the various Betz methods, it was also necessary to
552
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 45. Plan view of swept wing used to generate vortex wakes along with #ap settings for various con"gurations [10].
Fig. 46. Span-load distributions on various con"gurations of swept-wing model as predicted by vortex-lattice method [10]; a "83.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 47. Illustration of vortex meander at a given downstream station.
remove the in#uence of the opposite vortex in the pair, whose location is uncertain. Fig. 48 presents the "nal structure of a typical measurement along a curved path that had passed through or near a vortex center. The velocity "eld of the opposite vortex in the pair has been removed, so that the curves shown in Fig. 48 represent the structure of an isolated vortex. It is noted that the measured streamwise component of the velocity di!ers from the free-stream velocity only in the vortex core region and then, by less than 10%. Five such sets of data from "ve di!erent passes of the rotor arm through the vortex wake of the con"guration being tested were then averaged to obtain a representative velocity distribution for the vortex trailed by a particular con"guration of the wake-generating wing (Fig. 49). The data for the various con"gurations has been normalized (divided) by the free-stream velocity and the measured lift coe$cient on the generating wing to remove lift as a variable in the comparisons. It is noted in Fig. 49 that the maximum circumferential velocity, and the radius at which it occurs (i.e., the core radius of the vortex) are di!erent between the various con"gurations tested. As expected, the vortex with the largest core was produced by the swept wing with the #aps de#ected to produce a type of tailored loading. An averaged curve for the swirl velocity shed by the sawtooth loading is not presented, because each pass of the hot-wire probe through the wake yielded a di!erent velocity pro"le with several possible vortex centers. It is believed that the wake consisted of about seven vortex pairs so that a pro"le for the swirl velocity could not be correctly represented by a single vortex pair. Since the data in Fig. 49 for the swirl velocity has had the contribution of the companion vortex removed, the
553
Fig. 48. Example of variation of radial and circumferential velocity components with radius [10]; wing planform tailored 40%, a "123, C "0.85. *
results can be compared with estimates of vortex structure obtained by use of the basic-Betz rollup theory and the computed vortex-lattice solutions obtained for the span loading on the wake-generating wings from Fig. 46. When the measured and Betz-predicted circumferential velocity distributions are compared, the agreement is quite good in the outer parts of the vortex (Fig. 50). The di!erences that often occur near the vortex center are attributed to the choice of how the vortex sheet shed by the wing was assumed to roll up. If a di!erent rollup sequence had been assumed, the agreement could sometimes be improved. For example, in the case of the landing con"guration, the theory should assume that two vortices instead of one formed initially. Two vortices did form near the wing, but the #ow visualization with smoke indicated that these two merged before they reached the measuring station in the wind tunnel. The Betz theory used to predict the vortex structure in Fig. 50 does not account for vortex merging. Also, the method does not account for the boundary layer on the wing that enters the core region near the center of the vortex. The comparison indicates that the direct-rollup theory is adequate for many purposes, because the predictions are quite accurate for the outer part of the vortex, even though they are not always reliable near the center. 6.3.3. Span loading The span loadings predicted by vortex-lattice theory are compared in Fig. 51 with those predicted by the inverse-Betz theory using the measured swirl-velocity distributions. These comparisons were made by adjusting the span loading calculated by the vortex-lattice theory, so that the area under span loading curve is the same as that predicted by the inverse-Betz method. The results
554
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 49. Radial distribution of circumferential velocity as measured in wind tunnel for various con"gurations [10].
Fig. 50. Comparison of measured circumferential velocity in vortices with that predicted by the direct-Betz rollup method [10] using theoretical span-loadings presented in Fig. 46.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
555
Fig. 51. Comparison of span loading predicted by vortex-lattice theory with that predicted by the inverse-rollup theory [10] using measured vortex structures in Fig. 49.
in Fig. 51 show that the inverse theory can recover the span loading on the generating wing fairly accurately. With almost all con"gurations, a di!erence occurs near the wing tip as a result of the "nite core size of the vortex and the solid-body type rotation near r"0 due to the boundary layer on the wing. The magnitude of the distortion in span loading depends on the size of the core, which is in#uenced by the character of the boundary layer on the wing and on the viscous and turbulent shear forces in the vortex itself. In most cases, these distortions appear to be small and to occur largely in the vicinity of the wing tip. The agreement between theory and experiment found for the inverse-Betz method is better, in some cases, than for the direct-Betz method. It is believed that this is caused by the di!erence in the integration process, which tends to suppress inaccuracies for small radii for the inverse-Betz, and to amplify them in the direct-Betz. This di!erence occurs because the integral for the inverse-Betz method, Eq. (45), contains the radius in the numerator, which tends to suppress inaccuracies near the center of the vortex. The equation used for the direct-Betz method, however, Eq. (40), has small values of radius (or C (y)) in the vicinity of the wingtip or vortex center. Therefore, in the direct-Betz, inaccuracies are suppressed at large radii. Examination of the #ow visualization results obtained in the wake shed by a wing designed for sawtooth span loading indicates that the same instability and vortex linking occurs there also. The wake dynamics was most apparent in experiments conducted by Ci!one [91}93] in a water tow tank with a generic wing of 2 ft (61 cm) span with seven #ap segments on each side, i.e., a scaled down version of the wing used in the wind tunnel (Fig. 45). In one case, the #aps were de#ected alternately up and down across the span in order to generate sawtooth loading. It was found that, shortly behind the wing, the vortices formed pairs that executed large across-stream
excursions that "nally led to linking and loop formation, much like some of those shown in Fig. 43b. When a wing with the same shape was tested in the 40;80 ft Wind Tunnel, it was found that the torque on a following wing was much reduced until the lift on the wing became large enough to dominate all of the subvortices from the de#ected #aps. These results indicate that large #ap de#ections are required for large amounts of alleviation at lift coe$cients of interest for landing and takeo!. Hence, such an alleviation scheme becomes unwieldy and ine$cient if the landing #aps are not used judiciously to generate the vortices of opposite sign. When the vortex pairs are of comparable strength, they interact to bring about large excursions and loop formation between vortices so that wake vorticity is quickly dispersed. However, when the angle of attack of the wing is increased to the point where the wing-tip vortex becomes dominant, wake organization is restored causing alleviation to be diminished. It remains therefore, to develop guidelines for the design of lifting surfaces that produce highly dispersive multiple vortex wakes. The penalties associated with these designs can then be evaluated to determine the practicality of such an alleviation scheme. 6.3.4. Measured rolling moment Rolling moment measurements were made with the experimental setup (Fig. 44b) and the wake-generating wing (Fig. 45). As shown in Fig. 44b, the test-section length is su$ciently long to allow separation distances between generator and follower up to about 80 ft (24.4 m). The generator wing is mounted through a strain-gage balance to a "xed strut in order to measure the lift and drag exerted on it by the free stream. The following wing is also mounted onto a strut through a strain-gage balance to measure the rolling moment induced on it by the vortex wake of the leading wing. The strut could be raised and lowered, and moved laterally, to "nd the
556
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
location where the rolling moment was a maximum. The following wings were made of balsa wood to ensure a high-frequency response to the imposed torques of the meandering vortices. The analog signal from the straingage balance was "ltered with a low-pass "lter at 10 Hz to suppress unwanted electrical noise that occurs at higher frequencies. The three wings used as the follower model all had the same chord length, but a di!erent span in order to study the e!ect of the ratio of the span of the follower wing to that of the generator. The procedure for recording a data point started by "rst setting the #aps on the wake-generating wing at the angles desired for the con"guration, and then setting the angle of attack of the wing itself. The vertical and lateral locations of the follower wing were then set, and the wind tunnel conditions established. Since the wind tunnel airstream contains turbulence, the vortex moves about (meanders) causing the rolling moment induced on the following wing to change with time. This time-varying signal was recorded on a light-beam, strip-chart recorder. It was found that a data record of 1 min duration was su$cient to obtain a record wherein a maximum rolling moment for that location occurred at least three times. The procedure was then repeated at successive lateral and vertical positions of the follower wing (at 2}4 in increments) to determine the maximum value of the rolling moment for the entire wake for each test condition and each con"guration. (The nature of the vortex meander was such that the time-averaged rolling moments would be too facility dependent to be of much value, and therefore they were not recorded.) It was reasoned that the maximum &instantaneous' rolling moments would also represent the maximum rolling moment during a sustained vortex encounter. The measured maximum rolling moments on the following wing were converted to coe$cient form through the equation rolling-moment C " , (47) J q Sb where S and b are respectively the planform area and span of the following wing. After the measurements were obtained for the various wing con"gurations, the rolling moment data were plotted as C /C to better compare the various con"guraJ * tions at the same lift (Fig. 52). Such a parameter would theoretically not change with angle of attack if the span loading did not change. However, the #ap settings used in the present test cause some changes in the span loading when the angle of attack changes. As a consequence, the data in Fig. 52 are, in most cases, a function of C . It will be noted that, for comparison purposes, * a con"guration of the generating wing with wingtip spoilers was also tested (Fig. 52). The three parts of Fig. 52 include the e!ect of span ratio b /b on the wake-induced rolling moments. An expected decrease in
Fig. 52. Rolling-moment parameter as a function of lift on a swept-wing generator for various con"gurations [10].
maximum rolling moment with increasing span of the follower wing is not clearly apparent. Also, for the smallest following wing, it was found that sawtooth loading or the addition of a spoiler to the #ap 03 con"guration were both more e!ective than tailoring the wing. Note that aircraft typically have the capability to create a rolling-moment coe$cient of about 0.04}0.06 by use of ailerons. Hence, any imposed torque by a vortex that causes C to exceed about 0.06 will cause the encounterJ ing aircraft to roll even when full counter-roll control is imposed. When the smallest following wing is immersed in the wake of the swept wing con"gured to develop sawtooth loading (Fig. 52a), the generation of multiple vortices in the wake appears to be quite e!ective for reducing the rolling moment at low lift coe$cients. However, a large part of the e!ectiveness disappears as the lift increases above C "0.4, for the #ap settings used in the *
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
experiment. Some alleviation was achieved on the larger follower (b /b "0.29) with sawtooth loading, but not to the extent realized with the smallest following wing. A 2 ft (61 cm) span version of the swept wing was tested by Ci!one and Orlo! [91] by towing the wing through a water tank. Their test showed that the vortices shed by the sawtooth loading at C "0.7 undergo large excur* sions in the wake which are on the order of one-half of the span of the generating wing, and very similar to the excursions predicted in Fig. 43. In the water tow tank tests, the vortex pairs appeared to cause destructive interactions that tended to disperse the wake vorticity rapidly enough to substantially reduce the wake hazard at low angles of attack. At higher angles of attack, the overall lift on the wing seems to dominate the less intense vortices shed by the various #aps, so that vortex excursions are suppressed and a fairly strong single vortex pair then persists in the wake indicating that the vorticity shed by the generating wing is not being dispersed to the desired large amount. 6.3.5. Predicted rolling moment The methods used to predict the rolling moment induced on a wing as it encounters a wake are restricted here to penetrations that are parallel to the axis of the vortex (Fig. 53). The axial velocity in the vortex is assumed to be the same as the free-stream velocity. It is also assumed that the vortex encountered is straight, and that
557
the #uid is incompressible and inviscid. In the cases considered here, the up- and down-wash velocity distributions on the following wing are set equal to the measured circumferential or swirl velocity in the vortex wake (Fig. 49). In order to account for both vortices in a pair, the contributions of the port and starboard vortices are added. Even with these restrictions on the problem, it was not straighforward as to how to proceed with a computation. As background, when the test was conducted in the early 1970s, very little experience was available on the reliability of computational methods for estimating the loads induced on a wing when it encounters a vortex wake. At that time, emphasis was placed on the reliability of simple and quick methods that could be used in #ight simulators to study the #ight dynamics of aircraft as they encounter vortex wakes. Therefore, the analysis of torque or rolling moment on an encountering wing was restricted to the following methods [10]: 1. Two-dimensional strip theory. 2. Strip-theory with empirical lift-curve slope correction. 3. Vortex-lattice theory; #at-wing and #at-wake approximation. The two-dimensional strip theory assumes that the lift on each spanwise element is given by its two-dimensional value, or l(y)"C q c(y)sin a(y), *?
Fig. 53. Theoretical model used to analyze vortex impinging on following wing [10].
(48)
558
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
where C is the two-dimensional lift-curve slope of the *? airfoil section at that spanwise station, sin a(y)+w/; is the #ow inclination relative to the airfoil section at the spanwise station, and c(y) is the local chord of the wing. When the quantity yl(y) is integrated across the span of the wing, the rolling-moment coe$cient becomes
C @ C " *? (w/; )y dy. (49) J b \@ The values presented in Table 5 were found by numerically integrating Eq. (49) after setting w/; equal to the sum of the measured v /; contributions from the port F and starboard vortices. For two-dimensional wings, the lift-curve slope, C , is *? often taken as 2p. As noted in Table 5, the predictions made with Eq. (48) are then generally too large because the local angle of attack at each wing element does not account for the induced angles of attack caused by the vortex wake shed by the following wing as it experiences the #ow "eld of the vortex. A correction for this e!ect can be obtained by adjusting the lift-curve slope for the encountering wing by means of a formula introduced by Jones [137] and a modi"cation to it by Maskew [138]. The formula derived by Jones for wings of general planform is 2p AR , C " *? P AR#2
(50)
where AR is the aspect ratio and P" (semi-perimeter/span) of the wing. Maskew [138] reasoned that the spanwise station on the wing where the vertical velocity vanishes serves the #ow "eld in the same way as a wingtip. The following wing is therefore divided into separate spanwise segments for the computation of the
lift-curve slope by the use of Eq. (50). The strip-theory results presented in Table 5 were obtained by use of the Maskew adjustment to the Jones formula, and were found to be in good agreement with rolling moments calculated by use of vortex-lattice theory for the same upand down-wash distributions. The study showed that such an approximation provides much more realistic lift-curve slopes for the wing when it encounters a vortex wake than the straight two-dimensional strip theory. Comparison of the values calculated by use of the modi"ed strip theory with an empirically adjusted lift-curve slope are noted in Table 5 to be in good agreement with the vortex-lattice theory, which are also in good agreement with the experimental results. The di!erences in Table 5 between the vortex-lattice theory and experiment may be due to any of the following reasons: the way that the measurements of rolling moments were made; di!erences in the vortex velocity data; a combination of both; or unsteady aspects of the wind-tunnel measurements which were assumed negligible. Nevertheless, the foregoing results indicate that either the vortex-lattice theory or the simple strip theory with the lift-curve slope, C , determined by the *? Jones}Maskew formula provides reasonable estimates for the rolling moment induced by a vortex on a wing penetrating a vortex wake of another aircraft. The fairly good agreement between the predicted and measured values in Table 5 also suggests that the steady-state approximation is probably satisfactory for near-axial penetrations of the vortex wake. As experimental equipment and procedures improved, the ability to predict loads induced on wings that encounter vortex wakes was studied further [163]. By use of the empirically adjusted strip theory, the rolling moment and lift induced on a wing were
Table 5 Comparison of predicted and measured rolling-moment coe$cients [10] Con"guration
a
C *
b /b
R
Normalized rolling moment, C /C J * Strip theory
Vortex-lattice theory
Measured
C ?"2p *
Empirical C ? *
Flat-wake approximation
Flaps 0H Flaps 0H plus spoiler Landing Landing plus spoiler Tailored
8H 8H 6H 8H 10H
0.75 0.70 0.85 0.86 0.82
0.29 * * * *
5.84 * * * *
0.092 0.053 0.081 0.081 0.105
0.222 0.184 0.243 0.163 0.246
0.110 0.091 0.120 0.081 0.122
0.109 0.085 0.117 0.071 0.111
Flaps 0H Flaps 0H plus spoiler Tailored
8H 8H 10H
0.75 0.70 0.82
0.14 * *
2.82 * *
0.099 0.023 0.074
0.317 0.154 0.173
0.101 0.049 0.055
0.090 0.038 0.042
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
calculated at a large number of points in the wake. From these points, contours of equal rolling-moment and lift coe$cient were drawn (Fig. 54) for one vortex pair when the ratio of the span of the following wing to that of the wake-generating wing, b /b is 0.29. Only one quadrant is presented because the #ow "eld is symmetrical vertically and anti-symmetrical about the wake centerplane. Although the contours are not as precise as if determined by vortex-lattice theory, they do indicate the nature of the area over which high values of rolling moment occur. As expected, the maximum rolling moment occurs when the encountering wing is centered on the vortex. The area in Fig. 54a inside the contour labeled 0.06 is the region where overpowering rolling moments are to be experienced. Similarly, the results in Fig. 54 indicate that large values of positive and negative lift are induced on the following wing by the vortex wake depending on its location relative to the vortex pair. As expected, the shape of the curves of constant torque and lift change with both the vortex structure and with the span of the following wing. 6.4. Application of sawtooth loading to aircraft 6.4.1. Ground-based tests About the same time that the foregoing preliminary experiments were being carried out, the NASA spaceshuttle program purchased a surplus Boeing 747 subsonic transport aircraft. The ultimate use of the aircraft was to carry the space shuttle from Dryden Flight Research Center, where the space shuttles were expected to land, to Kennedy Space Center where the space shuttles were expected to be launched. Since space-shuttle operations had not yet started, the aircraft was assigned to the wake-vortex program for use in #ight tests. In order to obtain wake data on the B-747, several 0.03 scale models
559
were built for use in ground-based tests at Langley and Ames Research Centers and at the Hydronautics Inc. water tow-tank facility. The standard landing con"guration was "rst tested in the various ground-based facilities to establish a reference hazard against which alleviated con"gurations could be compared, and to establish the kind of agreement to be expected [164]. Since the aircraft had an on-board capability to independently deploy either the inboard or outboard #aps separately, three con"gurations were chosen for consideration during the test program; namely, the standard landing con"guration with all #aps fully deployed (i.e., the (303, 303) con"guration), and two modi"ed-landing con"gurations. One modi"ed landing con"guration had the inboard #aps fully deployed and the outboard #aps stowed (i.e., the (303, 03) con"guration). The third con"guration had the opposite #ap schedule (i.e., the (03, 303) con"guration). Only those #ap settings were chosen, because the ground-based experiments described in the previous section indicated that the tailored-loading concept would not provide the magnitude of alleviation required. Results obtained for wings with sawtooth loading, however, indicated that the concept should be explored [10]. At that time, the computations and some water tow-tank experiments by Ci!one and Orlo! [91,92], and some wind tunnel experiments published later [61,96] indicated that the alleviation mechanism instigated by sawtooth loading was brought about by the large excursions made by vortex pairs that usually ended in a linking of the vortex cores across the pair, i.e., large self-induced across-stream vortex excursions. Uncertainty existed then (and still exists now), however, as to the number of vortex pairs, and the magnitude of vortex strengths required to produce the large-scale mixing, and subsequent wake alleviation needed to decrease in-trail spacings by the amount desired.
Fig. 54. Contours of equal rolling moment and lift induced on a following wing by wake of swept wing with tailored loading [10]; b /b "0.29. (a) Rolling-moment parameter, C /C ; C /C "0.122. (b) Lift parameter, C /C ; C /C "!0.88. J * J * * * * *
560
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
With the foregoing information as background, a decision was made to test the conventional con"guration, and the two sawtooth options that were available by deploying either the inboard or the outboard #aps separately while leaving the other #ap stowed. Since no other span loading options were apparent at the time, the choice was somewhat obvious. The various con"gurations to be tested were designated the conventional landing or #aps (303, 303) con"guration, the modi"ed landing or (303, 03) con"guration, and the (03, 303) con"guration. The span-load distributions estimated for the various con"gurations by use of vortex-lattice theory [60,139] are presented in Fig. 55. It is to be noted that the variations in the span-load distributions achieved by independent #ap de#ections are a substantial portion of the entire lift. Tests with separate B-747 models began in the 40;80 ft Wind Tunnel and in the Hydronautics Water Tow Tank facility at about the same time [60,61]. Somewhat later, tests were also conducted in an air-tow facility (i.e., Vortex Research Facility [66,67,156,164] and in the 14;22 ft (4.42;6.63 m) Wind Tunnel which are both located at Langley Research Center [62,63]. In the water tow tank, the turbulence in the free stream is very near zero at the beginning of a run, and the model is mounted right-side up with a strut attached to the top of the model fuselage. In the 40;80 ft Wind Tunnel, the turbulence level in the free stream is about 0.5%, and the model was at "rst also mounted right-side up. The rightside up mounting of the model in the wind tunnel required that the strut be attached to the bottom of the fuselage so that the vortex wake of the model would mix with the wake of the mounting strut. As a consequence, the "rst results in the wind tunnel for the modi"ed landing or (303, 03) con"guration, were inconsistent. That is, during a given run, the wake-induced rolling moment on a following wing would jump from a level just below that produced by the conventional landing con"guration (i.e., a small amount of alleviation) down to a low level near the one measured in the water tow tank (i.e., a large amount of alleviation), thereby indicating two curves for the same con"guration. It was later discovered in some #ight tests that the reason for the #uctuating rollingmoment results was caused by the in#uence of the mounting strut on the wake-vortex structure. The mechanism by which the viscous wake of the mounting strut in#uenced the vortex wake of the model was not discovered until later [61]. The remedy for the interference from the strut was, of course, to mount the wake-generating model upside down in the wind tunnel so that the vortex wake of the model moves upward away from the viscous wake of the strut holding the model (Fig. 56). As disconcerting as the #uctuating results were, they did provide guidance for the #ight tests. Since the mounting strut added turbulence to the vortex wake along its strut when the generating model is mounted
Fig. 55. Span loading on wing of B-747 model for various #ap settings as computed by vortex-lattice theory; Corsiglia et al. [61].
right-side up, and that resulted in inconsistent results, it was suggested to the #ight-test group that the "rst tests of the (303, 03) con"guration of the B-747 be carried out with all of the landing gear stowed, and with no yaw of the aircraft. After that, the same con"guration should be tested with landing gear extended. The #ight results were consistent with the wind tunnel results in that the alleviation of the (303, 03) con"guration was extensive when the landing gear were stowed, but not nearly as e!ective when any part or all of the landing gear was extended. The same was also true when the aircraft was #own at zero yaw and with yaw. The experiences with the two methods of mounting wake-vortex models in a wind tunnel led to the decision to mount wake-generating models only by use of a streamlined strut attached to the fuselage upper surface,
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
561
Fig. 56. Experimental setup in Ames 40;80 ft Wind Tunnel [61].
so that the model appears upside down in the wind tunnel. By use of the experimental setup shown in Fig. 56, the rolling moments imposed on the following two models are presented in Figs. 57 and 58 as a function of the lift coe$cient on the B-747 subsonic transport model. For conventional #ap con"gurations, the rolling moment on the following model increases nearly linearly with C up * to the beginning of stall on the generator. This result is expected, because, the shape of the span-load distribution is nearly independent of lift over the range of C tested, * and only the magnitude of the loading changes with angle of attack. Since the vortex structure depends directly on the span loading, only the total vortex strength changes with C thereby yielding a nearly linear rela* tionship between C and C . Note in Fig. 57 that the J * various curves for the conventional con"gurations lie on approximately the same line. This implies that there is no major change in the vortex structure (except for magnitude) among the conventional #ap con"gurations. It is noted in Fig. 57 that, at low angles of attack, the wake-induced rolling moments behind the (03, 303) con"guration are greater than those measured for the standard landing con"guration. Analysis of the span-load distribution for the (03, 303) con"guration indicates that such a result is to be expected, because the vortex shed by the wingtip, and by the outboard end of the outboard #ap, merge before the two #ap vortices can interact to create the large excursions that lead to dissipation through linking. Hence, when the two outboard vortices (i.e., wingtip and outboard #ap) merge early in the rollup process, their combined strength dominates the #ow "eld. The combined circulation brings about a stronger and more concentrated vortex than is shed by the standard landing con"guration at the same lift coe$cient. At
Fig. 57. Maximum rolling-moment coe$cients on following wings in wake of B-747 for various #ap settings as measured in 40;80 ft Wind Tunnel [60,61]; x /b "13.
higher angles of attack, the curve for the rolling moment turns over to make the con"guration more appealing. It is believed, however, that this outboard-loaded con"guration at the higher loadings began to stall thereby producing low energy #uid that migrates to the vortex core. The larger core diameter reduces C for following J models of small span. No further consideration was given to the (03, 303) con"guration, because it did not produce a signi"cant reduction in wake-induced rolling moment. In contrast, when the (303, 03) con"guration was tested upside down, so that the vortex and strut wakes did not mix [60,61], it produced a substantial reduction in the rolling moment on the smaller trailing wing (Fig. 58a)
562
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 58. Variation with lift coe$cient of measured maximum rolling-moment coe$cients on following wings in wake of B-747 for two #ap settings with landing gear stowed as measured in 40;80 ft Wind Tunnel [60,61]; x /b "13. (a) b /b "0.2, (b) b /b "0.5.
Fig. 59. Variation with downstream distance of measured maximum rolling-moment coe$cients on following wings in wake of B-747 for two #ap settings with landing gear stowed as measured in 40;80 ft Wind Tunnel, and in Hydronautics Inc. water-tow facility [60,61]. (a) b /b "0.2, (b) b /b "0.5.
and a modest reduction on the larger trailing wing (Fig. 58b). In Fig. 58a, the data from the water tow tank and the wind tunnel for the small following wing are not in good agreement, whereas the data are in good agreement in Fig. 58b for the large following wing. Consideration of the data presented in Fig. 59a indicates that the alleviation mechanism appears to require a di!erent amount of time to go to completion in the two facilities
[61]. That is, the water tow-tank data taken at 14 spans behind the wake-generating wing is seen to be in fair agreement with those measurements for the (303, 303) con"guration, but not for the (303, 03) con"guration. However, at 30 spans downstream and beyond, the water tow-tank data for C is 50% of the (303, 303) J con"guration, which is in agreement with the wind tunnel results.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
563
Fig. 60. Photographs of wake con"gurations shed by B-747 with its inboard #aps fully deployed and with outboard #aps stowed [61]. (a) Landing gear stowed. (b) Landing gear extended.
It is now believed that the time for the alleviation mechanism to be completed is longer in the water tow tank than it is the wind tunnel, because the free-stream turbulence level in the tow tank is near zero, whereas it is about 0.5% in the wind tunnel. It is now known that the alleviation is brought about by a sinusoidal mutually induced instability that involves the two vortices o! the ends of the inboard #ap which eventually go into a linking process between the two vortices (Fig. 60). Since the instability is non-linear, and requires a "nite disturbance to initiate it, wave growth is slow to start in the quiescent tow tank, but begins immediately in the more turbulent environment of the wind tunnel airstream, even with the landing gear extended. If some low energy #uid from the landing gear, or from a wind tunnel strut, is ingested by the vortex cores, the vortices become more rigid, and do not go into a mutually induced instability unless they are given a large input from free-stream turbulence. In quiescent conditions, like the early morning quiet atmosphere present at the time of the #ight tests, the disturbances present to initiate the sinusoisal instability are not strong enough to do so (Fig. 60b). 6.4.2. Flight tests The #ight tests were conducted shortly after sunrise under low wind conditions in an attempt to minimize
atmospheric variations between test days. The #ight experiments were made with the full-scale B-747 aircraft mentioned previously which could be #own with the #ap con"gurations discussed here, with or without the landing gear extended. Both a Lear Jet and a T-37B aircraft were used to probe the vortices of the generator. The span ratio of the smaller of the trailing wings used in the ground-based tests to the span of the B-747 model, are about the same as that of the two probe aircraft relative to the B-747 used in the #ight tests; namely, b /b "0.186. Since the probe aircraft were free to move about in response to the induced velocity "eld of a vortex wake, wake penetrations were often along a path that did not include a vortex center. The vortex encounter data was therefore random in character, and required an interpretation that was less straightforward than with windtunnel data. The #ight and data-interpretation procedures used during the #ight tests are described by Jacobsen and Short [159], Barber et al. [58], Jacobsen and Barber [160], and Smith [55]. Information in those papers will be summarized here in order to give the reader an understanding of the di$culties of the #ight tests and of the nature of the data obtained. A great deal of information on the aircraft used in the tests is contained in the various papers, along with other information on the tests, which will not be described here.
564
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Measurements of the upset, or rolling-moment response, during a wake encounter were made by both probe aircraft, and the measurements of the velocity pro"les through vortex wakes were made with the Lear Jet. The results obtained with the Lear Jet are reported by Barber et al. [58], Jacobsen and Short [159], and Jacobsen and Barber [160], and the T-37B results are reported by Smith [55]. The B-747 aircraft was equipped with smoke (or vaporize oil) generators on each wingtip, and near the outboard edges of both the inboard and outboard #aps, so that the lift-generated vortices would be visible for the pilots of the probe aircraft. When a second series of tests over Rosamond Dry Lake near Dryden Flight Research Center in California were conducted, smoke generators were added at the inboard ends of the inboard #aps. The B-747 aircraft was equipped with a modi"ed Distance-Measuring-Equipment (DME) unit to allow direct measurement of the range to the probe aircraft. The Lear Jet aircraft was instrumented to measure the aircraft motions, and its control surface de#ections. Air speed, altitude, and angles of attack and sideslip were measured by use of an instrumented boom on the nose of the aircraft. A three-component hot-wire anemometer was also mounted on the nose boom for measuring the velocities in the various wakes of the B-747. The data were recorded on magnetic tape on board the aircraft. The response measurements were recorded in digital form, while the hot-wire anemometer measurements were recorded in analog form because of their high-frequency content. More information on the aircraft and test procedures are presented in Barber et al. [58], Jacobsen and Short [159] and Jacobsen and Barber [160]. The #ight tests were conducted at an altitude of approximately 12,500 ft (3800 m) (or 10,000 ft above ground level) at indicated air speeds that ranged from 150 to 180 knots. The gross weight of the wake-generating aircraft ranged from 480,000 to 600,000 lb (217,000 to 272,000 kg), so that the lift coe$cients ranged from 1.0 to 1.4. The test procedure used to obtain measurements was carried out by having a probe aircraft enter the wake at a separation distance large enough to assure safety. While the pilot attempted to keep the aircraft at or near the center of a vortex, the distance behind the wakegenerating aircraft was decreased until judged by the pilot, or through assessment of the loads on the aircraft, to be too hazardous to continue. The resulting motions during the various penetrations were then analyzed to determine the rolling moments imposed on the aircraft. Since the severity of the encounter depends strongly on the location of the probe aircraft relative to the vortex, a large number of encounters was required to ensure that the maximum upsets possible were obtained. Once the data from the large number of upsets had been reduced, an upper bound (or envelope) to the data was constructed and assumed to represent the maximum upset that
a particular wake produces on the probe aircraft. Since the velocity of the probe aircraft was usually higher than that of the B-747, the measured responses were corrected to the velocity of the wake-generating aircraft. Since the response of the probe aircraft usually involved rotation about all three axes, questions were raised as to whether the hazard index should consist of the rolling moment parameter alone, or one that included the three degrees of rotation of the probe aircraft, i.e., yaw, pitch and roll. In order to explore which hazard index was more appropriate, Jacobsen and Short [159] de"ned a spin control parameter written as XQ "[(p /p )#(q /q )#(r /r )] , (51) B B B where the subscript m identi"es the maximum control authority available on the probe aircraft for each rotation direction. The simpler hazard index involves only the ratio determined by dividing the roll acceleration due to the vortex by the roll acceleration brought about by full de#ection of the ailerons, PQ "p /p B or, in terms of rolling moment coe$cient,
(52a)
PQ "C /C B . (52b) J J When the roll-control ratio, PQ , is equal to one, the probe aircraft is able to just hold its own against the vortexinduced rolling moment, if the controls are applied instantaneously as needed. In order to determine which of the two parameters was more signi"cant for the encounter of aircraft with a vortex, Jacobsen and Short [159] reduced the data, so that comparisons could be made by use of both parameters (Fig. 61). The data set chosen for the comparison was obtained with the Lear Jet in the wake of the B-747 in its standard landing or (303, 303) con"guration, with the landing gear stowed, and thrust set for level #ight at C "1.4. It is noted in Fig. 61 that when the encounter * is near the vortex core, as evidenced by the larger control ratios, the combined-axes upsets are not signi"cantly greater than the roll upsets alone, the average increase being about 5%. When the encounter is closer to the edge of the vortex (i.e., lower values of the control ratio) the measurements indicate large upsets can occur in the pitch and yaw axes and they should be included in the probe aircraft response measurements. It is speculated that the spin control ratio would be a more adequate measurement of the response for a non-axial wake encounter. However, since the maximum upsets were of most interest in the program, and the roll-acceleration parameter is much simpler and easier to use, the roll-control ratio, PQ , came into common use rather than the spin-control parameter. Figs. 62}66 are reproduced from Jacobsen and Short [159] to show the large number of encounters that were used to develop rather crude boundaries for the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
565
Fig. 61. Comparison of rolling-moment control ratio with total spin control parameter for Lear Jet aircraft encountering wake of B-747 with #aps (303, 303), gear up, and thrust for level #ight at C "1.4; Jacobsen et al. [159]. *
Fig. 62. Variation with separation distance of rolling-moment coe$cient measured in #ight on Lear Jet aircraft in wake of B-747 at various lift coe$cients (303, 303), gear up, and thrust set for level #ight; Jacobsen et al. [159]. (a) #aps (303, 303), (b) #aps (303, 03).
various con"gurations that were tested. The data in those "gures are summarized in Fig. 67. The vortex-induced upset responses of the Lear Jet determined for several values of the lift coe$cient on the B-747 are shown in Fig. 62, where the vortex-induced
rolling-moment coe$cient, C , is plotted as a function of J the separation distance between the generating and probe aircraft. Even though it is expected that the higher lift coe$cients of the B-747 would produce larger upsets because of the increased circulation in the vortices, no
566
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 63. Variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 for two #ap settings and several lift coe$cients with gear up and thrust set for level #ight; Jacobsen et al. [159].
Fig. 64. E!ect of extension of landing gear on variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 for (303, 03) #ap settings and several lift coe$cients with thrust set for level #ight; Jacobsen et al. [159].
e!ect of the change in C from 1.0 to 1.4 is discernible for * either the normal landing #ap (303, 303) con"guration (Fig. 62a) or for the modi"ed landing (303, 03) con"guration (Fig. 62b). This result disagrees with the wind-tunnel results, but agrees with the #ight tests reported by Smith [55]. Two methods used to make the measurements may
account for some of the di!erences. In the wind-tunnel, the following wings are held "xed, whereas in #ight the probe aircraft is allowed to move in a dynamic encounter. The data in Fig. 62 are replotted in Fig. 63 to show the e!ect of the inboard and outboard #ap con"gurations. It
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
567
Fig. 65. E!ect of engine thrust on variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 with gear retracted for two #ap settings and several lift coe$cients with thrust set for level #ight; Jacobsen et al. [159]. (a) #aps (303, 303), (b) #aps (303, 03).
is noted that the vortex encounters were more severe behind the (303, 303) con"guration. Also, the wake shed by the (303, 303) con"guration was so persistent that, even though the separation distance was twice as large, it was still roughly equivalent to the wake of the (303, 03) con"guration. Included in the "gure are the corresponding wind-tunnel data. The #ight test results con"rm the alleviation of the vortex strength with the (303, 03) con"guration, as measured in the wind tunnel at a scaled separation distance of 0.5 n mile (0.85 km). The #ight-test results, however, do not show the increase in C with lift J coe$cient that was measured in the wind tunnel. The adverse e!ect of extending the landing gear on the (303, 03) con"guration is shown in Fig. 64. This e!ect is also shown in the data of Smith [55]. Included in Fig. 64 for comparison is a dashed line that indicates the upper boundary of the data in Fig. 62a for the gear up (303, 303) con"guration. The e!ect of the de#ected outboard #ap is greater than the e!ect of the landing gear, and both con"guration changes increase the magnitude of the
upset responses in the wake of the (303, 03) alleviated con"guration. The e!ect of engine thrust of the B-747 on the upset response of the Lear Jet probe aircraft is shown in Fig. 65 for three engine settings: (1) all engines at level #ight thrust; (2) the inboard engines at idle thrust and the outboard engines at thrust for level #ight; and (3) the inboard engines at thrust for level #ight and the outboard engines at idle. In general, it appears that the vortex encounter is more severe behind the (303, 303) con"guration with engines at idle than with all engines at level #ight thrust (Fig. 65b). This e!ect is not evident behind the modi"ed landing (303, 03) con"guration, however (Fig. 65b). No de"nitive di!erence is apparent between the con"guration with inboard engines idle, and the con"guration with the outboard engines idle. In the present investigation, no measurements were taken with all engines at idle thrust, but the results by Smith [55] indicate a strong adverse e!ect with all engines idle for the (303, 303) #ap con"gurations of the B-747.
568
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 66. E!ect of sideslip of B-747 with gear retracted on variation with separation distance of measured rolling-moment coe$cient on Lear Jet in wake of B-747 for various #ap settings and several lift coe$cients with thrust set for level #ight; Jacobsen et al. [159].
The e!ect of sideslip angle of the B-747 in the (303, 03) con"guration is presented in Fig. 66 for sideslip angles of about $23. Larger upsets were measured for the case of positive sideslip than for either zero or negative sideslip. It is not known which wing vortex was penetrated during each encounter. Although data are available for only a limited range of separation distances, they indicate that the resulting upset is approximately 50% greater with sideslip than for a comparable separation distance with no sideslip, which is in agreement with the results presented by Smith [55]. The pilots of the probe aircraft reported that, from 4.8 to 8.0 km (3 to 5 n mile) behind the aircraft, the trailing vortices, which were marked by smoke, appeared far more concentrated and well de"ned for the (303, 303) con"guration than for the (303, 03) con"guration. Furthermore, as a result of #ying in the wake at various ranges, they identi"ed a separation requirement which was much greater for the (303, 303) con"guration than for the (303, 03) con"guration. Fig. 67 is a summary of pilot qualitative separation requirement for following aircraft [58,61]. With the landing gear retracted to correspond to the ground-based experiments, the separation requirement was reduced substantially for the (303, 03) con"guration compared with the (303, 303) con"guration (Fig. 67a). Deployment of all or any part of the landing gear, however, increased the separation requirements for all con"gurations and especially for the (303, 03) con"guration. Sideslip was also found to adversely a!ect the wake alleviation when the landing gear was stowed (Fig. 67b). Flow visualization obtained during the #ight test provided some insight into the cause of the landing-gear e!ect. Fig. 60 shows the smoke trails from the B-747 for the (303, 03) con"guration with the landing gear both up and down. With the landing gear up, a well-de"ned
vortex pair is shed from the inboard edge of the inboard #aps, and these vortices undergo large-amplitude mutually induced interactions that lead to linking between the two #ap vortices. When the landing gear is deployed, these same vortices appear to be more di!use, and no instability or wave growth or linking between the two vortices appears to occur. The reason why the (303, 03) con"guration of the B-747 was so adversely a!ected by deployment of landing gear or by yaw was essentially explained by the photographs in Fig. 60. A method for making the alleviation mechanism work under all #ight conditions was, however, not found even though a number of attempts were made to "nd a solution. Therefore, since a simple method is not available to initiate the wave instability in the atmosphere on a consistent basis, the (303, 03) con"guration was considered not useable. It might at "rst seem that, if the (303, 03) con"guration of the B-747 had worked as well with gear down and with yaw as it did in the clean and unyawed condition, a solution would have been available for at least one aircraft in the #eet, and might be applicable to others. Such would not have been the case however, because a study by the Boeing company found that the (303, 03) #ap settings reduced the load carrying capability of the aircraft, because it restricted the travel of the center of gravity of the aircraft. When only the inboard #aps are deployed, the aircraft must be loaded more forward which restricts the available aircraft payload distributions and consequently, the e$ciency of the aircraft would be substantially reduced. The Boeing study also concluded that the reduction in lift for landing, imposed by the (303, 03) #ap settings, required both a higher landing velocity and a higher angle of attack at touchdown. The higher landing velocity would produce more stress and wear on the tires and landing gear, and the higher
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
569
Fig. 67. Pilot qualitative estimate of separation requirement for a Lear Jet or T-37B aircraft following a B-747 in level #ight; Corsiglia et al. [61].
angle of attack would risk more tail dragging incidents. These disadvantages would have rendered the aircraft less useful, so that it would not have been competitive with other aircraft in the market. The velocity in the #ow "eld of the wake shed by the standard landing (303, 303) con"guration was also measured by Jacobsen and Short [159] by use of a threecomponent hot-wire anemometer probe mounted on a nose boom of the Lear Jet probe aircraft. After the motions of the probe aircraft have been removed, the three components of the velocity in the vortex wake at 2.9 n mile (5.4 km) behind the B-747 in its (303, 303)
con"guration are presented in Fig. 68. Velocity measurements were also made at a distance of 2.2 n mile (4.1 km). Since the path of the hot-wire probe through the vortex is uncertain, the measured vortex structures were matched to a Lamb mathematical model for a vortex to aid in the interpretation of the data presented in Fig. 68. The reason for the di!erence in the vertical velocity in the port and starboard vortices in Fig. 69 is attributed to a di!erence in the probe path between the two measurements, and their distances from the vortex centers. It was noted by Jacobsen and Short [159] that their method provided a consistently good representation of
570
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 68. Variation of vertical, lateral and axial velocity components in wake of B-747 in standard landing con"guration as measured with hot-wire probe on Lear Jet aircraft as it traverses wake; Jacobsen et al. [159].
the maximum tangential velocities in the vortices (Fig. 70). Both the decay of the vortices with distance behind the generating aircraft, and the e!ect of raising the outboard #ap can be seen by observing the change in the tangential velocity as given by the vortex models matched to the data. This parameter is plotted in Fig. 70 where both variables have been normalized in the manner suggested by Iversen [101]. The mean line through the data correlated by Iversen is also shown in Fig. 70 as a dashed line. It is evident that the dimensionless maximum velocities for the (303, 303) con"guration are representative
Fig. 69. Velocity components in wake of B-747 standard landing con"guration from hot-wire results using Lamb vortex model to interpret data; Jacobsen et al. [159]. (a) Vertical velocity, (b) Lateral velocity.
Fig. 70. Peak tangential velocity in various wakes of B-747 as measured by hot-wire technique as a function of separation distance; Jacobsen et al. [159].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
of the values for other aircraft used in the correlation. The results also show a marked reduction in peak tangential velocity when the outboard #ap is retracted to produce the (303, 03) con"guration, which is consistent with the response measurements of the probe aircraft, and with results from ground-based experiments.
7. Mutually induced instabilities in single pair 7.1. Introduction The results presented in the previous section, and especially the discussion regarding Fig. 60, indicate the importance of the alleviation that can be achieved if the mutually induced instability can be mobilized for a vortex pair. Therefore, consideration is given in this section to the mutually induced instability for a vortex pair. Some background on the mutually induced instability is "rst presented, and then some computations are described that illustrate the dynamics that come about when a vortex pair is given a variety of initial sinusoidal displacements. As mentioned previously, large-scale vortex instabilities bring about mixing on a scale such that vorticity is rapidly convected not only within the wake but also across the centerplane and into regions beyond the wingtips of the wake-generating aircraft. After such a mutually induced instability has gone to completion, the intense and coherent swirling motions associated with the vortex cores shed by conventional span loadings are thereby rapidly changed into incoherent slowly rotating con"gurations which posed a much reduced wake hazard. The mixing action of the vortex motions also spreads the downwash over an area larger than the wingspan of the wake-generating aircraft which reduces the concentration of the downwash momentum in the wake. Study of the sinusoidal or mutually induced instability was carried out to understand the instability better, and to develop guidelines for the design of lifting systems that bring about a rapid onset and completion of instabilities in the vortex "laments. In the 1950s, the mutually induced instability was identi"ed by Scorer [120,165] in condensation trails left by aircraft #ying at cruise altitudes. At that time, Scorer attributed the instability to buoyancy di!erences along the vortex "laments and not to the mutual induction between the two vortices in the pair. Scorer [120] assumed that the buoyant gas from engine exhaust in the core region of the vortices accumulated at the crest of the waves, thereby making those parts of the "laments more buoyant than the troughs. It was reasoned that the warm exhaust gases would drift along the vortex cores from those parts at lower elevations to the crests of the waves, causing the amplitude of any waviness present along the vortex axes to grow. An explanation for the tilt
571
of the wave planes relative to the vertical was not presented. Photographs taken at 15 s intervals from directly below a typical mutually induced event are presented in Fig. 71 [38,49]. As explained in the caption below the "gure, the vortex cores are made visible by condensation of water vapor in the engine exhaust. Another good sequence of photographs of the instability in a vortex pair is presented by Bisgood et al. [47] for the wake of a Comet aircraft. In each of these sequences, the vortex "laments slowly recede and draw together in a nearly anti-symmetrical and sinusoidal pattern until they connect to form a train of irregularly shaped vortex loops. The loops then become more complex in shape and break up causing the wake to disintegrate into a number of incoherent aerodynamic motions. In a landmark paper, Crow [49] presents the correct explanation for the mutually induced instability for a vortex pair (Fig. 71) by analyzing the time-dependent motion of a vortex pair. His analysis correctly attributes the dynamics of the instability to the self-induced velocity "eld of the vortices on each other when they have waves along their length. The analysis was carried out for the cases when the waves on two vortices of opposite sign were in phase, and out of phase. Crow's analysis explains
Fig. 71. Photographs taken at 15 s intervals from below condensation wake of B-47 in cruise con"guration to illustrate mutually induced instability of a vortex pair (from Crow [49] and Van Dyke [38], courtesy of Meteorology Research, Inc.).
572
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the growth of the waves, their tilt relative to the vertical, and predicts a range of preferred wavelengths for the instability. Observations made of the vortices in the laboratory and those shed by transport aircraft at cruise altitude, and marked by the condensation of exhaust vapors, are in agreement with Crow's predictions [34,47,48,50,58,108,166}169]. Not only were the results of Crow's study of great signi"cance for the understanding of the dynamics of vortex wakes and their demise, but Crow's analysis also provided a method of analysis for the dynamics of various three-dimensional time-dependent motions of systems of vortex "laments. Analyses carried out by Hackett and Evans [170] illustrate how the sinusoidal instability exhibits itself in vortex wakes composed of multiple pairs, in agreement with results expected for sawtooth loadings described previously [90}93,151]. Shortly thereafter, Crow and Bate [74] estimated the time required for the instability waves to be initiated by atmospheric turbulence, and to develop to the point where the wake is estimated to be harmless. They also suggested ways to accelerate the onset of rapid wave growth. In recognition of his contributions to the understanding of the mutually induced instability of a vortex pair, the event is justi"ably often referred to as the Crow instability. At the time of the appearance of Crow's "rst paper on the sinusoidal or mutually induced instability, the e!ect of the structure of the vortices (i.e., radial distribution of swirl velocity) on the growth of the waves was unknown. Widnall et al. [171] studied the in#uence of #ow along the axes of the vortices on the growth of the instability waves. It was found that if axial #ow is part of the vortex structure, it would slow wave growth. The physical reason by which #ow along the axis of the vortices slows wave growth was found to be related to the work required to divert the streamwise momentum in the core into a curved path. An experimental study by Bilanin and Widnall [155] of wave growth when the span loading on the generating wing is given a time-dependent oscillation found that, even though fairly large waves could be induced in a pair of wake vortices, the waves would not grow in amplitude enough to bring about the crosslinking between vortices. Without cross-linking, the vortices remain hazardous, because the destructive part of the process which brings an end to the organization of the wake did not occur. As more experimental and theoretical information accumulated on the initiation, growth and culmination of the mutually induced instability, it became apparent that turbulence in the #ow "eld where the vortices are embedded must be of a size and intensity to initiate the instability. The analysis of Crow and Bate [74] pointed out that wave initiation and growth thrive when atmospheric eddies or disturbances are not only present but of a size large enough to be comparable with the preferred wavelengths for maximum instability. Since then a num-
ber of experiments and analyses have been carried out in order to better de"ne the e!ect of free-stream turbulence on the dynamics of the mutually induced instability [50,80,84,97}99,172}175]. In some of the studies, it was found that su$cient turbulence would initiate vortex breakdown (i.e., a rapid destructive enlargement of the vortex core diameter) before the onset of the mutually induced instability [84]. In some other studies, it was found that low levels of free-stream turbulence caused the vortices to meander with time, but did not observe vortex bursting or the mutually induced instability [89]. An example of informative research that illustrates the progress being made in the experimental study of vortex #ow "elds was carried out by Liu [80,98,99] in a water tow tank. The study observed the dynamics of vortex pairs generated by lifting wings to obtain detailed information on the mechanism at work when a vortex pair interacts with various aspects of the atmosphere such as ambient turbulence, wind shear, strati"cation and the proximity of the ground. The study of ambient turbulence [80] is of particular interest here, because it reports on how a pair of trailing vortices behave as the freestream turbulence is increased from very low values obtainable in water tow tanks to very intense turbulence from a towed grid. The scale and magnitude of the turbulence along with strati"cation of the #uid in the tow tank were changed systematically over a wide range of each parameter. Even though the wake-generating wing is small (5.1 cm chord by 10.2 cm span), interesting and informative results were obtained. Photographs presented by Liu [80] of vortex "laments in plan view at various times after being generated are reproduced with permission in Figs. 72}74. Turbulence generated by the wing itself appears to initiate local small amounts of core bursting even when the tow-tank #uid is quiescent (Fig. 72). The dominant mechanism for destruction of the #ow "eld of the vortex pair, however, is certainly the mutually induced instability. In the presence of turbulence generated by the larger grid, linking is still the dominant mechanism even though core bursting is more apparent on the vortices (Figs. 73a and b). Liu points out that more intense levels of turbulence in the free stream also shortened the preferred wavelength of the mutually induced instability. The core bursting exhibited in Fig. 73 at the locations of maximum amplitude along the waves is also frequently observed in the exhaust-condensation trails behind subsonic transports #ying at cruise altitudes. When the turbulence level is increased even further, as also found by Sarpkaya and Daly [84], core bursting appears to be the dominant mechanism for destruction of the organization of the #ow "eld of the vortex pair (Fig. 74). The e!ect of ambient turbulence was found by Liu to decrease the dominant wavelength for linking as the dissipation rate is increased (Fig. 75). Lui [80] also presents hot-wire data on the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
573
decay characteristic of vortex pairs in a turbulent and strati"ed ambient #uid. When it was observed in the air-tow facility at Langley Research Center that temperature-gradient e!ects in the air basin appeared to have a signi"cant e!ect on test results, Greene [176] carried out an analysis on the e!ect of atmospheric structure on wake decay. In order to obtain simple and useful guidelines, the analysis was one that could be characterized as a global analysis of the problem. That is, details of the vortex structure are set aside in the formulation, and attention is given to an extended model of the vortex oval (Fig. 76). It is "rst assumed that the vortex oval, due to viscosity and turbulence at its periphery, spills circulation from both sides of the oval, so that the enclosing streamline is not symmetrical above and below the vortex oval as shown on the left side of Fig. 76. (When the #ow is inviscid and nonturbulent, spillage does not occur.) The amount of circulation shed or spilled per unit time is then assumed to be proportional to the drag of the equivalent body shown on the right-hand side of Fig. 76. The Brunt}Vaisala frequency, N, is introduced as Fig. 72. Sequential photographs of development of mutually induced instability in a quiescent, neutrally stable water tow tank; linking is initially the sole mode of instability; Liu [98].
N"
g do g ! , o dz a
(53)
where g is the acceleration due to gravity, o the air density, dz the altitude change, and a the speed of sound.
Fig. 73. Sequential photographs of development of mutually induced instability in presence of ambient turbulence generated by large grid; linking is still dominant mode of instability with a few bursting events; Liu [80]; note time scale of wake decay. (a) e*+0.2; (b) e*+0.4.
574
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 76. Equivalent cross-section assumed for vortex pair in analysis of vortex decay in the atmosphere by Greene [176].
Fig. 74. Sequential photographs of development of wake instabilities in presence of stronger ambient turbulence (eH+0.5); both linking and bursting take place and preferred wavelength of mutually induced instability is smaller; Liu [80].
The parameter, N, is the frequency at which a buoyant #uid element at one elevation will oscillate about its equilibrium altitude. The motion of the hypothetical oval (Fig. 76) in the vertical direction is then analyzed to
develop predictions for the dynamics of vortex pairs (such as the mutually induced instability) for a wide variety of circumstances. For a given set of atmospheric conditions, Greene's #ow "eld model has been found to quite accurately interpret the response of a vortex pair with good accuracy in a number of circumstances. These successes include measurements in the air tow facility [176] and some laboratory experiments designed to check the validity of the theory [97]. The applicability of Greene's analysis is especially surprising because, in practice, the vortex oval does not have a velocity discontinuity across the streamline that encompasses the oval so that a shear layer is not generated. Spillage of circulation from both vortices in the pair must then come about, because turbulence eddies generated in the outer layers of the vortices transport circulation through the interface between the
Fig. 75. Variation of the dominant wavelength of vortex-linking instability as dissipation rate increases; Liu [80].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
#ow inside the oval into the freestream of the outer #ow which goes past the oval. It is therefore unexpected that the drag of the cross-section shown on the right-hand side in Fig. 76 would represent so closely the spillage of circulation found in practice. Some recent ground-based experiments and numerical results to test the theoretical relationships indicate remarkably good agreement [97]. The study shows again that models of the global type like Greene's [176] will on occasion provide very useful results even though they are based on #ow models that are quite approximate. Recently, Greene's model has been extended by Kantha [177,178] to provide more realistic modelling of the detrainment of the circulation from the vortex oval and across the interface between the two vortices in the pair by use of the Monin}Obukho! similarity laws. Kantha's model includes ground e!ect and the more rapid decay of the vortices when in the proximity of the ground. It is also designed to simulate the tilt of the oval and vortex bounce. 7.2. Numerical method The numerical technique used to compute the results to be presented is patterned after the incompressible, inviscid technique used by Crow [49]. That is, the wake vortices are broken into straight-line segments that approximate the curved "laments. The shape and locations of the vortex lines are monitored by following the points where adjacent segments or links are connected. The velocity components at these points are calculated as a summation of the separate contributions of all of the vortex links in the #ow "eld } except for the two that touch the point itself, and thereby have indeterminate contributions. Since the velocity contributions induced by the two adjacent links are not included, the vortex lines are essentially cut o! at a distance of one link length, ds, on both sides of the point in question. The length of the link, and consequently the cut-o! distance, are chosen so that the numerical results agree with the velocity of propagation of a vortex ring. That is, the link length, ds, in the present numerical method is adjusted until the velocity of propagation of a vortex ring agrees with the closed-form expression given by Lamb [9] for a ring with a small but "nite core. The core is assumed to have uniform vorticity over a diameter, d , comparable with the vortices trailed by transport aircraft. Agreement is achieved with the present numerical method when ds"0.36d . Based on these values, a link length of ds"0.2b is used throughout the computations to be presented. The symbol, b, is the initial spanwise separation between the vortices. The foregoing guidelines work well for a vortex pair. The spacing guidelines just described become more complex when a vortex wake is composed of more than one vortex pair. In those cases, care must be exercised to be
575
sure that the guideline for link length of ds"0.2b is a maximum and not violated during the dynamic motions of wakes composed of multiple vortex pairs. If such a situation does occur, the closely associated vortices may numerically undergo a local rapid wave growth that might be mistaken for a realistic vortex interaction. This type of rapid wave growth has been studied and found to occur whenever the spacing between vortices decreases, so that a link length approaches half the distance between any two vortices. The resulting instability has been referred to as a spur-type instability and has been shown to be associated with the numerical analysis and not with the #uid mechanics of the vortex interactions [179]. The computations are begun by placing sinusoidally shaped waves of amplitude, a , on the "laments in the G vortex pair so that, at the beginning of each case, the waves on the port (or left) vortex "lament have a phase angle, , between 0 and 1803 relative to the waves on the starboard vortex. For comparison purposes, the initial amplitude, a , of the waves is set by the magnitude G expected at the wingtips when the wake-generating aircraft rolls through an angle b"73. A value of 73 was chosen because that is the magnitude of the oscillations used to study wake alleviation in the #ight tests at Dryden [59,112]. The pitch oscillations used to generate the wave pattern for the in-phase case are assumed to be of a magnitude such that the same displacement magnitude is achieved at the wingtips as when the aircraft undergoes roll oscillations like those used in the #ight tests. Hence, those cases are also given a b label to signal that the amplitude of the waves are comparable. Di!erent initial amplitudes are then taken as multiples, or fractions, of the 73 case. All of the wavelengths are held "xed at six spans, which corresponds roughly to the streamwise length of the oscillations experienced in the #ight experiments. In order to reduce the computation time, only "ve wave cycles were considered in the analysis of each case. The beginning and end of each wave set was blended smoothly into the straight-line portions of the vortices by use of one-quarter cycle of sine-squared variation in the displacement of the vortex links. Flexibility of the wavy portion of the "laments was enhanced by placing two spans of links between the ends of the waves, and the single link that projects o! to the far reaches of the wake. In the "gures to be presented, only the three center waves on each "lament are shown, because they are believed to be insulated well enough from the starting and stopping parts of the waves that they represent the dynamics to be experienced by an in"nite wave train. This conclusion is supported by the fact that a signi"cant di!erence between the shape of the center and of the two adjacent waves on a "lament is not detectable. The strength of the vortices in dimensionless form, C"circulation/b; , is held "xed at 0.1, which approximates transport aircraft in their
576
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
landing con"guration. When a matrix of values has been computed, the results are used to determine the e!ect of the relative phase of the waves on the two vortices in the pair on their wake dynamics. 7.3. Vortex-pair instability 7.3.1. Introduction A systematic study is presented in this section to determine the e!ect of phase on wave ampli"cation, i.e., does a di!erence in phase of the input waves on the port and starboard vortices a!ect the growth rate of the wave amplitude [180]. The study was prompted by #ight-test results obtained with a B-747 and a L-1011 aircraft. Of interest here is the portion of the test devoted to roll- and pitch-oscillation maneuvers by the aircraft to "nd out if the wake hazard increased or decreased as measured with a following aircraft [59]. The #ight results, to be treated in more detail in Section 7.4, indicate that the phase of input waves on the vortices in the wake does have a profound a!ect on the resulting dynamics of the vortices as in#uenced by the mutually induced instability. The signi"cance of the question is apparent when it is noted that turbulence in the atmosphere might in#uence a vortex wake, so that the initial disturbances to the vortices could be in phase, out-of-phase, or somewhere in between. The investigation to be presented considers the entire range of possible phase-angle di!erences between the input waves on the port and starboard vortices. 7.3.2. Isolated vortex Before investigating the dynamics of a vortex pair with initial disturbance waves along their length, the timedependent motion of an isolated vortex is considered when it has displacement waves along its axis [180]. When analyzed by use of the foregoing numerical method, it is found that an isolated vortex "lament with sinusoidal waves impressed on it rotates without much change in shape as time progresses. Fig. 77 illustrates how the rotation rate is a!ected by the amplitude of the waves. In the computations, it is noted that the plane of the input waves rotates counter to the direction of the vortex rotation (i.e., retrograde direction) with no appreciable change in amplitude. Some small distortions do take place at the crests and troughs of the waves. These distortions are largely perpendicular to the plane of the disturbance waves, and oscillate in the fore and aft directions of rotation. That is, the oscillations consist of small changes in the shape of the waves in the direction normal to the wave plane. Since the angle of the wave plane was measured along the line from the crest to the trough, the rotation angles plotted in Fig. 77 re#ect a change in shape together with any change in rotational speed. It is observed in Fig. 77 that when b is 143 or more, the rotation rate is approximately constant with time and with initial amplitude even though the waves do curl
Fig. 77. Variation with time of rotation of plane of sinusoidal waves impressed on an isolated vortex with various initial amplitudes [180].
a little at the crests in the direction perpendicular to the wave plane. At smaller initial wave amplitudes, both short- (b"3.53) and long-term (b"73) variations occur in the apparent rotational rate. These results provide some background characteristics on the rotation rate, and on the changes in wave shape from the initial sinusoidal one in order to help di!erentiate between the various dynamics brought about on the "laments by the mutually induced interactions between the "laments [180]. The primary conclusion is that the plane of sinusoidal waves along the axis of an isolated vortex "lament will rotate in a retrograde direction with little change in shape, i.e., a second vortex is not necessary to induce rotation by the plane of the waves. However, if growth in the wave amplitude is to occur, a second vortex of opposite sign, (so that its wave planes rotate in the opposite direction) must also be present for wave growth. That is, as the wave planes of the port and starboard vortices rotate, the wave troughs are brought closer together, so that those parts of the waves have their amplitudes increased by mutual induction. At the same time, the crests move apart, so that mutual induction is small causing the amplitude of those waves to remain almost unchanged. If the amplitude of the waves on both vortex "laments is very small, the waves on each "lament in a pair rotate without growth. Without the rotation of the wave planes that a wavy vortex "lament induces on itself, it is unlikely that wave growth would occur. 7.3.3. Vortex pair; waves in phase, "03 The initial wave pattern on the "laments for this case could be thought of as having been generated by executing small pitching or plunging motions with the wake-
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
generating aircraft. Fig. 78 presents the shape of the vortex "laments at three di!erent times after the beginning of the event. The dimensionless time, ¹"t; /b, indicated on each "gure, represents the vortex spans of travel of the wake-generating aircraft from the beginning of the event. The wakes are displayed on a 303/303/903 oblique view to yield a three-dimensional perspective of the wake, and as an end view. The end views are plotted at four times the scale used for the oblique views to more clearly indicate the shapes of the vortex planes. The foregoing numerical method was used to calculate a range of input wave amplitudes to study the characteristics of the in-phase wave pattern. These results are summarized in Figs. 79 and 80 for the wave amplitude, A"a/b, and the angle of the wave planes, h. The larger initial amplitudes lead to faster growth rates and to di!erent rotation rates of the wave planes (Fig. 79). The decrease observed in the angle of the wave plane, h, when the time, ¹, exceeds about 80 occurs because of the way that the angle is measured. That is, the measurement is made on a secant from the crest to the trough of the wave, so that as the wave grows rapidly in the trough region,
577
the apparent plane of the wave becomes more vertical. It is also noted in Fig. 79b that, at the smaller initial amplitudes, the wave planes rotate at di!erent rates. However, if b is over 143, the wave planes rotate at about the same rate independently of the initial amplitude. If the dynamics of the interaction were linear, the curves in Fig. 79a would collapse to a single line when plotted as the ratio of the input amplitude, a , rather than G vortex span b. As indicated in Fig. 80, the wave growth is nearly linear with the input amplitude during the initial stages of the event. As time progresses, however, the larger inputs appear to be more productive, because they are the ones that bring the troughs of the waves close together most quickly, so as to bene"t from the large mutual induction brought about by the proximity of the two vortices at those axial stations where the wave troughs occur. Not shown in the "gures are the disconnecting and linking parts of the instability which occur after the numerical simulation has been terminated. As mentioned previously, the present method is not capable of simulating those #uid-dynamic processes. The results in Figs. 79 and 80 illustrate the importance of large
Fig. 78. Oblique and end views of vortex pair which has an initial displacement of sine waves that are in phase [180]; "03, wavelength"6b, initial amplitude"0.23b (b"143).
578
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 79. Wave characteristics as a function of time for various input amplitudes when waves are in-phase [180]; "03.
Fig. 80. Wave amplitude ratio, a/a , as a function of time to test for linearity of the vortex dynamics to input amplitude when input waves G are in-phase [180]; "03.
input-wave amplitudes for consistent and rapid wave growth during the mutually induced instability. 7.3.4. Vortex pair; waves out-of-phase, "1803 The disturbance waves are now initially located on a circular cylinder as if the vortices had been shed by an
aircraft executing a series of roll oscillations. As a consequence, the phase of the waves on the port vortex is shifted one-half cycle, "1803, relative to the waves on the starboard vortex in order to study the out-of-phase or anti-symmetric case. Another representation of the anti-symmetric case could be made by placing the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
"laments in vertical planes rather than on arcs. A number of events were also calculated using such an initial con"guration. It was found that the results di!ered only slightly, and that no di!erence in the stability characteristics appeared. Since the circular-arc con"guration more closely approximates the #ight situation, only those results are presented. The wave shapes at three instances of time are presented in Fig. 81 for a typical event. The wave amplitude is noted to grow as the wave planes rotate in the retrograde direction, as predicted by the stability analysis of Crow [49]. However, at the latest time shown, the wave planes have just passed the horizontal, and are beginning to shrink. It is noted that counter rotation of the two wave planes for this case bring neither the wave troughs nor the crests closer together. Also, the wave tips at the inboard ends are taking on a slight curl which contributes a small amount to the rotation angle and to the amplitude reduction. The results for a series of such events are summarized in Figs. 82a and b by plotting the dimensionless amplitude, A"a/b, and the change in the angle, h, of the wave planes. Fig. 82a illustrates how the wave amplitude "rst grows to a maximum value, which occurs at about ¹"90, and then decreases. At about the same time (Fig. 82b) the wave planes reach the
579
903 rotation angle. Linearity of the wave dynamics for the out-of-phase wave pattern is tested in Fig. 83 by comparing the amplitude history for the various values of b on the basis of the input amplitude. All of the cases fall along a single line, except for the small amplitude case of b"3.53. A similar observation is noted in Fig. 82b for the rotation of the wave planes. The results indicate that an out-of-phase disturbance causes the initially nearly vertical waves to rotate to the horizontal plane and remain there as a stable vortex con"guration. The result is a vortex trail wherein the two vortices appear as a railroad track that waves back and forth sinusoidally in the horizontal plane (Fig. 81). An example from #ight tests of the wake-vortex dynamics associated with the roll-oscillation case is presented in Fig. 84. (The contrast, brightness, background and smoke trails in the photographs were adjusted electronically to better de"ne the vortex trails taken from 16 mm "lm.) The two scenes were taken from frames in motion pictures of the smoke trails taken during the #ight tests conducted by Barber and Tymczyszyn [59]. The initial multiple-pair vortex wake of the L-1011 changes quickly into a single pair of nicely formed vortices. The planes of the vortices, which were initially vertical, then rotate to an approximately horizontal
Fig. 81. Oblique and end views of a vortex pair which has been given initial sinusoidal displacement waves that are out-of-phase ( "1803) on circular arcs as if trailed by an aircraft executing roll oscillations [180]; wavelength"6b, initial wave amplitude"0.23b; b"143.
580
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 82. Wave characteristics as a function of time for various input amplitudes when waves are out-of-phase [180]; "1803. (a) Peak-to-trough amplitude. (b) Rotation of wave planes from initial vertical attitude.
Fig. 83. Wave amplitude ratio, a/a , as a function of time to test G for linearity of the vortex dynamics to input amplitude when input waves are out-of-phase [180]; "1803.
Fig. 84. Photographs from below of vortex wake of L-1011 following roll-oscillation of about 73 amplitude [180]. (From motion pictures of #ight tests conducted by Barber and Tymczyszyn [59]; courtesy of M. R. Barber and R. M. Rhine.) (a) "rst photo; (b) about 1 min later.
attitude while the wave amplitude grows a small amount. Thereafter, the vortices change only a little and do so slowly. As a consequence, the two vortices then appear roughly as a parallel sinusoidal pair which could have been generated by an aircraft executing a series of yaw oscillations. These #ight results con"rm at least the qualitative nature of the dynamics of the vortex wake predicted by the numerical analysis and do much to clarify
the wake dynamics to be expected from various wave inputs. The foregoing results also show that atmospheric disturbances to a vortex pair that are out-of-phase do not result in destructive mutually induced wave growth. The numerical predictions are in agreement with the #ight test results, because it was found that there was no sign of any kind of unlimited wave growth for the out-of-phase
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
581
case similar to that which occurs in the symmetric or in-phase case. It is concluded, therefore, that the antisymmetric or out-of-phase case does not lead to any destructive vortex interactions. The out-of-phase case does produce a vortex con"guration that is stable and therefore much more persistent than even a parallel, non-disturbed wake shape. These results are con"rmed by #ight tests [59] which include observations of the "laments and penetrations vortex wakes. 7.3.5. Vortex pair; intermediate phase angles, 03( (1803 When the waves on the starboard vortex "lament are shifted forward to yield intermediate phase angles, the vortex dynamics is a combination of the in-phase and out-of-phase cases. The mid-phase case of "903, shown in Fig. 85, illustrates the mixture of the two kinds of dynamics such that the waves appear as loops in the end views. As time progresses, the troughs or lower parts of the waves grow in amplitude in very much the same way as the in-phase case. If the numerical simulations were continued, the vortex "laments would probably (in the presence of other disturbances) go into the disconnecting and linking parts of the instability that lead to loop formation and the disruption of the orderliness of the wakes. The curves shown for the amplitude of the input waves as a function of time (Fig. 86) illustrate how phase angle a!ects the growth rate for b"143. It is found that any initial input of that magnitude would eventually go into the rapid wave growth in the wave troughs which is typical of the in-phase dynamics if the phase angle is between 03 and about 1503. Even though the wave amplitude reaches a maximum and then begins to decrease, the vertical extent of the wave continues to grow so that the loop in the end view of the vortex opens up more and more. As time increases further, the troughs of the waves get deeper until the mutual-induction process of disconnecting and linking occurs. It then appears that the in-phase instability comes about for a broad range of phase angles, but a longer time is required for the cases with larger phase-angle di!erences, just as more time is required for the smaller input wave amplitudes. During the early parts of the event, the vortex motions in general resemble more closely those of the case at one end of the range than the other, depending on which is closest. Hence, any out-of-phase disturbances grow more slowly and inconsistently than the in-phase disturbances. 7.3.6. Concluding remarks on the ewect of phase The study of the e!ect of the phase of input waves on the growth of the instability has shown that growth is in#uenced by several parameters in addition to wavelength. First, the phase of the input waves on the port and starboard waves should be the same if rapid growth is expected from the mutually induced instability.
Fig. 85. Oblique and end views of vortex pair which has an initial displacement of sine waves which are midway between in-phase and out-of-phase [180]; "903, wavelength"6b, initial amplitude"0.23b; b"143.
Furthermore, only when the input waves are nearly in phase does the instability proceed to linking and loop formation for disintegration of the wake. That is, wave growth occurs initially if the input waves are out of phase, or nearly so, but the growth stops after the plane of the waves has rotated through 903. Secondly, the growth rate of the waves are more rapid for larger input wave amplitudes than for smaller ones. As illustrated in the tow tank experiments of Liu [80], strong turbulence in the ambient #uid accelerates the decomposition of
582
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 86. Wave amplitude as a function of time for various input phase angles, , of the impressed wave pattern [180]; b"143.
a vortex wake and permits the linking instability to occur at shorter wavelengths. Also, no new destructive mechanisms appear to be initiated by any of the in-between values of the phase angle. It is concluded that any out-of-phase wave components only contribute to the delay of the onset of the rapid growth part of the in-phase instability. That is, the farther that is from 03, the more time is required for the onset of the rapid growth associated with the inphase case. When the port and starboard waves are approximately out-of-phase, destructive wave growth appears to be delayed inde"nitely.
8. Multiple-pair instabilities 8.1. Introduction If the spanwise distance between the vortices in the pair is based on the span of the wing, the amount of time required for the mutually induced instability to go to completion is too long to help with the solution of the capacity problem at airports. If, however, the mutually induced instability can be initiated in multiple vortex wakes, as demonstrated with sawtooth loading in Section 6, which employs multiple vortex pairs, the time required for wake alleviation may be brought into the useful range. That is, the wake interaction is still based on the spanwise distance between vortices, but, in the case of vortex wakes which are composed of multiple pairs, the e!ective vortex span is the #ap length rather than the wing span. Hence, the distance or time required for wake decomposition to become completed can easily be reduced by a factor of 4 or more. Since systematic guidelines have not been developed for the design of vortex
wakes, span loadings, or wing structures that accomplish the desired wake disruptions, any investigation directed towards such a goal is complicated by at least the following factors: (1) the number of parameters available for variation is large; (2) the vortex interactions are a combination of several kinds of dynamics including the inphase and out-of-phase ones; and (3) the analysis method to be used must be capable of treating "nite disturbances, large vortex distortions, and the e!ect of viscosity and turbulence on wave growth. E!orts have been made, therefore, to ensure and to accelerate the onset of the mutually induced instability by manipulating control surfaces [49,74,155,172], or the entire aircraft [59], in order to impress large initial wave amplitudes on the vortex lines as they are generated. The objective, of course, is to reduce the time required to achieve rapid growth in wave amplitude and wake disruption. Large initial wave amplitudes are e!ective in reducing the time for completion of the mutually induced instability but mutiple-#ap vortices proceed more rapidly. Since the mixing achieved with multiple vortex pairs is on a scale of the span of the #ap and not of the wing, they bring about more rapid linking, and the vortex wake appears to be even more unstable, e.g., Section 6. In several of the cases studied [64,69], it was found that two vortex pairs were unstable enough downstream of the wing so that mutually induced, in-phase waves on the vortices grew quickly and then linked across the span to form vortex loops that destroy the coherence of the wake. The short lifetime of the coherent character of vortex wakes comes about primarily, because of the reduced spanwise distance between vortices of opposite sign. For example, the small distance between vortices, as produced by sawtooth loading, makes them more unstable so that wave growth is easy to initiate. Also, the reduced spanwise distance in the vortex pair reduces the time scale for the mutually induced instability, so that the time required for complete disorganization of the wake is reduced by the ratio of the spanwise distance between the vortices to the span of the wing. Since the wakegenerating wing used in the fundamental experiments with sawtooth loading had seven #aps per side, or 14 #aps in all, the reduction in time to wake destruction is 1/14th of that required for the wing with the #aps zero con"guration. In this section, an analysis is presented of the wakes shed by the (303, 03) and the (303, 303) con"gurations of the B-747 with outboard spoilers deployed con"gurations. The objective of the analysis is to show how reduced span between vortex pairs accelerates the demise of lift-generated wakes. It is found, however, that in practice the mutually induced instability is not initiated unless the aircraft is put through rapid roll oscillations to generate large amplitude waves on the vortices shed by the inboard #ap and wingtips [181].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
8.2. Overview of yight tests An illustration of rapidly dispersing wakes that work with landing gear extended and #ight spoilers deployed was obtained inadvertently during the latter part of the #ight test program with the B-747 and L-1011 aircraft by Barber and Tymczyszyn [59] at Dryden Flight Research Center. The primary purpose of the research program at that time was to evaluate the e!ectiveness of turbulence injection by use of spoilers already on each of the aircraft as suggested in wind-tunnel studies [62,63]. The spoiler con"gurations were "rst tested in straight and level #ight to determine how much alleviation of the wake hazard could be achieved. A T-37B aircraft was used to probe the wake to determine the level of hazard posed in comparison with the aircraft in its normal landing con"guration. After the straight and level tests had been completed on both the B-747 and L-1011 aircraft, #ight tests were conducted to determine if the alleviation achieved with #ight spoilers was altered by turning or rolling maneuvers. That is, the #ight tests were conducted in order to answer the question, `do either turning and rolling maneuvers adversely a!ect the hazards posed by the wakes produced by the aircraft with spoilers deployed?a In the #ight experiments, it was found that the wake hazard behind both a B-747 and L-1011 aircraft was signi"cantly altered when the roll-oscillation maneuver was added to their #ight procedure (Table 6). Unfortunately, the roll-oscillation maneuver applied to two different aircraft brought about two very di!erent responses, and neither was anticipated. A theoretical e!ort was then undertaken to "nd an explanation for the #ight results. In summary, the #ight tests showed that, when either the B-747 or the L-1011 aircraft was #own in
583
straight and level #ight, the wake-induced rolling moments with spoilers deployed was about one-half to twothirds of the value when spoilers were not deployed. When the B-747 aircraft was #own with the combination of spoilers deployed and roll oscillations, vortex interactions were generated that reduced the wake-induced rolling moments on a following aircraft to about one-eighth to one-fourth of the value observed for the conventional landing con"guration. That is, the combination of spoilers and roll oscillations with the B-747 reduced the wake overturning moments induced on a T-37B probe aircraft during a direct following encounter to the point where the probe aircraft did not experience an uncontrollable coherent rolling moment at separation distances as small as one and one-half nautical miles behind the wake generator. The pilots reported that the ride during penetration of the wake was like that with a car over a bumpy road, with no coherent rolling moment. In contrast, the vortex wake of the L-1011 aircraft responded in a dramatically di!erent way from the B-747 response, when spoilers were deployed and the aircraft executed roll oscillations. That is, when the roll-oscillation maneuver was added to the landing con"guration with spoilers deployed, the wake hazard did not decrease as with the B-747, but became both more intense and more persistent [59]. As explained in the previous section, the roll-oscillation maneuver of the L-1011 imparts an initial set of wave displacements that are out of phase (i.e., "1803), rather than in phase. Analysis of a set of waves on vortex "laments, suggests that the vortex pair goes from the input shapes to a stable con"guration. The stable con"guration comes about after the wave planes on the two vortices in the pair roll through 903, so that the vortex cores appear in the horizontal plane as
Table 6 Information on #ight tests conducted with roll or pitch oscillations [59] Con"guration Aircraft
Flaps
Spoilers
Maneuver
Results
B-747
303/03
Locked in retracted position
Straight and level #ight
Wake attenuated by about a factor of 2
B-747
303/303
2, 3 & 4 AT 453
Straight and level #ight
Wake attenuated by about a factor of 2
B-747
303/303
2, 3 & 4 AT 453
Roll oscillations at 6 s/cycle
Wake devoid of coherent rotary #ow at 3 n mile
B-747
303/303
Locked in retracted position
Roll oscillations at 6 s/cycle
Wake similar to unattenuated wake shed during straight and level #ight
L-1011
333
2, 3, 4 & 5
Roll oscillations at 4.6 and 9.2 s/cycle
Did not change wake hazard from straight and level #ight character. Very di!erent from B-747 results
L-1011
333
2, 3 & 4
Pitch oscillations at 2.3, 4.6 and 9.2 s/cycle
Excites and changes period of ScorerCrow instability
584
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
snaking railroad tracks (Figs. 81 and 84). The vortices now both lie approximately in the horizontal plane which is a more stable form of the vortices than the one laid out during straight and level #ight, and is therefore more persistent. In other words, the analysis in the previous section explains the #ight results obtained with the L-1011. The analysis to follow provides an explanation for the #ight test results obtained with the B-747 during roll oscillations [181]. Since an immediate explanation for the test observation with the L-1011 aircraft was not available, e!orts were made to determine an explanation for the alleviation achieved. It was even thought that the unexpected and unusually large change in the hazard posed by the vortex wake of the B-747 executing roll oscillations might be a new and possibly important vortex wake instability. An analysis by Holbrook [182] explored the possibility that the sinuous shape of the vortices was large enough that the probe aircraft would have only intermittent encounters with the hazardous portions of the wake. The overturning moments would also then be intermittent. It was thought that the rolling moments perceived by the pilot would then be reduced, even though the peak values had not been changed appreciably. In another study carried out in the Langley Air Tow Facility, Jordan [156] approximated the #ight experiment by activating the same control surface motions, but without allowing the aircraft model to roll. He found that the time-dependent changes in lift across the span caused the vortices generated at the #ap edges to cross the centerline of the aircraft #ight path each time the roll controls were reversed. The observations made in Jordan's experiments did not indicate whether a new kind of wake instability had been
triggered or whether already known vortex mechanisms were responsible for the wake dynamics that were observed. 8.3. Estimate of steady-state span loadings The normalized steady-state span loadings on the B-747 and L-1011 are presented in Fig. 87. The approximate weights of the aircraft (263,000 kg (580,000 lbs) for the B-747 and the 159,000 kg (350,000 lbs) for the L-1011) during the #ights at an altitude of about 10,000 ft above sea level at an indicated velocity of 150 kts were used to determine the lift coe$cients and angles of attack on the aircraft. The span loadings presented in Fig. 87 were then used to determine the strengths and locations of the vortices for both aircraft in their various #ap con"guration (Table 7). Since a reliable method for determining the span loading when spoilers were deployed was not available, the span loadings and the vortex distributions on the aircraft were estimated in those cases by assuming that the lift on the wing where the spoilers are deployed is reduced. For example, the loading on the B-747 with spoilers 2, 3, and 4 deployed is assumed to be approximated by the span loading when the #aps are set at (303, 03). Not approximated is the higher level of turbulence introduced by the spoilers. Similarly, the wake of the L-1011 with its #aps at 333 and spoilers activated is approximated by the vortices listed in Table 7. It should be noted that the strong vortex shed by the inboard edge of the inboard #ap on the B-747 is not present on the L-1011. The di!erences in the #ap design and placement on the wings of the two aircraft probably account for the di!erences in the two wakes in
Fig. 87. Estimated span loadings for test aircraft [181].
!0.061
0.188 #0.046 Q Approximate values
0.185 #0.052 0.060 Q Approximate values !0.063 !0.021 !0.063 0.058 0.225 0.058
#0.110 #0.065 #0.110 #0.0545 !0.020 #0.045 0.219 0.346 0.219 0.225 0.266 0.18 #0.130 #0.064 #0.054 #0.064 #0.0765 #0.103 #0.097 0.381 0.455 0.465 0.455 0.464 0.433 0.41 1.38 1.38 1.38 1.38 1.33 1.33 1.33 03/03 303/03 303/303 303/303 03 333 333 B-747 B-747 B-747 B-747 L-1011 L-1011 L-1011
Stowed Stowed Stowed 2, 3, 4 at 453 Stowed Stowed 2, 3, 4 & 5 deployed
c c c c c >
>
C2 C1 C *
8.4. Two-dimensional simulation of wakes
Flaps
Spoilers
585
the landing con"gurations. Another di!erence which appears to impact the wake-vortex hazard potential, is the somewhat tapered span loading on the B-747 as compared with the more elliptical loading on the L-1011. Experience indicates that alleviation is easier to achieve on tapered loadings than on wings which shed strong wingtip vortices.
Aircraft
Con"guration
Table 7 Locations and strengths of wake vortices trailing from starboard half of wing [181]
>
C3
Vortex
>
C4
>
C5
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Two-dimensional simulations of the wakes of the B-747 and L-1011 are "rst presented as background information, and to show the di!erences in the wakes under steady and level #ight conditions [181]. It is, of course, assumed that the vortex strengths do not vary signi"cantly in the #ight direction. The two-dimensional computations do not include the three-dimensional effects of the mutually induced instability nor the vortex dynamics that goes with it. Comparison of the twodimensional predictions with those computed for the three-dimensional dynamics helps to identify any vortex dynamics instigated by roll- and pitch-oscillation maneuvers. The lines shown in Figs. 88 and 89 depict an end view of the trajectories taken by the vortices from their initial positions listed in Table 7 to their locations 60 spans behind the generating wing. A distance of 60 spans is about two nautical miles behind the B-747 and about 1.53 n mile behind the L-1011. Intermediate distances are not marked on the "gures. The single vortex pair shed by the B-747 with #aps (03, 03) descends unchanged (Fig. 88a). Four of the 5 pairs of vortices shed by the aircraft in its landing con"guration (i.e., #aps (303, 303); Fig. 88b), orbit about one another to form periodic cauli#ower patterns. The "fth and most inboard pair "rst moves downward and inboard until the in#uence of the other vortices has diminished to the point where they can move upward as an isolated pair. In #ight, turbulence from the fuselage, engines and landing gear would cause the inboard vortex pair to coalesce. A contrasting vortex motion develops when the outboard #ap is withdrawn on the B-747 so that only three vortex pairs remain in the wake (Figs. 88c and d). The tip vortices move downward to form an isolated pair but the two #ap vortices execute large circular orbits and then they re-associate to form new pairs of vortices that move o! separately. The e!ect of turbulence, "nite core size, three-dimensional interactions, and changes in vortex strengths from those estimated here can all a!ect the details of the trajectories presented in Figs. 88c and d. However, the presence of the negative inboard vortex pair and its ability to in#uence strongly the other #ap vortices suggests that the large vortex excursions needed to explain the #ight results observed at Dryden Flight Research Center might be produced thereby.
586
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 88. End views of two-dimensional trajectories of vortices in wakes [181] of B-747 from initial locations to positions at ¹"60 (or ¹"100 as noted).
Fig. 89. End views of two-dimensional trajectories of vortices in wakes [181] of L-1011 from initial locations to positions at ¹"60. (a) Roll oscillations of 73 amplitude. (b) Pitch oscillations with same wingtip amplitude as roll oscillations in Fig. 90a.
The wakes shed by the various L-1011 con"gurations consist of either two or three vortex pairs. Since the vortices in the two-pair cases are both of the same sign,
the vortices simply rotate about one another while the entire wake descends (Figs. 89a and c). The presence of a third vortex in the #aps 333 con"guration produces
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
587
Fig. 90. Oblique and end views of wake of B-747 #aps (03, 03) con"guration at three time intervals after beginning of maneuver [181].
a di!erent pattern from the two-pair cases, but the trajectories resemble the pattern in Fig. 88b more than the ones in Figs. 88c and d. The results of the two-dimensional computations indicate that large vortex excursions appear not to be expected for the L-1011 #aps 333 case, because the locations, signs and relative magnitudes of the vortices are not the ones needed for alleviation. 8.5. Three-dimensional simulation of wakes: B-747 The three-dimensional time-dependent dynamics of the wakes shed by the B-747 aircraft during pitch and roll oscillations are now discussed [181]. The dynamics of the vortex wakes were computed by use of the method described in Section 7.2, where the e!ect of phase of the input waves on a vortex pair was studied. Once again the wake was assumed to be generated as a function of time as if the aircraft entered the "eld of view at the left side of the "gure, and exits on the right, moving at one coordinate marker per unit time. As a result, the dimensionless time indicated in each "gure represents the spans of travel of the wake-generating aircraft from the beginning of the event. As done previously, the wakes are displayed on a 303/303/903 oblique graphical view to
yield a three-dimensional perspective of the wake. Only the #exible portions of the wake are displayed. The end views of the wake are again presented at a larger scale (i.e., four times) to show more clearly the size of the waves and their change in shape with time. Also, symbols are placed on the "laments every two spans to assist in the understanding of the vortex shapes. In order to compare the cases more readily and to simulate the #ight experiments, the numerical results presented here assume that one oscillation cycle is completed within six spans of travel by the aircraft, and a roll amplitude of 73. Since the aircraft #ew at 150 knots, or 1.28 spans/s, the theoretical oscillation period is about 4.7 s for the B-747 [59]. As indicated in Fig. 88a, the wake of the B-747 does not undergo any signi"cant changes for 60 spans (or 3 n mile) or more when no #aps or spoilers are deployed, and when no disturbances are imposed on the wake. However, when the same con"guration (i.e., cruise con"guration or #aps (03, 03)) executes a series of roll oscillations, the planes of the disturbance waves rotate through 903 while the wave amplitude grows from about 0.09b to about 0.4b , in roughly 60 time units (Fig. 90a). There after, the wave shape and size appears to stay the same from ¹"60 to 100 and probably until the wake decays
588
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
by di!usion; just as predicted in the previous section in the study of the e!ect of phase. The vortex "laments then simulate a wake trailed by an aircraft executing lateral oscillations, i.e., a snaking motion. It is interesting to note that the initial growth of the waves that was predicted does occur, but the amplitude appears to reach a maximum after the wave planes have rotated in a retrograde manner to an approximately horizontal plane. If only one sinusoidally shaped vortex "lament were present in the #ow "eld, it would rotate almost unchanged. Addition of the second vortex appears to bring about an increase in the wave amplitude by about a factor of four, while the planes of the waves rotate from the vertical to a horizontal attitude, and come to rest. For comparison purposes, the wake of the B-747 #aps (03, 03) con"guration executing pitching oscillations is presented in Fig. 90b. The wave planes of the vortices are noted to rotate slowly in a retrograde motion until they reach an angle of about 453 to the centerplane. The waves then grow in amplitude until the lower part of the vortex waves approach each other closely. By that time, the amplitude of the waves has grown considerably, and is still continuing to grow at a fast rate. In a #ight situation, the vortices would then disconnect and link across the pair to form irregularly shaped loops of vortex "laments. As mentioned previously, the vortex wake of the B-747 when both #aps (303, 303) and spoilers 2, 3, and 4 deployed (Tables 6 and 7) is approximated by the span loading of the (303, 03) con"guration. It is noted that the lift-generated wake then consists of three vortex pairs; that is, a tip vortex and two fairly strong vortices that are shed by the ends of the inboard #ap. The wake dynamics initiated by rolling and pitching #ight maneuvers are presented in Fig. 91. A di!erent response by the vortex wake is noted for the two di!erent initial displacements imposed on the wake. The roll oscillations instigate growth in the waves placed in the two #ap vortices much like those shown in Fig. 90a. As the waves grow, the vortices orbit, and the planes of the waves rotate from nearly vertical to curved diagonal planes. Wave growth "rst occurs while the planes of the two vortices are nearly parallel. During the later stages of the event, a linkingtype interaction appears to be taking control of the vortex motions. The present numerical results therefore suggest that the initial sinusoidal displacements of the vortex "laments brought about by the roll oscillations executed by the B-747 lead to vortex interactions which greatly amplify the vortex displacements at those stations where each wingtip is at its highest position. The numerical results suggest that periodic linking and loop formation may also be starting to occur at about ¹"32. Examination of the motion picture taken of smoke #ow visualizations during the #ight tests of Barber and Tymczyszyn [59] indicates the same kind of vortex motion and thus supports the proposed explanation.
Once again, however, the amplitude appears to be reaching a limit if the linking process does not begin between each set of #ap vortices. It was not possible to discern in the #ight #ow visualizations whether linking actually took place or not, because intense mixing in the #ow "eld was taking place. The ingredient which seems essential for growth of the waves after roll oscillations is the presence of the two vortex pairs that are of opposite sign and of comparable strength. The vortex pair shed at the wingtips does not become involved in the swinging interaction of the #ap vortices, but simply moves inboard and then descends as predicted by two-dimensional theory without the appearance of signi"cant wave growth or instability. These characteristics were also observed in the #ight #ow visualizations. The similarity of the numerical results, and the #ight #ow visualizations, suggests that the span loading and subsequent wake vortex distributions assumed in the numerical work are not too far from the one that occurred in #ight. The results presented in Fig. 91b for pitching motion illustrate an interaction that is a version of the Crow process. The small waves on the vortices appearing on the older parts of the wake (left-hand side of the "gures) are the beginnings of waves that will probably lead to linking. Presence of the third vortex pair does not seem to enhance or hinder the wave growth nor the approach to the linking process. If the aircraft is #own on a straight and level path, the end views of the vortex wakes are about the same as predicted by two-dimensional theory until the vortices undergo the wave growth that leads to linking. The occurrence of this sequence of vortex interactions was con"rmed by #ight test at Rosamond Dry Lake with the B-747 in the (303, 03) con"guration with the gear up and spoilers stowed (Fig. 60). Not so obvious was the "nding that a small amount of turbulence injected into the wake by deployment of any of the landing gear, or by slight yaw, was su$cient to inhibit the growth of the disturbance wave so that linking and loop formation do not occur (Fig. 60). The results obtained from the #ight tests that used roll oscillations suggest that, if an initial displacement of su$cient amplitude is given to the waves on the wake vortices, wave growth does occur to the point where linking and loop formation and the "nal demise of the organized wake results. It is concluded, therefore, that the dynamics observed in the wake of the B-747 following roll oscillations can be attributed to the span loading, which is responsible for the special wake-vortex structure that destroys the wake organization. 8.6. Three-dimensional simulation of wakes: ¸-1011 The three span loadings and vortex wakes presented in Table 7 for the L-1011 were used to carry out numerical simulations of the #ight tests. However, only the #aps (333), spoilers-deployed case is presented, because the two
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
589
Fig. 91. Oblique and end views of wake of B-747 #aps (303, 03) con"guration at three time intervals after start of maneuver [181].
other cases were quite similar, and showed no signi"cant wave ampli"cation that was new. It is to be noted in the three-dimensional computations shown in Fig. 92 that the vortices shed by the L-1011 (with #aps and spoilers deployed) rotate around each other in much the same way as indicated by the two-dimensional theory and shown in Fig. 89. Distortions of the initial shape of the "laments due to roll oscillations of the generating aircraft are again superimposed on the paths. It is di$cult to determine in the end views just what kinds of vortex interactions are taking place. The computations show that, throughout the computational interval, the vortices stay grouped together closely enough that they would probably coalesce into a single pair much the same as they do when the roll-oscillation maneuver is not being used. Subsequent examination of the #ow visualization sequences taken during the #ight test by Barber and Tymczyszyn [59] show that the vortices trailed by the L-1011
coalesce fairly quickly into a single pair at about 0.5 mile or so behind the aircraft. The lack of another vortex pair in the merged wake, which is of comparable strength and of opposite sign, made the wake dynamics observed in #ight appear almost the same as the numerical results displayed in Fig. 90a. That is, the wake of the L-1011 responded to roll oscillations of the generator aircraft as if it were composed of a single pair. Wake alleviation was not sensed by the probe aircraft, because destructive vortex interactions did not occur. In fact, the single vortex pair goes through the dynamics explored previously in the section on the e!ect of wave phase on vortex interactions. As illustrated in Figs. 81 and 84, the planes of the vortices roll through 903 so that the pair forms a sinuous trail in the horizontal plane that is more stable than without the roll-oscillation maneuver. In other words, the wake is more hazardous when a rolloscillation maneuver is executed with the L-1011 than when the aircraft #ies straight and level.
590
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 92. Oblique and end views of wake of L-1011 #aps (333) with spoilers deployed at three time intervals after start of maneuver [181]. (a) Setup in 40;80 ft Wind tunnel. (b) Water tow tank and carriage arrangement at Hydronautics, Inc.
and possibly quantify further the wake ingredients necessary to bring about the di!ering responses of the B-747 and L-1011 wakes to the roll-oscillation maneuver. Based on the results presented in this section and the corresponding #ights tests at Dryden, it is concluded that two ingredients in the vortex wakes of the test aircraft appear to cause the di!erent responses to the roll-oscillation maneuver. First, the B-747 sheds a fairly strong vortex near the fuselage, and the L-1011 does not. Secondly, the L-1011 sheds a vortex near its wingtip that is stronger relative to the #ap vortices than the B-747. These two factors combine to bring about an unstable vortex con"guration behind the B-747 that leads to linking and destruction of the organization of the wake. In contrast, the roll-oscillation maneuver of the L-1011 brings about a stable vortex-wake con"guration that persists. The roll-oscillation maneuver is responsible for both sets of wake dynamics, because it places large initial sinusoidal waves on the "laments that bring about interactions and dynamics that lead to the observed motions. It should also be noted that, even though the present analysis is based on fairly crude estimates of span loadings, and the vortex wakes that they trail, comparison of the numerical results with the #ight motion pictures of smoke visualization shows that the dominant features of the wake dynamics behind the two wake-generating aircraft have been well simulated. It is also concluded that the vortex-wake instability is not of a new type, but just a combination of the symmetric and anti-symmetric mutually induced instabilities that result from multiplevortex interactions.
9. Wake alleviation by wing 5ns 8.7. Concluding remarks on multiple vortex pairs
9.1. Introduction to wing xns
It is concluded that, for multiple-pair vortex wakes, wave ampli"cation requires at least two vortex pairs (four vortices in the wake) of comparable and opposite strength. The separation distances between the vortices must also be large enough spanwise to enable a linkingtype interaction that produces large-scale mixing in the wake. This approach can be tested by adding a vortex pair of opposite sign and of comparable strength near the fuselage of the L-1011. Modi"cation of the inboard #aps on a model of the aircraft to produce such an extra vortex pair leads to two-dimensional trajectories like the ones shown in Figs. 88c and d. Two-dimensional computations carried out during this study, but not presented here, showed that only the stronger fuselage vortex cases show promise. Since the strong tip vortex shed by the L-1011 tends to dominate the wake dynamics, the degree of alleviation to be expected will be less than that achieved with the B-747. Ground-based tests with con"gurations having fuselage vortices would help to clarify
Several con"gurations already described demonstrate that certain vortex interactions are able to bring about large-scale mixing in vortex wakes for substantial reductions in the rolling-moment hazard posed by lift-generated vortices. Since none of the designs discovered so far have negligible penalties, and are therefore currently considered to be unacceptable, a more generalized approach was taken in the search for an ideal wake-alleviation scheme [105,183]. Research was directed at "nding another way to bring about the vortex interactions desired. It was reasoned that not only should the spanwise distribution of wake vorticity be used to control wake dynamics, but a vertical distribution of vorticity should also be used to assist in bringing about the desired rapid disintegration of the wakes. That is, conventional wings shed a vortex sheet that is approximately #at (i.e., in the z"0 plane), and that has a small vertical depth. As a consequence, in conventional wakes the rollup begins at the ends of the vortex sheet near the wingtips, and proceeds
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
inboard. Since the vortex sheet is thin, the sheet winds up in a tight spiral that tends to concentrate the vorticity near the center of the spiral. Whatever vertical depth is present in the initial vortex sheet due to boundary layer on the wing and #aps winds up in the spiral tending to reduce the concentration at the vortex center. It was reasoned, therefore, that addition of vertical lifting surfaces to the largely horizontal wing surface would not only add vertical depth to the vortex wake at the wing trailing edge, but would also impart immediate horizontal motion to some portions of the vortex sheet shed by the wing. The optimum or preferred placement, size, etc. of these vertical surfaces, or wing "ns, and the e!ect that they have on the hazard posed by lift-generated wakes shed, became the subject of several research e!orts in the large wind tunnels at NASA Ames Research Center [105,106,183,184] which are summarized in this section. Although the foregoing reasoning was used to begin the exploration of wing "ns as wake-alleviation devices, the wake-dispersion mechanism appears to be more complicated and, as yet, not amenable to analysis. As a consequence, the study and any optimizations achieved have been carried out experimentally. As more computations were carried out, and when some test results became available from a water tow tank, #ow visualization and wake measurements indicate that the wake is already de-intensi"ed very near the wing trailing edge [93]. It also appears that the wake does not change much thereafter. As a consequence, e!orts so far have provided only a rough concept for the alleviation achieved with wing "ns. Since the results do indicate a great deal of promise
591
for e$cient and rapid wake dispersion, the study carried out so far on wing "ns is described. 9.2. Experimental setup in 40;80 ft Wind Tunnel Since the 40;80 ft Wind Tunnel at NASA Ames was readily available for tests of short duration during the 1970s, several wind tunnel entries were made in order to test the wing-"n concept, and to determine design guidelines experimentally [105,183]. In addition, in cooperation with Langley Research Center, test time was rented in the water tow tank operated by Hydronautics Inc. near Laurel, MD. Diagrams of the experimental setup in the two facilities are presented in Fig. 93. The crosssections of the test sections in both facilities are large enough that wall a!ects on a model with a span of 70.5 in (1.79 m), or 3% scale, are negligible. However, downstream distances available to study the lift-generated wake of a B-747 model are limited in the wind tunnel by the length of the test section and in the tow tank by the depth of the water and the length of the tank. The tow tank is 410 ft (125 m) long, 24 ft (7.6 m) wide, and 12.5 ft (3.8 m) deep. Tests were conducted in the wind tunnel at a free-stream velocity of ; "131 ft/s (40 m/s, q " 20 lb/ft), and at a velocity of 12.5 ft/s (3.8 m/s) in the tow tank. In both facilities, a B-747 wake-generating model (0.03 scale) is mounted from the top of the fuselage by a slender, streamlined strut. In the wind tunnel, the model is mounted near the entrance to the test section, and in the tow tank it is mounted on the forward carriage (Fig. 93b). A plan view of the B-747 model used as the wakegenerating aircraft is presented in Fig. 94. The model had
Fig. 93. Facilities used to obtain data on wing "ns [183].
592
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
its landing gear extended, its leading-edge slants fully deployed, and the wing was designed so that the #aps could be deployed in their stowed, takeo!, or full-landing position. The horizontal tail was set at 03 relative to the fuselage, or aircraft reference plane (i.e., the horizontal tail is at 03 when the aircraft is at 0). A rectangular wing (b "13.1 in (33 cm), AR "5.5, b /b "0.186) was used to represent the following aircraft used in the #ight program (either the Gates Lear Jet or the T-37B). As indicated in Fig. 93, in the wind tunnel, the following model is placed at the downstream end of the test section on a support strut mounted onto a tower which could be raised and lowered and also translated across the airstream. Movement of the following model permits a survey to be made of the energetic part of the vortex wake shed by the wake-generating aircraft, so that the maximum value of the rolling moment can be found, and contours of equal rolling moment determined. The downstream tower could be located at distances as large as 80 ft (24 m or 13.6 generator spans) behind the wakegenerating aircraft, or at any closer distance. Based on the 70.5 in (1.79 m) span of the B-747 model, the 80-ft station corresponds roughly to a 0.5 mile scale distance behind a full-scale aircraft. As explained in Section 6.3, during a typical run, the following model is held "xed at various vertical and lateral positions in the wake for 1 min. The rolling moment at each position #uctuates due to turbulence in the free stream of the wind tunnel which causes motion or meander of the wake as it trails from the wake-generating model [161]. A survey of the wake cross-section is then made wherein the maximum value measured at each location is "rst recorded. The maximum value of all of the measurements taken is then used as the maximum rolling moment in the wake for that con"guration. The distribution of maximums is also used to map out rolling-moment contours. In the wind tunnel, a few con"gurations were tested at a "03, 43, 83, and 123. Most however, were tested only at 43 (C "1.2) to expedite * the investigation of a wider variety of con"gurations. In the water tow tank, the following model is mounted on a second carriage that maintains a "xed distance behind the forward carriage. Since the turbulence level, and consequently the vortex meander, is negligible in the tow tank, the #ow "eld is surveyed for maximum rolling moment by placing the following model at a "xed spanwise station during a run. In order to carry out a vertical survey at the chosen spanwise station, the following model makes a vertical traverse through the wake during a traverse along the channel. In the wind tunnel tests, the devices used to inject vortices on top of and below the vortex wake shed by the wing consisted of vertical surfaces, or "ns, mounted on the wing at a large angle of attack to the free-stream direction (Figs. 94 and 95). A variety of "n shapes were tested in the wind tunnel at the spanwise and chordwise
locations shown as dots in Fig. 94. In the water tow tank, the only "n design tested was the circular-arc planform (Fig. 95e) because it was determined as the best design and limited test time was available. Circular-arc "ns were chosen for the research program because Zimmerman [185] found that wings of circular planform did not stall even at large angles of attack. A study by Moghadam [186] found that planforms of elliptical planform might be even more e!ective as wing "ns, but they have not been tried as yet, because the "n e!ectiveness was found to not increase appreciably when the "n height exceeded a given height. The "n angle of attack was taken as positive when the vortex it sheds had the same direction of rotation as the nearby wingtip vortex. The "rst part of the optimization process explored whether "n performance was best when they were mounted on the upper or lower surfaces of the wing. As expected, a search technique showed that "n locations on top of the wing were much more e!ective than those mounted on the bottom surface of the wing. It is believed that the greater e!ectiveness on top of the wing is attributable to the higher dynamic pressure over the wing as compared with that under the wing. The higher velocity over the top of the wing produces a greater lift on a "n (and consequently a stronger vortex) than if it were mounted under the wing. Therefore, all of the data to be presented for wing locations, angles of attack, etc., were obtained with a "n or "ns mounted on the upper surface of the wing. The search for the optimum location, size, etc., for the various shapes of "ns shown in Fig. 95 was begun with the #at-plate "ns of rectangular planform, and then broadened to include all of the "n shapes shown in Fig. 95.
Fig. 94. Plan view of B-747 wake-generating model [183].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
593
Fig. 95. Fin shapes used in tests [183]. (a) Rectangular and triangular "ns. (b) Rectangular and circular-arc "ns.
9.3. Test results 9.3.1. General comments Wake-hazard data were obtained with a wide variety of "n sizes and shapes to study the e!ect of changes in the angle of attack, location, chord and height on wake hazard. The "rst of the two papers cited in the reference list was restricted primarily to "ns of rectangular planform [105], whereas the second paper considered a wider range of "n designs, and also explored the various "n parameters in more detail [183]. Material contained in both papers is summarized here. As mentioned previously, all of the tests were conducted with the "ns mounted on top of the wing. The test results will be presented for "ns with a planform of rectangular and triangular shapes at the same time, because both were used in the optimization process. 9.3.2. Fin angle of attack The "rst design parameter chosen for study was the angle of attack of the "n. Two sets of data are presented in Fig. 96, and in "gures to follow, so that variations with "n design can be illustrated. Since the "ns were all of low aspect ratio, it was not certain whether or not they would stall at the higher angles of attack. In Fig. 96, the angle of attack was varied from !123 to #363, where the positive sign means that the "n is shedding a vortex of the same sign as the nearby wing tip. According to the data presented in Fig. 96, the "n rapidly decreases the wake hazard as its angle of attack is increased and stall of the
"n, if present, does not appear to a!ect alleviation performance. At "rst it appears that negative angles of attack are ine!ective. However, in tests conducted later in the 80;120 ft Wind Tunnel at NASA Ames [184], negative angles of attack were found to produce similar results. However, the required angle of attack must be larger by about 303 on a swept wing to achieve the same rollingmoment reduction because of the spanwise #ow on the upper surface of the wing due to sweep. The larger negative angles of attack required for the same alleviation carry with them a drag penalty over and above that carried by positive angles. Di!erent "n shapes yield about the same result, and as expected, smaller "ns will produce comparable results if they are placed at higher angles of attack, e.g., circular arc "ns. It is noteworthy that the e!ectiveness of wing "ns for alleviation of vortex wakes is approximately proportional to the angle of attack used. Wing "ns are the only wake alleviation mechanism known to have such a proportional characteristic. 9.3.3. Spanwise location The next parameter studied was the spanwise location of the "n, mounted on the upper surface of the wing (Fig. 97). Various "n sizes were tested at several spanwise locations, and all showed a distinct preference for the location near a point midway between the aircraft centerline and the wingtip. When the results for the circular "n are added to Fig. 97, it is found that smaller "ns have the same characteristics, but that the bucket has
594
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 96. Wake-induced rolling moment on following wing with angle of attack of "ns [183].
Fig. 97. Wake-induced rolling moment on following wing with spanwise location of "n [183]. (a) Rectangular and triangular "ns; h /b "0.085, a "123. (b) Rectangular and circular-arc "ns.
a smaller spanwise extent and smaller bene"t (Fig. 97). As a consequence, more testing is required to be certain that the smaller "ns are in their optimum location. All of the "n con"gurations exhibited the same sensitivity to spanwise location. It was found that the optimum location of a "n was insensitive to the lift on the wing, or to the angle of attack of the "n.
9.3.4. Chord of xn The variation of the wake-induced rolling moment with the chord of the "n for several "n con"gurations is shown in Fig. 98. As the length of the chord of the "ns is increased, the alleviation once again also increases almost linearly up to about c /b "0.08. Above that value an increase in chord appears to be no longer bene"cial. All "n shapes are noted to provide almost linearly increasing alleviation with an increase in chord up to some point where further increases in the "n parameter yield little bene"t.
9.3.5. Height of xn A similar linear trend is found for "n height (Fig. 99), but the bene"t of "n height is limited to values up to around h /b "0.04. This "nding tends to indicate that the original idea for the use of wing "ns to add depth to the vortex wake is not the basis for the success achieved by use of wing "ns. In fact, the decrease in bene"t as h /b increases above 0.08 indicates that the proximity of the vorticity shed by the "n to the wing surface is important in the reduction of the wake-induced rolling moments. Such a variation with "n height is of bene"t, because small heights have less penalty in drag than tall "ns. It is noted in Figs. 98 and 99 that two "ns of a given shape (indicated by a double line) are usually more e!ective than a single "n, but not necessarily superior to a single rectangular "n of the same wetted area. If wing "ns are to be folded down into or onto the wing for cruise, two smaller "ns might be easier to handle than one large "n.
9.3.6. Circular-arc planform As indicated previously, one pair of circular-arc "ns was made with the Clark-Y airfoil section to duplicate the wings studied by Zimmerman [185]. Another pair of wing "ns was also made with the GA(W)-2 section to "nd out if a more recent airfoil design would yield improved performance. A measurable di!erence was not found, but the use of two circular arc "ns at the same time was found to be advantageous. Since preliminary results were promising, these two "n designs were tested more thoroughly in the wind tunnel than other designs, and they were the only ones investigated in the water tow tank. Data from the two test facilities are compared in Figs. 96}100 with the data for other "n shapes. None of the tests indicated that one airfoil shape was to be preferred over the other. Any airfoil shape is believed to be superior to #at-plate cross-sections.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
595
Fig. 98. Wake-induced rolling moment on following wing with chord of "ns [183]; a "43.
Fig. 99. Wake-induced rolling moment on following wing with height of "ns [183]; a "43.
The circular-arc "ns were placed at larger angles of attack than any of the other "ns, because the data of Zimmerman [185] indicated that wings of circular planform do not begin to stall until they reach an angle of attack of 453. Since the #ow angularity over the generator wing is uncertain, the true angle of attack of the "n is unknown. It is known that the local #ow angle over the upper surface of the wing is such that positive "n angles of attack are actually larger than its angle relative to the free-stream direction. The data in Figs. 98}100 show that two "ns with semi-circular planform and Clark Y airfoil sections provide as much or more alleviation than one #at-plate rectangular "n of the same dimensions. Furthermore, two circular-arc "ns, located within about one "n chord of each other, may be easier to install onto #ight hardware than one large "n. The rolling-moment data are presented in Fig. 100 on an expanded scale, so that a comparison can be made of the data from the two facilities. In general, there is little change in the level of the rolling-moment coe$cient, C , J over the range of downstream distances that were tested in the two facilities. Where substantial di!erences do occur, it is believed that the optimum "n position in one
Fig. 100. Comparison of wind tunnel and water tow tank measurements with B-747 model equipped with circular-arc "ns [183]; following wing C 1.
596
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
facility was not the same as in the other, because of the changes in span loading on the wing in the water tow tank due to the nearness of the free-surface of the water. From an overall view, the two sets of data do not di!er appreciably even though the downstream distance to the follower is over three times as large in the tow tank as in the wind tunnel, and the tow-tank model is only 0.4b from the free surface of the water. The experimental optimization process did indicate that the smaller circular-arc "ns provide the needed alleviation with less penalties in lift and drag. This result is consistent with the test results that indicate that those "ns with circular arc planform yield the strongest vortex for the smallest "ns. The best con"guration found for the B-747 in the test time available was a combination of two circular-arc "ns on both the port and starboard wings as shown in the photograph in Fig. 101. The circular-arc "n was found to be the best amongst those tested [185]. If an application is to be tried, it is suggested that "ns of elliptic planform also be tested to "nd out if they do have superior performance when used as vortex injection devices [186]. The lift and drag on the B-747 model is shown in Fig. 102 for the rectangular and circular-arc "ns. Results to be described indicate that properly designed "ns can reduce the associated penalties, and in fact, can increase the lift and reduce the drag of the conventional B-747 landing con"guration. It is felt that the vortices shed by the "ns enhance the velocity "eld over the wing so that any #ow separation on the #ap elements is reduced and
the overall #ow improved. Penalties due to weight and installation costs of a "n still exist, but the results obtained with the smaller "ns indicate that further optimization may lead to con"gurations wherein the wake rolling moments have been reduced to the desired level, and the lift and drag penalties are negligible. The lower drag measured in the water tow tank as compared with wind tunnel measurements is attributed to the lower turbulence and higher Reynolds number in that facility relative to the wind tunnel. The drag data presented in Fig. 102 also calls attention to the fact that contoured airfoils with rounded leading edges achieve leading-edge suction, so that the drag penalty associated with the circular arc "ns is less than the #at plate rectangular "ns. In fact, future tests in the study of the aerodynamics characteristics of wakes shed by aircraft should have been carried out only by use of "ns with airfoil shapes. Fins made of #at metal plate were used however, because they are much less expensive.
9.3.7. Multi-element xns Several "n con"gurations, which had several airfoil sections in close proximity (Figs. 95b and d), were tested in the wind tunnel. Some of these results are listed in the tables presented in Ref. [183], but are not shown graphically, because the alleviation was inferior to simpler "n con"gurations. Although the section lift coef"cients achievable with multi-element airfoils is usually higher, they may lose their advantage at low aspect ratios
Fig. 101. Photograph of model of B-747 mounted upside down on support strut with best "n con"guration (i.e., two circular-arc "ns mounted midway out on each wing) [183].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
597
Fig. 102. Variation of lift and drag with "n height of B-747 model when equipped with rectangular or circular-arc "ns [183]; a "43.
Fig. 103. Variation of wake-induced rolling moment with "n size for various "n con"gurations [183].
or when placed on a re#ection plane like the generator wing which has a boundary layer.
full-landing con"guration was held constant at 43 during the tests, so that the lift coe$cient was approximately, C "1.2, in both test facilities. The data fall in a band * about the rectangular "n data. Of most interest are those that are lowest, namely, the circular-arc and the blown#ap con"gurations. The data point in Fig. 103 for the "n with a blown #ap does not, however, necessarily represent the lowest rolling moment achievable with that "n, because the time needed to optimize its spanwise location, angle of attack, etc., was not available. Since the water tow tank facility was not set up to test blown-#ap con"gurations, those particular tests concentrated on the circular-arc "ns. All of the results indicate that the stronger the vortex shed by the "n, the more alleviation can be achieved. In order to have information on how the wake-induced rolling moment on a small following wing changes with distance across the vortex wake of a "nned con"guration, enough measurements were taken to draw contours of equal rolling moment for a wake shed by both a conventional and a "nned con"guration (Fig. 104). The rollingmoment contours for the "n-modi"ed wake are shaped quite similar to those of the unmodi"ed wakes. A signi"cant di!erence occurs, however, in the magnitudes of the contours in the inner and more hazardous parts of the wake. The "n appears to redistribute the wake vorticity, so that the interior of the vortex has reduced swirl velocities, but the outer parts are hardly changed because the contours for C "0.01 are about the same for both J con"gurations. Even though the contours for C "0.01 J are nearly the same, the rolling moment for the conventional wake is over 0.12 at the center, whereas the "n-modi"ed wake rises to only about 0.04 over a small region near the center. Such a large di!erence in rolling moment for a small change in span loading indicates that alleviation can be accomplished by designing the lift distribution to promote favorable vortex interactions.
9.3.8. Fins with blown yap Since the optimum spanwise location for a "n is in the vicinity of the inboard engine on the B-747 model, it seemed likely that high-pressure air from the engine could be used to enhance the lift or side-force capability of the "ns by chordwise blowing (Fig. 95f ). At the end of the test period, a single blown-#ap con"guration was tested at one location on the wing. The results are presented in the tables in Ref. [183] for two "n angles of attack at the maximum blowing available with the test set up (i.e., a blowing coe$cient based on "n planform of 0.5). The "n at the larger angle of attack did provide signi"cant alleviation, but there was not time available to carry out tests that would have optimized the various "n parameters. These preliminary results do indicate, however, that further consideration should be given to the "n location on the generator wing and to its angle of attack to "nd out if greater alleviation can be achieved with "ns having blown #aps. Also, the use of two or more "ns on each wing should be tried as a method for reducing the size or wetted area of the "n con"guration. 9.4. Discussion of xn conxgurations One means for comparison is to specify that the optimum "n is one that reduces the wake rolling moment a given amount, and that also causes a minimum penalty in lift, drag, weight, etc. (Fig. 103). The measured rolling moment for the devices tested is shown as a function of the ratio of the wetted area of the "ns to that of the wing. A data point as near as possible to the origin is desired, so that both the wake-induced rolling moment and the required "n size are small (a small "n is presumed to impose a smaller penalty than a larger "n). In this comparison, the angle of attack of the B-747 model in its
598
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 104. Contours of equal rolling-moment coe$cient as measured on following wing in wake of B-747 model [183]; a "43.
9.5. Ewect of rectangular xns on span loading It should "rst be noted that wing "ns are the only device discovered so far that produces alleviation in direct proportion to the size, de#ection of the "n and other factors that in#uence the strength of the vortex that it sheds. The alleviation produced by a "n con"guration has also been found to behave in an orderly way without any reversals of performance. The mechanism by which wing "ns achieve alleviation is not clear. It appears that the "ns modify the #ow over the wing so that the vortex wake distribution is modi"ed for rapid dispersal, but the details and concepts behind this process are unknown. As indicated previously, the "ns redistribute the loading on the wing as estimated by vortex-lattice theory (Fig. 105). It is noted that the larger rectangular "n changes the loading substantially over a portion of the span, but the smaller rectangular "n makes only small local changes. The alleviation brought about by the two "n heights is noted in Fig. 100 to be about the same, suggesting that some characteristic other than span loading may be the dominant factor in producing the alleviation achieved by "ns. 9.6. Concluding remarks on wing xns Various theoretical and experimental studies of the performance of aircraft models with "ns mounted on
their wings have not yet identi"ed the #uid-dynamic mechanism responsible for their e!ectiveness nor led to theoretical guidelines for their optimization. It is believed that the wing "ns impart horizontal or spanwise motion of vortex elements to bunch up and to spread out wake vorticity in order to generate interactions to rapidly disorganize and disperse vortex wakes. Several design features of wing "ns for alleviation of the hazard posed by vortex wakes were identi"ed by the test program. First the "n or "ns should be designed to produce the strongest vortex possible while minimizing the penalties associated with the design. The e!ectiveness of a "n design is strongly dependent on its spanwise location on the wake-generating wing. The mechanism of alleviation appears to require vortex placement and strength as well. If the "n is to achieve vortex generation by developing lift in the local airstream around the wing, it develops much more lift when mounted on the upper surface of the wing than on the bottom of the wing. The "ns should be made with an airfoil cross-section (rather than with #at plates) to decrease the drag of the device and increase its e$ciency. Finally, an improved understanding is needed for the details of the mechanism responsible for the rapid modi"cation of the vortex wake to a less hazardous con"guration, so that the design process can be optimized.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
599
Fig. 105. Span loadings as estimated by vortex-lattice theory for wing of B-747 landing con"guration equipped with various "ns con"guration [183]; a "43, c /b "0.085, C +1.18. *
10. Measurements in 80ⴛ120 ft Wind Tunnel 10.1. Introduction In the 1980s, the 40;80 ft Wind Tunnel at NASA Ames Research Center was modi"ed to increase the maximum velocity in the test section from 200 to 300 knots, and to add a large low-speed branch onto its circuit. The added branch has a test section that is 80 ft high, 120 ft across (24.4 m;36.6 m) and about 200 ft (61 m) long with a maximum velocity of 100 knots. The portion of the circuit devoted to the large test section is called the 80;120 ft Wind Tunnel. It is now the largest NASA facility, and consequently, has the greatest downstream test distance, which is the characteristic of interest to the wake-vortex program. A plan view of the wind tunnel (Fig. 106) illustrates the intersection of the test section and constant area di!user with the circuit of the 40;80 ft
Wind Tunnel. The test section alone is long enough that wake measurements can be made at downstream distances that simulate scale distances up to one mile (1.61 km) when models of 0.03 scale are used. Therefore, two tests of about three months duration each were conducted to obtain data on two models of subsonic transport aircraft (i.e., B-747 and DC-10). The purpose of the tests was to expand the database available from wind tunnels on the characteristics of vortex wakes shed by various con"gurations of subsonic transport aircraft [106,184]. As with previous wake vortex tests, the two wind-tunnel entries were designed to evaluate the potential hazard posed by various subsonic transport aircraft in the airport environment, and to develop guidelines for the design of high-lift systems of aircraft, so that their wakes disperse rapidly enough to allow in-trail spacings between aircraft to be safely decreased.
600
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 106. Plan view of test section region of 80;120 ft Wind Tunnel [184].
In both 80;120 ft Wind Tunnel test entries, a 0.03 scale model of the Boeing 747 with a span of 70.5 in (1.79 m) was again used as a wake-generating model. In the second test entry, a 0.03 scale model of the McDonnell Douglas DC-10 with a span of 59.5 in (1.51 m) was also used as a wake-generating model. The test conditions are listed in Table 8. As noted in Table 9, the con"gurations tested include the conventional landing and several modi"cations of it. The purposes of the tests were to provide data for estimating the interaction of following aircraft with the wakes of standard landing con"gurations, and to develop a database on how various wing-design parameters a!ect the wake-vortex structure and its decay with time or distance behind the wake-generating aircraft. In order to assess the characteristics of vortex wakes, the following wings were tested or analyzed that range in size from 0.186 to 1.21 times the span of the wake-generating model (Table 10). Also, a two-component hot-"lm anemometer probe was used to determine the up- and down-wash distributions in the wake at both 81 and 162 ft (24.7 and 49.4 m) downstream measuring stations. An overview of the information obtained during the two test entries, and several applications of the data are presented in this section. 10.2. Experimental setup in 80;120 ft Wind Tunnel The test setup used in the 80;120 ft Wind Tunnel is about the same as, but better equipped than, the one Table 8 Test conditions [184] used in 80;120 ft Wind-Tunnel (24.4;24.4 m) Free stream velocity"131 ft/s Dynamic pressure"20 lb/ft Distances to following models"81 and 162 ft
Table 9 Data on wake-generating models [106,184] B-747 Model Scale of model "0.03 Wing span b "70.5 in Average chord of wing cN "10.1 in Reynolds no. based on cN Re "660,000 Aspect ratio AR "6.96 Wing area S "4.94 ft Horizontal stabilizer angle "03 Landing gear extended Flaps and slats fully deployed
DC-10 Model
"0.03 "59.5 in "7.92 in "518,000 "7.5 "3.56 ft "03
used in the latter part of the 1970s test program in the 40;80 ft Wind Tunnel (Fig. 107). In order to carry out a test, one of the wake-generating models, B-747 or DC-10 (Fig. 108 and Table 9), is mounted through a strain-gage balance to a strut in order to measure the lift, drag and pitching moment exerted on it by the free stream. Instead of locating the experiment on or near the centerline of the wind tunnel, as was done during the 40;80 ft Wind Tunnel tests, the models are now located o! to the side of the 80;120 ft Wind Tunnel centerline (Figs. 106 and 107). The o!-center mounting is used because the 80;120 ft Wind Tunnel merges with the circuit of the 40;80 ft Wind Tunnel along a diagonal junction (Fig. 106). Including the di!user, the constant area region is therefore longer on one side than on the other. Consequently, in order to maximize the downstream distance available for a test, the wake-generating models and following wings are mounted on that side of the test section. In the test sequences, the experimental equipment was con"ned to the test section wherein a 162 ft (49.4 m) separation distance is achieved by
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
601
Table 10 Data on following wings [184] No.
b (in)
C * (in)
C (in)
K *# (deg)
K 2# (deg)
AR
S (ft)
f (Hz)
f (Hz)
1 2 3 4 5
13.12 13.13 6.00 35.97 72.04
2.41 2.84 6.00 7.86 15.67
2.41 0.85 6.00 2.41 4.72
0 30 0 30 30
0 15 0 15 15
5.44 7.14 1.00 7.00 7.06
0.220 0.168 0.250 1.283 5.100
156.0 156.0 190.0 30.5 12.0
13.0 13.0 12.0 11.5 7.3
Fig. 107. Diagram of experimental setup in 80;120 ft Wind Tunnel [184].
locating the wake generator in the forward part of the test section and the survey rig for the follower model at the end of the test section. An 81 ft (24.7 m) separation distance is achieved by locating the generator model just o! to the side of the turn table and not moving the following model and its traversing gear. In this way, the much larger and more cumbersome traverse mechanism that supports the following model need not be moved in order to change the separation distance. An inverted mounting of the generator model is again used to minimize interference of the strut wake with the vortex wake of the generator model (Fig. 107). The model wake then moves upward away from the strut wake, which tends to go straight downstream. The angle of attack of the wake-generating model is set remotely through an actuator and indicator mechanism. The landing con"gurations of the wake-generating models (Fig. 108) include extended landing gear along with fullydeployed leading-edge slats and trailing-edge #aps. As in the past, and as indicated in Table 9, a designation of
#aps (303/303) is used to indicate that the B-747 wakegenerating model is in its full landing con"guration with the leading-edge slats, landing gear, and trailing-edge #aps fully deployed. The other two con"gurations are again part of the study to "nd design guidelines that will make it possible to build e$cient aircraft with acceptably alleviated wakes. In the (303/03), or modi"ed landing con"guration, the inboard landing #aps are fully deployed, and the outboard ones are stowed. The rest of the model is in its full landing con"guration. The third con"guration that was tested, Table 9 and Fig. 108, consists of the conventional landing con"guration with a fairly large "n, like those discussed in Section 9, mounted on the upper surface of each side of the wing to accelerate the dispersion of the vortex wake. The models used as following wings are all made with a NACA 0012 airfoil section and have the planforms shown in Fig. 109 and the characteristics indicated in Table 10. The planforms for the swept wings are based on an average value obtained for the leading- and
602
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 108. Plan view of wake-generating models to illustrate #ap arrangements and locations of wing "ns [184].
Fig. 109. Overhead photograph of following wings used in test program [184].
trailing-edges and taper ratio of a large number of the wings of subsonic transport aircraft now in service. In this way, the following wings used in the tests are representative of subsonic transports, but do not resemble any of them closely. The models are constructed of wood and aluminum, and then covered with "berglass to ensure a smooth, durable "nish along with structural rigidity and adequate frequency response. As a result, the natural frequencies in roll and pitch of the model-balance combinations are several times larger than the lift and rollingmoment frequencies encountered. The trailing model or wing is mounted on a sting (Fig. 107) that can be raised and lowered over a height range of about 8 ft (2.44 m). The vertical traverse mechanism is attached to a tower that can be translated laterally, or spanwise, across the airstream over a range of about 18 ft. The following-wing or wake-encountering model is attached to its sting through a strain-gage balance located inside the centerbody of the wing, so that
the wake-induced lift and rolling moment can be measured. Both a 1 and a 2 in internal-type balance were used in the tests to more adequately cover the wide range of loads that occur when the smallest to the largest following wings encounter a vortex wake. As a result, the natural frequencies in roll and pitch, f and f , of the model-balance combinations (Table 10), are several times larger than the lift and rolling-moment frequencies encountered. As a reference, the natural frequency in roll of the model/balance combination tested during the 1970s was 30 Hz, i.e., when a wing equivalent to model C1 was used. Because the physical distance between the wakegenerating model and the following model is quite large (81 or 162 ft, 24.7 or 49.4 m), a probe to measure the dynamic pressure (i.e., total and static pressure) was attached to the support strut of each model. A correction could then be applied to the coe$cients of the follower if the variations were too large. It was found that the dynamic pressure near the wake-generating model always agreed within measuring accuracy with the test section value, but that the dynamic pressure at the following model was about 1% larger. An analysis of the e!ect of a di!erence in dynamic pressure between the two stations showed that both the lift and rolling-moment coe$cients should be adjusted by a factor that is about the one-fourth power of the ratio of the two dynamic pressures. Since the correction for these test results is then 1.0025, an adjustment in the data was not made. 10.3. Test procedures The procedure used to measure the rolling moment on the following wing consists of several steps. The
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 110. Lift and drag on con"gurations of B-747 wakegenerating model as a function of angle of attack [184].
generator model is "rst set up in its desired con"guration and angle of attack. After the loads on the wake-generating model are recorded (Fig. 110), the following wing is placed at various locations in the vortex wake of the generator model. Since the airstream is not perfectly uniform, the position of the vortex wake moves about with time to cause di!erent amounts of lift and rolling moment to be induced on the following wing. The analog signals from the strain gage balances in the wakegenerating and in the following wings are "ltered with a low-pass "lter at 10 Hz in order to eliminate electronic noise and high-frequency oscillations of the models. (The hot-wire signals were also "ltered in the same way.) Since the "ltered signals also varied with time, the time-varying rolling moment indicated by the strain-gage instrumentation is recorded during a test interval of 1 min. Data samples are then taken of the time-varying "ltered record every 0.1 s, so that 600 data samples are recorded from the 1 min test interval. The permanent or retained record consists of the maximum and the minimum of all of the 0.1 s values that occurred during the 1 min test interval, and also the average or mean value of all 600 samples. A total sample of about 1 min in duration was found to be long enough that two to four peak values of about the same magnitude would occur at the 81 ft test station, but, as will be explained later, is believed to be inadequate at the 162 ft station. If the airstream is perfectly uniform and the vortex wake is steady, di!erent locations of the following wing relative to the wake-generating model cause di!erent amounts of lift and rolling moment to be induced on the following wing. Furthermore, the induced loads would not vary with time. In most wind tunnels however, the induced loads change with time as the wake vortices move about in the wind tunnel in response to the turbu-
603
lent eddies in the airstream. Since these perturbation velocities have a substantial distance (81 or 162 ft), or time, over which to in#uence the vortex positions, movement or meander of the vortex wake may not be negligible at the station where the following model or wing is located. In the 80;120 ft Wind Tunnel where the two tests were conducted, the vortices appear to meander from their time-averaged location up to about 2 in (5 cm or 0.0284b ) at a distance of 81 ft (13.8b ) behind the wake-generating model [162]. At the 162 ft station (27.6b ), the meander distance is twice as large or about 4 in (10 cm or 0.0568b ) from their time-averaged location. Hence, measurements vary considerably with time when made in or near a vortex with a small core radius. For these reasons, data are taken at a sequence of points in a grid as illustrated in Fig. 111 to "nd the location where the rolling moment is a maximum. If the span of the following model is small relative to the span of the generator model, the largest rolling moment is assumed to occur when the centerline of the following model is aligned with the axis of one of the vortices in the wake. These values are then used as the elevations at which spanwise surveys are conducted with various following wings or with a two-component hot-"lm anemometer probe. Since the vortex centers are usually located at di!erent elevations on each side of the centerline (Fig. 111), the survey elevation on each side of the wake is changed at the centerline, so that both surveys pass through the vortex center for their respective sides. The centers of the vortices are indicated as y and
z , because they are identi"ed as the locations where
the rolling moment on a small following wing is a maximum for that side of the centerline. 10.4. Comparison of data from two large wind tunnels Since the 80;120 ft Wind Tunnel had not been used previously for wake-vortex research, and since the
Fig. 111. Illustration of grid pattern used to "nd maximum rolling moment in vortex wakes.
604
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
wake-generating models and the following models, center bodies, strain-gage balances and support hardware were all new, it seemed prudent to "rst compare the new results with those obtained in the 40;80 ft Wind Tunnel. Therefore, the test program was begun by measuring the rolling moment on several con"gurations of the B-747 that had been tested previously. When the data from the two facilities are compared, it was found that they agreed well within the data scatter, or within about $5% [106]. 10.5. Ewect of span ratio on rolling moments As indicated in Fig. 109, the three following wings used in the tests include the swept wings, C2, C4 and C5, that all have the same planform which is a generic average of many of the subsonic transports now in service. Since they all have the same planform but di!erent spans, it is possible to study how the ratio of the span of the follower to the span of the wake generator, b /b a!ects the magnitude of the wake-induced rolling moments. Measurements were taken in the port and starboard portions of the vortex wakes for the three generator con"gurations of the B-747 (Fig. 112). As mentioned previously, the maximum values are believed to be representative of the most hazardous rolling moments in the wake. The data for both the port and starboard sides of the wake are presented as positive values in Fig. 112 so that both sides can be compared more easily. A dashed line at C "0.06 is used to indicate the approximate rollingJ moment capability typical of subsonic transport aircraft. Any points above the C "0.06 line indicate situations J where a following aircraft would have insu$cient rollcontrol capability on board to resist that imposed by the vortex wake of the generator. In fact, an analysis by Rossow and Tinling [104] of results obtained with #ight
Fig. 112. Maximum rolling moments induced on following wings of swept planform in vortex wake of B-747 con"gurations [184]; x "81 ft (24.7 m).
simulators suggests that an encounter with a wake near the ground is probably deemed unsafe by pilots unless the imposed rolling moment is down to about half of the roll authority on board the follower. Such a restraint leaves a reserve of control power available to compensate for the surprise of the encounter and to allow enough roll control by use of ailerons to bring the following aircraft back to a level attitude. As indicated in Fig. 112, when the wake generator is in its conventional landing or (303, 303) con"guration, the rolling-moment coe$cients decrease about linearly as the span ratio, b /b , increases. A similar response does not occur when the wake is shed by a con"guration designed to have a more benign alleviated wake. Since the swirl velocities have been reduced and the vortex core diameters increased, it was at "rst uncertain whether the rolling moments would increase or decrease with span ratio. It is gratifying, therefore, that in the alleviatedwake cases, the wake-induced rolling-moment coe$cients do not change signi"cantly with span ratio. The general trend of the plotted results tends to indicate that if an alleviated wake is safe for small following aircraft it is also likely to be safe for larger aircraft. The approximately constant rolling moment induced on following wings of various sizes by vortex wakes of alleviated con"gurations prompted a study by Rossow [187] of wing e$ciency that will be described in Section 12. Another observation to be noted in the data presented in Fig. 112 is the fact that when the following wing is the same size as the span of the wake generator, the imposed roll is about the same as the typical roll-control available with ailerons. This characteristic of wake encounters has been noted in the past by test pilots #ying in the wakevortex program. When the encounter of the aircraft with a vortex is of short duration or intermittent, a follower of the same size as the generator (or larger) should not experience overpowering rolling moments. A sustained encounter could, however, be judged to be marginally safe or unacceptable during landing or takeo!. The e!ect of the size of the following wing on its susceptibility to a vortex wake is illustrated for both the B-747 and the DC-10 in Fig. 113a as a function of the span ratio, b /b , and in Fig. 113b as a function of inverse span ratio, b /b . The ratio of rolling moment induced on the follower to the lift on the generator tends to deemphsize the e!ect of lift coe$cient on the results. Also, the use of span ratio on the abscissa accounts for the di!erence in relative size of the two wake-generating models. Included in Fig. 113 are two dashed curves that were obtained by use of the up- and down-wash curves at the 81 ft station for the DC-10 wake-generating model as input for a vortex-lattice code. As pointed out in Ref. [184], at some locations in the wake the method overpredicts the maximum rolling moments by up to 10}15% when the following wing is about half the size of the generating wing, and about 30% when the two wings are
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
605
Fig. 113. Comparison of wake-induced rolling moments on swept following wings as a function of span ratio and inverse span ratio [184]; x "81 ft (24.7 m).
about equal. Therefore, the fact that the computed values are above the measured ones is attributable at least partly to the computational method. The use of the inverse span ratio, b /b , permits com parison of the measured data with equations derived in Section 4 which estimate the lift and rolling moment induced by a line vortex (i.e., all circulation concentrated at the center). The closed-form expressions for the maximum values are given by Eqs. (17) in Section 4.2. Since these equations are a linear function of b /b at low aspect ratios, an estimate for the maximum rolling moment induced on a wing by a line vortex is a straight line through the origin in Fig. 113b. Extrapolation of the experimental data to b /b "0 indicates that the closed form expression, Eq. (17b), has the correct form. 10.6. Rolling-moment results: conventional landing conxgurations
model at only 43 angle of attack and with following wing C1. The purpose of the experiment was to determine how much, if any, the vortex wake of the aircraft model was changed due to values of yaw much larger than any possible error in alignment that might have occurred in the setup of the models and struts. Such a question was raised by previous tests which noted a signi"cant di!erence in the port and starboard magnitudes of the rolling moment imposed on following models, even though the model was aligned with the wind tunnel centerline within about $0.13. In order to be sure that the asymmetry in the wake was not due to small errors in yaw placement of the wake-generating model, tests were carried out at yaw angles of b"!23, 03, and #23. A 23 increment was chosen because it far exceeds the accuracy with which the yaw angle of the model can be placed during the setup of the experiment. The results presented in Fig. 114 show
The presentation of the results for the two wakegenerating models is divided into two groups. The "rst group, which will be discussed here, includes the conventional landing con"gurations. The second group, includes those con"gurations wherein modi"cations were applied to the wings of the wake-generating models in an e!ort to reduce the magnitude of the rotary velocities in the wake to alleviate the wake hazard for aircraft which might encounter them. 10.6.1. Ewect of yaw of the wake-generating model Since alignment of the model with the wind tunnel centerline could only be done within 0.13, and since the local airstream may not be exactly aligned with the wind tunnel centerline, a sequence of runs was carried out to examine the e!ects of yaw on the relative strengths of the port and starboard sides of the wake. The sequence of runs was carried out with the B-747 wake-generating
Fig. 114. E!ect of yaw angle on measured rolling moment on following wing C 1 in wake of B-747 model [184]; a "43, x "81 ft (24.7 m).
606
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
that small angles of yaw do not account for the asymmetries in the structure of the lift-generated vortices. It is concluded therefore that di!erences in the vortex wakes on the port and starboard sides are probably due to di!erences in the shapes of the two sides of the wing. 10.6.2. Ewect of angle of attack of the wake-generating model In the past, only a few run sequences were carried out wherein the angle of attack, a , was varied. As indicated in Figs. 115a and b, and as expected, the magnitude of the rolling moments induced on following wing C1 by the wake increase as the lift increases. The results for both the B-747 and the DC-10 at x " 81 ft (24.7 m) and 162 ft (49.4 m) are o!set indicating that some wake decay probably occurred. The larger di!erences at the lower angles of attack are believed to be caused by the turbulence introduced into the wake by the slats and #aps which operate there at signi"cant o!-design conditions. Past experience has shown that introduction of turbulence into the wake of a wind tunnel model can cause the wake-induced rolling moments to decrease by 5}30%. At the upper end of the angle of attack range, the rolling moments are about the same at the two downstream stations, indicating that wake decay is small when the wake-generating wing is operating at near-design conditions. A characteristic not observed in previous tests is a small amount of hysteresis that occurs in the lift on the generator model as the angle of attack is approached from above rather than from below. Once this characteristic was identi"ed, the angle of attack on the generator model was set by approaching the desired angle from above. In this way, the lift at a given angle of attack was the greatest obtained at a given angle of attack. The angle of attack is determined by an indicator fastened to the inside of the wake-generating model in order to eliminate
uncertainty in the angle of attack due to freedom of movement in the drive linkage. If only the intensity of (and not the distribution within) the vortex changes with angle of attack, the maximum rolling moment induced on a following wing would be proportional to the lift on the wake-generating wing. In order to test this possibility, the ratio of rolling moment to lift, "C "/C , is plotted as a function of the angle of J * attack (Fig. 116). Such a linear relationship appears not to exist with either aircraft model. Some of the reason for the non-linearity may be caused by #ow separation on the wake-generating wings at low angles of attack. It is believed however, that the primary cause is attributable to the changes in span loading as the angle of attack changes. The span loading changes with angle of attack, because the inboard parts of wings have large #ap de#ections and the outboard parts near the wingtip do not. A direct comparison of the wake-induced rolling moments produced by the two wake-generating models suggests that, at a given angle of attack, the larger B-747 has a somewhat more intense wake than the DC-10 (Fig. 117a). The more appropriate way in which to compare the results (which removes the sensitivity to C ) is * to plot the ratio, "C "/C as a function of the angle of J * attack (Fig. 117b). The rolling-moment intensity of the two wakes then appears to be comparable. The descent distances of the vortices below the generating wing at the 162 ft station were approximately twice the amounts measured for the 81 ft station becoming about 1.1b at a "103 for both the DC-10 and the B-747. 10.7. Rolling-moment results: alleviated landing conxgurations Another way in which to study the wakes of aircraft is to explore how sensitive or susceptible their lift-generated wakes are to changes in the planform of, or to
Fig. 115. Maximum rolling moment induced on following wing C 1 by wakes of standard landing con"guration of wake-generating models as a function of angle of attack [184].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
607
Fig. 116. Reduced maximum rolling moment, "C "/C , induced on following wing C 1 by wakes of standard landing con"guration of J * wake-generating models as a function of angle of attack [184].
Fig. 117. Comparison of maximum rolling moments induced on following wing C 1 by vortex wakes of the two wake-generating models in their standard landing con"guration [184]; x "81 ft (24.7 m).
devices attached to, their wings. The objective here is to determine whether changes observed in the wake of the B-747 that were found to be successful on the B-747 would also be successful in reducing the intensity of the rotary velocities in the wake of the DC-10 model. 10.7.1. Ewect of span of trailing-edge yaps Early in the wake-vortex research program of the 1970s, it was discovered that the wake intensity of the B-747 could be substantially reduced by changing the standard landing con"guration to the so-called (303, 03) #ap con"guration. The con"guration is achieved by placing the inboard #aps in their standard landing con"guration and the outboard #aps in their stowed position
(a simple form of sawtooth loading). In order to obtain more data on the characteristics of the mechanism produced by the special #ap arrangement, several #ap con"gurations were tested on both the B-747 and the DC-10 models wherein the spanwise extent of the outboard #ap was varied. In this way, the con"gurations tested include, at one limit, the outboard #ap as fully stowed, and at the other limit fully deployed. The intermediate spanwise #ap sizes that were tested include lengths of the outboard deployed #ap that are 25, 50, and 75% of the standard length. Once again, in order to reduce the in#uence of the magnitude of the lift on the rolling-moment data, the data are presented as "C "/C in Fig. 118. The measured J * data obtained with both aircraft models show that the
608
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 118. Variation of wake-induced rolling moments with spanwise size of outboard trail-edge #aps [184]; x "81 ft (24.7 m); a "43 for B-747; a "63 and 83 for DC-10.
induced rolling moment is a minimum when the outboard #ap is completely stowed (e.g., the (303, 03) #ap con"guration of the B-747). The higher value of rolling moment on the port side of the B-747 is consistently observed with this model, and is believed to be caused by the fact that the alleviation mechanism does not go to completion on that side of the centerline within the 81 ft distance from the generator to the following model. The maximum rolling moments are noted to be largest when both #aps are fully deployed. The test results also indicate that intermediate #ap sizes are not to be preferred. It was not possible to determine whether the vortex-linking mechanism attributed to the alleviation on the B-747 (Fig. 60) also applies to the DC-10. 10.7.2. Ewect of wing xns The mechanism by which lift-generated wakes are alleviated when vertical surfaces (wing "ns) are placed on the upper surface of wings is not clearly de"ned. It is, however, the one wake-alleviation scheme that has indicated substantial reductions in the wake-induced rolling moments for the B-747 model when it was tested over a range of wing-"n con"gurations (e.g., Fig. 97). It is of interest to now apply the wing-"n concept to the DC-10 to determine its characteristics and potential level of e!ectiveness on another aircraft with a di!erent high-lift system. The curve in Fig. 119 for the rolling moment as a function of spanwise location of a "n on the B-747 wing indicates that the optimum location for a "n is near the half-way point between the wingtip and centerline [106,183]. A similar result is also found for the DC-10 model (Fig. 119) whether the "n is at a positive or negative angle of attack. A di!erence occurs in the preferred magnitude of the angle of attack of the "n, because
Fig. 119. Variation of wake-induced rolling moment with spanwise location of "ns mounted on upper surface of wings [184]; following wing C 1, x "81 ft.
due to wing sweep, the #ow direction over the upper surface of the wing where the "n is located has a strong inboard component. The optimum spanwise location is about the same on both aircraft models. Any di!erences between the results for the two models may be due to the nature of the two wings, but it is believed to be more likely due to a di!erence in the relative sizes of the two sets of "ns used in the experiment. That is, when the B-747 model was tested, the "n size was 0.0567b ;0.0851b . When the DC-10 model was tested, the "n size was 0.0336b ;0.0672b . The smaller relative "n size was used on the DC-10, because larger sizes degraded the performance a disproportionate amount.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
It is concluded that the mechanism of wake alleviation by wing "ns is probably the same on the two wake-generating models, and that the magnitudes can be made comparable by changes in "n design. The approximately equal e!ectiveness of the "ns on the two models is not surprising. Although the two wing planforms appear to di!er somewhat, both were no doubt designed for minimum weight at a given lift to yield quite similar span-load distributions. If such is the case, the span loadings and the vortex wakes shed by the two models are similar enough that they are about equally susceptible to the in#uence of wing "ns. A number of wing-"n con"gurations were tested on both the B-747 and the DC-10 models at both the x "81 ft and the x "162 ft stations. Fig. 120 presents a summary of the rolling moment data obtained for the wide variety of con"gurations of the two wake-generating models as a function of downstream distance. If the curves were all parallel, the decay rate of the vortices would then have all been about the same. As is evident in Fig. 120, no general pattern appears to exist. The sets of curves for the two models indicate that the vortex intensity sometimes increases and sometimes decreases between the two stations. It is concluded that vortex stretching (and the associated intensi"cation) can account for some of the increase in rolling moment with downstream distance. Decay of the swirling velocities may also have occurred in some cases. The results presented in Fig. 120 will be discussed further in Section 13 to follow along with other information on the decay of vortices. 10.8. Measured spanwise distributions 10.8.1. Overview of data Spanwise surveys through the vortex wakes were made for several reasons. The most important reason was to obtain data on both the wake-induced loads and on the
609
velocity distribution in the wakes to determine the accuracy of the vortex-lattice theory used to calculate wakeinduced loads on encountering aircraft. When the lift and rolling-moment loads induced on following wings are known along with the up- and down-wash distributions at the same locations, the two should be connected by a theory for the loads, as demonstrated in the next section. The precision of the connection will determine the accuracy of the method and of the experimental measurements. If unexplained disagreements occur, #aws in either the theory or the measurements, or both, would need to be found. Another important reason for the measurements is the need for spanwise distributions of both loads and velocity for estimations of the dynamics of aircraft as they encounter vortex wakes. That is, the data will be used in ground-based simulators to study the encounters of aircraft with wake vortices. Other uses for the data include the modelling of vortex wakes as they form, the development of numerical methods for wake dynamics, and to study the characteristics of vortex wakes as they age in the #ow "eld a short distance behind the generating wing (i.e., up to 1 mile). In the surveys taken, each side of the vortex wake was treated separately (Fig. 121) because the vortex center (i.e., the location of the largest rolling moment) is usually at a di!erent elevation on each side of the centerline, i.e., by amounts from zero to 0.06b (Table 11). As described previously, the surveys are carried out by sequentially placing the wing at a number of spanwise locations from the centerline of the generator out to well beyond its wingtip (usually out to about 1.5b ) to establish the upwash in the outer parts of the vortex. Once again, the data taken were the maximum, the minimum, and the mean or time average of the lift and rolling moment imposed by the vortex wake on the following wing at each spanwise location. The same technique was used to measure the up- and down-wash distributions.
Fig. 120. Reduced maximum rolling moment induced on following wing C 1 by wakes of various con"gurations as a function of downstream distance [212].
610
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 121. Illustration of elevation change at wake centerline of path used to carry out spanwise surveys with following models and with hot-"lm anemometer probe [163].
Table 11 Locations of maximum rolling moments and lateral surveys [184] Con"guration of generator
Landing, #aps (303/303)
Modi"ed landing, #aps (303/03)
Landing, #aps (303/303) with "ns, a "183, y /b "0.480
Run no.
Following wing
Port side
Starboard side
>
Z
>
Z
!0.370
!0.471 !0.471 !0.471 !0.471 !0.471
#0.427
!0.342
#0.370 #0.370
!0.342 !0.352
13 28 19A 35 36
1 3 4 5 Hot "lm
15A 17 34 38
1 4 5 Hot "lm
!0.475 !0.475 !0.430
!0.627 !0.627 !0.627 !0.627
#0.501 #0.501 #0.398
!0.426 !0.426 !0.482
23 25 26 33 37
1 3 4 5 Hot "lm
!0.372
!0.512 !0.512 !0.512 !0.512 !0.512
#0.431
!0.400
#0.457 #0.340
!0.400 !0.454 !0.400
!0.342 !0.367
!0.397 !0.313
Spanwise survey taken.
After the locations of the vortex centers were found with following wing C1 as discussed previously (Table 11), spanwise surveys were made with it (Fig. 122) with several of the other following wings and with a hot"lm anemometer probe. Typical data points are shown in Fig. 122 to illustrate their distribution and scatter. In "gures to follow, however, in order to reduce the clutter in the "gures, the symbols are omitted and only a line between the measured points is shown. In the hot-"lm surveys, only the streamwise and vertical velocity components were measured. The two velocity components were
then combined to yield the distribution of up- and down-wash angle, w/u, across the wake. A single spanwise survey was made with Model C3 (the following wing with a 6;6 in planform) in order to "nd out if a wing of small span would produce more accuracy, and a better representation of the vortex wake being surveyed than following wings of larger span. Only one survey was made because the loads were too small to achieve acceptable accuracy with the strain-gage balances chosen for the test. An obvious extension of the smaller-is-better argument is to go to an upwash sensor of the smallest size
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
611
Fig. 122. Typical measured loads on following wing C 1 as it makes a lateral traverse through wake of standard landing con"guration of B-747 model [106]; a "43.
possible; namely, a hot-wire or hot-"lm probe. As a result, lateral surveys of upwash were made with a hot-"lm anemometer probe. After the data had been collected, various adjustments and corrections were applied to the results before they were used in the computations. An increment, *y" 0.028b (i.e., 2 in or 5 cm), was "rst applied to the span wise location to correct for a lateral o!set to align the centerline of the data with the centerline of the wakegenerating model. Various other adjustments were also applied to the data to correct for such items as local #ow angularity in the wind tunnel, any non-zero angle of attack of the following wing or hot-"lm gage relative to horizontal, and possible de#ections of the support sting, traverse tower and rail assembly due to air loads from the free-stream velocity. Although these displacements are each small, the combination appears to be enough to cause an o!set in the measured curves of about C "0.02 and C "0.002. The o!set in the torque dis* J tributions is determined so that the curves for rolling moment far from the centerline have about the same magnitude of rolling moment. Such an adjustment is based on the assumption that a slight twist or lateral asymmetry in the following wings causes a bias in the data [163]. 10.8.2. Up- and down-wash velocity distributions The data taken with a hot-"lm anemometer probe (Fig. 123) provide the up- and down-wash velocity distributions that are used with the vortex-lattice method to
Fig. 123. Up- and down-wash distributions measured with hot"lm probe along a lateral traverse through vortex centers of wakes shed by B-747 model [163]; a "43.
compute the spanwise lift and rolling-moment distributions on the various following models. Table 11 lists the con"gurations of the wake generator, the various following wings or hot-"lm anemometer probe for which a survey was taken, and the locations where the most intense rolling moments occurred on each side of the wake centerline. In the hot-"lm surveys, only streamwise and vertical velocity components were measured. The two velocity components were then combined to yield the distribution of up- and down-wash angle, w/u, across the wake (Figs. 123}126). An obvious feature in Fig. 124 is that the data at x "162 ft is not as smooth as the data at x "81 ft. The increased size of the #uctuations in the velocity distributions at x "162 ft is believed to be caused by the larger meander distances of the vortices at the greater downstream distance. The irregularities in the downwash data indicate a need for longer data-sampling times at downstream distances much greater than 81 ft to determine improved time-averaged and maximum and minimum values for the downwash; e.g., sample lengths of 2}4 min
612
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 124. Downwash distributions in wakes of the two wakegenerating models in standard landing con"guration at two downstream stations [184].
rather than 1 min. The longer sampling period allows more time for the center of the vortex to meander over the entire region for a more complete and consistent time-averaged value of the velocities at the measuring point. A longer sampling period would also help to determine an improved value for the time-averaged location of the vortex center. Even with scatter, the di!erences between the maximum and minimum data curves in Fig. 124 provide an indication of not only the variations in the velocity at a given point in the #ow "eld, but also of the lateral or spanwise displacement of the vortex center as it meanders about. Examination of the maximum and minimum curves in the vortex core region indicates that the vortex meanders sideways about 4 in (i.e., a 2 in radius) at the 81 ft station in both large wind tunnels, and about 8 in (or a 4 in radius) at the 162 ft station in the 80;120 ft Wind Tunnel. Such a variation is expected, because the greater downstream distance allows twice as much time for the turbulent eddies to convect, and to distort the vortices from their time-averaged locations. As long as the velocity of meander is not too rapid, the analog data coming from the hot-"lm anemometer is not signi"cantly altered by the 10 Hz low-pass "lter in the circuit. At 10 Hz, the wavelength of an eddy in the
airstream is about 13 ft (i.e., between 2 and 3 spanlengths). The most surprising feature of the data presented in Fig. 124 is that some of the up- and down-wash velocities in the vortices are noticeably higher at x "162 ft than at x "81 ft. These increases in the swirl velocity with downstream distance indicate that vortex intensi"cation rather than decay occurred. As can be seen in Fig. 120, the maximum measured rolling moments were sometimes less and sometimes greater at the x "162 ft station compared with values at the x "81 ft station, which is an indication that vortex changes with downstream distance are not consistent. Therefore, the rolling moment and the downwash velocity data are consistent with each other, because the instantaneous rolling moments calculated by use of the measured maximum velocity distributions are larger than the measured ones at either the x "162 ft station or at the x "81 ft station. In support of the alleviation e!orts described in the previous paragraph, measurements were also made in the wakes of the B-747 and DC-10 models when con"gured with wing "ns and in the modi"ed landing con"guration (Figs. 123, 125 and 126). In Fig. 123b, data are presented only at the 81 ft station for the B-747 model equipped with rather large wing "ns. In Fig. 123c, the B-747 model had its outboard #ap stowed for the modi"ed landing con"guration. Unfortunately, results were not obtained at the 162 ft station for these two con"gurations. Data were obtained at both stations for several other wing-"n con"gurations of the B-747 and DC-10 models at the 81 ft station (Figs. 125 and 126). The smaller "n sizes in Figs. 125 and 126 were used in an e!ort to "nd more e$cient alleviated con"gurations and to "nd out if the vortex wakes of alleviated con"gurations decay or decompose more rapidly than those of conventional landing con"gurations. It is concluded that, once formed, conventional and alleviated wakes decay at about the same rate unless some sort of three-dimensional instability causes the coherent nature of the wake to break up before the wake decays completely. 10.8.3. Diagnosis of velocity measurements Certain characteristics observed in the data presented in Figs. 123}126 are related to the environment in which the vortex wakes are immersed [162] and to the way that the hot-"lm anemometer data were taken. It is recalled that the time-averaged data presented in Figs. 123}126 represent the measurements taken during a 1-min period at a given point, while the vortex center moves about randomly. In the data-taking process, the 1-min period is divided into intervals of 0.1 s to yield 600 data samples. The maximum and minimum data points are obtained as the two extremities of the 600 samples taken during the 1 min. If the wind tunnel airstream had no turbulence (and therefore no meander), the time-averaged, maximum and minimum data would all be the same
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 125. Downwash distributions at two downstream stations in wakes of two con"gurations of B-747 wake-generating model equipped with small wing "ns [184]; a "43; y /b "0.24, c /b "0.085, h /b "0.014.
Fig. 126. Downwash distributions at two downstream stations in wakes of two con"gurations of DC-10 wake-generating model equipped with small wing "ns [184]; a "83; y /b "0.24, c /b "0.057, h /b "0.017, a "#183.
(Fig. 127a). Since the wind tunnel airstream does contain turbulence, the vortex moves about (meanders), and is stretched and compressed to change the magnitude of the swirl velocities in the vortex; thereby leading to the three curves in each part of Figs. 123}126. In order to understand the e!ect of the meander and of the stretching processes on the relative shapes of the time-averaged, maximum and minimum curves, "rst consider the hypothetical case where the vortex meanders only in the vertical direction. When the vortex moves vertically away from its time-averaged location, the vertical velocity measured along a line across the wake through the time-averaged center of the vortex simply decreases everywhere. The envelope of the absolute value of all such measurements is then the same as if the vortex were stationary (Fig. 127a).
613
If the vortex meandering motion is restricted to the lateral direction only, and does not stretch or compress (i.e., the vortex remains straight, and moves about as a long rod), the velocity curves would all have the same shape, but would be displaced laterally as illustrated in Fig. 127b for the time-averaged, and the two extremities of motion. If a number of instantaneous curves were plotted for all amplitudes of meander, the extremities of the maximum and minimum curves would form an envelope with a #at top and bottom. As the meander distance increases, the #at top and bottom of the envelope would also increase in the lateral direction, but not in magnitude. Next consider the hypothetical case illustrated in Fig. 127c wherein eddies in the airstream combine to bend and stretch the vortex locally, but do not move the vortex center from its time-averaged location at the measuring station. In that case, a lateral or vertical displacement of the center of the velocity curves does not occur. However, the amplitude of the velocity increases in the core region, because vortex stretching reduces the core radius, and by conservation of angular momentum, increases the swirl velocity (Fig. 127c). Since vortex intensi"cation occurs over only the core region, which is usually small, the imposed rolling moment is not changed appreciably, if at all, provided the span of the following wing is more than several core diameters. Small-scale eddies immersed in the vortex would probably cause small instantaneous variations in the pro"le of the swirl velocity (Fig. 127d). It is noted in Fig. 124 that the amplitude of the instantaneous velocity is increased primarily in the core region, and that some broadening of the velocity pro"le also occurs. Since the maximum and minimum curves in Figs. 123}126 are made up of the envelopes of the extremities of the data taken at each survey point, they would include all of the enhanced velocity variations due to vortex motion, stretching, and eddies. The complexity of the interaction of the vortices with the airstream turbulence makes it di$cult to estimate the amount of vortex enhancement to be expected, but it seems that the processes discussed in the foregoing paragraphs, and illustrated in Fig. 127, could account for the larger velocities at the x " 162 ft station. That is, it is conjectured that both meander and vortex stretching occur to form an envelope of the maximum and minimum velocity curves that can have amplitudes and spreading that increases with downstream distance } at least for once. At the 162 ft station, evidence of vortex stretching is believed to be associated with rolling moment measurements found at the periphery of the meander region rather than at the time-averaged location of the vortex center. It is believed that a series of experiments designed to explore the foregoing conjectures is needed to clarify the various characteristics in the data associated with vortex meander and stretching. It should
614
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 127. E!ect of turbulence and vortex dynamics on downwash velocity distributions [212]. (a) (303/303); (b) (303/303) "ns; (c) (303/03).
be remembered that, as aggravating as vortex meander is in the wind tunnel when high-quality measurements are desired, the same or similar phenomenon is often present in the atmosphere [50,122,160]. An improved understanding of how turbulence a!ects the intensity and decay of vortices in the wind tunnel would no doubt enhance the understanding of vortex behavior in the airport environment. A beginning towards a correction or adjustment by which measurements in a turbulent airstream could be converted to velocity distributions for a uniform non-turbulent free stream has been tried with modest success by Baker et al. [89], but was not tried here. Consideration was also given to the possibility that some of the vortex motions at the measuring stations were due to the self-induced ampli"cation of meander, but insu$cient data was available to indicate a connection. Improved and other measurement techniques should be brought to bear on the need for more information on vortex structures [111,188]. 10.8.4. Lift and rolling-moment loads A number of lift and rolling-moment distributions were measured at both downstream stations [106,184]. In order to present the data more compactly, it seemed best to present a shortened version of these distributions at the same time that the data is used to examine the validity of a vortex-lattice method for the computation of the loads on aircraft when they encounter a vortex wake [163]. Therefore, the data and the comparisons are presented in the next section.
11. Validation of vortex-lattice method 11.1. Introduction Throughout the wake-vortex research program, e!ort was, and still is, directed at the development of reliable models and tools for the representation and prediction of the structure and dynamics of vortex wakes, and their interaction with aircraft. As a part of this e!ort, the study reported in this section was carried out in order to obtain an improved understanding of the accuracy of an available computer code to calculate loads on lifting surfaces embedded in the rotary and rotational #ow "elds of vortex wakes [163]. In order to be able to test or validate a computational method for the loads induced on a wing embedded in a vortex wake, the 80;120 ft Wind Tunnel was used to obtain data on the up- and down-wash distributions across the vortex wakes of several con"gurations, as presented in the previous section. The time-averaged velocity distribution data is used as the input #ow "eld for the computer code at the location of the wing in the #ow "eld. The lift and rolling-moment loads on various following wings are also measured at the same locations in the #ow "eld, i.e., along the same line as used to obtain the velocity distributions. Comparison of the measured and predicted loads with each other should then be connected by a single link, i.e., a method for predicting the loads. Not only does such a comparison provide a validation of the computational method, but it also provides a check on
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the "delity of the experimental equipment, and methods used to obtain the data. It was reasoned that the method to be chosen for study must be easy to apply to a large variety of con"gurations, because the number of aircraft con"gurations in the subsonic transport #eet is large. Another reason for simplicity is that the method must not use much computer time (i.e., it should be fast), so that a large number of solutions can be obtained quickly for spatial analyses and for simulation of the dynamics of aircraft-wake encounters. Along with the foregoing requirements, the method should also be accurate enough, so that given a reliable velocity "eld as input, the computed lift and rolling moment fall within the scatter of the values measured in the wind tunnel. A method developed by Hough [139] that ful"ls these requirements is the same vortexlattice method used in various wake-vortex studies [10,60]. 11.2. Applicability of vortex-lattice method A variety of theoretical methods could have been tested as the link between the computed and measured lift and rolling moments. Only the vortex-lattice method is used in the comparisons to be presented, because it is simple to apply, is robust and reliable for many con"gurations, and has the capability to include a variety of wing shapes and vortex structures. Therefore, all approximate methods such as those based on strip theory [10], and those based on global-type arguments [176}178], were discarded as too unreliable for the comparisons being made, even though they can provide insight into vortex/wing interactions. The vortex-lattice method chosen for this study is based on potential #ow theory which assumes that the #ow "eld is steady with time, incompressible, inviscid, and that #ow separation or stall is negligible [139]. Since the velocity "eld that interacts with the following or encountering wing is brought about by a vortex wake, the #ow "eld is solenoidal (or rotational) and not potential. Therefore, if a potential-#ow method, like the vortex-lattice method, is to be used in lift-generated wakes, it must either be modi"ed in some way, or the #ow "eld must be reinterpreted, so that it conforms with potential#ow theory. If the velocity "eld is impressed by a vortex system, the boundary conditions on the various lattices that represent the wing may be speci"ed by (1) assuming that each panel responds to the local #ow angle; or (2) that the wing panels are inclined at an angle to a uniform free stream. The inclination of each lattice panel is assumed to be equal to the angle of attack in the #ow "eld at the control point of the panel. The second interpretation changes a rotational problem into a potential one thereby making the mathematics and #ow "eld consistent. No matter which interpretation is used, the strengths of the vortice-lattice panels are adjusted, so
615
that there is no #ow through the encountering wing at the control points, and the "nal results are the same. In the vortex-lattice method, the lifting panels are constructed by superposition of horseshoe vortices. The cross-stream component of the horseshoe is swept or unswept in order to best "t the planform of the wing, while the other two legs of the horseshoe extend in the downstream direction to in"nity. All three legs of the horseshoe lie in a z"constant plane, which is where the wing camber and the up- and down-wash distribution are applied, i.e., a thin-wing boundary condition. The method employs only one layer of lattices, and does not include a separate lattice or panel system to separately represent the upper and lower surfaces of the wing or tail surfaces being considered. When the geometry of the horseshoe lattice has been established, the strengths of the horseshoe vortices are set in combination by a matrix inversion, so that the boundary conditions on the wing are satis"ed everywhere. When such a potential #ow technique is applied to a wing placed in a rotating and rotational (or solenoidal) #ow "eld, the applicability of the predictions is, at least academically, open to question. That is, since the #ow "eld of the vortices is rotational and not potential, the use of a potential-#ow method is, in principal, not valid even though a reinterpretation is applied. Also, it is reasoned that the oncoming stream may not be considered as a shear #ow composed of a spanwise distribution of vertical velocity. If such an assumption is made, not only is the shear #ow solenoidal and not potential, but the vertical momentum in each vertical shear layer is in"nite rather than "nite, as in a vortex. If however, it is assumed that the #ow "eld and wing are recon"gured, so that the free stream is uniform rather than rotational, and that the wing is twisted to match the angle of attack imposed by the vortex system, the simulated problem is potential. Discussions in the literature justify the assumptions needed to treat the loading on the encountering wing as if the oncoming stream were uniform, rather than rotational, and that the vortex downwash "eld is interpreted as wing twist (or as local angle of attack) [163,189}192]. 11.3. Comparison of predicted and measured loads 11.3.1. Lift The measured time-averaged spanwise distributions of up- and down-wash angle presented in Fig. 123 were used as input into a vortex-lattice code [139] to predict the lift on following wings C1, C4, and C5 (Figs. 128}130) as they encounter the vortex wake shed by one of three con"gurations of the wake-generating model. In each part of the "gures, the computed time-averaged distributions (solid lines) are compared with the measured timeaveraged distributions (data shown as open-circle symbols). It is to be noted that the comparisons have been
616
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
restricted to the time-averaged data, because their use is more straightforward than either the maximum or minimum data sets. In general, the comparisons in Figs. 128}130 indicate that the lift distributions computed by use of the vortexlattice method are in good agreement with the measured values. The agreement of the results in Fig. 128 for following model C1 are very good considering the complexity and unsteady character of the #ow "eld. The comparisons made for the larger following models, C4 and C5, are not as good in the region at and between the vortex centers. A systematic e!ort was made to be sure that the discrepancy between the results was not due to misalignments or adjustments in the data nor to approximations in the mesh size, spacings, etc., in the vortex-lattice code.
Fig. 129. Comparison of measured lift induced on following wing C4 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
Fig. 128. Comparison of measured lift induced on following wing C1 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
Examination of the comparisons for following model C1 indicate that the predictions follow the measured data well within experimental accuracy. The larger than usual discrepancy for following model C1 in the port vortex behind the (303/03) con"guration is not unexpected, because the alleviation mechanism for that wake did not go to completion for that side of the wake. As a result, two vortices are in close proximity causing the wake to be very unsteady, and the rolling moments to be somewhat higher. The generally good agreement in Fig. 128 for following model C1 indicates that the assumptions made in order to apply the potential-#ow vortex-lattice method to the rotational #ow "eld of vortex wakes are valid approximations for small span ratios, b /b . Furthermore, since following model C1 is the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
617
Fig. 130. Comparison of measured lift induced on following wing C5 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
smallest of the three following wings, it is the one expected to su!er most from #ow separation or stall whenever the vortex #ow "eld impresses a large angle of attack on the following wing. Since no such deviation is noted for following model C1, #ow separation probably is not the cause of the discrepancies that appear for following models C4 and C5 in Figs. 129 and 130. It is concluded therefore, that the di!erences between the computed and measured data are due to some characteristic of the #ow "eld that is not included in the vortex-lattice method or in the application of the boundary conditions. Since the agreement of the predicted and measured data for following wing C1 is very good, it is also concluded that the experimental and data reduction techniques are adequate and produce reliable data. 11.3.2. Rolling moment The sequence used for the comparisons presented in Figs. 131}133 for rolling moment parallel those presented previously for lift. Once again the rolling-moment distributions computed for following model C1 (Fig. 131) are in very good agreement with the measured data. The values computed for following model C4 (Fig. 132) are also in quite good agreement in most regions except near the vortex centers, where the magni-
Fig. 131. Comparison of measured rolling moment induced on following wing C1 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
tude of the predictions are again too large. The same comments can be made for the comparisons presented for following model C5 (Fig. 133) but the magnitude of the discrepancy has increased over that observed for the two smaller encountering wings. Once again, the discrepancies are believed to be due not to #ow separation, nor to lack of accuracy of the application of the vortex-lattice method, but, as discussed in the next section, due to one or more #ow-"eld characteristics not included in the method. 11.4. Assessment of assumptions As mentioned previously, a systematic e!ort was made to be sure that the discrepancy between the results was
618
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 133. Comparison of measured rolling moment induced on following wing C5 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
Fig. 132. Comparison of measured rolling moment induced on following wing C4 as it traverses laterally through the wake of various con"gurations, with that predicted by use of measured downwash and vortex-lattice theory [163].
not due to misalignments or adjustments in the data nor to approximations in the mesh size, spacings, etc., in the vortex-lattice code. It was found that the computed values usually changed less than 1% at any place along the span due to any of the items tried. After the foregoing possibilities had been tested and eliminated as being responsible for the discrepancy between computed and measured distributions, the assumption made in the application of the vortex-lattice method regarding the streamwise downwash distribution was investigated. That is, when the vertical velocity at each control point is set, it is assumed that the value is constant for all control points at the same spanwise station; i.e., the downwash is assumed to be the same for
each column of streamwise panels or lattices, and an allowance for distortion of the oncoming vorticity distribution is not made. If so, changes in the solenoidal character of the oncoming stream by the encountering wing are ignored by the theory used to compute the loads. It is believed that this approximation is the most logical reason for the discrepancy between the computed and measured lift and rolling-moment distributions. In support of this conjecture, it is again noted that the vortex-lattice method is quite accurate when the following wing is small, and that the error increases as the following wing increases in size. Similarly, the trend in predictive accuracy follows the fact that small following wings (i.e., small values of b /b ) cause small or negligible distortions to a vortex wake, whereas larger wings (i.e., large values of b /b ) cause larger distortions in the structure of the vortex wake. Since little distortion is expected when the following wing is small, like following wing C1, the vortex-lattice method would be expected to be reliable with only small or negligible error. However, when the following wing is large, like C4 and C5, the distortion of the vorticity "eld, and the resulting downwash distribution is expected to be larger, and perhaps even quite signi"cant.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
It remains to con"rm that the discrepancies between computed and measured data are caused by vortex-wake distortions brought about by the in#uence of the penetrating wing. The "rst requirement is that it can be shown that wake distortion is able to bring about the changes in magnitude and distribution observed between the predicted and measured quantities for the larger wings. It would then be desirable to develop an e!ective method to properly analyze the wing/vortex}wake interaction, and apply it to the test con"gurations studied here. The distortion of the oncoming vortex wake by the presence of the following wing is not taken into consideration by the vortex-lattice method. That is, an assumption is made that the oncoming stream is potential, and not solenoidal. An estimate of the distortion that can be brought about by a wing/vortex}wake interaction is relatively simple to obtain by use of a Tre!tz-plane type of analysis [163]. The computations in Fig. 134 were carried out by analyzing the motion of two-dimensional point vortices arranged in a circular distribution, and with a strength distribution designed to approximate the vorticity distribution typical of lift-generated vortices. The boundary conditions on the motion of the vortices are applied so that, prior to the x/b "0 station, the vortices move as if in two-dimensional free space. Downstream of x/b "0, the vortices above z/b "0 move as if they are over an in"nite #at plate, and those below z/b "0 move as if they are under an in"nite #at plate. Both of these two
619
motions are simulated in the Tre!tz plane by use of images. At each of the x/b stations speci"ed in Fig. 134, the in"nite plate is assumed to end. The downwash distribution is then calculated for the position of the vortices at that station as if the plate (and the images) were not there. The various parts of Fig. 134 represent the amount of interaction for following wings of di!erent sizes as indicated by the x/b values noted in each part of Fig. 134. That is, the upper "gure for x/b "0 represents the downwash induced in the free stream by the undisturbed vortex wake. Each "gure that follows illustrates the distortion in the wake caused by a following wing of larger size, and the downwash induced by the new wake shape. The example presented in Fig. 134 assumed that the leading edge of the #at plate was sharp and thin enough to divide the vortex in half as it encounters the wing, without otherwise distorting the impinging vortex structure. Therefore, the calculations presented in Fig. 134 do not simulate the bluntness of the leading edge of the following wings. Since the small following wings are thin compared to the depth of the wake, a zero thickness is a valid approximation. However, when the following wing is large, the bluntness of the leading edge and the thickness of the wing might be enough to cause the high-speed vortex core to stay intact and to pass either above or below the wing rather than being split in half as assumed in Fig. 134. If this occurs, sample computations indicate that the resulting downwash distributions are as
Fig. 134. Distortion of vorticity distribution in a vortex wake as it encounters a #at plate of various downstream sizes [163].
620
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
a whole about the same as the thin-wing results, but the distributions di!er in detail. It is noted in Fig. 134 that those point vortices on top of the #at plate or wing move outboard with time, and those under the #at plate move inboard with time, just as anticipated intuitively. This movement redistributes the vorticity in the wake so that the downwash in the spanwise region between the two vortex centers is reduced, just as observed with the lift for the larger following wings. Furthermore, the outboard distributions of downwash are slow to be altered, just as observed with the lift comparisons. Also, it is noted that the total change in downwash velocity across the vortex centers is slow to be altered, so that the rolling moment on an encountering wing would also be slow to be changed by wake distortion. Computations were also carried out for vortex distributions that approximate solid-body rotation, and the results were about the same but took longer to come about.
12. Wake energy, span e7ciency and span loading 12.1. Introduction The characteristic of non-hazardous wakes to be discussed here is their e$ciency, or lack thereof, and possible techniques to remedy the problem. The discussion uses the relationship between e$ciency of the lifting surfaces, and the kinetic energy in the wake that the wing sheds. If a non-hazardous wake con"guration is to be found, it must have a wake that has much less energy than conventional designs for two reasons. First, a nonhazardous wake must have low velocities and therefore low energy. Secondly, an e$cient wing sheds a lowenergy wake. From basic aerodynamics, the wake energy, span e$ciency and span loading, are all connected. Therefore, this section considers lifting wings that are designed so that the desired lift is generated with a low level of wake energy, and a corresponding high span e$ciency [187]. A goal of the study was to "nd optimum con"gurations. However, a procedure for optimization was not found, because a relationship between span loading, vortex wake structure and energy was not available. Such a relationship becomes very complex and nonlinear, because it must include vortex interactions and viscous forces which reform the multiple vortex wake at the wing trailing edge into a single vortex pair. The study began with the observation that alleviatedwake con"gurations often shed vortex wakes that induce about the same rolling-moment coe$cient on following wings of all sizes [187]. As shown in Fig. 112, the windtunnel data indicates that, when a wing is embedded in an alleviated wake, the maximum vortex-induced rolling moment on a wing is very nearly constant with span ratio for several di!erent alleviation mechanisms. Computa-
tions carried out by use of vortex-lattice theory, and the downwash data in Fig. 123, con"rm that the spanwise vertical velocity distributions also re#ect the low and nearly constant value of wake-induced rolling moments for the alleviated con"gurations over a wide range of span ratios, b /b , and for di!erent wing planforms. In order to investigate the possibility as to whether the span loadings had special characteristics that would lead to new wing designs, a study was made of the vortex wakes at the downstream station where the measurements were made, i.e., at 81 ft or 0.5 mile scale distance behind the wake-generating model [187]. In order to determine the span loadings that correspond to these downstream vortex wakes, the analysis "rst "nds the vortex structures that make up the measured downwash distributions. An inverse Betz method described in Section 5 is then used to derive the corresponding span loadings. Analysis of these span loadings, and consideration of the induced drag and the energy in various wakes, yields information on some of the characteristics and penalties associated with the design of wings for less hazardous wakes. It is recommended that tools be developed for an optimization process that includes drag, wing-root bending moment, weight, complexity, etc., and the design of vertical and horizontal lifting surfaces for vortex wakes that have an acceptable hazard. The discussion to follow considers the energy in idealized wing designs, their e$ciency, criteria that should be used to determine e$ciency, and what factors need to be considered in the design of a wing with low or negligible hazard due to its vortex wake. 12.2. Estimated span loadings In order to provide an estimate for the structure of the vortex wakes being studied, the span loadings on the various wake-generating con"gurations, were calculated by means of vortex-lattice theory for the wing of the wake-generating model at 43 angle of attack (Fig. 135). Since the two alleviated wakes to be analyzed in this study (Fig. 123b and 123c) have gone through strong two- and/or three-dimensional vortex interactions after they were generated, and before the measurements were taken, the relationship of the "nal vortex wake to the original span loading on the wake-generating model has become obscure. That is, because of the vortex interactions, the vortex wake far downstream behind the wing has taken on an alleviated form. If the "nal vortex wake had been generated directly from a monotonic span loading, the span loading would no doubt be quite di!erent from the one that actually generated the wake. A question to be answered in this section is whether the "nal vortex wakes that are benign can be interpreted by use of inverse rollup theory for span loadings that have the same lift but less penalties than the original alleviated wing design.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 135. Comparison of parabolic span loading with those estimated for the wings of the con"gurations of B-747 model tested in wind tunnel [187]; a "43.
12.3. Analysis of downwash data 12.3.1. Vortex structures The procedure used to "nd the time-averaged structure of the vortices that make up a wake consists of several steps. First, a determination is made as to how many vortices are present in the wake, and roughly where their centers are located. In the cases being analyzed here, only two vortices, or a single pair, are present in the wake when it arrives at the measuring station located at x "81 ft. One possible exception is the port side (nega tive y values) of the modi"ed landing or (303, 03) con"guration (Fig. 123c). Such a possibility was observed during the data-taking process when the measurements indicated two peaks in rolling moment that were both higher than measured for the starboard side of the wake. Therefore, for the modi"ed landing case, the velocity survey, and the analysis presented here were carried out as if only one vortex was present on each side of the centerline. Since the lateral velocities are negligible on a path through the vortex centers, only the vertical and streamwise velocity components were measured. Since a vortex pair induces a downward velocity on itself, the next step in the analysis is to remove the proper amount of downwash at each spanwise station from the measured distributions in Fig. 123. The velocity "eld of each vortex is then evaluated as if it was isolated from the opposite vortex in the pair. The procedure used assumes that, near the vortex center, the #uid motion is nearly axisymmetric after the downward velocity of the pair has been removed. If the #ow "eld is symmetrical about each vortex center, the data inboard and outboard of the
621
vortex center should yield the same swirl velocity. However, since a vortex pair is present in the #ow "eld, two processes in#uence the location and shape of the streamlines (Fig. 30). The "rst process to be considered is caused by the opposite vortex in the pair. Its presence changes the concentric streamlines for an isolated vortex to be shifted outboard to form a series of circular streamlines whose centers are shifted outboard by increasing amounts as the streamline radius increases (Fig. 30b). If such a streamline pattern is to be preserved, the vortices must be held in place by force, which does not occur in a vortex wake. The second process which causes the streamlines to be di!erent from the concentric circles for an isolated vortex is brought about by the downward motion of the pair when they are released (Fig. 30c). A steady-state streamline system is achieved by superimposing a uniform upward free-stream velocity on the #ow "eld, so that the #ow around the vortex pair has an internal part inside the oval that is usually rotational (i.e., contains circulation) and an external part that is irrotational when the #ow is approximately inviscid. The streamlines of interest in the present analysis are those inside the vortex oval (Fig. 30c). Fortunately, the lateral displacement of the streamlines due to the opposite vortex, and the compression of the rotational part of the #ow "eld into the interior of the oval by the downward motion of the vortex pair, combine to produce nearly concentric streamlines as assumed for isolated vortices (Fig. 30c). The radial (or lateral) location of a particular element of circulation from the wing as deposited in the vortex oval con"guration is probably not the same as if the vortex being analyzed were really isolated. In the analysis to follow, the vortices are treated as if they are symmetrical inboard and outboard of their centers, which appears to be a good approximation for the vortex oval. As will be seen in the results of the analysis, symmetry does exist at smaller distances from the vortex center but not for the outer parts of the vortex structure. Since the hot-"lm anemometer probe is "xed relative to the wind tunnel, the velocities measured include the self-induced downward motion of the vortex pair, and the velocity "eld of the opposite vortex. For this reason, an iterative procedure is used to adjust the data for the downward motion of the vortices, and to determine the structure of isolated vortices that make up the downwash distributions (Fig. 123). Since the downwash adjustments needed are not known at the outset, they must be found iteratively. The process begins by assuming a location for the vortex center and an estimated value for the in#uence of the opposite vortex. The swirl velocities on the two sides of the vortex center are then compared. If they are not about the same in the vicinity of the vortex center, a change in the overall upwash increment is made. The computations are then iterated upon until they agree within experimental accuracy. After each revised upwash
622
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
distribution has been found, a new vortex center is located by interpolating along the up- and downwash curve through the core region of the vortex to "nd the spanwise location where the downwash velocity passes through zero. The entire process converges in about "ve iterations. The foregoing procedure was used to determine the time-averaged vortex structures for the three con"gurations of the B-747 model for which wake-surveys were taken. As mentioned in the previous paragraph, the downwash data in Fig. 123 was "rst divided into port and starboard structures. Each of those data sets were again divided at the center of the vortex into two groups (Fig. 136). One group includes the data located between the vortex center and the centerline of the wake, and the other group includes all of the data outboard of the vortex center. Therefore, Figs. 137, 138, and 139 present curves for both the port and starboard sides of the wake and for both the inboard (dashed curves) and the outboard data (solid curves) sets. The inboard and outboard data sets are in quite good agreement near the vortex centers, but at larger radii the two sometimes di!er considerably. The alleviated wake shed by the (303, 303) with-"ns con"guration is noted to have smaller swirl velocities and a smaller swirl velocity gradient through the core regions (Fig. 138) than the wake vortices shed by the standard landing con"guration (Fig. 137). The modi"ed landing con"guration has smaller swirl velocities, but the gradient through the core is still quite steep (Fig. 139). 12.3.2. Span-load distributions from isolated vortex structures The simple method introduced by Betz and described in Section 5, relates the span loading on a wing, or the vortex sheet that it sheds, to the rolled-up vortex far downstream. The inverse-Betz method, also described in Section 5, relates the structure of the fully de-
Fig. 136. Division of measured upwash distributions at center of vortex and at centerplane of wake for calculation of isolated vortex structures.
veloped vortex to a span loading that could have generated the vortex. That is, from Section 5, the bound circulation in the wing at the spanwise station, y, is related to the circulation in the "nal vortex by Eq. (45). The isolated-vortex structures, presented in Figs. 137}139, were inserted into the foregoing equations for the inverse Betz method to retrieve the span loadings from the measured data (Figs. 140}142). The retrieved span-load distributions have been made dimensionless by dividing the circulation bound in the wing by the circulation in a pair of vortices that is required for rectangular or uniform span loading when the lift on the wing and the distance between the vortex centers are the measured ones, i.e., a reference circulation, C . That is, C /b ; "C /(2AR (*y/b )), (54) *
Fig. 137. Vortex structures derived from the time-averaged downwash data in Fig. 123a for the standard landing con"guration [187]; #aps (303, 303).
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
623
Fig. 138. Vortex structures derived from the time-averaged downwash data in Fig. 123b for the standard landing con"guration with "ns mounted on top of wing [187] at y /b "0.254; h /b "0.057, c /b "0.083, a "183; #aps (303, 303).
Fig. 139. Vortex structures derived from the time-averaged downwash data in Fig. 123c for the modi"ed landing con"guration [187]; #aps (303, 03).
where *y/b is the spanwise distance measured between the port and starboard vortex centers. It is noted that the ratios of circulations, C(y)/C , all reach or exceed 1.0, which indicates that the vortices do contain the circulation needed to account for the lift on the wakegenerating wing. The spanwise locations where C(y)/C +1.0 are displaced spanwise from the wing centerline because the cross-plane streamlines are o!set due to the presence of the opposite vortex and compressed by the downward motion of the vortex pair (Fig. 30). Since the streamlines are o!set, the circulation they contain is also o!set causing the ratio C(y)/C to become about one at spanwise locations other than the centerline. 12.3.3. Discussion of retrieved span loadings It is "rst noted that the span loadings retrieved from the measured wakes (Figs. 140}142) do not resemble very closely the ones calculated for the wing con"gurations (Fig. 135). The most apparent di!erence is the disappearance of the humps and valleys predicted by vortex-lattice theory due to the lift on the #aps and wing "ns. Such a result is expected, because the vortices shed at the ends of the #aps are often close to each other, and since they are of opposite sign, they interact destructively to smooth out the original variations in the strength of the vortex sheet being shed. Furthermore, the swirl of separate vor-
tices of the same sign in the wake near the trailing edge of the wing interact to smear or smooth out the vorticity concentrations in the wake. Also suppressed in the rollup process is the abrupt fallo! in lift at the wingtip, because the low-energy boundary layer on the wing and #aps migrates to the core regions of the vortices [146]. For the foregoing reasons, the retrieved span loadings taper monotonically from a maximum near the wing centerline to zero at the wingtip. Any characteristic in the original vortex sheet caused by the #ap ends or the wing "ns appears to have been obliterated. This result ful"lls one purpose of the study which was to "nd out how much complex vortex sheets shed by wings change as they roll up into a vortex wake in the far "eld. Comparison of the results presented in Fig. 135 with those in Figs. 140}142 indicates that the changes can sometimes be large. In spite of uncertainties in the data and in the methods used to compute the retrieved span loadings, they still appear to have de"nable characteristics. In the case of the standard landing or (303, 303) con"guration (Fig. 140), the retrieved loadings closely resemble the one shown for parabolic loading in Fig. 135. It is also noteworthy that the loadings are quite similar to the one derived by Jones [152] through an optimization process based on lift and wing-root bending moment for a wing span 1.15 times that of an elliptically loaded wing.
624
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 140. Span loadings derived from vortex structures in Fig. 137 for the standard landing con"guration [187]; #aps (303, 303).
Fig. 141. Span loadings derived from vortex structures in Fig. 138 for the standard landing con"guration with "ns mounted on top of wing [187]; y /b "0.254, h /b "0.057, c /b "0.083, a "183; #aps (303, 303).
Fig. 142. Span loadings derived from vortex structures in Fig. 139 for the modi"ed landing con"guration [187]; #aps (303, 03).
In the case of the wake of the (303, 303) con"guration with wing "ns, the retrieved span loadings (Fig. 141) also resemble the one that was designed by Jones [152] as optimized to have minimum drag for a given span and a given wing-root bending moment, i.e., his design for a wing span that is 1.3 times as large as the one for elliptic
loading. When such an optimization is carried out, the corresponding vortex sheet at the wing trailing edge has an initial downwash velocity distribution wherein the outboard parts of the vortex sheet rotate as a solid body. The speci"cation of solid-body rotation by the vortex sheet was also suggested as a means for preventing the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
vortex sheet from rolling up into a concentrated vortex with an intense core, i.e., a span loading tailored for a benign wake. In the inverse Betz method, it is assumed that a vortex sheet tailored in this way would roll up from the wingtip inboard. In reality, it rolls up from the center of the sheet to form a somewhat more intense but still benign vortex. The third con"guration studied was the modi"ed landing or (303, 03) con"guration of the B-747 model, produced by withdrawing the outboard #ap to its stowed position on the standard landing con"guration. The span loading predicted for such a wing at 43 angle of attack (Fig. 135) has only the one hump at the spanwise station where the inboard #ap is fully deployed. The corresponding retrieved span loading (Fig. 142) appears to be approximated by a parabolic pro"le [144,145] much like the retrieved span loadings for the (303, 303) con"guration (Fig. 140). The two cases di!er in that the (303, 303) wake is much more hazardous than the (303, 03) wake. As pointed out previously, the vortex sheet shed by such a span loading does roll up from the wingtip as assumed by the Betz' method. It is believed that the addition of the low-energy wakes produced by the landing gear and yaw of the aircraft migrates to the centers of the vortices, so that their core diameters increase in size. The increased core diameters make the vortices more rigid, so that the mutually induced instability that leads to threedimensional linking between vortices does not occur (e.g., Fig. 60). 12.4. Wake hazard and induced-drag As stated in the introduction to this section, the primary objective of the research being reported is to "nd new ways to design wings that are e$cient, and that shed non-hazardous vortex wakes. Since the energy in the vortex wake of a wing is well known to be proportional to the drag due to lift, or the induced drag, one way to
625
investigate the e$ciency of a wing is to study the distribution of kinetic energy in its vortex wake. In this analysis, it is assumed that the velocity in the free-stream direction is roughly constant, so that the kinetic energy of the wake vortices is contained only in the across-stream velocity components. The relationships to be derived will be applied to components typical of vortex wakes; namely, a vortex pair composed of two equal and opposite vortices with cores that rotate as a solid body (Rankine vortices), and a pair with vortex cores that have constant swirl velocity (Fig. 143). A vortex pair is used to model the wake, because the energy content for a single vortex goes to in"nity as the outer limit of integration becomes large, whereas, the energy integral remains "nite for a pair of equal and opposite vortices. An expression for the kinetic energy content for vortex wakes in general is di$cult to derive, but the case for a single pair of Rankine vortices has been evaluated by Spreiter and Sacks [193]. In their analysis, the #ow "eld is divided into an irrotational or outer part, and a rotational or inner part that contains the circulation of the vortices (Fig. 144). The integral for the energy in the irrotational part of the #ow "eld is then given by [193]
o E " 2
(v#w) dy dz.
(55)
1
Since the outer part of the #ow "eld is irrotational, it can be expressed by a potential function, u, and the integration over the surface, S, can be changed into the contour integration, C, as shown in Fig. 144: o E " 2
!
u
Ru ds. Rn
(56)
The quantity s is the distance along the contour, and n is in the direction perpendicular to the contour surface. In order to simplify the contour integration, the circulation is assumed to be contained within the circles whose
Fig. 143. Idealized vortex structures for study of energy distributions in vortex wakes [187].
626
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
drag of a wing as
Fig. 144. Idealized vortex pair and contour, C, used to integrate for kinetic energy in irrotational part of #ow "eld [193].
centers are o!set from the b spanwise spacing, so that they correspond to the streamlines induced by a pair of point vortices (located a distance b apart) (Fig. 144). The kinetic energy of the #uid in the irrotational part of the #ow "eld was found by Spreiter and Sacks [193] as
oC b !2r #(b #4r . E " ln 2p b #2r !(b #4r
(57)
The energy inside the vortical region of the vortices is calculated by use of the integral [193] as
o P E " 2prv dr. 2 F
(58)
When the vortex core rotates as a solid body, as it does for a Rankine vortex, v ) "rC/2pr, the kinetic energy F in the core is given by oC E ) " . 8p
(59)
Similarly, when the vortex core rotates with a constant swirl velocity, v ) "C/2pr , the energy in the rotational F part of the #ow "eld is oC E ) " . 4p
(60)
The total kinetic energy in the vortex wake is then given by the sum for the two regions as E"E #E .
(61)
The last relationship needed is that between the energy in the wake, and the induced drag which is found from the expressions for lift and for the induced
4AR b C C " , (62) "G ep b b; where e is the span e$ciency. Since the induced drag and the kinetic energy are both proportional to the square of the circulation in the vortices, they are proportional to each other and can be used interchangeably when various con"gurations are being compared. It is "rst noted that the energy in the &Rankine' and &constant-swirl-velocity' vortex cores, Eqs. (57) and (58), are both proportional to C and independent of the core radius, r . Hence, in both of these cases, if C is the same for two core sizes, the large vortex core has the same energy as the small core. The induced drag is then also proportional to the square of the circulation shed by the wing, but the vortex-induced rolling moments are proportional to the "rst power of the circulation, and how it is distributed. Since the energy in both a large and a small core are the same (i.e., for the same circulation but not necessarily the same lift), the di!erence in the total energy for a concentrated vortex (i.e., a small core radius) and for a dispersed (i.e., a large) vortex core is given by the energy in the #ow "eld between the two core radii, as if the #ow were potential, or
b !2r #(b #4r oC *E " ln 2p b #2r !(b #4r
b #2r !(b #4r , (63) b !2r #(b #4r where r and r are respectively the radius of the small and of the large cores. Another interesting feature of the energy relationships for large and small core sizes is that it takes a larger increment in energy to enlarge a small vortex core a small radial amount than it does to enlarge a large core by the same radial amount. Furthermore, a non-hazardous or large-core vortex contains less energy, and consequently corresponds to a smaller induced drag than a vortex with a small core. In other words, if a lift-generated wake can be designed to shed vortices with large cores, for the same centerline circulation as with elliptic loading, its induced drag would be less, as demonstrated by Jones [152] when he designed span loadings based on wing-root bending rather than on "xed span. Before discussing span loadings for alleviated wakes further, induced drags computed for several candidate types of span loadings are compared in the upper part of Table 12 on the basis of a "xed span without any other restraints placed on the design. Such a comparison is based on the fact that, if the span of the wake-generating wing is held constant, the optimum span loading is elliptic with the span e$ciency e equal to 1. The induced drag for each span loading listed in Table 12 is proportional to ;
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the inverse of the span e$ciency, or the quantity p"1/e, where e"1 for elliptic loading as shown in the table. If, for example, the span loading is designed to produce a vortex wake with a reduced intensity in its core, the centerline circulation needs to be increased to o!set the triangular character of the loading and thereby produce the same lift as an elliptically loaded wing of the same span. Therefore, the span e$ciency decreases, and the drag for a given lift is p times the induced drag for elliptic loading. Therefore, the induced drag is larger for triangular loading (Table 12). In addition, the increased total circulation in the vortex also increases the swirl velocities and the energy in the vortex wake, so that the desired alleviation is not achieved, i.e., if the design is optimized only on the basis of span and induced drag. If, however, the drag of alleviated con"gurations is based on a minimization based on wing-root bending moment instead of span as suggested by the optimization studies carried out on the span loadings for planar wings by Jones [152], the results are quite di!erent. In Jones' paper, a series of designs are derived that optimize the span loading for minimum induced drag while holding the lift and the wing-root bending moment constant, i.e., the span of the wing is allowed to change. As a result, one of the solutions found increases the wing span by 15% over that for elliptic loading, and thereby achieves 15% less induced drag while holding the lift and the wing-root bending moment constant; lower part of Table 12. If the span of the wake-generating wing is increased by 30%, or to 1.3 times that for an elliptically loaded wing, the induced drag is again about 15% less than for an elliptically loaded wing, and the lift and the wing-root bending moment are the same (Table 12). As mentioned earlier, this span loading is very similar to the span loading retrieved for the "nned-wing con"guration (Fig. 140). The foregoing results point out that an appearance of being ine$cient by one set of design criteria may turn out to be more e$cient by another set of criteria. This suggests that an optimization for alleviated wings should utilize a more complete set of parameters. Such a process may provide wing span loadings for benign wakes that have acceptable or greater e$ciency than wing designs in current use. In addition, the results found here point out that the optimization process should include not only horizontal lifting surfaces, but vertical surfaces that lift sideways as well. At this time, it is not clear what parameters should be used in such an optimization scheme nor exactly how the structure of the vortex wake is related to wing geometry. The results presented in Figs. 135 and 140}142 illustrate the complexities that can occur between vortex wake structures at the wing trailing edge, and at the station where the vortices are fully developed. Most of the discussion in this paper has been directed at the wake hazard rather than at alleviation. The two
627
Table 12 E$ciency factors for various span loadings [187] Loading type
Span e!., e
Ezciency based on span Elliptic 1.00 Parabolic 0.91 Triangular 0.73 Min. root bend. 0.66 Solid-body rot. 0.38
p"1/e
Span
1.000 1.101 1.366 1.524 2.612
1.00 1.00 1.00 1.00 1.00
Ezciency based on wing-root bending moment Min. root bend. 1.18 0.85 Min. root bend. 1.18 0.85
1.15 1.30
terms di!er in that wake hazard refers to the vortex wake directly, whereas alleviation assumes that a given loading on the wing has had something added to it, taken from it, or done with it, to reduce the hazard posed, i.e., it has been alleviated. Most current conventional wing designs probably shed a hazardous wake-vortex pair that contains a larger amount of energy (i.e., rotational kinetic energy) than does a benign vortex wake with the same circulation per vortex. However, an aircraft with an alleviated wake may have more drag (i.e., kinetic and heat energy in its wake). Such is the case, because the span loading on the wing "rst generates an energetic vortex wake. Work or energy must then be expended to modify the vortices, so that they become non-hazardous. This is usually accomplished by removing or dispersing the kinetic rotational energy to alleviate the hazard posed. When such a wake has been alleviated to reduce the swirl velocities, some of the original energy in the wake plus the energy expended in making the conversion has been turned from kinetic energy into heat energy thereby making the remaining swirl velocities less hazardous. A good illustration of such a process is the use of drag-type devices to inject turbulence into the vortices to di!use their cores [62,63,67]. Such an observation again points out the need for procedures that design the wing lifting surfaces directly for all of its desired factors, such as the lift, e$ciency, minimum weight, and an acceptable wake-vortex hazard.
13. Vortex decay 13.1. Introduction The term vortex decay implies a steady monotonic decrease with time in the magnitude of the swirl velocity distribution in the vortex. As indicated in the foregoing text, the #ow "eld of a vortex pair is non-linear, and especially in the presence of atmospheric turbulence, can
628
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
undergo a wide variety of dynamic motions that usually accelerates the demise of the #ow "eld. The measurements by Ci!one and Orlo! [91,92] of vortex decay in a water tow tank with very little ambient turbulence (Fig. 2) found that the maximum swirl velocity in a vortex "rst tends to remain constant before beginning a prolonged decay process roughly as t\ . The development of a second-order closure tubulence model by Donaldson [32,141}143] led to numerical simulation of the decay of isolated vortices that predicted the same type of decay pattern. The numerical studies carried out on the decay of vortex pairs found that the decay of vortex wakes was best predicted when the turbulence in their numerical codes was turned o!. It was concluded that the "nite grid sizes used in the numerical procedures introduced a redistribution of vorticity that simulates viscous and turbulent forces. Although the transfer of energy by the numerical procedures used in the computations is small, it is large enough to yield decay rates comparable with or greater than the observed ones. Computational procedures for vortex wakes that have been developed since that time appear to have now either suppressed or avoided the di!usion of vorticity associated with numerical procedures used in the earlier codes [35,72,75,76,86,97,173,175,194}196]. In each of these studies, the e!ect of turbulence on the #ow "eld is modelled by techniques that consider the in#uence of swirl and rotary shear on the magnitude of transfer of momentum. Laboratory measurements of the turbulent structure of vortices provide a means for testing the various theories being developed [79,80,89,154,168, 197,198]. The development of improved sensors are dealt in papers [100,111,188,199]. The in#uence of swirl and shear on turbulence are treated in detail by Zeman [200] in a study of the decay of isolated vortices. In his study, the ability of vortex #ow "elds to smear and damp out turbulence is identi"ed and analyzed. He describes the process as one wherein the self-generated turbulence within a vortex exists, but the radial transfer of momentum is so e!ectively damped by the swirl velocities and their gradients that vortex decay is dominated by viscous stress rather than by turbulent transfer of momentum. It is believed that it is for these reasons that vortex #ow "elds behind even large aircraft appear to be of a laminar rather than turbulent type when substances are injected into the #ow "eld to visualize the streamlines. It also explains why vortices persist as if the #ow "eld were laminar rather than turbulent, and why vortex instabilities usually break up the coherent #ow "eld of the vortices well before viscous and turbulent decay processes cause their demise. The swirling shear velocities tend to damp out turbulent eddies thereby bringing about a laminar character to the vortex #ow "eld. The laminar character of the inner part of vortices, even when embedded in a turbulent environment, is frequently observed by means of #ow visualization.
Fig. 145. Diagram of distortion caused in turbulence eddies by swirling shear #ow "elds of vortices [61].
When smoke or marker #uids are injected into the vortices, they are observed to not disperse for long periods of time, but continue to mark the cylindrical patterns of #uid motion up until the vortex #ow "elds break down due to instabilities or atmospheric disturbances. Observations of this kind indicate that the slow decay of swirl velocities and dispersion of vorticity must be associated with shear forces that are more nearly laminar than turbulent. A possible mechanism by which the e!ectiveness of turbulent eddies is made vanishingly small is illustrated in Fig. 145. Just as the laminar sublayer of the boundary layer on a #at plate damps out eddies near the surface, the swirling and shearing #ow of a vortex causes a circular eddy to be distorted into a #at, high aspect ratio ellipse, which is readily damped to ine!ectiveness. Therefore, existing small-scale turbulence introduced into the vortex by the viscous wake of the aircraft wing of the vortices causes nearly circular eddies to become distorted into long narrow slits that are ine!ective in transferring momentum radially, and that are damped quickly. If however, the eddies introduced into the vortical #ow "eld have a scale that, like atmospheric turbulence, is large compared with the part of the vortex that has a laminar character, the vortices are convected into sinuous shapes that grow with time and bring about breakdown of the vortex structure at the sharp bends in the vortices as illustrated very nicely in Fig. 37 of Garodz and Clauson [50]. The decay of lift-generated wakes is discussed in the text to follow along with methods which may be used to study the nature of the decay process. A discussion will also be presented in Section 16 on attempts to use of the injection of turbulence into vortex wakes as a means to accelerate their demise by destroying the organized structure of the swirling motions.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
629
13.2. Natural decay
assumed that the swirl velocity in a turbulent vortex may be written as an extension of Lamb's model as
13.2.1. Simple models for decaying vortices One of the oldest and simplest equations for the decay of an isolated vortex is the Oseen/Lamb formulation [9] given by
!r C , v " 1!exp F 2pr 4t(l#e)
C !r v " 1!exp . F 2pr 4lt
(64)
Eq. (64) was found by Lamb through an adaptation of a solution presented by Oseen for the di!usion of an isolated two-dimensional line source with time. Eq. (64) is commonly referred to as the Lamb vortex structure. An isolated vortex is chosen for study, because the problem is a two-dimensional one which involves only time and the radial variation of velocity on streamlines which are concentric circles. Since the radius at which the maximum swirl velocity occurs changes as the vortex ages, a relationship is now found for the radius at which the slope of the velocity function in Eq. (64) is zero. The radius at which the swirl velocity is maximum is usually de"ned as the core radius of the vortex. Di!erentiation of Eq. (64) to "nd the radius at which the velocity is a maximum yields r "1.25643121 4lt
(65a)
or r "2.24181(lt. The maximum swirl velocity may then be written as C v "0.71533 . (65b) F 2pr Eq. (65a) predicts the t\ decay rate indicated by data taken in #ight and in water tow tanks [90}92,101]. The plateau region vanishes for this formulation, because all vortices are assumed to have their circulation concentrated at r"0 when the vortex begins its decay process. Since vortices generated by lifting wings, water jets, etc., in the laboratory or in #ight, have zero swirl velocities at their centers, the function of the plateau region in Fig. 2 appears then to be an adjustment region which brings the curve for the decay of the maximum swirl velocity with downstream distance out into the vicinity of the t\ curve. Although such an interpretation is intuitively correct, its application has many variations that depend on the nature of the vortex-generating wing and on the environment in which the vortices are embedded. In the 1950s, Squire [201] extended Lamb's result to include vortices whose turbulence could be characterized by the circulation content of the vortex, because as he states, `the simplest formula is usually as good as any othera. He meant, of course, that such a model is useful as a "rst approximation, and when better information is not available. In order to obtain a simple result, Squire
(66)
where C is the entire circulation content of the line vortex. In Squire's model, the turbulence does not vary with radius. In simpli"ed terms, Squire substitutes the quantity (l#e) for the laminar value of the kinematic viscosity, l, where e is de"ned as an eddy viscosity which is taken as e"aC , (67) where a is a constant. The decay process predicted by both Eqs. (65a) and (66) has the t\ character. A more realistic approach to the turbulent structure of vortices is to conduct an analysis that includes the selfgenerated turbulence in the vortex and the turbulence in the ambient #uid. Several such analyses include a global type formulation by Greene [176] which predicts the demise of vortex pairs in various types of atmospheres. A more rigorous approach by Kuzmin [202] derives equations for the interaction of self-generated and ambient turbulence with the vortex structure for an evaluation of the decay rate of vortices for various wind conditions. In one of the earliest and simplest analysis of vortex decay, a simple formulation was derived by Ho!man and Joubert [51] for the structure of a turbulent vortex. In their analysis, an expression for the Reynolds stress is derived by use of the conservation of the moment of momentum of the concentrically circular #ow "eld of the vortex. As an outcome of their analysis, a relationship for the variation of the circulation with radius is derived in the form C(r)/b ; "A ln(r/b ), (68) where A is a constant. If a linear variation of the circulation with the logarithm of the radius is found in the data for a measured vortex, it is assumed that the turbulence model used by Ho!man and Joubert to derive Eq. (68) applies to the vortex structure. In what may be labeled as a fourth method, is the development of simple analytical relationships for the distribution of swirl velocity in an isolated vortex. The functions developed simply approximate measured distributions, and usually do not have a physical basis that permits estimates to be made of the decay process [203}205]. The functions derived often apply to vortices shed by either rotors or wings. One such function with considerable latitude is given by r/r C v" , (69) F 2p [1#(r/r )L]K where n and m are arbitrary and r is the core radius of the vortex. If m"1/n, the maximum swirl velocity occurs
630
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
at r and decays as 1/r in keeping with conventional vortex structure [205]. Although some of the equations used in the "t to measured data are interesting, and provide an equation that approximates measured vortex structures, their use in the interpretation of data, and their use for the determination of a decay rate for the vortex is not clear. 13.2.2. Numerical simulations Even though this overview is not intended to include numerical simulations, the large amount of e!ort devoted to the subject suggests that mention must be made of research in this area. The large amount of e!ort directed at the development of computer codes is an attempt to satisfy the need for an accurate representation of the development of the vortex wake as it leaves the liftgenerating surfaces of the aircraft, and proceeds through decay and decomposition to a harmless state. If a code were available that could simulate with a high con"dence level any portion of the wake history accurately, the experimental measurements could be guided much more judicially, and solutions to various aspects of the wakevortex problem could be found more readily. Most of the simulations appear to solve special or idealized problems to provide some guidance and intuition. Since wakevortex dynamics is non-linear, and can on occasion respond to viscous and turbulent features of the #ow "eld in a seemingly erratic way, numerical simulations are very di$cult to accomplish accurately for the general case. Nevertheless, development of computer codes to do so should be attempted with short term goals that ful"ll less ambitious objectives. One of the "rst attempts at the development of a computer code for the simulation of the entire wake history of lift-generated wakes was carried out by Teske et al. [206] as an extension of the work of Donaldson and Bilanin. The code followed the development of the lift-generated wake from the trailing edge of the wing into the far "eld where the mutually induced instability of Crow sets in and pinches o!, and the wake decays. As time progressed, the computer codes began to use "nite-di!erence methods to better simulate the dynamics and internal processes of the vortices and their interactions. For the interested reader, some of the research e!orts on the development of numerical simulations for vortex wakes are presented in some of the references listed [32,34,51,72,73,75,76,78,79,86,89,97,141,142,175, 188,194,196,197,200,207}210]. Some of the articles treat not only the convective, viscous and turbulent processes within lift-generated wakes, but they also include e!ect of convective and turbulent processes in the ambient #uid on the wake dynamics. Several of the papers include comparisons with experimental measurements. A numerical simulation was carried out by DaclesMariani et al. [196] of the vortex wake shed by the
standard landing con"guration of the B-747. The intent of the simulation was to "nd out how well a newly developed computational method [195] could simulate the changes observed in the vortex wake structure measured in the wind tunnel. The downwash data measured in the wake of the standard landing con"guration of the B-747 model at 81 ft (Fig. 124a) was used as input. Two versions of a computer code were then used to predict the structure of the wake at the 162 ft station (Fig. 146). The "rst version of the code uses the full Navier}Stokes formulation to predict the downstream #ow "eld. The second version, Model II in Fig. 146, is also based on the Navier}Stokes equations, but some simplifying assumptions, suitable for vortical #ows, are made in its formulation to make the code run more quickly. The results from the computations made by use of the full Navier}Stokes formulations are included to show that the more approximate and faster method, Model II, yields about the same result. The computer code assumed that the free stream was uniform and contained no turbulence. The numerical results presented in Fig. 146 indicate that the two numerical results only di!er slightly from each other, and both predict only a small change in the downwash distribution across the wake between the 81 and the 162 ft stations. When the computed distributions are compared with the time-averaged measured distribution, the agreement is quite good on the starboard side, but not so good over much of the port side of the wake. Two explanations for the di!erences between the computed and measured results seem to apply. First, the experimental downwash was a!ected by the turbulence in the wind-tunnel airstream which was not simulated in the computations. Second, the measurements were not made correctly. Since the computations and the measurements are in
Fig. 146. Comparison of upwash distributions as computed by use of Navier-Stokes simulation with time-averaged distribution as measured in 80;120 ft Wind Tunnel at x "162 ft. Input data for computation from x "81 ft (24.7 m) (From Dacles Mariani et al. [196]).
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
good agreement on the starboard side of the wake, and over a portion of the port side, it is believed that improvements need to be made in the measurement techniques at downstream distances larger than 81 ft. Improved techniques were used on the starboard side, which probably explains the good agreement there. It is also possible that segments of the two pro"les on the starboard side of the wake are in quite good agreement, because the survey was made through the center of the meander region, whereas the port side survey was made through the point of maximum rolling moment. Since the computed result and the experimental measurements are in good agreement over much of the starboard side and a portion of the port side, it is concluded that improvements in the measurement techniques and procedures would probably bring the wind tunnel data into better agreement with the calculated pro"les over the entire wake. 13.3. Observations of decay 13.3.1. Swirl velocity The information presented here is intended to draw together information presented previously in this overview in order to assist the reader in an overview of the decay of swirl velocity with time or distance behind the wake-generating wing. First recall that the changes in the maximum swirl velocity with downstream distance as measured in a water tow tank (Figs. 2 and 3) indicated that the maximum swirl velocity is "rst nearly unchanged and then decays roughly as the inverse of the square root of time, or 1/t . Since the background or ambient turbulence is vanishingly small, the decay process follows the process expected according to the Lamb}Oseen relationship, Eq. (65a), (65b). As the turbulence level in the ambient #uid increases, the wake vortices change from having nearly straight to highly sinuous axes. As pointed out by Crow and Bate [74], Liu [80,98,99], and others, the background turbulence has the capability to initiate natural instabilities in vortex wakes, and thereby hasten the destruction of the coherent nature of the vortices. Not only does the ambient turbulence initiate instabilities in the wake, but it also helps to disperse the vorticity in the wake. Therefore, whenever attempts are made to make measurements in vortex wakes, the lateral motions of the #ow "eld make it di$cult to separate the decay process from vortex changes with time. It is to be remembered that the in-trail wake-vortex separation problem in the airport environment is usually one that involves vortices embedded in some sort of ambient turbulence. Since the interaction of vortex wakes with the ambient turbulence is complex, simple rules for conversion of vortex results obtained in a turbulent environment to a non-turbulent one, and vice versa, are not available, so that numerical simulation is necessary [72,75,208,209].
631
Since the NASA 40;80 ft and 80;120 ft Wind Tunnels have a free-stream turbulence level of about 0.5%, the vortices take on a sinuous shape which causes the #ow "eld of a vortex to meander about at a given downstream distance [161,162]. As discussed in Section 10, the meandering motion, and the in#uence of the ambient turbulence on the vortices was such that it was not possible to discern a clear downstream trend in the swirl velocity (Fig. 120). For example, the downwash data at the two separation or downstream distances, x "81 and 162 ft, presented in terms of #ow-"eld angularity, w/u, in Figs. 122}126, is that the data at x "162 ft is not as smooth as the data at x "81 ft. The increased size of the #uctuations in the velocity distributions at x "162 ft are believed to be caused by the larger meander distances of the vortices at the greater downstream distance. It is believed that some of the irregularities in the downwash data can be suppressed by longer data-sampling times. The most surprising feature in the data presented in Fig. 124 is that some of the up- and downwash velocities in the vortices are noticeably higher at x "162 ft than at x "81 ft. These increases in the swirl velocity with downstream distance indicate that vortex intensi"cation rather than decay occurred, which is opposite to intuition. It would be hoped that the vortex wakes measured in the wind tunnel could be compared with data from other sources. In the search for data on the same or similar con"gurations it was noted that several pro"les measured in water tow tanks are quite similar to those in Fig. 124 even though the wake-generator was a #at wing of rectangular planform (e.g., Fig. 2 of Baker et al. [89] and Fig. 4 of Jacob et al. [174]) and not similar to the wings shown in Fig. 108. Even though the lifting surfaces di!er considerably, the downwash "elds appear very similar to one another. The data developed for helicopter rotors by Leishman and Bagai [41], and McAlister [42] for isolated wingtips also appears to be similar to the vortex structures shed by aircraft, but appears to decay much faster. A simple way to evaluate vortex intensity is to compare the vortices on the basis of maximum swirl velocity as done previously [91,92,101]. For example, measurements on the landing con"gurations tested in the 80;120 ft Wind Tunnel can be compared with those available from #ight experiments [15,17,122]. Measurements made in #ight behind a B-747 in its landing con"guration indicate a maximum swirl velocity [15,17] of about v "0.5; as compared with values around F 0.2; or less in the wind tunnel (Figs. 122}126). Other tower-#yby experiments obtained values in excess of 1.2; for the B-727, B-757 and the B-767 in their landing con"gurations [50]. Lidar measurements were taken by Hallock and Burnham [122] at 24 s (1 mile) after the passage of a B-747 in its conventional and in an alleviated con"guration (#ight spoilers deployed). They
632
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
measured maximum swirl velocities of 0.2; and 0.1; , respectively. Those values are close to those measured in the wind tunnel. At 24 s the following distance is about 1 mile, or about the same scale distance as in the 162 ft station in the wind tunnel. For the conventional landing con"guration, the lidar data presented by Hallock and Burnham [122] appears to indicate a larger core size followed by a constant swirl velocity out to about r/b "0.09 which is not observed in the wind-tunnel data. At larger radii the swirl velocity falls o! at about the same rate as measured in the wind tunnel. In other analyses of full-scale data obtained in #ight, Abramson and Burnham [110], and Sarpkaya [211] present information on a variety of con"gurations. Some of the wide variations in maximum swirl velocity can probably be attributed to Reynolds number and scale di!erences between the models and #ight hardware. The small scale of the wind tunnel models probably results in #ow separation on the wing and on the #ap elements, which is probably much greater than that which occurs on the full-scale aircraft. Even small amounts of #ow separation are known to cause the core size of the shed vortex to be larger than without #ow separation, which in turn reduces the swirl velocity. However, it is questionable whether the large di!erences noted here can be entirely attributed to di!erences in #ow separation that came about in the various tests. 13.3.2. Vortex-induced rolling moment As mentioned in Section 10, a number of con"gurations of the B-747 and the DC-10 models were tested for rolling-moment hazard in the 80;120 ft Wind Tunnel at both the x "81 and the x "162 ft stations. Fig. 120 presents a summary of the rolling moment data obtained for the wide variety of con"gurations of the two wakegenerating models as function of downstream distance. Since the curves do not all even slope the same way, the changes with downstream distance appear to include both decay and ampli"cation. It is concluded that vortex stretching (and the associated intensi"cation) can account for at least some of the increase in rolling moment with downstream distance. Decay and restructuring of the swirling velocities may also have occurred in some cases. It is not surprising then that similar occurrences are present in the #ight data. Since the #ight data has very large scatter due to the di$culty with penetration paths not always being along the path of most intense encounter, the "nal curves were usually drawn through only the highest data points obtained. Quite often the data did indicate a decrease with distance behind the wake-generating aircraft. However, on some occasions the probe aircraft would encounter a vortex at large downstream distances, and "nd that the encounter was even more intense than experienced at stations nearer the generating aircraft. Since pilot input can make the response of the aircraft appear to be caused by a vortex
more intense than expected, and the penetration path is uncertain, the higher rolling moment responses were "rst dismissed as a bad data point. However, when several cases of excessive rolling moment had been experienced, some of the data points were included in the reporting [55]. These results suggest that some of the inconveniences of ambient turbulence in the free stream of groundbased facilities are o!set by the fact that they do simulate experience in #ight tests. Since it is easier to repeat tests and to perform diagnostic tests in ground-based facilities, the ability to chase down the causes of unexpected data is increased.
14. Tests for similitude in vortex structures 14.1. Introduction The data obtained in the 80;120 ft Wind Tunnel at the two downstream stations where velocity surveys were taken are now used to "nd out if the vortex structures have approached or have made the transition from their rolled-up structure to a similarity pro"le [212]. The objective of the investigation is to "nd out if any features associated with vortex decay can be identi"ed in the wind-tunnel data. In particular, the theoretical vortex models used are those of Lamb/Squire [9,201] or the Ho!man}Joubert [51] to "nd out if a particular pattern or universal characteristic is evident in the vortices that make up the measured downwash distributions reported in [106,184]. First of all, it is not obvious, nor is it required, that vortex structures (which are very di!erent from each other when "rst rolled up) should all go to a self-similar type of structure and stay in such a relationship throughout the decay process. The problem is even more complicated by the fact that the wind tunnel, and the atmosphere, have turbulence in the ambient #uid which causes the vortices to become sinuous and to have increased radial transport of angular momentum; especially at the periphery of the vortex structures. If similitude exist, it may be easier to identify and quantify the changes with downstream distance between the 81 and the 162 ft stations in the wind tunnel. Not only are the changes with distances slow, but the changes due to decay are hard to separate from those that occur due to the sinuous motion of the vortices which causes stretching and compression of the vortex cores. The velocity pro"les for the isolated vortex structures (Figs. 137}139) are now analyzed to determine if similitude exists according to one of two models. Only the data from one side of the wake (i.e., the side with the most data points and with the smoothest distribution) are reported to reduce the number of "gures to be presented. Results from the other side of the wake produced about the same results. The objective is to determine whether the pro"les
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
of swirl velocity correspond to or can be approximately represented by either the Lamb/Squire [9,201] or the Ho!man}Joubert [51] model for a universal structure of turbulent vortices. If the data "t either criterion, the information may be of use in the generation of a selfsimilar representation for vortex structure and decay. Research similar to that to be reported here has also been carried by Eisenhuth et al. [118] and Owen [213]. The likelihood of the occurrence of similitude by means of a summation of a number of exponential parameter like the Lamb/Squire model for a turbulent vortex was studied by Iversen [214]. Based on the turbulence model assumed to exist in the vortices analyzed, his results indicate that the early structure of vortices shed by wings of various shapes and span loadings lose their distinctive character and all structures eventually tend towards a universal pro"le like the Lamb/Squire vortex structure. Such an assumption is supported by the results presented in Section 12. Since the downstream distance available in the large wind tunnels is limited to about 162 ft, some viscous and convective restructuring of the vortices will probably have occurred, but it seems doubtful that viscosity and turbulent forces would have had enough time to bring the vortex structures close to a universal character. Nevertheless, the data presented in "gures to follow indicate that some sort of representation may exist. Since the data quality is questionable in some cases, and the downstream distances available are not large enough, it is not certain whether the vortices are on the way to a universal structure or whether the close agreement is fortuitous. In a somewhat related study, Rossow [215] attempted to "nd the vortex structure from measured rolling moments by approximating the vortex structures with a series of Lamb vortices. Thereby, a measured rolling-moment distribution across a wake could be interpreted for the corresponding up- and down-wash distribution that generated the rolling moments. It was found that the process was feasible, but lacked accuracy in the retrieved velocity distribution because it was not close to those estimated for the wakes by Betz' method. It was concluded that whenever possible direct measurement of the velocity "eld with a hot wire is much more accurate and e$cient. The Lamb vortex representation also was not useful in the determination of viscous e!ects. 14.2. Oseen/Lamb/Squire structure As presented in Section 13 on vortex decay, a solution presented by Lamb [9] for the di!usion of an isolated two-dimensional line vortex over time was extended by Squire [201] to include vortices whose turbulence could be characterized by the circulation content of the vortex. Based on Squire's analysis, the swirl velocity in a turbulent vortex may be written as an extension of
633
Lamb's model as Eq. (66) in Section 13.2.1 as v "(C /2pr)[1!exp(!r/4t(l#e))], where C is the F entire circulation content of the line vortex. In simpli"ed terms, Squire justi"es the substitution of (l#e) for the laminar value of the kinematic viscosity, l, where e is de"ned as an eddy viscosity which is given by Eq. (67) in Section 13.2.1 as e"aC where a is a constant. Since the laminar solution and Squire's turbulent solution have the same form, a test to "nd out whether a vortex resembles a univeral self-similar pro"le or not can be made by rewriting Eq. (66) as
1 C G(r/b )"(r/b ) ln " , 4tb(l#e) C !C(r)
(70)
where C(r) is given by C(r)"2prv . F
(71)
In the analysis of the data available, a variety of exponents on the parameter (r/b ) were tried. Since most of the results corresponded best with either the "rst or second powers of (r/b ), only the results for those two exponents are presented here. Therefore, the equations used to "nd out if a vortex pro"le resembles one that is universal and of the form of the so-called Lamb vortex (or Squire's version of it) are plotted as a function of radius when written as
G(r/b ) 1 C " ln , (r/b ) (r/b ) C !C(r)
(72a)
G(r/b ) 1 C " ln . (r/b ) (r/b ) C !C(r)
(72b)
14.3. Howman}Joubert structure A second method by which an organized structure of a turbulent vortex can be represented was derived by Ho!man and Joubert [51] and shown to be applicable to the vortex wakes shed by a wide variety of aircraft [118,213]. As mentioned previously, an expression for the Reynolds stress is derived by use of the conservation of the moment of momentum of the concentrically circular #ow "eld of the vortex. As an outcome of their analysis, a relationship for the variation of the circulation with radius is derived which has the form given by Eq. (68) presented in Section 13.2.1 as C(r)"A ln(r/b ), where A is a constant. In order to obtain the most straightforward test, the axes for the graph should be chosen to provide for a straight-line character in the data. A formulation for the constant A will not be done, because the analysis becomes too uncertain. Therefore, in "gures to follow, the circulation will simply be plotted as a function of ln(r/b ) with the constant A set equal to one.
634
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
14.4. Sample results from similitude tests Vortex data formulated to test the two similitude parameters are presented in Figs. 147}150. The structure of
the isolated vortex derived from the measured downwash distributions are presented in Figs. 137}139. The tests for similitude (or for a universal character) according to the Lamb/Squire model with an exponent of one or two are
Fig. 147. Tests for similitude on data taken in starboard side of wake of B-747 model in standard landing con"guration [212].
Fig. 148. Tests for similitude on data taken in starboard side of wake of DC-10 model in standard landing con"guration [212].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
635
Fig. 149. Tests for similitude on data taken in starboard side of wake of B-747 model in standard landing con"guration with large "ns [212]; x "81 ft (24.7 m).
Fig. 150. Tests for similitude on data taken in port side of wake of B-747 model in modi"ed landing con"guration [212]; x "81 ft (24.7 m).
636
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
presented in the upper parts of the "gures as indicated, and the tests for the Ho!man}Joubert model are presented in the lower parts of the "gures, also as indicated in each. A great deal of credence should not be placed on data taken near the vortex centers, because the data are not as reliable as those at larger radii. It is reasoned that small errors in the lateral location of the data points can cause a large percentage change in the determination of the circulation. It is "rst noted in the tests carried out for the Lamb/Squire model that more of the vortex data have a more nearly linear relationship with the parameter de"ned in Eq. (72a) than with the quadratic de"ned by Eq. (72b), even though the quadratic is the theoretically preferred quantity. That is, the curves are more nearly constant in the upper part of Figs. 147}150 than they are in the lower part of the "gures. The conclusion to be drawn from those "gures is that neither the Lamb nor the Squire vortex model provides a realistic approximation to the data. It therefore seems unlikely that the shear forces between radial layers of #uid can be represented by a constant value of laminar viscosity or turbulence like the one proposed by Squire [201]. In only the one case (Fig. 149) does the quadratic variation hold, and then only approximately. Even then, it is not possible to determine an apparent eddy viscosity, e, because the time t"0 (at which the vortex could be considered a line vortex) to establish a virtual or apparent beginning point for the vortex history is not known. Also, a determination of e by use of corresponding vortex pro"les for the 81 and the 162 ft stations could not be found, because the data are not reliable enough to carry out an evaluation. The tests for the straight-line character of the graphs for the Ho!man}Joubert test are presented in the lower parts of Figs. 147}150. It appears that almost all of the data studied (including some not presented here) have a straight-line character over a portion of their pro"les. These results suggest that a turbulence structure along the lines assumed by the Ho!man} Joubert analysis is probably present in the cases tested. It is also noted that the straight-line similitude characteristic occurred for a wide variety of con"gurations and span loadings. The radial extent over which the straightline characteristic persists does not seem to be much larger for the data taken at the 162 ft station than at the 81 ft station. Such a result probably re#ects the fact that vortex decay, and vortex change, with downstream distance are very slow once the vortex has rolled up behind the wake-generating wing. The foregoing tests for similitude indicate that the turbulent shear forces between streamlines in a vortex are large enough that they need to be included in the decay of vortices. Furthermore, the data suggests that the tubulence formulation should have the character of the model proposed by Ho!man and Joubert [51].
15. Vortex instabilities 15.1. Introduction Some of the decay processes discussed in the previous section assumed that the ambient #uid is so quiescent that the vortices decay by gradually spinning down without any other type of motion being instigated or imparted to the vortex. When a vortex, or a pair of vortices, is embedded in a real environment, like the atmosphere, random motions of the air cause the vortex axis to become sinuous in shape. Also, small-scale eddies in#uence the vortex by convecting rotary momentum from one radial location in the vortex to another to enhance the di!usion process. Of interest in this section are the instabilities in a vortex that can be initiated by disturbances from within the vortex wake or from the ambient #uid. Vortex instabilities are studied, because they have the potential to grow to a large enough amplitude to quickly destroy the coherent structure of an isolated vortex or the entire vortex wake. A good example of a vortex-wake instability that brings about large-scale mixing is the mutually induced instability in a single vortex pair analyzed by Crow [49] which has been discussed in Sections 7 and 8. Since the mutually induced, or Crow, instability has already been discussed at length, it is mentioned here as an example of the mixing that can be brought about in vortex wakes to destroy the initially coherent structure of the wake. The study of the stability of vortex wakes is continuing in the hope of "nding other wake instabilities that proceed more rapidly, more reliably, and more destructively than presently known instabilities for lift-generated wakes. An example of instabilities that are usually not e!ective in alleviating vortex wakes, is the phenomenon known as vortex breakdown or bursting wherein the radius of the vortex core is suddenly enlarged by several fold. Vortex core bursting usually occurs in response to a persistent pressure gradient along the vortex axis. Such an instability is most applicable to the vortices that form over highly swept wings at high angles of attack, and the corresponding loss of lift associated with vortex breakdown or bursting. It appears that the destruction of the vortex is con"ned to regions near its axis, and that the angular momentum in the #uid is preserved, so that wake-induced rolling moments are not dramatically decreased [216]. Since catastrophic breakdown or bursting has not been observed in vortex pairs that trail from transport aircraft, and computations indicate that bursting lowers the wake-induced rolling moment by only a small amount, vortex bursting does not compete with the mutually induced instability for rapid and thorough destruction of vortex wakes. A wide variety of instabilities can a!ect vortex structure, e.g., photographs of instabilities on vortex structures in Van Dyke's book [38]. The "rst example presented on
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
his p. 59 consists of small-scale distortions on the hollow core of a buoyancy-driven vortex. The spiral variations in the core diameter are inertial waves that propagate along the vortex core at about the stream velocity, and do not appear to initiate distortions of the core that grow to large enough amplitude to eventually destroy the coherent structure of the vortex. Another photograph on p. 67 of Van Dyke's book, illustrates how small-scale waves form on the core region of ring vortices and grow rapidly with time. In a short period of time, the periodic distortions grow large enough to destroy the entire #ow "eld of the ring vortex. First identi"ed by Widnall [36], the instability has rightfully become associated with her name [38]. The mutually induced instability of Crow mentioned previously, which is frequently observed in vortex pairs that trail from aircraft in cruise con"guration at high altitude, is illustrated in Fig. 71 (from Crow [49] and Van Dyke [38]) and in Figs. 72}74 (from Liu [80,98,99]). It is noted that the vortex cores marked by condensed water vapor in engine exhaust, or by dye, remain nearly intact throughout the growth stage of the instability. The core of the vortices only disappears near the end of the event where the vortices become signi"cantly stretched and bent. The instability has the virtue that it involves both vortices in the pair and promotes vigorous mixing throughout the wake by means of the sinuous shapes of the vortices and the irregularly shaped loops that form. 15.2. Small-scale vortex instabilities As the foregoing discussion indicates, the name smallscale instability implies that the vortex #ow "eld promotes the growth of small disturbances, usually in the region of the vortex core or near the center or axis of a vortex. If the instability is predicted theoretically, it is usually necessary to determine the ultimate growth of the distortions experimentally, because the resulting dynamics is usually so complicated that it must be followed numerically or experimentally. If the "nal sizes of the disturbances are restricted to the core region of the vortex, the swirling #ow "eld does not lose much of its hazard potential [216]. If however, the distortions grow large enough to be comparable with the size of the wing span, the hazard posed by the wake may be reduced to an acceptable level. One of the "rst analyses carried out on possible smallscale instabilities in the core region of vortices was carried out by Lessen et al. [217], Lessen and Paillet [218], and Zalay et al. [219]. Experiments conducted to test the instability used both the rotor blade of a helicopter, and a "xed wing to generate the vortex. The disturbance to the vortex core was produced by a jet of air directed into the vortex near its axis. It was found that any smoke or #uid markers introduced to follow the #uid motions were
637
rapidly di!used by the blowing, and that the maximum swirl velocities in the vortex were reduced substantially. However, the rolling moment induced by the resulting vortex on a following wing was almost unchanged [220]. It is concluded that either the turbulence generated by the jet of air along the vortex axis, or the resulting instability, produced chaos only in the core region of the vortex. In either case, the rest of the vortex was left nearly intact, so that its hazard potential remained. In a related study, the e!ect of engine exhaust and landing gear extension on vortex dispersion was examined by use of measurements of the vortex-induced rolling moment on a following wing both in #ight and in ground-based experiments [58,61,66,220]. Even though there was some scatter in the data, the results indicated that the vortex-induced rolling moment on a following wing or aircraft is attenuated by engine thrust by up to 10}20%. The alleviation was, however, found to be inadequate for a decrease in the in-trail spacing between aircraft for arrival and departure at airports. Similar results were found for disturbances introduced into the wake by drag devices [58,62,63,87,88]. It is believed that the reductions in wake intensity observed when disturbances (i.e., turbulence) were injected into vortex wakes are caused by the enhanced di!usion of the circulation in the wake vortices, and not by any catastrophic vortex instability. Such a result is not surprising, because as mentioned in Section 12 on wing e$ciency, a great deal of energy is required to change the diameter of an energetic vortex core. Before vortex instabilities are discussed further, two forms of vortex dynamics observed in condensation trails will be described. Both were noted in the #ight tests conducted with the B-747 at Dryden Flight Research Center in the 1970s. The "rst, appearded to be an orderly modi"cation of the core region of vortices shed by the B-747 and illustrated in Fig. 151. It was observed only twice and then only for short periods of time, i.e., about 5}10 s. To the author's knowledge, a photograph of the event has not been taken. As illustrated in Fig. 151, the vortex contorts itself much like a rubber band being wound ever tighter. That is, instead of winding up or spinning within the same tubular space, the vortex core appeared to wrap around itself by jumping out into a tight spiral around its original location. The new core con"guration then has a radius which is larger by about
Fig. 151. Diagram of small-scale distortion on vortex core in wake of B-747 that appears similar to knots which form on rubber band as it is wound ever tighter.
638
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
a factor of two or three and that appears to have a central core and a tight spiral wrapping over it that is on the outside of the original tubular core. The outer vortex **windingsa appeared to wrap sequentially and progressively in one direction along the original vortex on the outside of the original tube. The wrappings proceeded along the core only a short distance until the core region, and the newly wrapped core region, lost their identity and became turbulent. This process caused only the core region of the vortex to become incoherent and left the outer part of the vortex intact until some other process in the wake caused the organization in the wake to be destroyed. A second form of vortex dynamics observed in the #ight tests involved not only the core but also the outer parts of the vortex. The event is a common one that might be called a form of core breakdown, and was observed in almost every wake. Britton [167] describes the event as another type of instability in which vortex burst occurs in the outer part of the vortex leaving a core behind, i.e., the burst does not entirely destroy the vortex. As sketched in Fig. 152 from observations of the wakes trailed by the NASA B-747 in over#ights at NASA/ DFRC, the event consists of a swirling type of radial #ow that appears to come from the core region of the vortex. It also appears that the #ow inside the core is toward the breakdown point from both directions along the core. The disk-shape region lies in a plane perpendicular to the vortex axis. The #ow visualization provided by vaporized mineral oil indicated that the air in the core region of the vortex #owed along the core from both directions to the location of the event. The axial #ow occurring along the core then turns from an axial direction to one in a radial direction, where the air #ows away from the vortex axis in spiral fashion. The radial #ow at the sharp bend appeared to interupt the vortex at that station, so that breakdown of the #ow "eld of the vortex was initiated. When the mutually induced instability did not lead to linking of the vortex pair, and when the vortices became sinuous because of atmospheric eddies or self-induced motions, such a disk-type breakdown mechanism at sharp bends in the vortex axes was the "rst part of a general mixing whereby vortex wakes break up. In fact, in the airport environment where aircraft are con"gured in their landing con"guration (as was the case in the Dryden tests), the vortex wakes are most often dispersed by the action of atmospheric eddies that caused the vortices to become more and more sinuous with time until the disk-type of breakdown (Fig. 152) occurs. Photographs of the event are presented for several events in a water tow tank by Liu [80] in Figs. 72}74, and in #ight by Britton [167], Crow [49] and in Fig. 3 of MacCready [221], and in a tow tank by Olsen [158]. On occasion, the breakdown event consists of a single diskshaped region where the swirling radial #ow is obvious, but more often it consists of a number of events adjacent
Fig. 152. Diagram of #ow from vortex core when it is bent sharply thereby causing the #ow "eld of the core region to decompose. Compare with Figs. 72}74.
to each other along the vortex core so that the region appears as an old fuzzy bottle brush with bristles of irregularly length as indicated in the "gures just mentioned. 15.3. Large-scale vortex instabilities Consideration is given here to vortex instabilities that, when initiated, bring about mixing in vortex wakes on a scale the size of the wing span of the wake-generating aircraft or larger. The instabilities must then have a scale or wavelength much larger than the core size. In addition to providing a large amount of mixing in the wake, the wing con"guration required to implement the instability should either maintain or increase the e$ciency of the aircraft. A vigorous search for those kinds of vortex mechanisms has been in progress for over 25 years with some success, but without one or more clearly de"ned solutions. The following subsections describe some of the e!orts that have been made. Most of the instabilities to be described rely on turbulence in the ambient #uid, or in the wind-tunnel airstream, to initiate the instability. The turbulence in ground-based facilities is consistent and reliable, but turbulence in the atmosphere is quite variable and unreliable. Therefore, ground-based tests are good developmental screening tools, but "nal proof-ofconcept must be made with #ight tests under a wide variety of operational situations. 15.3.1. Stability of single vortex pair As pointed out in Sections 7 and 8, one of the "rst mechanisms observed to bring about the complete disintegration and dispersion of a single pair of wake vortices is the mutually induced instability identi"ed by Scorer [165,120] and correctly explained by Crow [49]. As pointed out in Sections 7 and 8, the alleviation process is e!ective, but the time required to accomplish the needed wake spreading of the sinuous vortex "laments is unacceptably long for the airport environment. Therefore,
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
e!orts have been made to ensure, and to accelerate the onset of the Crow or mutually induced instability by manipulating control surfaces [155,172] or the entire aircraft [59,158]. The objective was to impress waves of large amplitude on the vortex lines as they are generated in order to reduce the time required to achieve rapid growth in wave amplitude and wake disruption. It was found that the process occurs most readily when the generating aircraft is in an aerodynamically clean con"guration, so that the vortex cores are small and the rotary velocities high. When the vortex cores are large due to the entrainment of low-energy #uid that trails in the wakes of landing gear and #aps, the growth rate of the instability waves is slow, or may not occur at all. A theoretical and experimental study was carried out by Leweke and Williamson [222] on the instability of a single pair of counter-rotating vortices. Their study extends the analysis of Crow by including disturbances that are of shorter wavelength, which are on the order of the vortex core diameter rather than the spanwise spacing between the vortices. The paper is especially interesting, because it provides the theory for the instabilities, and then also demonstrates the modes experimentally. In the "gures presented, Leweke and Williamson point out that the vertical and spanwise displacements of the vortices are in phase and not in re#ectional symmetry. The "gures presented show that the long wavelength instability of Crow is in progress, and has not yet progressed to the point of vortex linking. It is interesting to note that the instability is illustrated in the pictures of vortex "laments taken of the vortex loops formed shortly after linking, and the subsequent formation of waves of short wavelength (e.g., Fig. 71 from Crow [49], Figs. 1 and 2 in MacCready [221], and Fig. 13 in Scorer and Davenport [120]) are close to re#ectionally symmetric. This behavior in condensation trails at high altitude appears to be fairly consistent, and is frequently observed. It is believed that the paper of Leweke and Williamson contributes substantially by calling attention to the short wavelength counterpart of the long-wavelength version of the mutually induced instability. The #uid dynamics associated with the short wavelength instability does not appear to be related to either of the #uid motions illustrated in Figs. 151 or 152. It is also not clear whether the short wavelength instability leads to mixing that is restricted to the region near the core of the vortex, or whether the outer part of the vortex #ow "eld experiences mixing with regions beyond the wingtip region. 15.3.2. Stability of multiple vortex pairs In order to expand the knowledge on the instabilities and mixing that occurs in wakes like those shed by a wing with sawtooth loading (e.g., Fig. 43), Hackett and Evans [170] conducted a numerical study of the wake dynamics expected for several con"gurations. The analysis method was directed at prospective mutually induced
639
instabilities that might occur in wakes composed of multiple vortex pairs. Their more comprehensive analysis con"rmed the results predicted by the Tre!tz-plane type of analysis carried out earlier, and gave insight into the dynamics expected in more complex liftgenerated wakes. In a recent paper, Crouch [223] extends the analysis carried out by Crow [49] for one vortex pair to liftgenerated wakes composed of two vortex pairs. For these muliple-vortex con"gurations, Crouch identi"es a variety of mutually induced instabilities between the various vortices. The distortions in the axes of the vortices include both symmetric and antisymmetric modes which are of shorter wavelength than those that occur on a single vortex pair. It is found that the growth rates of the instabilities are greater for two pairs than for a single pair. Since the spanwise distance between vortices is much less in the cases analyzed by Crouch than usually found for a single vortex pair, the wavelengths of the instabilities are much shorter, and the time required for the dynamics of the wave instability to proceed through linking and dispersion is much shorter than in the single pair case. The vortex shapes presented in Fig. 11 of Crouch's paper are very similar to the #ight photographs shown in Fig. 60 of the wake shed by the (303, 03) con"guration of the B-747 which sheds three vortex pairs. When the vortex dynamics does proceed to completion, the alleviated wake was described by the pilots of penetrating aircraft as one that induced a bumpy ride, but also one that appeared to have little or no coherent rotary motion [59]. These #ight experiments support Crouch's predictions of very high growth rates, and demonstrate that the mutually induced instability in multiple vortex wakes is able to bring about a nearly complete loss of coherence in the wake within a short time behind the wake-generating aircraft. Crouch's analysis was not, however, able to predict the sensitivity of the instability to deployment of any of the landing gear nor to yaw of the aircraft, which were found in #ight to reduce the e!ectiveness of the instability by a considerable amount (e.g., Fig. 60). In a series of numerical simulations of two vortex pairs, Rennich and Lele [69] obtained wake dynamics which appears to be in agreement with Crouch's results. Both analyses point out the possibilities for large-scale mixing that are generated by sawtooth-type loadings [151]. These results coupled with the #ight test results obtained with the (303, 03) con"guration of the B-747 (Sections 7 and 8) indicate that under certain circumstances it is possible to design a lift-generated wake that disperses rapidly enough that wake-vortex spacings at airports can be reduced [58,59,181]. Further support for the concept, and for some of the limitations of the concept, are provided by the experimental results obtained in the 40;80 ft Wind Tunnel and in a water tow tank with a wing equipped with seven pairs of #aps [10,91]. The
640
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
#aps enabled the wing to shed eight vortex pairs that interacted quickly to produce chaos in the wake. However, the mixing mechanism became subdued as the lift on the wing was increased enough to make the #ap vortices subordinate to the pair shed by the wingtips. The advantages gained when large input disturbance waves are imposed on a vortex wake is illustrated by an example described in Section 8. Some of that information is repeated here to again indicate the uniqueness and di$culty with the concept. As pointed out previously, the event occurred near the end of the #ight test program at Dryden. As a last-minute check on the resilience of vortices that had been alleviated by means of turbulence injection by use of spoilers, several #ights were made where the wake-generating aircraft executed a series of roll-oscillation maneuvers. The roll oscillations were used to simulate the curving structure of vortices that might occur as the aircraft rolls and turns when a wave o! is given during landing. To everyone's surprise, the alleviation achieved with spoilers deployed during roll oscillations was far greater than that achieved with the spoilers deployed during straight and level #ight. It was found that the larger input disturbance waves were able to initiate a mutually induced instability in the two vortices shed by the inboard #ap, so that the wake structure became incoherent, according to numerical simulation of the #ight experiments with vortex "laments. In the numerical results, the wake was simulated with vortex "laments based on the assumption that deployment of the spoilers modi"ed the span loading, so that it could be approximated by the (303/03) con"guration. The vortex strengths were therefore based on computed span loadings, and showed that the large initial "nite displacements of the "laments by the roll oscillations activates a mutually induced instability that leads to rapid decomposition of the entire vortex wake [181]. The wake alleviation achieved with the B-747 by use of spoiler deployment and roll oscillations was not achievable with any other con"guration of the B-747 or the L-1011 [59]. The example just described is interesting from a research point of view. It is not, however, applicable to subsonic transport aircraft, because the required rapid rolling maneuvers causes passenger comfort and safety to be compromised, and because the dynamic loads imposed on the generating aircraft produce unacceptable structural fatigue. 15.4. Vortex injection by use of wing xns The wing-"n concept for wake alleviation has already been treated in Section 9, and so is only mentioned here because the mechanism that brings about the reduction in swirl velocity is not yet known. It is believed that it is some form of mutually induced instability, but how the instability proceeds to achieve large reductions in wake
intensity that are roughly proportional to the "n angle of attack is unknown.
16. Turbulence injection 16.1. Introduction The introduction or addition of turbulence into a liftgenerated wake in order to more rapidly di!use the intense swirling velocities, or to initiate an instability, was tried with much e!ort during the early part of the wake-alleviation program in the 1970s. The topic was left until near the end of the paper not only because the technique was not very successful, but also because the information in previous sections was needed to put the investigations into perspective. For example, when the wake-vortex program of the 1970s began, several well-known aerodynamicists believed and expressed their strong opinions that nothing signi"cant could be done to make a lift-generated wake non-hazardous. Their reasoning was that the wing had to produce lift to enable the aircraft to #y, and the production of lift by a wing of "nite span requires that appreciable downward momentum is imparted to the air. Since the downward moving air has side edges, vortices result. As described in a previous section, part of the statement is wrong, because the hazard posed by wakes of conventional wings has been signi"cantly reduced by more than just one method. The problem with the alleviation successes found so far is that the e$ciency of the wake-generating aircraft is degraded by an unacceptable amount, or the alleviation was unreliable. In order to illustrate the types of concepts that were tried, an overview of several experimental programs will be described. Work began on turbulence injection devices soon after the initial series of #ight tests being used to determine spacing distances between aircraft at airports were being completed by the FAA and NASA. The #ight data indicated that, without some sort of modi"cation to vortex wakes, the decay rate is too slow in the airport environment for e$cient use of runways. Research e!orts were then started to "nd ways to bring about a more rapid decomposition of the vortices, so that aircraft could be safely spaced more closely for landing and takeo!. Since #ow visualization of vortices behind aircraft indicated that the vortices had what appeared to be a laminar structure throughout much of its swirling motion, it seemed logical to introduce turbulence into the swirling regions to increase substantially the turbulence in the #ow "eld. It was reasoned that the increased turbulence would break down the laminar #ow making it turbulent, and thereby increase the rate of decay and dispersion of the vortices. Such a concept was supported by the observation that laboratory vortices were di$cult to generate, and to maintain if the ambient air was not
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
nearly quiescent, i.e., even small amounts of turbulence would disrupt the vortex structure. At the time when this research began (i.e., about 1970), the idea was primarily directed at the utilization of turbulence to more rapidly di!use the highly energetic parts of the vortices near their centers. An e!ort to trigger speci"c instabilities was not intended, but any instabilities that would have been initiated by the injected turbulence would have been gladly accepted. Research with turbulence injection devices covers a broad range of devices including spoilers, splines, wingtip jets and fans, and engine thrust. Results from investigations on these devices are presented in various papers included in conference proceedings [25,27}30,224]. Studies have also been conducted on the e!ect of various turbulent environments on vortex wakes [72,78,154,213,214]. In general, it was found that many of the devices tried were e!ective in reducing the rotary velocities in wake vortices, so that the maximum velocity in the plateau region of decay is reduced. Unfortunately, as exhibited by the curves in Fig. 2, a reduction in the initial value of the circumferential velocity generally leads to an increase in the downstream extent of the plateau region, so that the net decay of the vortex far downstream is not greatly in#uenced. A further disadvantage of turbu-
641
lence injection is that a reduction in the rotary velocities near the axis of the vortex does not greatly reduce the rolling moment imposed on following aircraft whose wing spans are substantially larger than the diameter of the vortex core; which includes most aircraft. Three devices tried in the NASA wake-vortex program of the 1970s are now discussed. Alleviation achieved with engine thrust has already been discussed in Sections 1 and 2. 16.2. Wingtip spoiler One of the "rst, if not the "rst, device tried was a spoiler mounted on the wingtip of a Convair 990 operated by NASA. A wind tunnel study by Corsiglia et al. [94] indicated that a relatively small wing tip spoiler was capable of reducing the maximum rotational velocity in the shed vortex by a factor of about three. When a full-scale version of the device was tested in #ight on one wingtip of a Convair 990 (Fig. 153), the pilot of the Lear Jet aircraft used to penetrate the wake could not distinguish the di!erence between the vortices shed by the treated and the untreated wingtips [94]. Instruments onboard the Lear Jet penetrating aircraft did show however, that the roll acceleration imposed on the probe aircraft by the vortex was lowered from 4.4 to 2.4 rad/s
Fig. 153. Convair 990 aircraft operated by NASA Ames Research Center with vortex dissipater mounted on left wingtip to disperse vortex wake; Corsiglia et al. [94].
642
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
as it moved from the untreated to the treated trailing vortex. Some of the di!erences between the two observations behind the two wingtips may have been due to a di!erence in the path of penetration by the probe aircraft. Since roughly the same result occurred on several penetrations, it is more likely that the results of the roll acceleration instrumentation do represent the alleviation achieved. It is believed that the correct explanation lies in the fact that both the alleviated and the nonalleviated vortex roll accelerations experienced by the pilot far exceeded the aileron-induced roll capability of the Lear Jet (1.15 rad/s). Under those circumstances, the pilot perceived that he was experiencing overpowering rolling moments from both the treated and untreated vortices, and the di!erence indicated by the instrumentation was not apparent to him. The foregoing experiment again points out the fact that e!ective alleviation must bring the wake-vortex induced rolling moments down to the point where the vortex-induced rolling moment is less than about onehalf of the roll authority on board the aircraft. Anything less will still be perceived as hazardous. The small change in rolling moment indicated by the #ight tests, even though the maximum swirl velocity in the vortex may have been reduced by a factor of three (as in the windtunnel experiment) is to be expected. The di!erence in results arises, because a reduction in swirl velocity only in the core region of the vortex does not achieve much change in the overall rolling moment induced on aircraft when the wing span is much larger than the vortex core diameter. 16.3. Wingtip spline In a second example of turbulence injection, the size of the device used to inject turbulence into the wake was increased in size relative to the aircraft in order to achieve an acceptable level of alleviation [67]. The con"guration consisted of a spline or umbrella-type apparatus that trailed just behind the wingtip of a four-engine propeller-driven transport (Figs. 154 and 155). When the modi"ed and unmodi"ed aircraft were tested in #ight, the wake-induced rolling moment on a small propellerdriven aircraft was found to be reduced by about 72%. As expected, #ight in the modi"ed vortex wake by the probe aircraft was found to be a controllable situation at separation distances of less than 2 n mile. The disadvantage of the spline device was that it increased the landing drag of the C-54 by about a factor of two. It is informative to examine the wake history of the con"guration, because as illustrated in Fig. 155, the reduction occurs almost immediately behind the C-54. As is typical of a plateau region, little or no decay occurs during the next 8 km. At that point, natural decay appears to have reduced the vortex intensity behind the unmodi"ed aircraft to the point where the two wakes have roughly equiva-
Fig. 154. Unmodi"ed C-54 wake-generating aircraft and wingtip spline assembly used to test vortex attenuation concept; Patterson et al. [67].
lent rolling-moment hazards. This result appears to again support the contention that turbulence injection a!ects the plateau region of vortex decay but not the far-"eld decay. Later in the wake-alleviation program, Patterson [68] proposed that a large propeller be placed behind the wingtip in place of the spline to remove energy from the vortex. Such a device could then extract rotational energy from the airstream with either a low drag penalty or by providing thrust. In a similar study, Snyder [71]
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
643
devices are of a size that is probably less than one-tenth of the span of the generating aircraft, which is too small to demolish the structure of the vortex wake. Furthermore, injection of turbulence increases the drag of the aircraft and may create unwanted dynamic loads on the aircraft structure which may cause premature fatigue failures. 16.5. Atmospheric turbulence
Fig. 155. Measured vortex-induced rolling moments induced on single engine probe aircraft to test vortex attenuation concept with splines in wind tunnel and in #ight; Patterson et al. [67].
studied the e!ect that a wingtip propeller and its direction of rotation would have on the vortex location and on the span loading. Since e$cient wing designs for jet transport aircraft shed a large part of their vorticity inboard of the wingtip, devices that work in the wingtip region fell out of favor.
The atmosphere is the best turbulence injection apparatus currently available. Not only does it provide large-scale turbulence in the lower atmosphere that has a scale and energy level capable of rapidly dispersing vortex wakes, but it is available at no cost [8,48,74,80,83,86,110,112,122]. Unfortunately, dispersion of vortex wakes as provided by the atmosphere is intermittent and does not always occur when needed. Since wake dispersion by the atmosphere is very e!ective, studies have been undertaken on how to best implement reduced aircraft separation distances during windy periods, and to use conventional spacings during calm periods.
17. Wake-vortex avoidance schemes 17.1. Introduction
16.4. Flight spoilers already on aircraft Both wind-tunnel and #ight tests were used to "nd out if spoilers already on board most large transport aircraft might serve as turbulence generators capable of reducing the hazard in vortex wakes to an acceptable level [62,63]. If any of the concepts was acceptable, the cost of implementation should be quite reasonable. The e!ect of the thrust of jet engines as turbulence injecting devices was also studied [66]. However, the alleviation achieved with spoilers, engine thrust, and other turbulence injection devices was found to consist primarily of a reduction in the rotary velocities near the core of the vortices, and did not seem to accelerate the decay of vortices in the far "eld enough to provide the needed alleviation. A number of other devices that rely on turbulence injection were also tested experimentally [25,220]. It was concluded, therefore, that in only one of the many con"gurations tested was enough alleviation produced to satisfy the requirement for 2 or 3 n mile spacings, but the spline device had unacceptably high penalties [67]. As far as future prospects are concerned, further improvements in wake-vortex alleviation by use of turbulence injection are not likely. The experiments carried out so far indicate that the concept is unacceptable, because the size of the mixing eddies needed to signi"cantly reduce the hazard posed by wake vortices at a 2}3 n mile goal needs to be on the order of the wing span. In contrast, eddies produced by on-board turbulence
Since lift-generated wakes of aircraft persist long enough to pose a hazard to following aircraft during approach and takeo!, the most obvious solution is to avoid the wake vortices of previous aircraft. If avoidance is to be accomplished on a consistent basis, and since vortices are not usually visible, a reliable method must be developed to be sure that the #ight corridors are free of hazardous vortices when an aircraft enters the airspace. The "rst e!ort at the development of an avoidance scheme began in the late 1960s with the #ight program by the FAA. On the basis of the information obtained by Garodz et al. [12}21] from the #ight program, and information from NASA and other sources, the separation guidelines were determined as listed in Table 1. Shortly thereafter, it was found that the separation guidelines were e!ective, because they allowed enough time for the vortices from one aircraft to move out of and away from the #ight corridor to be used by following aircraft. The foregoing decisions bene"ted from the fact that they were made at a time when the exhaust from jet engines of most transport aircraft contained noticeable amounts of soot particles. The soot particles served as #uid #ow markers that, quite often, made it possible for pilots of following aircraft to clearly see the core regions of vortices shed by preceding aircraft, and thereby avoid them. In the early 1970s, it was mandated that the turbulence in the burner cans be increased, so that the soot
644
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
output from the engines became negligible. As a consequence, lift-generated vortices are now seldom visible behind jet aircraft in the vicinity of airports. E!orts to "nd a way to visualize or detect in some way the presence and location of vortices have not yet produced a successful operational system [24,28,199]. A good review of work by the FAA on the development of vortex sensors for detection and measurement of vortices is presented by Abramson and Burnham [110] and Burnham [111,112]. A good overview of a number of detection systems under study at the time by a variety of other groups is available in the 1991 FAA Conference edited by Hallock [28]. At a 1997 wake-vortex meeting [225] held at Ottawa, Canada, presentations described a number of wakevortex avoidance systems now under development by France, Germany, Russia, United Kingdom, and the United States. Also described at the meeting were programs for the development of record-keeping systems for wake-vortex encounters. The purpose of the recordkeeping systems is to assemble data so that the weather conditions and circumstances under which vortex encounters occur can be identi"ed, and corrective measures taken. An overview is presented in this section on wakevortex avoidance systems. More information is provided in the 1997 conference proceedings [225] where abstracts, slides, and some discussions on the presentations are included. Since the various avoidance systems have some common components, but di!er in the details, and because the study of avoidance schemes is a side-issue for this paper, an overview will be presented of only two study programs, namely, the Vortex Advisory System (VAS), which was developed and tried in the late 1970s, and the Aircraft Vortex Spacing System (AVOSS), because it is a very broad based theoretical and experimental program. The Aircraft Vortex Spacing System (AVOSS) is now being designed and developed by NASA Langley Research Center for and in cooperation with the FAA. The reason for choosing this system for discussion is that it has been underway for probably the longest time, is the most comprehensive, and is developing the largest database of any of the programs [2,24,50,121, 123,124,211,226]. A discussion is then presented on various features of avoidance systems that appear to either simplify the task, or make it more di$cult. 17.2. Vortex Advisory System (VAS) In an e!ort to safely reduce all of the separation distances listed in Table 1 to a uniform 2 or 3 n mile during approach and depart of aircraft at airports, a vortex advisory system was developed in the 1970s by use of measurements made on vortices shed by aircraft as they arrive and depart at airports [30,227]. The measurements used in the determination included measurements
Fig. 156. Wind ellipse on which Vortex Advisory System (VAS) was based. Shaded region is safety region to allow for a transition from adequate wind to one of inadequate wind and vice versa; Wood [30].
with: an array of anemometers of over 50,000 landings (100,000 vortices) and 5000 tako!s; a monostatic acoustic vortex system of 15,000 landings and 2000 takeo!s; and a laser-doppler velocimeter of over 5000 landings. The measurements were made at Chicago O'Hare, New York JFK, London Heathrow and Denver airports. The data showed that after about one minute only 16% of the vortices were still in the vicinity of the #ight corridor. Further analysis showed that after 80 s (i.e., 3 n mile at a landing speed of 135 knots) the residual vortices all fell inside of the wind ellipse reproduced in Fig. 156 [30]. That is, after 80 s, the vortices were either blown out and away from the #ight corridor, or they were dissipated by ground turbulence when the local wind vector was outside of the ellipse shown in Fig. 156. The data made it possible to draw elliptic contours of wind velocity and direction outside of which an approach or departure #ight corridor becomes free of any detectable vortex. A second ellipse, with a shaded region between the two, was used to allow for a transition region between a hazardous and a non-hazardous situation. Designated the `Vortex Advisory Systema (VAS), the system was tried at O'Hare Airport near Chicago. The decision to test VAS at O'Hare was based on the fact that
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
the airport was near capacity, had a mixture of tra$c that included a large percentage of aircraft in the heavy category, and the area was often windy. Unfortunately, at the stage of development of the interfaces between VAS and the #ight control system already in place at O'Hare, the decision-making processes had not been developed thoroughly enough to be incorporated smoothly into the #ight-control procedures. As a consequence, airport capacity was decreased rather than increased. In retrospect, the implementation of the VAS concept should "rst have been applied at a relatively non-busy airport where it could have been re"ned into a complete smoothly-working system. Once re"ned, implementation at an extremely busy airport, like Chicago O'Hare, would have a much better chance for success. Since the concept failed on its "rst application, the VAS concept has been dismissed as unworkable, which was probably a big mistake for a number of reasons. First, it could have served as a pilot program for the various systems now under study, and could have provided information as to which should be rejected and which should be considered for implementation. Secondly, since the VAS concept is sound, further testing and development at a sequence of airports would no doubt have provided increased capacity at most airports until an improved replacement would become available. It might still be advisable to carry out practice implementation of a simple system like VAS to gain experience with vortex avoidance systems, because the more complex systems now being considered will no doubt have even more unexpected problems than encountered by VAS. 17.3. Aircraft Vortex Spacing System (AVOSS) After the VAS concept was dropped in the late 1970s, e!orts to make measurements on wake vortices at airports, and to "nd satisfactory alleviation methods for lift-generated wakes were signi"cantly scaled back by NASA and the FAA. In the early 1990s, a number of programs to develop wake-vortex avoidance systems were again started. Most concepts include the e!ects of the atmosphere on vortex persistence and location, and have as their goal a precision which permits a safe separation distance between aircraft under all weather conditions of about 3 n mile. As mentioned previously, probably the most ambitious of all of the programs is the Aircraft Vortex Spacing System concept being developed by NASA Langley Research Center. The research underway has the goal of enabling safe improvements in the capacity of the nation's air transportation system by bringing about a reduction in the in-trail spacing of airplanes. At the time that the program began, and to a large extent at the present time, the scienti"c basis does not exist to quantify the wake transport and decay properties of lift-generated vortices, nor the aircraft}vortex interaction dynamics, with su$cient accuracy to put into
645
use weather-dependent aircraft separations, that are signi"cantly di!erent from current standards. The major goal of the research at Langley is to provide the technology base and systems to permit the same airport capacity levels during instrument operations that are presently experienced during visual airport operations. In support of that goal, Hinton [2,123,124] presents a description of the components that make up the AVOSS. When completed, AVOSS will provide a system concept that uses available knowledge of aircraft wake generation, atmospheric modi"cation of those wakes, wakeencounter dynamics, and operational factors to provide dynamic wake-vortex spacing criteria for use at airports by Air Tra$c Control. In 1997, a decision was made to reduce the emphasis on wake-encounter dynamics and concentrate more on vortex avoidance. Several guidelines were placed on the characteristics of AVOSS. As described by Hinton [124] they are: (1) The "nal system must be such that it can be approved for operational use, including a large degree of robustness, reliability and cost realism. (2) The safety provided must be equal to or greater than the current system. (3) AVOSS will not require an increment in pilot skill level or training. (4) No aircraft structural or system modi"cation will be required. (5) AVOSS will not alter current pilot functions nor change airborne/ground responsibilities. (6) It is permissible to require special air tra$c control (ATC) or #ight procedures that are compatible with current skill levels. Within these constraints, the new system must increase airport capacity as much as possible. The AVOSS System Concept is illustrated schematically in Fig. 157 and the Predictor Subsystem in Fig. 158 to indicate the complexity of the problem. One of the most apparent uncertainties is the weather state at the airport when an aircraft arrives. Since aircraft spacing at the arrival airport must be known before the aircraft departs its originating airport, an ability to predict the weather state in advance by hours is required. Even the measurement of the weather and atmospheric state along the #ight corridor as a function of time is di$cult, whereas comparable accuracy for the same data several hours in advance seems impossible. As a consequence, an intense theoretical and experimental program of prediction and measurement of the atmosphere and of the dynamics of lift-generated vortices embedded in them has been underway for about "ve years. Measurements have been made at various airports in the vicinity of the #ight corridor for approach and departure and e!orts have been made to predict the motion and structure of the vortices [24,72,86,97,121,198,208,211,225,226]. The analyses and measurements will hopefully yield reliable solutions for the time-dependent weather at a given airport and for the weather several hours in advance. In addition, it must be possible to place error bounds on the various parameters that govern vortex transport and decay. The
646
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 157. AVOSS System Concept; Hinton [124].
Fig. 158. AVOSS Predictor Subsystem; Hinton [124].
di$culty of the task is awesome, and it seems that it may be necessary to bring other factors into the planned system to simplify the problem to one that can be solved satisfactorily in the near future.
18. Simpli5cation of vortex-avoidance systems 18.1. Overview A number of speci"cations are usually placed on vortex wake advisory or avoidance systems in order to insure that it "ts smoothly into the rest of the air transport system when it is implemented. It should be kept in mind that even a small change in some of the speci"cations can sometimes signi"cantly reduce the complexities of a wake-vortex avoidance system, and also improve safety. If, for example, the guidelines placed on the development of an avoidance system make it necessary to accommodate the entire conically shaped ILS region like the one illustrated in Fig. 159, unnecessary e!ort is required, as will be illustrated. The cross-section of the
Fig. 159. Illustration of conically-shaped #ight corridor used for Instrument Landing System (ILS) for approach.
approach corridor is small at runway threshhold, but becomes quite large at approach distances beyond the middle marker (5 n mi). For example, at 5 n mi the crosssection of the ILS conical corridor has a diameter of over 1500 ft. Since aircraft are permitted to locate themselves anywhere in the approach corridor, the wake-vortex
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
avoidance system must have the capability to guarantee to pilots of following aircraft that they will not encounter a wake vortex with enough strength to signi"cantly disrupt their approach path and touchdown throughout the entire conical region. Such a requirement is very di$cult to ful"ll and to still decrease spacing between aircraft on a regular basis. It seems logical then to design the approach and departure corridors so that the requirements on the wake vortex advisory system be eased. The text to follow describes a study of several design features of the air tra$c system that would simplify considerably the problems associated with the development of vortex avoidance systems [228]. A feature to be avoided is also described. 18.2. Flight corridor of small cross-section 18.2.1. Accuracy of global positioning system (GPS) Obviously, it is much easier for vortex wakes to move a small distance to vacate a #ight corridor than to move a large distance. This fact suggests that aircraft on approach to or departure from airports should be restricted to #ight corridors that are as small as practical in crosssection [228]. The size of the #ight corridor depends, of course, directly on the navigation systems on board subsonic transport aircraft to maintain accurate control of their #ight paths. A strong supporting reason for making a transition to #ight corridors of small crosssection is that the technology needed for implementation is currently available from the Global Positioning System (GPS) that operates by use of satellites orbiting earth. Although not its original purpose, GPS technology is ideally suited for the location and guidance of transport aircraft, and is in current use on many aircraft. Furthermore, research is underway to upgrade the accuracy of GPS so that aircraft will be able to execute zero visibility landings safely under all weather conditions. Consideration has therefore been given to the possible simpli"cations that can be derived by making the approach #ight corridors at airports as small as guidance technology for aircraft will permit [228]. The present aircraft guidance system used at airports is the Instrument Landing System (ILS). The ILS currently provides approach corridors which have a conical shape wherein the point of the cone is at runway threshhold, and the open end is at the beginning of the approach path for aircraft (Fig. 159). At touchdown the #ight corridor is quite small, but at the middle marker and beyond, the 33 conical #ight corridor becomes 1500 ft and larger in diameter. Since the #ight corridor has a large cross-section, it takes vortex wakes a long time to move out of it. If, however, the corridor were reduced in a size just within the capability of present aircraft guidance systems, like GPS, the wake vortices would have only a short distance to move before they were out of the #ight corridor.
647
Optimally, the cross-section of the #ight corridor should also be constant in size, rather than conical. The GPS currently in service is based on a satellite system that transmits location information at two frequencies. The "rst frequency is currently being used by non-military users, and the second is selectively available. It has recently been announced that the United States has the intention to remove selective availability on the second frequency by 2005 and to add a third frequency to the system (Aviation Week and Space Technology, April 6, 1998, p. 60). It is estimated that the availability of three frequencies should improve the precision of location, so that maximum errors decrease from 100 to 3}10 m. Prior to this decision, the FAA planned to use "xed reference stations along with the current satellite system to increase the accuracy of location near airports to achieve errors less than $33.5 m ($110 ft) in the horizontal direction, $9.5 m ($31 ft) in the vertical direction, and less than 1 m at the runway threshold [229]. Additional accuracy (down to several cm.) is also currently achievable by use of pseudo-satellites, or pseudolites, to essentially calibrate the GPS receivers near airports so that accuracies are based on fractions of a wavelength rather than on several wavelengths [230}232]. When these accuracies of location are coupled with some of the more accurate autopilot systems, it appears that it is possible to hold an aircraft on an approach path accurately enough to permit zero visibility landings. Since accurate location and guidance of aircraft will be available in several years for another purpose (zero visibility landings), it seems obvious to inquire how such a capability can be used to simplify the avoidance of lift-generated vortices at airports. A study conducted by Rossow [228] concludes that GPS should be utilized to design approach corridors that are long, slender and constant in cross-section, rather than conical. The small cross-sections of the #ight corridors should extend out from the runway threshold at the conventional approach angle used by aircraft (3.53 to the horizontal at the present time) as far as needed to bring aircraft safely into and along approximately the same #ight path. Since safety is assured once inside the #ight corridor, the distance from runway threshold at which the controlled corridor should end will probably be governed by the requirement that the altitude at that point must be high enough for aircraft to safely recover from a vortex encounter if one should occur. Some additional rationale behind the design of #ight corridors is described in subsections to follow. 18.2.2. Vortex transit times If GPS #ight corridors of small size are adopted for wake-vortex avoidance at the same time that they are adopted for zero visibility landings, the volume of atmosphere throughout which a vortex advisory system must keep track of lift-generated vortices is considerably
648
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 160. Contours of constant rolling-moment coe$cient for vortex wake to indicate boundary of hazardous region [228]; b "200 ft (61 m), C "1.5, b /b "0.29. J
reduced. The example used in illustrative computations by Rossow [228] was assumed to be 80 ft wide and 80 ft high (i.e., 24.4;24.4 m) but could be even smaller. The bene"t received from a #ight corridor of small crosssectional size is that, for a given situation, the time required for a vortex wake to vacate the corridor by the wind or by self-induced velocities is correspondingly small. An estimate of the self-induced downward velocity of a vortex pair shed by aircraft indicates a spread from several ft/s for small transports to about 10 ft/s for larger transports. However, the transit time involves not only the motion of the vortex centers, but also the hazardous region around the vortex pair, because the hazard associated with the vortex wakes is the item that must move out and away from the #ight corridor. The cross-sectional size of the hazardous region of a vortex pair was estimated by calculating the wakeinduced rolling moment on a following wing in the vicinity of a vortex wake over a range of locations. Points that have the same rolling moment are then connected to produce lines of constant rolling-moment coe$cient for the wake as shown in Fig. 160. The wake is assumed to be symmetrical above and below the vortex centers (located at y/b "0.4, z/b "0.0), and anti-symmetrical port and starboard. The center of the wake, and not the center of the wake-generating aircraft, is located at the origin. The contours presented in Fig. 160 are taken as representative of the wake structure from about seven spanlengths, or 1/4 mile, to about 80 spanlengths, or 3 mile behind the wake-generating aircraft. The computations are presented for C "1.5, and a ratio of the span of the following * wing to that of the generating wing of b /b "0.29, e.g., a wake-generating aircraft with a wing span of about
200 ft (61 m) and a following aircraft with a wing span of about 60 ft (18.3 m). The example presented is typical of a small aircraft behind a heavy aircraft and is not directly applicable to any two particular aircraft. Contours for aircraft more nearly equal in size to the heavy leading aircraft are similar to the example in Fig. 160 but have smaller induced rolling moments near the vortex centers [104]. By use of the information in Fig. 160, it is possible to de"ne a boundary outside of which the lift-generated wake does not pose a rolling-moment hazard. Identi"cation of the hazardous boundary begins with the observation that the maximum aileron-induced rolling moment is typically "C "+0.06 for subsonic transports [104]. JB The inner cross-hatched regions around the vortex centers and inside the "C ""0.06 contours then denote J those regions where the wake-induced rolling moments exceed the maximum aileron-induced rolling-moment of the encountering aircraft. Outside of these regions, the wake-induced rolling moment on the following aircraft is always less than 0.03, i.e., "C "40.03. Under those cirJ cumstances, it is estimated that the encountering aircraft has enough roll control power for the ailerons to cope with and recover from any vortex-induced roll excursion [104]. In order to be conservative, the hazardous region is taken as extending one span in the vertical and two in the horizontal direction in order to be well outside of the "C ""0.01 contours where an encounter would be barely J perceptible. Next, assume that the #ight corridor is small relative to the size of an aircraft of 200 ft span (61 m), and is centered on the corridor (Fig. 161). The hazardous region is then much larger than the #ight corridor, so that the
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
649
Fig. 161. Superposition of hazardous region of large transport aircraft and 80;80 ft (24.4;24.4 m) #ight corridor with centerlines aligned [228].
hazardous contours extend out well beyond the sides of the corridor, even when the wake-generating aircraft is centered on the corridor. If an approach or departure is to be safe from a vortex encounter, enough time must be allowed for the wake to move the maximum distances possible, either vertically or sideways to separate the two regions. The worst situation for lateral or vertical transfer is for the aircraft to be at the opposite side of the #ight corridor from the direction of travel of the wake. In equation form, the maximum horizontal and vertical travel distances are then given by [228] *y "B #B /2,
(73a)
*z "D #D /2,
(73b)
where B and D are the breadth and depth dimensions of the #ight corridor, i.e., for most subsonic transports, B "2b and D "b . Eqs. (73) point out the import ance of the size of the #ight corridors, because they can be changed but the size of the hazardous region cannot. Obviously, the minimum amount of time for the #ight corridor to become safe occurs when the #ight corridor is of zero size, that is, when the #ight of all aircraft are constrained to #y along a given line so that B "D +0. Any increase in the size of the #ight corridor to allow for deviations from a small corridor adds linearly onto the time for the hazardous region of the vortices to move out of the #ight corridor. In equation form, the time required for the hazardous region to vacate the #ight corridor is given by [228] *t "[B #B /2]/v , W
(74a)
*t "[D #D /2]/w , X
(74b)
where v is the velocity component of the wind across the #ight corridor, and w is the self-induced downward velocity of the vortex pair. For convenience, and to be conservative, the span of the largest aircraft in the current #eet (b +200 ft) is used for the reference hazardous re gion. If the #ight corridor is taken as 80 ft;80 ft, and the wind is not blowing, the hazardous region needs to move downward by (80 ft#100 ft) to vacate the #ight corridor. If the descent velocity of the vortex pair is taken as w "5 ft/s, 36 s are required for the wake to vacate the #ight corridor. A 1 min (or 3 n mile) spacing would then provide safe separation distances for aircraft [228]. When smaller wake-generating aircraft are considered, the self-induced velocity of the vortex pair is sometimes smaller. Some or all of their reduced downward speed is o!set by the smaller distance, B /2 or D /2, that the vortices have to travel in order to clear the #ight corridor and become avoidable. It is noted that the centerline (i.e., not necessarily the entire aircraft) of the following aircraft is constrained to the #ight corridor. Certain parts of the aircraft will usually protrude outside of the #ight corridor. It is not necessary, however, to allow extra time or space for the two regions to become separated, because the rollingmoment computations are based on the relative locations of the centerline of the wake, and the centerline of the following aircraft. Thus, the computations already take into account the entire velocity "eld of the vortex wake and the entire wing of the following aircraft. 18.3. Straight or curved yight corridors Consideration is given here to the preferred shape for the #ight corridor (i.e., straight versus curved). The desire
650
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
Fig. 162. Plan view of curved approach path in horizontal plane [228]. (a) Positive curvature. (b) Negative curvature.
for simplicity in any avoidance procedure almost dictates that straight-line #ight corridors be used, because any curvature of the #ight corridor complicates the programming for approach and departure operations. It seems prudent however, to at least consider curved corridors in case a particular shape has a decided advantage over the straight-line #ight path. The question to be answered then is whether curved #ight corridors lead to conditions that signi"cantly decrease the likelihood of a vortex encounter, and thereby merit the extra e!ort needed to execute them. Curved paths in the discussions to follow can mean a path with continuous curvature, or a path that has two or more straight-line segments that approximate a curve. When the curvature is only in the horizontal plane as the aircraft descends for landing or ascends after takeo!, the vortex hazardous region descends in still air as it would if the #ight path were straight. However, if a wind is blowing parallel to any part of the curved trajectory (Fig. 162), the downward motion of the vortex wake is in#uenced by a head- or tail-wind e!ect. The apparent descent of the vortex wake may then be enhanced or reduced depending on the wind direction and magnitude, and whether the aircraft is landing or taking o!. It is therefore concluded that a curved, or segmented turn in the horizontal plane while on approach or departure is more complex to monitor and has a higher risk for wake encounters than a straight-line #ight corridor. Finally, no
di!erence appears to exist between curvature due to a turn to the port or to the starboard. Consider next both positive and negative #ight path curvatures in the vertical plane (Fig. 163). Note that the angles of the #ight paths relative to the ground are much larger than actual ones to better illustrate possible hazardous situations. If all aircraft follow the same #ight corridor, and the vortex wakes descend in still air according to their self-induced velocity, the risk of an encounter with the hazardous-wake region is not increased for either type of #ight path. However, if a head- or tail-wind is blowing, the steeper parts of the #ight paths are more susceptible for the wake moving into the path of a following aircraft. It is therefore important to maintain a minimum slope along #ight corridors, which is provided by a straight-line #ight path from a given altitude to touchdown. Hence, once again a straight-line #ight path is less susceptible to wind-caused unacceptable motion on the part of the vortex wake than any curved path. Furthermore, if aircraft are allowed to follow either a straightline or one of the curved #ight paths shown in Fig. 163, the mixed trajectories cause the aircraft carrying out a straight-line #ight to cross the vortex wake of the preceding aircraft. In a study of a proposed two-segment approach, it was found that the mixture of straight-line and two-segment approaches were particularly hazardous; Kurkowski, Barber and Garodz [119]. Without going into other possibilities, it is apparent that #ightpath curvature in the vertical plane can also be more hazardous than a straight one, is more complex to operate, and certainly does not present an advantage over #ight corridors that are straight. 18.4. Relocation of yight corridors Consider here the case wherein the #ight paths of the wake-generating and following aircraft can each be controlled separately and precisely. A reduction in wakevortex spacing distances would then seem possible, because the system would be able to guide the following aircraft along an adjustable path where the vortices shed by the preceding aircraft will not be encountered, no
Fig. 163. Side view of curved approach path in vertical plane [228].
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
651
Fig. 164. Side view of relocation of #ight corridors along runway to illustrate large amount of space required [228].
matter how closely they follow one another [228]. For example, the #ight path of one aircraft would be laid out, so that it would land at or near the beginning of the runway. Since the vortex wake of the leading aircraft will descend when there is no wind, the next or following aircraft would be directed along a #ight path that is directly above the one used previously (Fig. 164). Such a procedure is one that has been used in the past during conditions when visual #ight rules can be followed. Similarly, if the wind is blowing, the following aircraft can avoid a vortex encounter by moving its #ight path to port or starboard, up or down, by an amount that depends on the magnitude and direction of the wind. The basic idea is to place the relative locations of succeeding #ight paths, so that the wind and the self-induced velocities do not allow vortices to move into the #ight path of following aircraft. The amount of relocation of each #ight corridor depends on the size of the crosssection of the #ight corridor and of the wake-vortex hazardous region, and magnitude in the wind and its uncertainties. In that way, each succeeding aircraft has its own #ight corridor located so as to avoid all other corridors and vortex wakes of other aircraft. Furthermore, the corridors should all be straight and parallel so that #ight paths do not cross the wakes of preceding aircraft. In principal, the foregoing process is the way that relocation of #ight corridors should work. However, relocation of the #ight corridors cannot be continued inde"nitely, because airports are of "nite size so that previous corridors must eventually be recycled. If a #ight corridor is to be reused, su$cient time must be allowed after relocation for the vortices to decay to a harmless level, or to move far enough away that they do not pose a hazard when a corridor is recycled. In addition, the time required for an aircraft to transit its entire approach or departure #ight path is usually longer than the time interval between aircraft. Several #ight path corridors will therefore need to be active at a given time for both landing and takeo!, which introduces more complications.
Before proceeding further, the most serious drawback is that succeeding #ight corridors must be shifted so that overlap with previous #ight corridors does not occur, and the amount to be shifted is not small. From Fig. 164, the intersection of a #ight corridor on approach with the runway surface is given by *x "D /tan h ,
(75a)
where D is the depth of the #ight corridor, which is taken as the vertical uncertainty in the location of the aircraft. If the size of the hazardous region is the determining factor, *x "D /sin h ,
(75b)
where D is the depth of the hazardous region perpen dicular to the #ight path, and not the vertical extent. The impossibility of the situation becomes apparent when, for example, the size of the intersection of an 80 ft;80 ft corridor with the runway is considered (Fig. 164). For approach angles of h "3 and 53, the footprint of the corridor intersection with the runway, is found by Eq. (75a), to be 1526 and 914 ft, respectively. If the corridor depth is based on the depth of the hazardous region for a large aircraft, its imprint along the runway is even larger. Similarly, the impracticality of the corridor relocation method is also apparent when lateral relocations are considered. In those cases, the relocation distance needs to be based on the width of the hazardous region, B , which is 2b in width, or about 400 ft (122 m) for a large aircraft. For comparison, commercial runways vary from 150 to 300 ft (46}91 m) in width and from 8000 to 12,000 ft long (2438}3658 m). The two runways at Mo!ett Field, CA, that are used by NASA Ames Research Center are both 200 ft (61 m) wide and are 8100 and 9200 ft (2469 and 2804 m) in length. Since a vortex is shed any time that an aircraft carries lift, the termination of the #ight corridor at the runway surface should include a region where the landing aircraft "rst touches down, loses it lift, and begins its rollout. Since a vortex hazard still exists in that region, the depth of the #ight
652
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
corridors should be increased to accommodate the added hazardous region. For the foregoing reasons, it is concluded that relocation of #ight-path corridors to avoid vortex wakes is impractical as a wake-vortex avoidance method. Similar conclusions are drawn when it is realized that aircraft landing while visual #ight rules are in e!ect often use a visual estimate to determine whether or not they are above the #ight path of the preceding aircraft. Since such a relative location is di$cult to judge without GPS determined #ight paths, it is easily possible that a pilot believes his aircraft to be above the #ight path of previous aircraft, when in reality it is below. 18.5. Atmospheric data monitoring All proposed wake-vortex avoidance systems require regular monitoring of atmospheric motions along the approach and departure corridors to determine the locations of vortex wakes, and the status of the atmosphere. Only with information on the magnitude and direction of the winds present in and around the #ight corridors can vortex avoidance be assured. The task is easier if the #ight corridors are small in cross-section, but data on local wind velocities are still advisable, if not required. The needed information on the atmosphere can be obtained from the aircraft in the corridors by use of equipment on board the aircraft. That is, the three components of the speed of the aircraft relative to the ground are determined by use of GPS equipment. The three components of the velocity of aircraft through the air can be measured with onboard aerodynamic instrumentation. The di!erence between the two measurements yields the wind velocity. When the two sets of measurements are transmitted to an airport ground station, the data can be processed for determination of atmospheric motions. It is therefore recommended that each aircraft in the corridor transmit the information on its location, orientation, and on its velocity relative to the air (and to the ground) to a monitoring station at the airport. The monitoring station checks the data for inconsistencies and accuracy, and then determines the velocity components of the winds along the #ight corridor. The wind data is then used to predict the locations of the vortex wakes ahead of each aircraft to be certain that a vortex encounter does not occur. If an unsafe condition is predicted, the aircraft that would be involved are noti"ed to make a go-around or to use another runway. If the computations predict that the #ight corridor is free of all vortex in#uences ahead of the aircraft, no messages are sent and aircraft are free to continue their approach and landing. All of the GPS systems mentioned previously are capable of yielding accurate values for the velocity of aircraft relative to the ground. It remains however to determine whether the aerodynamic instrumentation
currently on board subsonic transports provides the required accuracy or not. If current instrumentation is found to be insu$cient, improvements will need to be made.
19. Remarks on status of research The foregoing text indicates that one or more wakemodi"cation methods have been identi"ed that provide adequate alleviation of the hazard posed by vortex wakes. Of these, the wing-"n concept appears to o!er the most reliable and #exible approach to solutions that are acceptable to airframe manufacturers. In order to accomplish this goal, research is needed to develop design guidelines for e$cient lifting systems that shed benign wake}vortex systems. Experiences with the research conducted on the wakevortex problem indicates that progress is most rapid when theoretical tools are used to guide and interpret experimental results. Not obvious from the foregoing results is that preliminary results on ideas to be tried, and the veri"cation of theoretical models, are best carried out in ground-based facilities rather than in #ight. Groundbased facilities have the advantage that they can provide information in less time, and with less expense than #ight experiments. Also, ground-based experiments can be carried out on idealized con"gurations that are too hazardous to test in #ight. Lastly, any #ight experiments, even though not necessarily expensive, have high visibility to the scienti"c community. High visibility limits greatly the number of trials and errors, and high risk failures, that are tolerated by funding sources. Which prospects should be pursued in order to "nd a solution to the lift-generated vortex problem? Before a supposedly new prospective idea is proposed for study, it is very important to "rst become familiar with past e!orts, and to then follow the literature closely, so that wasted e!ort is avoided. In the past, the research areas have usually been divided into three categories. (1) How hazardous is the lift-generated wake shed by a given aircraft? (2) How can the wake be modi"ed to make it non-hazardous to following aircraft while still retaining the e$ciency of the generating aircraft? (3) How can vortex wakes be e!ectively and e$ciently avoided? A great deal of e!ort has gone into all three of these items. Item number one needs to be improved upon so that the hazard posed by any new aircraft design can be predicted before the design leaves the drafting board, or computer. This is not yet possible within satisfactory accuracy by use of current technology. As mentioned in the "rst paragraph of this section, more work is needed on item number (2), which relates to the development of guidelines for the design of aircraft so that they shed benign wakes. Admittedly, a satisfactory solution has not yet been found, but the research to date indicates that
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
a solution is possible. At this time, funding is being applied primarily to the development of wake-avoidance systems for airports, without much being devoted to the development of alleviation concepts. It is hoped that a more balanced program will come about in the near future. If support for research on wake-alleviation concepts becomes available again, it is suggested that the study of all concepts be enlarged to include a new variety of optimization parameters as indicated in Section 12 of this paper. In this way, designs for aircraft lifting systems will be found that simultaneously increase the e$ciency of aircraft, and make their vortex-wake benign. Most of the wake-vortex avoidance systems under study at this time do not include the use of the GlobalPositioning System to control the #ight of aircraft into and out of airports along narrow #ight corridors. It is believed that failure to include these features in the wave-vortex avoidance systems being developed is a big mistake. Indications are that such a technique must be employed to reduce the work load required to insure that vortex wakes are not in the #ight corridors being used by following aircraft. Preliminary study also indicates that a workable wake-vortex avoidance system can become available in the near future if the Global-Positioning System is used to bring about su$ciently accurate guidance of aircraft to make narrow #ight corridors practical. At this time, all of the problems associated with the use of GPS for guidance along #ight corridors of small crosssections have not been solved, but, since it is a relatively new and rapidly expanding technology, the remaining problems may be solved in the near future. In summary, the purpose of this paragraph is to point out that #ight corridors of small cross-sections are required if the design of a practical wake-vortex avoidance system is to be achieved. That is, one that safely increases the capacity of airports. Lastly, there is always room for improvement in the methods used to take data in experiments. Throughout this paper reference has been made to areas where the test techniques and procedures used in a test could be improved upon, or were inadequate. First and foremost, methods for data taking should begin to address in a more complete fashion the e!ect of turbulence in #ight, and in the wind tunnel, on the dynamics and persistence of vortex wakes. Some of the improvements will require a great deal of e!ort and innovation, and others will be easy to implement. One such technique that needs much improvement is an ability to better follow the development of vortex instabilities (like those of Crouch [223], Crow [49], and Leweke and Williamson [222]). Obviously, methods are needed to help identify and better diagnose the three-dimensional, timedependent wave motions on vortex "laments as they trail behind lift-generating wings in wind tunnels and water tow tanks. In addition, progress in the development of
653
new ideas and concepts like those suggested by various authors and described in this overview will be expedited greatly if ground-based facilities are readily available for use in the needed experimental parts of the investigations.
References [1] McGowan WA. Calculated normal load factors on light airplanes traversing the trailing vortices of heavy transport airplanes. NASA TN D-829, May 1961. [2] Hinton DA. Aircraft vortex spacing system (AVOSS) concept and development. In: Credeur L, Perry RB, editors. Proceedings of the NASA First Wake Vortex Dynamic Spacing Workshop, Langley Research Center, Hampton, VA, NASA/CP-97-206235, May 13}15, 1997, p. 11}22. [3] Bleviss ZO. Theoretical analysis of light plane landing and take-o! accidents due to encountering the wakes of large airplanes. Report SM-18647, Douglas Aircraft Co., Inc., Santa Monica, CA, 1954. [4] Kraft Jr CC. Flight measurements of the velocity distribution and persistence of the trailing vortices of an airplane. NACA TN 3377, March 1955. [5] Rose R, Dee FW. Aircraft vortex wakes and their e!ects on aircraft. Tech. Note No. Aero. 2934, British Royal Aircraft Establishment, December 1963. [6] Robinson GH, Larson RR. A #ight evaluation of methods for predicting vortex wake e!ects on trailing aircraft. NASA TN D-6904, November 1972. [7] Wetmore JW, Reeder JP. Aircraft vortex wakes in relation to terminal operations. NASA TN D-1777, April 1963. [8] Zwieback EL. Trailing vortices of jet transport aircraft during takeo! and landing. AIAA J Aircraft 1964;1(5):308}10. [9] Lamb, Sir Horace. Hydrodynamics, 6th ed. New York: Dover, 1945. [10] Rossow VJ, Corsiglia VR, Schwind RG, Frick JKD, Lemmer OJ. Velocity and rolling-moment measurements in the wake of a swept-wing model in the 40- by 80-foot Wind Tunnel. NASA TM X-62,414, April 1975. [11] Jacobsen RA, Drinkwater III FJ. Exploratory #ight investigation of aircraft response to the wing vortex wake generated by the augmentor wing jet STOL research aircraft. NASA TM X-62, 387, May 1975. [12] Garodz LJ, Schutz CM. Analysis of low atmospheric density wake turbulence characteristics for jet transport category aircraft, FAA Data Report, Project 177-621-04X, February 1968, NAFEC, Alantic City, New Jersey. [13] Garodz LJ. Measurements of the vortex wake characteristics of the Boeing 747, Lockheed C5A and other aircraft. FAA Data Report Project 177-621-03X, April 1970, NAFEC, Atlantic City, New Jersey. [14] Garodz LJ. Investigation of the relatively long timehistory characteristics of the CV-880 airplane in terminal area-type #ight operations. FAA Data Report Project 504-303-03X, November 1970, NAFEC, Atlantic City, New Jersey.
654
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[15] Garodz LJ. Measurements of Boeing 747, Lockheed C5A and other aircraft vortex wake characteristics by tower #y-by techniques. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st ed. New York: Plenum Press, 1971, p. 265}285. [16] Garodz LJ. Federal aviation administration full-scale aircraft vortex wake turbulence #ight test investigations: past, present, future, AIAA Paper 71-97, New York, 1971. [17] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the Boeing 747 trailing vortex system using the tower #y-by technique. FAA-RD-73-156. NAFEC, Atlantic City, NJ, June 1974. [18] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the Boeing 727 trailing vortex system using the tower #y-by technique. FAA-RD-74-90, NAFEC, Atlantic City, NJ, August 1974. [19] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the McDonnell-Douglas DC-9 trailing vortex system using the tower #y-by Technique, FAA-RD-74-173, NAFEC, Atlantic City, NJ, November 1974. [20] Garodz LJ, Lawrence DM, Miller NJ. The measurement of the Boeing 707 trailing vortex system using the tower #y-by technique, FAA-RD-75-15, NAFEC, Atlantic City, NJ, March 1975. [21] Garodz LJ, Lawrence DM, Miller NJ. Measurement of the trailing vortex systems of large transport aircraft using tower #y-by and #ow visualization (summary, comparison and application). FAA-RD-75-127, NAFEC, Atlantic City, NJ, May 1975. [22] Kuechemann D, editor. Progress in Aeronautical Sciences, vol. 7. London, England: Pergamon Press Ltd., 1966. [23] Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, New York: Plenum Press, 1971. [24] Credeur L, Perry RB, editors. Proceedings of the NASA First Wake Vortex Dynamic Spacing Workshop. Langley Research Center, Hampton, VA, NASA/CP-97206235, May 13}15, 1997. [25] Gessow A, editor. NASA Symposium on Wake Vortex Minimization. NASA SP-409, 1976. [26] Hall MG. Vortex breakdown. Ann Rev Fluid Mech 1972;4:195}218. [27] Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977. [28] Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } vol. 1 and 2, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, October 29}31, 1991. [29] Meier GEA. Chairman, AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. [30] Wood WD, editor. FAA/NASA Proceedings Workshop on Wake Vortex Alleviation and Avoidance, Report No. FAA-RD-79-105, U.S. Dept. of Transportation, November 28}29, 1978. p. 1-1 to 1-42. [31] Delery JM. Physics of vortical #ows. AIAA J Aircraft 1992;29(5):856}76.
[32] Donaldson CduP, Bilanin AJ. Vortex wakes of conventional aircraft, AGARDograph No. 204, May 1975. [33] El-Ramly Z. Aircraft trailing vortices } a survey of the problem. Technical Rept. ME/A72-1, Carlton University, Ottawa, Canada, November 1972. [34] Sa!man PG. Vortex interactions. Ann Rev Fluid Mech 1979;11:95}122. [35] Spalart PR. Airplane trailing vortices. Ann Rev Fluid Mech (Palo Alto, CA) 1998;30:107}38. [36] Widnall SE. The structure and dynamics of vortex "laments. Ann Rev Fluid Mech (Palo Alto, CA) 1975;7:141}65. [37] Vyshinsky VV (Project Mgr). Investigation of vortex wake evolution and #ight safety problems } collection of papers. Trudy TsAGI, vol. 2627, Publishing Dept. of TsAGI, Moscow, Russia, 1997. [38] Van Dyke M. An album of #uid motion. Stanford, CA: The Parabolic Press, 1982. [39] Hallock JN. Aircraft wake vortices } an annotated bibliography (1923}1975). Report FAA-RD-76-43, U.S. Dept. of Transportation, January 1976. [40] Hallock JN. Aircraft wake vortices: an annotated bibliography (1923}1990), Report DOT-FAA-RD-90-30, DOT-VNTSC-FAA-90-7, U.S. Dept. of Transportation, John A. Volpe National Transportation Systems Center, Cambridge, MA, January 1991. [41] Leishman JG, Bagai A. Challenges in understanding the vortex dynamics of helicopter rotor wakes. AIAA J 1998;36(7):1130}40. [42] McAlister KW. Measurements in the near wake of a hovering rotor. AIAA Paper 96-1958, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [43] McCroskey WJ. Vortex wakes of rotorcraft. AIAA Paper 95-0530, AIAA 33rd Aero Sciences Meeting and Exhibit, Reno, NV, January 9}12, 1995. [44] Andrews WH, Robinson GH, Larson RR. Aircraft Response to the Wing Trailing Vortices Generated by Large Jet Transports. NASA Aircraft Safety and Operating Problems, vol. I, NASA SP-270, May 1971, p. 115}26. [45] Andrews WH. Flight evaluation of the wing vortex wake generated by large jet transports. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed. New York: Plenum Press, 1971, p. 287}8. [46] Andrews WH, Robinson GH, Larson RH. Exploratory #ight investigation of aircraft response to the wing vortex wake generated by jet transport aircraft. NASA TN D6655, March 1972. [47] Bisgood PL, Maltby RL, Dee FW. Some work on the behaviour of vortex wakes at the royal aircraft establishment, Royal Aircraft Establishment Tech Memo 1244, August 1970. [48] Bisgood PL. In-#ight studies of vortex wakes, 1970}73. Establishment Tech Memo 1554, November 1973. [49] Crow SC. Stability theory for a pair of trailing vortices. AIAA J 1970;8(12):2172}9. [50] Garodz LJ, Clawson KL. Vortex wake characteristics of B-757-200 and B-767-200 aircraft using the tower #y-by technique; vols. 1 and 2. NOAA Technical Memorandum ERL ARL-199, NOAA Environmental Research Laboratories, Air Resources Laboratory, Silver Spring, MD, January 1993.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 [51] Ho!man ER, Joubert PN. Turbulent line vortices. J Fluid Mech. 1963;16 (Part 3):395}411. [52] McCormick BW, Tangler JL, Sherrieb HE. Structure of trailing vortices. AIAA J Aircraft 1968;5(3):260}7. [53] McWilliams IG. Hazard extent about aircraft trailing wake vortices-analytic approach. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference, Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 23}30. [54] Sammonds RI, Stinnett Jr GW, Larsen WE. Wake vortex encounter hazard criteria for two aircraft classes. NASA TM X-73,113, June 1976. (Also FAA-RD-75-206.) [55] Smith HJ. A #ight test investigation of the rolling moments induced on a T-37B airplane in the wake of a B-747 airplane. NASA TM-56031, April 1975. [56] Singh B, Kutty TM, Wentz Jr WH. Preliminary investigation of rolling moments induced by trailing vortices for several wing-tip modi"cations. Wichita State University Aeronautical Report 72-1, 1972. [57] Wentz Jr. WH. Evaluation of several vortex dissipators by wind tunnel measurements of vortex-induced upset loads. Wichita State University Aeronautical Report 72-3, 1972. [58] Barber MR, Hastings Jr. EC, Champine RA, Tymczyszyn JJ. Vortex attenuation #ight experiments. In: Gessow A, Editor, NASA Symposium on Wake Vortex Minimization, NASA SP-409, Feburary 25}26, 1976, p. 369}403. [59] Barber MR, Tymczyszyn JJ. Wake vortex attenuation #ight tests: a status report, NASA CP-2170, 1980, p. 387}408. [60] Corsiglia VR, Rossow VJ, Ci!one DL. Experimental study of the e!ect of span loading on aircraft wakes. AIAA J Aircraft 1976;13(12):968}73. [61] Corsiglia VR, Dunham RE. Aircraft wake-vortex minimization by use of #aps. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976, p. 305}38. [62] Croom DR. Low-speed wind-tunnel investigation of various segments of #ight spoilers as trailing-vortex-alleviation devices on a transport aircraft model. NASA TN D-8162, March 1976. [63] Croom DR. Low-speed wind-tunnel parametric investigation of #ight spoilers as trailing-vortex-alleviation devices on a transport aircraft model, NASA TP-1419, 1979. [64] Nikolic VR, Jumper EJ. Attenuation of airplane wake vortices by excitation of far-"eld instability. AIAA 93-3511, 11th AIAA Applied Aerodynamics Conference, August 9}11, 1993, Monterey, CA. [65] Nikolic VR, Jumper EJ, Nelson RC. Modi"ed, discretevortex method for studying wing-loading e!ects on wake dynamics. AIAA J Aircraft 1996;33(1). [66] Patterson JC, Jordan Jr FL. Thrust-augmented vortex attenuation. In: Gessow A, editor. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976. p. 251}70. [67] Patterson JC, Hastings EC, Jordan FL. Ground development and #ight correlation of the vortex attentuating spline device. In: Gessow A, editor. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976. p. 271}303.
655
[68] Patterson Jr JC. Exploratory wind-tunnel investigation of a wingtip-mounted vortex turbine for vortex energy recovery. NASA TP-2468, 1985. [69] Rennich SC, Lele SK. Method for accelerating the destruction of aircraft wake vortices. AIAA J Aircraft 1999;36(2):398}404. [70] Rossow VJ. Prospects for alleviation of hazard posed by lift-generated wakes. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } vol. 1, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD-92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, October 29}31, 1991. p. 22-1 to 22-40. [71] Snyder Jr MH. E!ects of a wingtip-mounted propeller on wing lift, induced drag, and shed vortex pattern. Ph.D. thesis, Oklahoma State University, Stillwater, OK, May 1967. [72] Ash RL, Zheng ZC. Numerical simulations of commercial aircraft wakes subjected to airport surface weather conditions. AIAA J Aircraft 1998;35(1):18}26. [73] Cantwell B, Rott N. The decay of a viscous vortex pair. The Phys of Fluids 1988;31(11):3213}24. [74] Crow SC, Bate Jr. ER. Lifespan of trailing vortices in a turbulent atmosphere. AIAA J Aircraft 1976; 13(7):476}82. [75] Devenport WJ, Zsoldos JS, Vogel CM. The structure and development of a counter-rotating wing-tip vortex pair. J Fluid Mech 1997;332:71}104. [76] Eaton JA, O'Flaherty MP. Flow"eld prediction of threedimensional wing trailing vortices using advanced turbulence models, AGARD 78th Fluid Dynamics, Conference Proceedings 584, Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Trondheim, Norway, Conference Proceedings 584, 20}23 May 1996. Paper No. 7, p. 7-1 to 7-7. [77] Follin GJ, Devenport WJ. E!ects on the turbulent structure of a counter-rotating vortex pair, AIAA Paper 96-1959, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [78] Kandil OA, Adam I, Wong TC. Far-"eld turbulent vortex-wake/exhaust plume interaction for subsonic and HSCT airplanes. Paper No. AIAA 96-1962, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [79] Graham JAH. Reynolds-stress measurements in a turbulent trailing vortex. J Fluid Mech 1984;147:353}71. [80] Liu H-T. E!ects of ambient turbulence on the decay of a trailing vortex wake. AIAA J Aircraft 1992; 29(2):255}63. [81] Miranda JA, Devenport WJ. Turbulent structure in the spiral wake shed by a lifting wing. AIAA J 1998; 36(4):658}60. [82] Moore DW, Sa!man PG. Axial #ow in laminar trailing vortices. Proc Roy Soc London Ser A 1973;333:491}508. [83] Rudis RP, Burnham DC, Janota P. Wake vortex decay near the ground under conditions of strong strati"cation and wind shear. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 11, p. 11-1 to 11-10.
656
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[84] Sarpkaya T, Daly JJ. E!ect of ambient turbulence on trailing vortices. AIAA J Aircraft 1987;24(6):399}404. [85] Vaughan JM, Brown DW, Constant G, Eacock JR, Foord R. Structure, trajectory and strength of B-747 aircraft wake vortices measured by laser. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 10, p. 10-1 to 10-10. [86] Zheng ZC. The e!ects of atmospheric turbulence on aircraft wake vortices. AIAA Paper No. 96-1954, 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17}20, 1996. [87] Corsiglia VR, Schwind RG, Chigier NA. Rapid scanning, three-dimensional hot-wire anemometer surveys of wingtip vortices. AIAA J Aircraft 1973;10(12):752}7. [88] Corsiglia VR, Rossow VJ. Wind-tunnel investigation of the e!ect of porous spoilers on the wake of a subsonic transport model. NASA TM X-73,091, January 1976. [89] Baker GR, Barker SJ, Bofah KK, Sa!man PG. Laser anemometer measurements of trailing vortices in water. J Fluid Mech 1974;65(Part 2):325}36. [90] Ci!one DL. Correlation for estimating vortex rotational velocity downstream dependence. AIAA J Aircraft 1974;11(11):716}7. [91] Ci!one DL, Orlo! KL. Far-"eld wake-vortex characteristics of wings. AIAA J Aircraft 1975;12(5):464}70. [92] Ci!one DL, Orlo! KL. Application of laser velocimetry to aircraft wake-vortex measurements. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976, p. 157}92. [93] Ci!one DL. Vortex interactions in multiple vortex wakes behind Aircraft. AIAA J Aircraft 1977;14(5):440}6. [94] Corsiglia VR, Jacobsen RA, Chigier N. An experimental investigation of trailing vortices behind a wing with a vortex dissipator. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, Plenum Press, 1971, p. 229}42. [95] Corsiglia VR, Orlo! KL. Scanning laser-velocimeter surveys and analysis of multiple vortex wakes of an aircraft. Proceedings of the Aircraft Wake Vortices Conference, March 15}17. Report FAA-RD-77-68, U.S. Dept. of Transportation, Transportation Systems Center, Cambridge, MA, 1977, p. 114}23. [96] Corsiglia VR, Iversen JD, Orlo! KL. Laser-velocimeter surveys of merging vortices in a wind tunnel. AIAA J Aircraft 1978;15(11):762}8. [97] Delisi DP, Greene GC, Robins RE, Singh R. Recent laboratory and numerical trailing vortex studies, AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 34, pp. 34-1 to 34-10. [98] Liu H-T, Srnsky RA. Tow tank simulation of vortex wake dynamics. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } vol. 1 and 2, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD-92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, October 29}31, 1991. p. 32-1-26.
[99] Liu H-T, Hwang PA, Srnsky RA. Physical modeling of ground e!ects on vortex wakes. AIAA J Aircraft 1992;29(6):1027}34. [100] Reinath MS. Doppler global velocimeter development for the large wind tunnels at Ames Research Center. NASA TM 112210, September 1997. [101] Iversen JD. Correlation of turbulent trailing vortex decay data. AIAA J Aircraft 1976;13(5):338}42. [102] Kirkman KL, Brown CE, Goodman A. Evaluation of e!ectiveness of various devices for attenuation of trailing vortices based on model tests in a large towing basin. NASA Contractor Report NASA CR-2202, December 1973. [103] Smith WG, Lazzeroni FA. Experimental and theoretical study of a rectangular wing in a vortical wake at low speed. NASA TN D-339, October 1960. [104] Rossow VJ, Tinling BE. Research on aircraft/vortexwake interactions to determine acceptable level of wake intensity. AIAA J Aircraft 1988;25(4):481}92. [105] Rossow VJ. E!ect of wing "ns on lift-generated wakes. AIAA J Aircraft 1978;15(3):160}7. [106] Rossow VJ, Sacco JN, Askins PA, Bisbee LS, Smith SM. Measurements in 80- by 120-foot wind tunnel of hazard posed by lift-generated wakes. AIAA J Aircraft 1995;32(2):278}84. [107] Iversen JD, Bernstein S. Trailing vortex e!ects on following aircraft. AIAA J Aircraft 1974;11(1):60}1. [108] Nelson RC. The dynamic response of aircraft encountering aircraft wake turbulence. Tech Report AFFDL-TR74-29, Air Force Flight Dynamics Laboratory, WrightPatterson Air Force Base, OH, June 1974. [109] Nelson RC. Dynamic behavior of an aircraft encountering aircraft wake turbulence. AIAA J Aircraft 1976;13(9):704}8. [110] Abramson S, Burnham DC. Ground-based measurements of wake vortices from landing aircraft at Airports. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Trondheim, Norway, Conference Proceedings 584, 20}23 May 1996. Paper No. 13, p. 13-1 to 13-7. [111] Burnham DC. Review of vortex sensor development since 1970. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 47}66. [112] Burnham DC. B-747 vortex alleviation #ight tests: ground-based sensor measurements. Report DOT-FAARD-81-99, U.S. Dept. of Transportation, February 1982. [113] Burnham DC. Wake vortex alleviation system requirements. Report DOT-TSC-FA427-PM-84-19, U.S. Dept. of Transportation, May 1984. [114] Burnham DC. Wake vortex avoidance systems: requirements analysis. Report DOT-TSC-FA527PM-84-46, U.S. Dept. of Transportation, November 1984. [115] Burnham DC. TSC hazard model for wake vortex encounters. Report DOT-TSC-FA627-PM-86, U.S. Dept. of Transportation, November 1985.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 [116] Burnham DC, Hallock J. Wake vortex separation standards: analysis methods. Report DOT-VNTSC-FAA97-4, U. S. Dept. of Transportation, Federal Aviation Administration, May 1997. [117] Condit PM, Tracy PW. Results of the Boeing company wake turbulence test program. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed. New York: Plenum Press, 1971, p. 473}508. [118] Eisenhuth JJ, McCormick BW, Nelson RC. Analysis of experimental measurements of trailing vortex systems of large jet transport aicraft. Proceedings of the National Aerospace Electronics Conference, Dayton, OH, May 17}19, 1971, p. 28}35. [119] Kurkowski RL, Barber MR, Garodz LJ. Characteristics of wake vortex generated by a Boeing 727 jet transport during two-segment and normal ILS approach paths. NASA TN D-8222, April 1976. [120] Scorer RS, Davenport LJ. Contrails and aircraft downwash. J Fluid Mech 1970;43(Part 3):451}64. [121] Vicroy DD, Bowles RL, Brandon JM, Greene GC, Jordan Jr. FL, Rivers RA, Stewart EC, Stough III HP, Stuever RA. NASA wake vortex research. ICAS-946.2.2, 19th Congress of the International Council of the Aeronautical Sciences, September 19}23, 1994, Anaheim, CA. [122] Hallock JN, Burnham DC. Decay characteristics of wake vortices from jet transport aircraft. Paper No. AIAA 97-0060, 35th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6}10, 1997. [123] Hinton DA. Aircraft vortex spacing system (AVOSS) conceptual design. NASA TM 110184, Hampton, VA, August 1995. [124] Hinton DA. An aircraft vortex spacing system (AVOSS) for dynamical wake vortex spacing criteria. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. p. 23-1}23-12. [125] Hallock JN, Burnham DC, Tombach IH, Brashears MR, Zalay AD, Barber MR. Ground-based measurements of the wake vortex characteristics of a B-747 aircraft in various con"gurations. AIAA Paper 77-9, January 1977. [126] Hastings Jr EC, Keyser Jr GL. Simulated vortex encounters by a twin-engine commercial transport aircraft during "nal approach. SAE Technical Paper 800775, May 1980 (also NASA TM-81782). [127] Johnson WA, Rediess HA. Study of control system e!ectiveness in alleviating vortex wake upsets. Paper No. 141, Systems Technology, Inc, Hawthorne, CA, August 1973. [128] Johnson WA, Teper GL, Rediess HA. Study of control system e!ectiveness in alleviating vortex wake upsets. AIAA J Aircraft 1974;11(3):148}54. [129] Sammonds RI, Stinnett Jr GW. Hazard criteria for wake vortex encounters. NASA TM X-62,473, August 1975. [130] Tinling BE. Estimation of vortex-induced roll excursions based on #ight and simulation results. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference, Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977. p. 11}22.
657
[131] Tinling BE. Estimates of the e!ectiveness of automatic control in alleviating wake vortex induced roll excursions. NASA TM-73,267, August 1977. [132] Tinling BE. Estimation of the e!ect of the delayed #ap approach on the wake vortex hazard. NASA TM-73,179, September 1977. [133] Streeter VL. Fluid dynamics. New York: McGraw-Hill, 1948. [134] Talay TA. Introduction to the aerodynamics of #ight, NASA SP-367, 1975. [135] Rossow VJ. Estimate of loads during wing-vortex interactions by Munk's transverse-#ow method. AIAA J Aircraft 1990;27(1):66}74. [136] Munk MM. Fundamentals of #uid dynamics for aircraft designers, New York: The Ronald Press Co., 1929. [137] Jones RT, Cohen D. Aerodynamics of wings at high speeds. vol. VII. In: Donovan AF, Lawrence HR. editors. High speed aerodynamics and jet propulsion}aerodynamic components of aircraft at high speeds. Princeton University, NJ: Princeton University Press, 1957. [138] Maskew B. Numerical lifting surface methods for calculating the potential #ow about wings and wing-bodies of arbitrary geometry. Ph.D. Thesis, Loughborough Univ. of Tech., England, October 1972. [139] Hough G. Remarks on vortex-lattice methods. AIAA J Aircraft 1973;10(5):314}7. [140] Betz A. Verhalten von Wirbelsystem, ZAMM 1932; Bd. XII (3): 164}74. (Also available as NACA TM 713.) [141] Donaldson CduP, Sullivan RD. Decay of an isolated vortex. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed. New York: Plenum Press, 1971, p. 389}411. [142] Donaldson CduP, Snedeker RS, Sullivan Roger D. Calculation of aircraft wake velocity pro"les and comparison with experimental measurements. AIAA J Aircraft 1974;11(9):547}55. [143] Bilanin AJ, Teske ME, Donaldson CduP, Snedeker RS. Viscous e!ects in aircraft trailing vortices. In: Gessow A, editor, NASA Symposium on Wake Vortex Minimization, NASA SP-409, February 25}26, 1976, p. 61}128. [144] Brown CE. Aerodynamics of wake vortices. AIAA J 1973;11(4):531}6. [145] Rossow VJ. On the inviscid rolled-up structure of liftgenerated vortices. AIAA J Aircraft 1973;10(11):647}50. [146] Rossow VJ. Prediction of span loading from measured wake-vortex structure } an inverse Betz method. AIAA J Aircraft 1975;12(7):626}8. [147] Rossow VJ. On extended-Betz methods for rollup of vortex sheets. AIAA J Aircraft 1997;34(5):592}9. [148] Rosenhead L. The formation of vortices from a surface of discontinuity. Proc Roy Soc London A 1931;134: 170}92. [149] Westwater FL. The rolling up of the surface of discontinuity behind an aerofoil of "nite span. Aeronautical Research Council, London, Repts. and Memo. 1692, 1935. p. 116}31. [150] Rule JA, Bliss DB. Prediction of viscous trailing vortex structure from basic loading parameters. AIAA J 1998;36(2):208}18. [151] Rossow VJ. Theoretical study of lift-generated vortex wakes designed to avoid rollup. AIAA J 1975; 13(4):476}84.
658
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[152] Jones RT. The spanwise distribution of lift for minimum induced drag of wings having a given lift and a given bending moment. NACA Technical Note 2249, December 1950; see also, Collected works of Robert T. Jones. NASA TM X-3334, February 1976, p. 539}54. [153] Iversen JD, Brandt SA, Raj P. Merging distance criteria for co-rotating vortices. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 161}72. [154] Iversen JD, Park S, Backhus DR, Brickman RA. Hotwire, laser anemometer, and force balance measurements in cross-sectional planes of single and interacting trailing vortices. AIAA Paper No. 78-1194, 11th Fluid and Plasmadynamics Conference, Seattle, WA, July 10}12, 1978. [155] Bilanin AJ, Widnall SE. Aircraft wake dissipation by sinusoidal instability and vortex breakdown, AIAA Paper 73-107, 1973. [156] Jordan Jr FL. Flow visualization of the wake of a transport aircraft model with lateral-control oscillations. NASA TM 84623, June 1983. [157] McMillan OJ, Nielsen JN, Schwind RG, Dillenius MFE. Rolling moments in a trailing-vortex #ow "eld. AIAA J Aircraft 1978;15(5):280}6. [158] Olsen JH. Results of trailing vortex studies in a towing tank. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st ed. New York: Plenum Press, 1971. p. 455}72. [159] Jacobsen RA, Short BJ. A #ight investigation of the wake turbulence alleviation resulting from a #ap con"guration change on a B-747 aircraft. NASA TM-73, 263, July 1977. [160] Jacobsen RA, Barber MR. Flight test techniques for wake vortex minimization studies. In: Gessow A, editor. NASA Symposium on Wake Vortex Minimization, NASA SP409, February 25}26, 1976, p. 193}220. [161] Zell PT, Flack K. Performance and test section #ow characteristics of the National Full-Scale Aerodynamics Complex 40- by 80-foot Wind Tunnel. NASA TM 101065, February 1989. [162] Zell PT. Performance and test section #ow characteristics of the National Full-Scale Aerodynamics Complex 80- by 120-foot Wind Tunnel. NASA TM 103920, January 1993. [163] Rossow VJ. Validation of vortex-lattice method for loads on wings in lift-generated wakes. AIAA J Aircraft 1995;32(6):1254}62. [164] Stickle JW, Kelly MW. Ground-based facilities for evaluating vortex minimization concepts, NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976. p. 129}55. [165] Scorer RS. Natural aerodynamics. New York: Pergamon Press, 1958. [166] Bofah KK. Some remarks on aircraft wake vortex analysis. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 31}46. [167] Britton JW. Some remarks on en-route vortex encounters. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference. Report No. FAA-RD-77-68,
[168]
[169] [170]
[171]
[172]
[173]
[174]
[175]
[176] [177]
[178] [179]
[180]
[181]
[182]
[183]
[184]
[185]
U.S. Dept. of Transportation, March 15}17, 1977, p. 243}6. Eliason BG, Gartshore IS, Parkinson GV. Wind tunnel investigation of Crow instability. AIAA J Aircraft 1975;12(12):985}8. Tombach IH. Observations of atmospheric e!ects on vortex wake behavior. AIAA J Aircraft 1973;10(11):641}7. Hackett JE, Evans PF. Numerical studies of three-dimensional breakdown in trailing vortex wakes. AIAA J Aircraft 1977;14. Widnall SE, Bliss D, Zalay A. Theoretical and experimental study of the stability of a vortex pair. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st Ed., New York: Plenum Press, 1971. p. 305}38. Bliss DB. E!ect of unsteady forcing on the sinusoidal instability of vortex wakes. AIAA J Aircraft 1982; 19:713}21. Gerz T, Ehret T. Wake dynamics and exhaust distribution behind cruising aircraft. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 35, p. 35-1 to 35-12. Jacob J, Savas O, Liepmann D. Trailing vortex wake growth characteristics of a high aspect ratio rectangular airfoil. AIAA J 1997;35(2):275}80. Spalart PR, Wray AA. Initiation of the Crow instability by atmospheric turbulence. AGARD 78th Fluid Dynamics Panel Symposium on The Characterization and Modi"cation of Wakes From Lifting Vehicles in Fluids, Conference Proceedings 584, Trondheim, Norway, 20}23 May 1996. Paper No. 18, p. 18-1 to 18-8. Greene GC. An approximate model of vortex decay in the atmosphere. AIAA J Aircraft 1986;23(7):566}73. Kantha LH. Empirical model of transport and decay of wake vortices between parallel runways. AIAA J Aircraft 1996;33(4):752}60. Kantha LH. Empirical model of transport and decay of wake vortices. AIAA J Aircraft 1998;35(4):649}53. Rossow VJ. Spur-type instability observed on numerically simulated vortices. AIAA J Aircraft 1988; 25(9):835}41. Rossow VJ. Prospects for destructive self-induced interactions in a vortex pair. AIAA J Aircraft 1987; 24(7):433}40. Rossow VJ. Wake hazard alleviation associated with roll oscillations of wake-generating aircraft. AIAA J Aircraft 1986;23(6):484}91. Holbrook GT. Vortex wake hazard analysis including the e!ect of the encountering wing on the vortex. M.S. Thesis, George Washington Univ., Washington, DC, August 1985. Rossow VJ. Experimental investigation of wing "n con"gurations for alleviation of vortex wakes of aircraft. NASA TM 78520, November 1978. Rossow VJ, Fong RK, Wright MS, Bisbee LS. Vortex wakes of two transports measured in 80- by 120-foot Wind Tunnel. AIAA J Aircraft 1996;33(2):399}406. Zimmerman CH. Characteristics of Clark-Y airfoils of small aspect ratios. NACA TR 431, 1932.
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660 [186] Moghadam MM. Experimental investigation of vortices shed by various wing "n con"gurations. M.S. thesis (J. D. Iversen advisor), Iowa State University, August 1979. [187] Rossow VJ. Vortex structures and span loadings from alleviated-wake measurements. AIAA Paper 97-2262, 15th AIAA Applied Aerodynamics Conference, Atlanta, GA, June 23}25, 1997. [188] Desabrais KJ, Johari H. Direct circulation measurement of a wing tip vortex using ultrasound. Paper AIAA 980609, AIAA 36th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 12}15, 1998. [189] Barrows TM. Simpli"ed methods of predicting aircraft rolling moments due to vortex encounters. AIAA J Aircraft 1977;14(5):434}9. [190] Filotas LT. Vortex induced wing loads. AIAA J 1972;10(7):971. [191] Flax AH. Comment on &&Simpli"ed methods of predicting aircraft rolling moments due to vortex encounters''. AIAA J Aircraft 1977;14(11):1151}2. [192] Jones WP. Vortex-elliptic wing interaction. AIAA J 1972;10(2):225}7. [193] Spreiter JR, Sacks AH. The rolling up of the trailing vortex sheet and its e!ect on the downwash behind wings. Institute of the Aeronautical Sciences, Inc., J Aeronaut Sci 1951;18(1):21}32,72. [194] Bandyopadhyay PR, Stead DJ, Ash RL. Organized nature of a turbulent trailing vortex. AIAA J 1991;29(10):1627}33. [195] Dacles-Mariani J, Zilliac GG, Chow JS, Bradshaw P. Numerical/experimental study of a wingtip vortex in the near "eld. AIAA J 1995;33(9):1561}8. [196] Dacles-Mariani J, Hafez H, Kwak D. Prediction of wakevortex #ow in the near- and intermediate-"elds behind wings. Paper AIAA 97-0040, AIAA 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6}10, 1997. [197] Han YO, Leishman JG, Coyne AJ. Measurements of the velocity and turbulence structure of a rotor tip vortex. AIAA J 1997;35(3):477}85. [198] Ramaprian BR, Zheng Y. Measurements in rollup region of the tip vortex from a rectangular wing. AIAA J 1997;35(12):1837}43. [199] Back LH. Optical and physical requirements for #uid particles marking trailing vortices from aircraft. AIAA J Aircraft 1976;13(7):483}9. [200] Zeman O. Persistence of trailing vortices: a modeling study. Phys Fluids 1995;7(1):135}43. [201] Squire HB. The growth of a vortex in turbulent #ow. Aeronaut Quart 1965;XVI(Part 3):302}6. [202] Kuzmin VP. Estimation of wake-vortex separation distances for approaching aircraft. In: Vyshinsky VV (Project Mgr), Investigation of vortex wake evolution and #ight safety problems } collection of papers. Trudy TsAGI, vol. 2627, Publishing Dept. of TsAGI, Moscow, Russia, 1997, p. 209}24. [203] Vatistas GH, Lin S, Kwok CK. Theoretical and experimental studies on vortex chamber #ows. AIAA J 1986;24(4):635}42. [204] Vatistas GH, Lin S, Li PM. A similar pro"le for the tangential velocity in vortex chambers. Exp Fluids 1988;6(2):135}7.
659
[205] Vatistas GH, Kozel V, Mih WC. A simpler model for concentrated vortices. Exp Fluids 1991;11:73}6. [206] Teske ME, Quackenbush TR, Bilanin AJ, Wachspress DA. Vortex roll-up, merging and decay with the uniwake computer program. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference } Vol. 1 and 2, U.S. Dept. of Transportation, Federal Aviation Admin., DOT/FAA/SD-92/1.1, DOT-VNTSC-FAA-92-7.1, Washington, DC, Oct. 29}31, 1991. p. 33-1-20. [207] Phillips WRC. The turbulent trailing vortex during rollup. J Fluid Mech 1981;105:451}67. [208] Proctor FH. Numerical simulation of wake vortices measured during the Idaho Falls and Memphis "eld programs. AIAA Paper No. 96-2496, 14th AIAA Applied Aerodynamics Conference, New Orleans, LA, June 17}20, 1996. [209] Risso F, Corjon A. Direct numerical simulations of wake vortices in intense homogeneous turbulence. AIAA J 1997;35(6):1030}40. [210] Sa!man PG. Structure of turbulent line vortices. Phys. Fluids 1973;16(8):1181}8. [211] Sarpkaya T. Decay of wake vortices of large aircraft. AIAA J 1998;36(9):1671}9. [212] Rossow VJ. Measured changes in vortex wakes with downstream distance. AIAA Paper No. 98-2524, 16th AIAA Applied Aerodynamics Conference, Albuquerque, NM, June 15}18, 1998. [213] Owen PR. The decay of a turbulent trailing vortex. The Aeronaut Quart, 1970;XXI (Part 1):69}78. [214] Iversen JD. Inviscid to turbulent transition of trailing vortices. AIAA Paper No. 75-883, Hanford, CT, 1975 (also Iowa State University Report ISU-ERI-Ames 74241, November 1974). [215] Rossow VJ. Wake-vortex structure from lift and torque induced on a following wing. AIAA Paper No. 93-3013, 24th AIAA Fluid Dynamics Conference, Orlando, FL, July 6}9, 1993. [216] Bilanin AJ, Teske ME, Hirsh JE. Deintensi"cation as a consequence of vortex breakdown. In: Hallock JN, editor. Proceedings of the Aircraft Wake Vortices Conference, Report FAA-RD-77-68, U. S. Dept. of Transportation, March 15}17, 1977, p. 283}96. [217] Lessen M, Singh P, Paillet F. The stability of a trailing line vortex, Part I: inviscid theory. J Fluid Mech 1974;63(Pt. 4):753}63. [218] Lessen M, Paillet F. The stability of a trailing line vortex, Part II: viscous theory. J Fluid Mech 1974;65(Pt. 4):769}79. [219] Zalay AD, White RPW, Balcerak JC. Investigation of viscous line vortices with and without the injection of core turbulence, RASA Rept. 74-01, February 1974, Rochester Applied Science Associates, Rochester, NY. [220] Dunham Jr. RE. Unsuccessful concepts for aircraft wake vortex minimization. NASA Symposium on Wake Vortex Minimization, NASA SP-409, 1976, p. 221}50. [221] MacCready PB. An assessment of dominant mechanisms in vortex-wake decay. In: Olsen JH, Goldburg A, Rogers M, editors. Aircraft wake turbulence and its detection, 1st ed. Plenum Press, 1971, p. 289}304. [222] Leweke T, Williamson CHK. Cooperative elliptic instability of a vortex pair. J Fluid Mech 1998;360: 85}119.
660
V.J. Rossow / Progress in Aerospace Sciences 35 (1999) 507}660
[223] Crouch JD. Instability and transient growth for two trailing-vortex pairs. J Fluid Mech 1997;350:311}30. [224] Stickle JW. Wake vortex alleviation } the NASA program. In: Wood WD, editor. FAA/NASA Proceedings Workshop on Wake Vortex Alleviation and Avoidance. Report No. FAA-RD-79-105, U.S. Dept. of Transportation, November 28}29, 1978, p. 2-1-56. [225] Posluns H, editor. Proceedings of the International Wake Vortex Meeting. Ottawa, Ontario, Canada, 2}4 December 1997. [226] Stough III HP, Greene GC, Stewart EC, Stuever RA, Jordan Jr. FL, Rivers RA, Vicroy DD. NASA wake vortex research. AIAA Design, Systems and Operations Meeting, August 11}13, 1993, Monterey, CA, AIAA Paper 93-4004. [227] Spitzer EA, Hallock JN, Wood WD. Status of the Vortex Advisory System. Proceedings of the Aircraft Wake Vortices Conference, edited by Hallock JN, Report No. FAARD-77-68, U.S. Dept. of Transportation, March 15}17, 1977, p. 326}34. [228] Rossow VJ. Wake-vortex separation distances when #ight-path corridors are constrained. AIAA J Aircraft 1996;33(3):539}46.
[229] Loh R, Shively C, Swider R. Overview of the FAA's di!erential GPS CAT III technical feasibility demonstration program. AIAA Guidance, Navigation and Control Conference, August 9}11, 1993, Monterey, CA, AIAA Paper 93-3836-CP. [230] Cobb HS. GPS pseudolites: theory, design, and applications. SUDAAR Report 707, Stanford University, Dept. of Aeronautics and Astronautics, Palo Alto, CA, September 1996. [231] Lawrence DG. Aircraft landing using GPS: development and evaluation of a real time system for kinematic positioning using the Global Positioning System. Stanford University Dept. of Aeronautics and Astronautics, Palo Alto, CA, SUDAAR Report 690, September 1996. [232] Pervan BS. Navigation integrity for aircraft precision landing using the Global Positioning System. Stanford University Dept. of Aeronautics and Astronautics, Palo Alto, CA, SUDAAR Report 677, March 1996.