Wake vortex characteristics of transport aircraft

Progress in Aerospace Sciences 47 (2011) 89–134

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Wake vortex characteristics of transport aircraft C. Breitsamter n Institute of Aerodynamics, Technische Universit¨ at M¨ unchen, Boltzmannstraße 15, 85748 Garching, Germany

a r t i c l e in fo

abstract

Available online 30 November 2010

The flow and flight physics of wake vortex systems has been intensively investigated concentrating on a large variety of aspects. This paper gives a brief overview on past and present wake vortex research activities such as early studies, integrated programs, model and flight tests, numerical investigations, fundamental physical aspects and alleviation strategies. Then, detailed results of the properties of the wake near field and extended near field are presented addressing typical length and time scales and especially turbulence quantities. Progressing from the near field to the far field wake instability mechanisms are explained along with their relevance for wake vortex decay. Characteristic quantities are given for the short and long wave instabilities associated with vortex merging and wakes consisting of two and four trailing vortices. A non-dimensional frequency parameter is introduced to classify the main instability types. Means for wake vortex alleviation are described aimed at influencing the wake vortex turbulence field or triggering and amplifying the inherent instabilities. The methods discussed include passive means such as the effects of spoilers, differential flap setting and four-vortex systems and active means using oscillating flaps or auxiliary devices. & 2010 Elsevier Ltd. All rights reserved.

Contents 1. 2.

3.

4.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Research activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.1. Early studies and integrated programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.2. Small and large-scale tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 2.2.1. Near field–wind tunnel tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 2.2.2. Mid- and far-field–water tunnel and catapult tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 2.2.3. Flight tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.3. Numerical investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.3.1. Near field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.3.2. Far field and atmospheric influences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2.4. Fundamental physical aspects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2.5. Alleviation strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Near field characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.1. Classification and basic quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.2. Wind tunnel facilities, models and experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.3. Near field properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.4. Extended near field properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.5. Major findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Unsteady effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.1. Vortex merging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.1.1. Principle experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.1.2. Present investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.2. Instabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.2.1. Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.2.2. Long wave instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

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C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

4.2.3. Medium wave instabilities–four-vortex systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4. Short wave instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5. Present investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Major findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wake vortex alleviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Passive means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1. Spoiler elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2. Differential flap setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Active means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. Control surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2. Winglet flaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix. Lamb–Oseen vortex model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Wake vortices develop as a consequence of the lift an aircraft produced to fly [125]. For a wing generating lift, the pressure on the wing lower surface is higher than the pressure on the wing upper surface. Therefore, air flows around the wing tip from the lower surface to the upper surface resulting in a strong vortex, the so-called ‘‘wing tip vortex’’. Further, the fluid coming from the wing upper and lower surface shows a different sense of direction at the wing trailing edge. Thus, a free shear layer or vortex sheet develops, which is connected with the respective wing tip vortex in the span direction. This free shear layer rolls up due to its self-induction together with the wing tip vortex into a single rolled-up vortex for the left and right wings, respectively. Consequently, two counterrotating trailing vortices exist, which can exhibit cross flow velocities of up to 360 km/h in their core region depending upon flight conditions and airplane size. Those trailing vortices stay downstream up to hundred wing spans and more, before they decay due to instability mechanisms and/or due to atmospheric effects. This means that trailing vortices can have a lifespan of several minutes and a length of up to 30 km for large airplanes. The wake vortex system turns out to be far more complex in the near field region for high lift configurations, i.e. at takeoff and landing, if slats and flaps are deployed. Under such conditions further dominant vortices are present. In particular, very strong vortices may develop at the flap side edges, which still exceed the strength of the wing tip vortices [3,11]. An airplane affected by a vortex wake experiences, depending upon its position relative to the wake vortices, an upwind field, a downwind field (loss of lift) or an induced rolling moment (Fig. 1) accompanied by more or less strong velocity fluctuations [100,116,120]. In particular, for an airplane which is smaller than the one flying ahead serious consequences can arise from the wake impact: These are increased structural dynamic loads or loss of the stable flight condition, if for example, the available commanded rolling moment is not large enough to counteract the wake induced rolling moment. The strength of the two trailing vortices, which remains after the roll-up process, is proportional to the total circulation and thus to the lift, which compensates the aircraft weight. The safety margins for the longitudinal distance between two airplanes depend therefore on their maximum take-off weight (MTOW). This criterion has been introduced in the seventies by the International Civil Aviation Authority (ICAO) [41,42,79] (Table 1). Three weight categories exist: ‘‘light’’ (under 7.000 kg), ‘‘medium’’ (7.000 kg up to 136.000 kg) and ‘‘heavy’’ (over 136.000 kg). Depending on the combination of ahead flying and the following airplane a distance between the airplanes from 3 to 6 nautical miles (5.56–11.12 km) must be kept [96].

113 116 117 119 120 121 122 125 126 127 127 129 132 132

These safety margins limit already today the capacity of the runways at many airports, as for example Frankfurt/Main, and thus the capacity of the entire airport. This problem will continue to intensify in view of the further estimated high growth rates of civil air traffic and scarce surfaces for the extension of existing airports or building of new airports. Concerned are, on the one hand, the manufacturers of large airplanes, and on the other hand, air traffic control and airport operators, who want to reduce the aircraft separation distances during increase in density of traffic, with a strong mixture of different types of aircraft and thus different wake vortex types, under full retention of the safety standards. Also for military aircraft wake vortices are of particular interest because their impact can lead to considerably high structural dynamic loads [85,95]. Thereby, the formation flight, the approximation to the tanker aircraft for air refueling or flying through the wake of the opposing aircraft during air combat are of special interest.

2. Research activities 2.1. Early studies and integrated programs The three–class categorization of aircraft separation distances made on basis of the maximum take-off weight fulfills the safety standards to all experiences. In the seventies first extensive model studies and flight tests were carried out in context with the definition of the separation distances [42,5,6,15,17,59,62,80,113]. Different overview articles inform about earlier and current research work in the area of the wake vortex problem [36,52,66,120,126]. The work presented therein takes up fundamental physical questions regarding vortex modeling, instabilities and unsteadiness. Numerous studies are concerned with the development and application of methods for the experimental and numerical simulations to represent and analyze all stages of the wake vortex lifespan (Fig. 2). Also, means to influence the wake vortex system for reducing the wake vortex hazard are addressed. A further emphasis of the investigations is on the simulation and forecast of the wake vortex behaviour in the atmosphere as well as the development and use of detection and wake vortex warning systems. In the following, an overview of these research fields is given. In view of the relevance of the wake vortex problem for the European aircraft industry different research projects and integrated research programs were and are conducted, e.g. EuroWake (1996– 1999) [73], Wirbelschleppe I/II (1999–2006) [51], C-Wake (2000– 2003) [74–77], WakeNet2-Europe (2003–2006), WakeNet3-Europe (2008–2010) [140], AWIATOR (2002–2007) [63], IHK (2005–2007) [84] and FAR-Wake (2005–2007) [139]. They are concerned with the topics wake vortex forecast, detection and characterization and

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Nomenclature B

Relative increase in lateral distance between the two trailing vortices (m) b Wing span (m) b0 Lateral distance between the two trailing vortices (m) b~ 0 Lateral position of the free circulation center of multiple vortex systems (m) bH Lateral distance of main vortices of a four-vortex system (m) bN Lateral distance of minor vortices of a four-vortex system (m) CL Lift coefficient, L/qNF CL0 Lift coefficient at zero angle of attack CLa Lift slope Cl,f Wake vortex induced rolling moment coefficient c Chord (wing) (m) d Diameter (m) d Distance between neighbouring vortices (m) F Surface area (wing) (m2) f Frequency (Hz) fM Sampling frequency (Hz) fA Excitation frequency (Hz) Gn Circulation parameter Gopt Maximum growth rate for optimal perturbations g Gravitational acceleration, 9.81 m/s2 k Reduced frequency, f ðb=2Þ=U1 kA Reduced excitation frequency, fA(b/2)/UN kV Reduced frequency of vortex merging instability ka Axial wave number L Lift (N) l Length in chord direction (m) lm Wing mean aerodynamic chord (m) m Azimuthal wave number mA/C Aircraft mass (kg) N Number of sampled values; number of revolutions nb Number of frequency bands p Pressure (N/m2) 2 qN Freestream dynamic pressure, ðr1 =2ÞU1 (N/m2) Rb Ratio of lateral distances, bN/bH Rcv Ratio of viscous and vorticity radius, rc/rv RV,krit Critical ratio of viscous core radius to vortex distance at merging, rc/d RG Circulation ratio, GN/GH Relm Reynolds number, U1 lm =n ReG Vortex Reynolds number, G=n rc, rv Viscous core radius; vorticity radius (m) Suui Power spectral densities of velocity fluctuations uui [(m/s)2/Hz] s Wing half span (m) s Spanwise load factor, b0/b T Time interval (s) Tux, Tuy,Tuz Turbulence intensities, urms/UN, vrms/UN, wrms/UN t Time (s) tV Time for vortex merging (s) t0 Starting time; time scale of wake vortex downward movement (s) U, UN Flight speed; freestream velocity (m/s) Vx, Vr, Vy Axial, radial and azimuthal (circumferential) velocity (m/s) u, v, w Axial (streamwise), lateral (spanwise) and vertical velocity (m/s)

u,v,w

Axial (streamwise), lateral (spanwise) and vertical mean velocity (m/s) qffiffiffiffiffiffiffi u0 ,v0 ,w0 Fluctuation part of u, v, w; uui (m/s) urms, vrms, wrms rms velocities of u0 , v0 , w0 ; urms ¼ uu2 (m/s) w0 Wake vortex induced vertical velocity (m/s) x, y, z Cartesian coordinates xn, yn, zn Non-dimensional coordinates in axial, lateral and vertical directions, xn ¼ x/b, yn ¼2y/b, zn ¼2z/b a Angle of attack (deg.) b Angle of sideslip (deg.) b Constant of Lamb–Oseen vortex model d Winglet flap deflection (deg.) Df Frequency resolution (Hz) e Horizontal tail plane setting (deg.) er Radial deformation/shear (1/s) G Circulation (m2/s) G0 Root circulation (m2/s) GH, GN Circulation of main vortices; circulation of minor vortices (m2/s) Z Slat, flap and spoiler deflection angle, respectively (deg.) j25 Wing sweep (related to quarter line) (deg.) L Aspect ratio l Taper ratio l Wave length (m) n Kinematic viscosity (m2/s) nt Eddy viscosity (m2/s) y Azimuthal coordinate (deg.) y0 Inclination angle of instability propagation plane (deg.) r, rN Density, ambient density (kg/m3) s, sn Growth rate (1/s); non-dimensional growth rate t, tn Non-dimensional time o Angular frequency (1/s) o Vorticity (1/s) x Aileron deflection angle (deg.) x, xn Non-dimensional axial vorticity Subscripts: Ambient conditions Four-vortex system Four-vortex system with counter-rotating main and minor vortices A Excitation Crouch Crouch type instability Crow Crow type instability f Follower aircraft (wake encountering aircraft) IF, OF Inboard, outboard flap IS, MS, OS Inboard, midboard, outboard slat max Maximum min Minimum osc Oscillating rev Revolution Widnall Widnall type instability x, y, z Axial, lateral and vertical directions N 4WS 4WS–

Superscripts N n

4

Non-dimensional; normalized Non-dimensional; related to elliptical lift distribution Amplitude

91

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C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Abbreviations AWIATOR Aircraft WIng with Advanced Technology OpeRation DFS Differential Flap Setting DNW German–Dutch Wind Tunnels E403 Four engine large transport aircraft (LTA reference configuration 1) HTV Horizontal Tail plane Vortex ICAO International Civil Aviation Organization IFR Instrumental Flight Rules IFV Inboard Flap Vortex INV Inboard Nacelle Vortex LIDAR LIght Detection And Ranging

wake vortex alleviation, [63,72–77]. Thereby, the gained knowledge essentially aims at three partially competitive directions with the intention to adapt the current separation distances to the actual hazard situation: 1. Detection: A wake vortex encounter is a priori avoided by wake vortex detection with on-board systems [30,58] and/or ground based systems.1 2. Forecast: Based on the analysis of the actual situation, namely the combination of types of airplanes following each other, atmospheric conditions (weather) and airspace conditions (air traffic control, regulations), a forecast of the wake vortex hazard is made to adapt the separation distances [51,68,71, 106,112,118,121]. 3. Alleviation: The wake vortex hazard in terms of the induced rolling moment on a follower aircraft is diminished to a tolerable or uncritical value by configurational means [22,23].

2.2. Small and large-scale tests Configuration elements for wake vortex alleviation are typically studied in model tests. In the context of experiments using small scale models, the entire downstream development of the wake vortex system can be analyzed with today’s methods.

2.2.1. Near field–wind tunnel tests Because of the usually limited test section length, wind tunnel investigations concentrate on the near field, characterized by vortex formation and the roll-up process (Fig. 3). The measurements are performed using usually 5-hole-probes [32, 33] and/or ‘‘Particle Image Velocimetry’’ (PIV) [135], or regarding the determination of time-dependent flowfield velocities by means of hot wire anemometry [3,11]. Numerous works document velocity and vorticity fields for various configurations of typical transport aircraft, starting in the seventies until today [16,72–76,81,8,117]. Further, the interaction of the engine jets with the wake vortices is considered [23,48,78]. Also, the Reynolds number influence is studied with respect to transfer results of small scale tests to full scale configurations [75]. 1

Already developed ground based systems are: WSWS: ‘‘Wirbelschleppen– Warnsystem’’ [57]; AVOSS: ‘‘Aircraft VOrtex Spacing System’’ [64,65,101]; HALS/ DTOP: ‘‘High Approach Landing System/Dual Treshold Operation’’ [49,50]. Currently, none of these systems is in continous operational use.

LLF LTA LVV MTOW OFV OFIV ONV PIV QDV rms TAK WFV WRP WTV

Large Low-Speed Facility Large Transport Aircraft Low Vorticity Vortex Maximum Take-Off Weight Outboard Flap Vortex Outboard Flap Inboard Vortex Outboard Nacelle Vortex Partcile Image Velocimetry Quickly Decaying Vortex root mean square Twin aisle configuration (LTA reference configuration 2) Wing-Fuselage Vortex Wing tip Reference Point Wing Tip Vortex

2.2.2. Mid- and far-field–water tunnel and catapult tests Following the extended near field, the mid and far field define the regions where the trailing vortices persist for a long distance downstream and the vortex strength does not considerably decrease. The following decay range marks the more or less rapid destruction of the wake vortices. The analysis of the mid- and farfield region and the decay range succeeds in model tests, in particular, with the use of water towing tanks and optical measuring technique by means of PIV. Such tests need towing tanks featuring extremely long measurement sections, which found a new operational area in the context of the wake vortex problem as suitable test facilities, [54,76,134]. Contrary to the wind tunnel with incident flow and fixed model, the model is moved through the resting fluid in the towing tank. For the minimization of surface effects the model is in the depth of water within the range of one model span. It is held from above by a profiled model sting, which serves also as tow bar. Matching the correct flight situation the wake vortices move downward and are not affected by the suspension system. Due to the high forces acting on the model and for the avoidance of cavitation a driving speed of approx. 3–6 m/s (Relm E0.25  106–0.5  106) is commonly used. Far field ranges up to 150–200 spans are possible, whereby the influence of wall and end effects is to be avoided. Also catapult tests are used, which require however a clearly higher expenditure regarding the catapult model [22]. Apart from the developments of the required experimental techniques the investigations concentrate on the changes in the evolution of the wake vortices, i.e. vorticity dispersion and diffusion and mutual

Increased turbulence; increased structural dynamics loads

Upwash Downwash

Loss of lift: loss of altitude / reduced climb rate; increased turbulence Fig. 1. Wake vortex hazard, cf. [120].

Up-/ Downwash Induced rolling moment

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Table 1 ICAO separation distances for instrumental flight rules (IFR). Leader aircraft (max. take-off weight)

Follower aircraft

Separation (NM/km)

Time delay (s) (approach speed 70 m/s)

Heavy (4136.000 kg) Heavy (4136.000 kg) Heavy (4136.000 kg) Medium (r136.000 kg) ( Z7.000 kg) Light (o 7.000 kg)

Heavy Medium Light Medium Light Medium Light

4.0/7.4 5.0/9.3 6.0/11.1 3.0/5.6 4.0/7.4 3.0/5.6 3.0/5.6

106 132 159 79 106 79 79

The minimum radar separation refers to 3 NM (79 s) or 2.5 NM (66 s).

Extended near field

Near field

Decay region

Mid field / far field

x

U∞

b

b0

lµ

x/b ≤ 10

x/lµ = O(1)

x/b > 100

Γ0

b0

–Γ0

Vg Vθ

y

w

U∞ x

velocities in the real atmosphere the LIDAR technology (‘‘LIght Detection And Ranging’’) is used [133,61]. A laser beam operating in the invisible range reflects itself at aerosols, in particular, at those in the range of the detecting wake vortex, and the returned signal provides a measure for the wake velocity based on doppler shift. In practice, the Lidar beam scans alternating between two end positions and combs thereby the wake vortex range. Because of the strongly bundled ray of light always only a small cutout of the wake vortex is measurable at one time. Only more swivels seize the wake vortex within its entire range. From the sections of this onedimensional measurement the velocity profile of the wake vortex is built up in digital rework. Distortions due to vortex drift by strong air turbulence or cross-wind can be reduced by adjusting the scanning range. A clearly higher measure of accuracy results from a multiple arrangement of Lidar equipments (triangulation). Such an arrangement makes it possible to improve positioning and to derive a corresponding length information [86,87]. Considering the usually asymmetrical structure of the wake vortex the velocity profile depends furthermore on the angle, under which the wake vortex is cut by the ray of light, so that this has to be considered with the interpretation of the data. Also, pulsed Lidar technology is used which offers the advantage that only one Lidar is necessary for working at longer focal range (600–1200 m). It allows an installation at important commercial hub airports such as Frankfurt, Paris CDG, and London Heathrow.

2.3. Numerical investigations

Fig. 2. Stages of wake vortex lifespan.

z

93

u v

¨ Fig. 3. Wake vortex evolution and roll-up process, cf. Hunecke [73].

interaction occuring downstream. Especially, the interest is directed toward the instability mechanisms, which leads to the rapid decay of the wake vortices and the parameters determining this physical process.

2.2.3. Flight tests Finally, flight tests show the wake vortex behaviour for the real aircraft under atmospheric conditions, which can be treated in model tests only insufficiently. For measuring the wake vortex

A large number of investigations take place in the field of numerical simulations. The computation of the entire wake vortex system of an aircraft configuration, i.e. from vortex development and evolution up to the decay, exceeds also the today’s available computer capacities, particularly, if regarding realistic Reynolds numbers2 (Re  107). Therefore, the flow around the aircraft configuration, the wake vortex roll-up process in the near field and the wake vortex development in the mid- and far-field are treated usually as individual problems. The interfaces are frequently based on velocity or vorticity fields at defined wake positions. Thus, the integration and/or the comparison of experimental data is also possible. The sectional treatment permits also the use of differently efficient or complex computational tools in consideration of the necessary or desired accuracy for each case [138].

2.3.1. Near field For the simulation of the flow around the aircraft configuration and thus the computation of the wake vortex near field, Euler and Reynolds Averaged Navier Stokes (RANS)—methods are typically used [88,130]. The necessary grid resolution and the set-up of specific computational parameters are frequently calibrated with experimental data, in order to examine then purely computationally configuration variants or to provide spatially sufficiently resolved initial values for the calculations in the extended near field. On the basis of a given velocity or vorticity distribution and usually synthetic turbulence data the roll-up process can be simulated quasi two-dimensionally by large eddy simulation (LES) or Direct Numeric Simulation (DNS) in very good agreement with experimental data [129]. Considering real time simulation, also analytical tools like Betz methods are used [4,53,119]. 2 The required number of grid points (cells) is proportional to Re9/4, limiting the use of methods like ‘‘Direct Numerical Simulation’’ or ‘‘Large Eddy Simulation’’ to low Reynolds number cases and/or to simple geometries.

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2.3.2. Far field and atmospheric influences For the wake vortex development in the far field and the simulation of the wake vortex decay due to instabilities computational methods are used such as vortex filament methods [25,43,110]. Thereby, the linear range of instabilities can be modeled whereas nonlinear decay processes are not represented. For the latter it requires again the application of the LES simulation [83]. Individual cases were treated by highly expensive LES or DNS calculations using staggered grids [89,129]. Systematic investigations or parameter variations require therefore a compromise from necessary modeling degree and costs in the sense of computational effort and computational time. Further, comprehensive investigations and developments of simulation tools are dedicated to the description and forecast of the wake vortex evolution in the far field considering atmospheric conditions, like atmospheric stratification, turbulence, cross and shear winds and ground effects [18,19,31,69,70,94,97,60, 107–109,111,123].

2.4. Fundamental physical aspects A variety of research activities concentrate on the fine structures and details of the wake vortices [34] the merging of co-rotating vortices and the interaction of counter-rotating vortices [35,93,98], as well as on unsteady effects and turbulence, [82,99]. These investigations take place on basis of analytical and numerical representations typically using simplified model configurations (Fig. 4). The instability contributing to the actual decay of the wake vortex system is known as Crow instability [28], which becomes apparent in a sinusoidal distortion of the vortex trajectories with exponentially increasing amplitude of lateral deflection (Fig. 2). Crow made first time an analytical description of this phenomenon, which is derived from the mutual induction of the counter-rotating vortex pair exposed to an existing initial disturbance. Apart from the long wave Crow instability (wavelength is approximately the eightfold of the lateral wake vortex distance) instabilities with clearly smaller wavelengths can occur, for example, when two vortex pairs are present (e.g. flap and wing tip vortices in the extended near field). Further, instabilities with wavelengths within the range of the vortex core diameter can be detected [137]. Short wave instabilities play an important role for the wake vortex merging process at higher Reynolds numbers [92,98]. The instabilities mentioned reveal

themselves by characteristic frequencies in the power spectra of the measured velocity fluctuations [8,11]. 2.5. Alleviation strategies Fundamental ideas for the reduction of the wake vortex hazard are aimed to affect the spatial vorticity distribution in the near field, thus alleviating the induced rolling moment (low vorticity vortex, LVV), or to enhance inherent instability mechanisms of the vortex systems, in order to enforce an accelerated decay (quickly decaying vortex, QDV). A variety of passive means in the sense of additional or changed configuration elements, like wing fins, flap edge elements, spoiler elements, vortex plates, etc., were and are tested [23,38,102,105]. Further, special wake vortex topologies are regarded to trigger inherent instabilities [47,110,129]. In addition, active solutions like oscillating flaps and/or spoilers are studied [26,27]. The fact has to be stressed that for wake vortex reduction the suggested configurational means will not have any unfavorable effects on the flight characteristics and performance, i.e. in context of certification the flight envelope must remain unchanged. Furthermore, with all these considerations, the question is to be answered, to what extent the modifications made at the aircraft, i.e. in the near field, are still effective in the far field to rearrange the vorticity distribution for wake vortex alleviation and/or to enhance the wake vortex decay.

3. Near field characteristics The results of the experimental investigations presented herein are typically assigned to large transport aircraft high-lift configurations with regard to approach conditions. Section 3.1 gives an overview on wake vortex development and associated quantities used for wake vortex analysis. Section 3.2 informs about the main configurational details of the considered wind tunnel models ‘‘E403’’ (four-engine configuration; baseline/reference configuration 1) and ‘‘TAK’’ (twin aisle configuration; baseline/reference configuration 2) including the wake vortex related aerodynamic quantities. The evolution of the wake vortex system in the near field is discussed in Section 3.3, while Section 3.4 concentrates on the wake vortex development in the extended near field. The investigated configurations serve also as a reference for means of wake vortex alleviation discussed in Chapter 5. Section 3.5 summarizes the major findings. 3.1. Classification and basic quantities Considering the downstream development, a vortex wake can be divided into four regions (Fig. 2):

Viscous core radius

rc rv

Vorticity radius (outer core radius)

y w ( y)

b0 = s b Fig. 4. Definition of viscous core radius rc and vorticity radius rv for the pair of rolled-up trailing vortices (assumption in vortex models: counter-rotating axisymmetrical vortices of equal strength).

(i) The near field, x/br0.5, (x/lm oO(1)), which is characterized by the formation of highly concentrated vortices shed at all surface discontinuities. (ii) The extended near field, 0.5 ox/b r10, where the wake rollup process takes place and the merging of dominant vortices (e.g. shed at flap edge, wing tip, etc.) occurs, leads gradually to two counter-rotating vortices. (iii) The mid and far field, 10 ox/br100, where the wake is descending in the atmosphere and linear instabilities emerge. (iv) The dispersion region, x/b4  100, where fully developed instabilities cause a strong interaction between the two vortices until they collapse. The discussion and analysis of the wake vortex flowfields is based on the following quantities: Mean velocities. The velocity field is described by the time dependent axial, lateral and vertical velocities (u,v,w). They are

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

typically expressed by a mean (time averaged) value u and a fluctuation part u0 , shown here for the axial velocity component u(x,y,z,t): uðx,y,z,tÞ ¼ uðx,y,zÞ þ uuðx,y,z,tÞ

ð1Þ

The time averaged value and the mean square value yield: Z Z 1 t0 þ T 1 t0 þ T u ¼ lim uðtÞ dt ðaÞ; uu2 ¼ lim ½uðtÞu2 dt ðbÞ: t-1 T t t-1 T t 0 0 ð2Þ For the presentation of dimensionless quantities, the mean axial, lateral and vertical components, u,v,w, are related to the freestream velocity UN. Mean axial vorticity: The axial vorticity component ox ¼ ð@w=dy@v=@zÞ is used to quantify the strength of the wake vortices. Taking into account the freestream velocity UN and the wing half span b/2 leads to a dimensionless representation:

x¼

ox b 2U1

ð3Þ

Circulation: Based on straight level flight, the balance of lift 2 ðb2 =LÞ ¼ mA=C g. force and aircraft weight results in L ¼ CL ðr1 =2ÞU1 The root circulation G0 is then obtained applying the Kutta– Joukowski theorem, dL¼ rNUNG(y)dy, with L¼ rNUNG0b0. The quantity b0 denotes the lateral distance of the rolled-up vortices reflecting the left and right centers of the free circulation. Introducing the spanwise load factor s ¼b0/b, one obtains Z C U b 1 þ b=2 GðyÞ b0 ðbÞ ð4Þ G0 ¼ L 1 ðaÞ; s ¼ dy ¼ 2Ls b b=2 G0 b Regarding an qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

elliptical

circulation

distribution,

GðyÞ ¼

G0 1ð2y=bÞ2 , the spanwise load factor s results in s¼sn ¼ p/4. The corresponding root circulation is then given by

G0 ¼

2CL U1 b

pL

ðaÞ;

G ¼

G ðbÞ: G0

G0 2pb0

¼

CL U1 ðaÞ; 4pLs2

w0 ¼

4CL U1

p3 L

ðbÞ:

ð6Þ

The associated time scales t0 and t0 , respectively, define the time interval at which the vortex pair moves downward by a distance equal to the vortex spacing b0: t0 ¼

b0 2pðsbÞ2 Lb ¼ ¼ 4ps3 ðaÞ; CL U1 w0 G0

t0 ¼

p4 Lb ðbÞ 16 CL U1

ð7Þ

The timescale t0 is a measure of the ‘‘wake vortex age’’ depending strongly on the load factor s: t0  s3. The dimensionless time scales t and t* are obtained by

t¼

t x b 1 CL ¼ ¼ x 3 ðaÞ; t0 b U1 t0 s 4pL

Compared to the non-dimensional downstream distance x*¼x/b, the dimensionless time t allows an analysis taking load factor s, lift coefficient CL and aspect ratio L into account. The relation for t* refers to the elliptical lift distribution as aerodynamic reference loading. Then, CL and L remain as the only configuration parameters. Turbulence intensities: The root mean square (rms) values of the axial, lateral and vertical velocity fluctuations, u0 ,v0 ,w0 , are typically normalized with the freestream velocity UN. Here, they are denoted as Tux, Tuy and Tuz that are used to analyze the wake vortex turbulence characteristics: qffiffiffiffiffiffiffi qffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi uu2 vu2 wu2 ðaÞ; Tuy ¼ ðbÞ; Tuz ¼ ðcÞ: ð9Þ Tux ¼ U1 U1 U1 Turbulent shear stresses are presented in the following form: uuvu uuwu vuwu ; ; 2 2 2 U1 U1 U1

ð10Þ

Spectral densities: The power spectral densities Suu of the velocity fluctuations are inspected to identify dominant frequencies associated with specific unsteady effects or instability mechanisms, respectively. The power spectra are calculated applying Fast Fourier Transformation [7]. The dimensionless power spectral densities SN uu are normalized with the frequency resolution and the mean square value, as written exemplarily for the axial velocity fluctuations3 : SN uu ¼ Suu

Df uu2

;

Df ¼

fM 2nb

ð11Þ

Induced rolling moment: The wake vortex impact on a follower aircraft (index f) is typically quantified by the induced rolling moment: Z CLa,f Lf U1 þ 1 wðZÞ lf ðZÞ Cl,f ¼ ZdZ; Z ¼ 2y=bf ð12Þ 4 Uf 1 U1 bf

ð5Þ

The superscript (n) refers to the elliptical circulation or lift distribution, respectively. The associated relations are used to define a common basis when comparing wake vortex parameters to become independent of the actual lift distribution. Induced velocity and time scales: The two counter-rotating trailing vortices of nearly equal strength forms the aircraft wake after the roll-up process is completed (Fig. 3). Using the Biot– Savart law the induced velocity w0 on the vortex centers results in w0 ¼

95

t ¼

t 16CL ¼ x 4 ðbÞ: t0 p L

ð8Þ

This rolling moment coefficient depends on the wake vortex induced vertical velocity ðw=U1 Þ (Fig. 4), the velocity ratio of leading and following aircrafts (UN/Uf) and the lift slope CLa,f, aspect ratio Lf and the inverse relative span (lf/bf) of the follower aircraft. 3.2. Wind tunnel facilities, models and experimental techniques The wake vortex investigations are conducted in the wind tunnel facility C of the Institute of Aerodynamics (AER) at ¨ Munchen ¨ Technische Universitat (TUM) employing advanced ¨ hot-wire anemometry. The wind tunnel C is of the Gottingen type and has a closed test section of 1.8 m in height, 2.7 m in width and 21 m in length [8]. The test section length covers a wake distance of approximately 5–6 spans referring to half models with scales of about 1:20C1:30 regarding transport aircraft configurations. The test section ceiling is adjustable to control the axial pressure gradient along the test section. The turbulence level at the nozzle exit is less than 0.5%. Half models of typical four-engine (E4) Large Transport Aircraft (LTA) are investigated named ‘‘E403’’ and ‘‘TAK’’ (twin aisle configuration) representing the reference configurations 1 and 2 (Fig. 5). Overall dimensions and configuration details are 3 Here, a number of nb ¼ 1024 frequency bands are used resulting in a frequency resolution of Df ¼1.46 Hz.

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C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Wing tip Reference Point (WRP)

b/2 lµ

Peniche

±z

±y

±x

Traversing system

Triple sensor hot-wire probe

Test section: 1.8m x 2.7m x 21m Fig. 5. Half models of typical large transport aircraft serving as reference configurations 1 (model E403) and 2 (model TAK): (a) geometry; (b) reference configuration1 (model E403) mounted in test section of TUM-AER wind tunnel C and (c) reference configuration 2 (model TAK).

listed in Table 2. The models are made of stainless steel and equipped with fully adjustable flaps, slats, ailerons and horizontal tail plane. The experiments concentrate on the approach configuration, with the setting of the high-lift devices as given in Table 2. The horizontal tail plane (HTP) setting is chosen to match trim conditions. The engines are designed as through-flow nacelles and fitted with nacelle strakes in case of the E403 configuration. The models are positioned on the tunnel floor with the wing tip reference point (WRP) at about 2.6 m downstream of the nozzle exit, and the wing tip pointing upward (Fig. 5). The WRP is the position of the trailing edge at the winglet tip at an angle of attack of a ¼01, where x* ¼x/b¼0. A peniche of 0.095 m height is used to raise the model fuselage above the wind tunnel floor boundary layer. The model wing box is attached to the driven shaft of a computer controlled model support located below the test section floor, allowing a precise angle of attack setting (tolerance: Da ¼ 70.021). The test section of the wind tunnel C is further equipped with a three-axis probe traversing system giving minimum steps of 70.2 mm in axial, lateral and vertical directions. The vortex wake is measured in several cross flow planes orientated perpendicular to the freestream direction at distances of x*¼ 0.37, 1.0, 2.0, 3.0, 4.0, 4.5 and 5.6 downstream of the WRP. In regions of high flow gradients, i.e. in the areas of vorticity layers and vortex cores, the survey points are closely spaced with a relative grid resolution of 0.004 in spanwise and 0.006 in vertical direction based on the wing span. Outside these regions, the relative spacing is gradually enlarged to 0.024 laterally and 0.036 vertically. Regarding the susceptibility of vortical structures to intrusive measurements, it was found that

the presence of the hot-wire probe has no marked influence on the wake vortex formation and evolution [81]. In particular, a triple-wire probe is used that is operated by a multichannel constant temperature anemometer system to measure time series of axial, lateral and vertical velocities [7]. The tungsten wires are platinum plated and have a diameter of 5 mm and a length of approximately 1.25 mm. The wires are arranged perpendicular to each other to achieve best angular resolution. An additional temperature probe is employed to correct anemometer output voltages if ambient flow temperature varies. A sampling rate of 3000 Hz (Nyquist frequency 1500 Hz), a low-pass filter frequency of 1000 Hz and a sampling time of 6.4 s were chosen. The sampling time corresponds to 19,200 values per wire and survey point. The signals are digitized with 16 bit precision through a 16 channel simultaneous sampling A/D converter. The sampling parameters are achieved by preliminary tests to ensure that all relevant flowfield phenomena are detected. The anemometer output signals are converted into the time-dependent velocity components u, v and w using a lookup table previously obtained from the direct velocity- and angle-dependent calibration of the hot-wire probe [7]. Based on statistical error evaluation, accuracies are in the range of 1% for mean quantities, 2.5% for rms quantities (turbulence intensities) and 4% for spectral densities [8]. Since the wake measurements are carried out in wind tunnel C, limited to a continous maximum freestream velocity of UN ¼25 m/s, the model is fitted with transition strips placed along the wing leading-edge and in the front section of fuselage and

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

half model tests, the maximum loads refer to 1500 N in the axial direction, 73000 N in the normal direction and 7700 Nm in pitching moment. Therefore, minimum detectable loads for axial force, normal force and pitching moment are 0.38 N, 1.5 N, and 0.18 Nm, respectively, resulting in an accuracy in the lift coefficient of DCL ¼0.003–0.012 for the present tests. The lift polars indicate that there is no significant difference in the lift coefficients between the two Reynolds number cases which hold even for the high lift and stall regimes (Fig. 6b). Regarding the present wake vortex analysis, the lift coefficients attributed to approach flight conditions are far below the maximum lift values. Corresponding wool tuft analysis demonstrates that attached flow is present on wing and control surfaces (Fig. 6a). The following features characterize the wake vortex system of the four-engine large transport aircraft in approach configuration considering the near field and extended near field. The related basic vortex parameters are collected in Table 3.

nacelles (Fig. 6a). Thus, fully turbulent boundary layers are enforced on the wing as well as on fuselage and nacelles, especially to avoid laminar separation at higher lift levels. Due to the high adverse pressure gradients turbulent boundary layers exist on slats and flaps without tripping. The Reynolds number influence on the aerodynamic coefficients is studied in wind tunnel A (test section dimensions: 1.8 m  2.4 m  4.8 m) undertaking force measurements at freestream velocities of UN ¼25 m/s (Relm ¼ 0:525  106 ) and UN ¼ 50 m/s (Relm ¼ 1:05  106 ) [8]. Measurement accuracies related to the underfloor six-component wind tunnel balance are 0.025% based on maximum nominal loads of the balance load cells. Conducting

Table 2 Geometric and configurational data of LTA half models E403 and TAK. Large transport aircraft half models Scale

E403 1: 22.5

97

TAK 1: 19.25

3.3. Near field properties Wing and fuselage Wing Span Half span Mean aerodynamic chord Surface area Aspect ratio Taper ratio Sweep (25% line)

b s lm F

j25

2.602 m 1.301 m 0.323 m 0.7278 m2 9.302 0.289 29.801

2.982 m 1.491 m 0.357 m 0.8804 m2 10.100 0.300 31.281

Fuselage Overall length Diameter

lR dR

2.605 m 0.124 m

2.907 m 0.293 m

High lift devices Slat Inboard slat Midboard slat Outboard slat

ZIS ZMS ZOS

19.61 23.01 26.01

19.61 23.01 23.01

Flap Inboard flap Outboard flap

ZIF ZOF

26.01 26.01

26.01 26.01

Aileron Inboard aileron Outboard aileron

xI xO

10.01 10.01

5.01 5.01

Approach conditions Angle of attack Horizontal tail plane setting

a e

9.51  9.51

7.01  6.01

L l

Axial vorticity and vortex topology: The wake near field of a transport aircraft in high lift configuration is characterized by a heterogeneous vortex system (x* ¼0.37, Fig. 7a). Besides the wing tip vortices, there are also vortices shed at the side edges of slats, flaps and ailerons. In addition, strong nacelle vortices develop due to the oblique flow on the nacelle caused by wing sweep and inclination. Further, nacelle strakes, slat horns, flap track fairings and other geometric discontinuities create a variety of concentrated small scale vortices. Focusing on the dominant single vortices of the wing half span domain, the near field is typically characterized by six main vortices, namely the wing tip vortex (WTV), the outboard flap vortex (OTV), the outer and inner engine nacelle vortices (ONV and INV), the wing-fuselage vortex (WFV) and the horizontal tailplane vortex (HTV). The WTV, OFV, ONV and INV have the same sense of rotation which is here of positive sign, i.e. positive vorticity or circulation, referring to the right wing of the lift producing configuration. The WFV and HTV are characterized by an opposite sense of rotation or negative vorticity. For the WFV, this negative vorticity is caused by the change in the circulation gradient at the wing-fuselage junction, while for the HTV the tailplane produces negative lift with respect to a trimmed configuration. A qualitative representation of the spanwise circulation distribution G(y) and the circulation

2 Transition strips

1.8 1.6 1.4

CL

1.2

Rel = 1.050 · 10 Rel = 0.525 · 10

6

6

1 0.8 0.6 0.4 0.2

Baseline, U∞ = 25m/s Baseline, U∞ = 50m/s

0 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 α [deg] Fig. 6. Wool tuft flow visualization on wing and lift polar CL(a) of the reference configuration TAK (‘‘TAK baseline’’): (a) wool tuft flow visualization and (b) lift polar CL(a).

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C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Table 3 Wake flow parameters for LTA half models E403 and TAK. Large transport aircraft half models Freestream conditions Velocity Reynolds number Wake vortex parameters Lift coefficient Circulation Induced velocitiy

TAK

UN Relm

(m/s) –

25 0.475  106

25 0.525  106

CL

– (m2/s) (m/s) – (s) –

1.76 7.835 0.610 0.024 3.349 0.461  106

1.44 6.767 0.460 0.018 5.903 0.389  106

G0 w0 w0 /UN t0 ReG

Time scale Vortex Reynolds number

E403

Dominant vortices:

0.37 1

INV: INV Inboard Nacelle Vortex WFV: WFV Wing Fuselage Vortex

5.56

4

x* 1.1

WTV

1 0.9

ξ−levels 17.80 15.90 14.00 12.10 10.20 8.30 6.40 4.50 2.60 0.70 –1.20 –3.10 –5.00

0.8 0.7

ONV

0.6

y*

ONV: ONV Outboard Nacelle Vortex

3

U∞

WTV: WTV Wing Tip Vortex OFV: OFV Outboard Flap Vortex

2

OFV

0.5

INV

0.4 0.3

HTV

0.2

WFV

0.1 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

z* Axial vorticity distribution ξ

HTV: HTV Horizontal TailplaneVortex

Shedding of dominant near field vortices

Γ U∞

y

d Γ/dy ONV INV WFV

WTV OFV Fig. 7. Non-dimensional axial vorticity distribution at xn ¼ 0.37 for reference configuration 1 (E403 model) and shedding locations of dominant near field vortices: (a) vortex topology and (b) qualitative circulation distribution.

gradient dG/dy is given in Fig. 7b. Marked changes in the circulation gradient reflect the evolution of the main near field vortices described above. The dominant wing vortices are linked by the wing vortex sheet emanating from the trailing-edge due to the difference in the lateral velocities of wing upper and lower side. The overall near field vortex topology for both configurations E403 and TAK is very similar as the wing geometry and high lift elements of these configurations are characterized by the same features (Fig. 8). In particular, the TAK nacelle vortices exhibit higher axial vorticity peaks than those of the E403 configuration. This holds also for the TAK flap vortex. But the axial vorticity maxima attributed to the wing tip vortices show nearly the same peak values for both configurations, which is also the case for the horizontal tail plane vortex. It must be considered that the TAK

wake vortex system is not as ‘‘old’’ as that of the E403 configuration, which is expressed by comparing the related time scales:     t0,TAK w0,TAK t ¼ 0:6575 ðaÞ; ¼ TAK   t0,E403 w0,E403 tE403 x ¼ const    CL,TAK LE403 ¼ ¼ 0:7535 ðbÞ ð13Þ CL,E403 LTAK x ¼ const

This situation is further indicated by the downward movement of the wing vortex sheet, which is less advanced in case of the TAK compared to the E403 configuration (Eq. (13)). Also, the counterclockwise rotation of the OFV around the stronger ONV is slightly delayed for the TAK model.

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

99

ξ–levels 0.3

0.3 0.2

E403–baseline

WTV 58

0 -0.1

WFV -6.5

HTV -36

TAK–baseline

0.1

HTV -39

0 -0.1

-0.2 -0.3

ONV 55

z*

z*

0.1

0.2

INV 30

OFV 17

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

WTV 57 ONV 70

WFV

-0.2 INV

-0.3

OFV 27.6

57 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

Fig. 8. Field distributions of non-dimensional axial vorticity x at xn ¼0.37 for reference configurations 1 (E403 model: tn ¼ 0.012) and 2 (TAK model: tn ¼0.009).

accuracy to the locations of the axial vorticity and turbulence intensity maxima, also used to determine center positions of the dominant vortices. The remaining wing  vortex sheet is marked by 2  a lateral shear stress band of vuwu=U1 4 0:0002, clearly distinguishing this layer from the undisturbed flowfield.

Turbulence intensities and Reynolds stresses: The near field wake vortex sheet is indicated in the cross flow plane by a lateral band of increased velocity fluctuations (Fig. 9). In addition to the turbulent wing boundary layer it results from the shear layer due to the difference in direction of the lateral velocities at the confluence of the wing flow from upper and lower side at the trailing edge. Further contributions to the turbulent wake are associated with local flow separation due to the wing geometric discontinuities (side edges, etc.), leading to the formation of large and small scale vortices. The lateral zone of increased turbulence intensity is clearly separated from the surrounding flowfield. The latter shows very low turbulence levels of about 0.5% according to freestream conditions while the turbulence levels of the wing vortex sheet are in the range of 5–7%.4 These levels characterize the intensities of the velocity fluctuations in axial, lateral and vertical directions (Tux,Tuy,Tuz: Fig. 9a–c). The overall spanwise patterns of the turbulence intensity fields in the three coordinate directions exhibit no significant differences but local variations can be detected at the areas of the embedded dominant near field vortices. At the plane of symmetry (y* ¼0, z* E 0.1), the interfering turbulent boundary layers of wing and fuselage influence the wake vortex evolution creating a larger zone of increased turbulence intensity. Local turbulence maxima can be attributed to the dominant near field vortices where the turbulence peaks indicate the vortex cores. The turbulence intensities of the vertical velocity fluctuations reach levels of Tuz E10–13% for the engine nacelle vortices (INV and ONV), Tuz E7 9% for the flap vortex (OFV) and Tuz E8 9% for the wing tip vortex (WTV). The gradients and curvatures in the mean axial and radial vortex velocity profiles contribute to the increase in turbulence, but also the phenomenon of ‘‘meandering’’ is of relevance representing random fluctuations of the vortex center around a mean position [34,82] (cf. Fig. 36.) The distribution of the non-dimensional Reynolds stress 2 component of the cross flow plane, vuwu=U1 , is illustrated in Fig. 10 including a carpet and contour plot. The latter is aimed to highlight the differences in sign. The discussion concentrates on this component because it refers to the in-plane fluctuations v0 and w0 . Each of the dominant vortices is characterized by a turbulent shear stress structure consisting of four peaks. They can be grouped in two pairs of the same sign placed along a diagonal through the vortex center where the change in direction of the lateral and vertical velocities is the largest. Thus, there is a 901 shift between the positions of the shear stress peaks, where the location of the sign change represents the vortex center. The vortex centers determined in this way correspond with good

The roll-up process of the wing vortex sheet with the merging of co-rotating vortices and the interaction of counter-rotating vortices characterizes the extended near field. This process is completed when just a single vortex remains for the left and right wings. The roll-up process typically extends over a downstream distance of about 10 wing spans. Axial vorticity and axial velocity: The main near field vortices induce cross flow velocities the maximum values of which are in the range of 25% of the freestream velocity. The non-dimensional axial vorticity distribution indicates for the reference configuration E403 the merging of the outboard flap vortex (OFV) with the outboard nacelle vortex (ONV) at x*E1.00 and t*¼0.031, (Fig. 11a). Before merging, the ONV vorticity level is much higher than that of the OFV (cf. Fig. 7a). The flow physics associated with the merging of co-rotating vortices is explained in detail in Section 4.1. The spanwise (lateral) position of the resulting main vortex OFV–ONV is approximately at y*¼y/(b/2)E0.72.5 This position reveals that the OFV–ONV is located closely to the actual center of the free circulation representing the center of the roll-up process. The axial vorticity distribution further shows that also for the TAK configuration the merging of OFV and ONV takes place at x*E1.00 (Fig. 11d). The two remaining dominant vortices of positive vorticity, namely the wing tip vortex (WTV) and the inner nacelle vortex (INV), rotate counter-clockwise around the main vortex system OFV–ONV. The latter exhibits nearly the same axial vorticity level for both the E403 and the TAK configurations. Compared to the TAK case, the E403 higher lift coefficient means an ‘‘older’’ wake vortex system where the process of passing circulation from the WTV to the main vortex system has already started. Thus, the WTV peak vorticity of the E403 configuration is lower compared to the TAK one. From the two single vortices with negative sense of rotation, the wingfuselage vortex (WFV) decreases strongly in strength when progressing downstream because the higher turbulence intensity in the fuselage region enhances its dissipation. Contrary, the horizontal tailplane vortex (HTV) remains concentrated and changes hardly its lateral position. With the on-going roll-up process the counter-clockwise rotation of the wing tip vortex (WTV) and the

4 These values correspond to the turbulence intensity levels measured typically for the flat plate turbulent boundary layer.

5 For an elliptical circulation distribution the center of the free circulation or roll-up center, respectively, is at y* ¼0.7854 according to s ¼ p/4, cf. Eq. (4).

3.4. Extended near field properties

100

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

a

0.3

E403 Baseline - x* = 0.37

E403 Baseline 0.2

0.007

WTV

0.006

z*

0.1

OFV ONV

0.005

ONV

0

0.004

HTV

WFV

WFV region

0.003

-0.1

WTV INV

0.002 0.001

-0.2

0

OFV

-0.001

INV

-0.3

-0.002

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

-0.003

y*

E403 Baseline 0.2 WTV ONV HTV

z*

z*

0.1 WFV

-0.1 -0.2 OFV INV

-0.3 0

0.1

0.2

0.3

0.2

0.4

0.6 y*

0.8

1

-0.6

-0.4

-0.2 z*

0.2

0

b

0.3

0

0

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

y*

0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

Blue:

E403 Baseline Baseline E403

v’w’/U2 < 0

WTV ONV

HTV

Red: v’w’/U2 > 0

OFV INV

0

0.1

0.2

0.3

0.4

Quadrupel extrema: pairs of positive/negative sign 0.5

0.6

0.7

0.8

0.9

1

1.1

y* 2 Fig. 10. Field distributions of non-dimensional turbulent shear stresses vuwu=U1 at xn ¼0.37 (tn ¼ 0.012) for reference configuration 1 (E403 model): (a) Carpet plot and (b) contour plot to highlight differences in sign.

0.3 E403 Baseline 0.2 WTV

z*

0.1 ONV

0

HTV

WFV

-0.1 -0.2

OFV INV

-0.3 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

y* Fig. 9. Field distributions of axial, lateral and vertical turbulence intensities, Tux, Tuy, Tuz, for the reference configuration 1 (E403 model: tn ¼ 0.012): (a) axial turbulence intensity Tux, (b) lateral turbulence intensity Tuy and (c) vertical turbulence intensity Tuz.

inboard nacelle vortex (INV) around the main vortex (OFV–ONV) continues (Fig. 11b and e). In case of the E403 configuration the distance between the WTV and the OFV–ONV decreases whereas the distance between INV and OFV increases. The reverse trend exists for the TAK configuration due to the lower aerodynamic loading on the outboard wing section. The axial vorticity distribution of the most downstream located cross flow plane (x*¼5.56; t*¼ 0.173) shows that merging of the WTV with the main vortex OFV–ONV is far advanced in case of the E403 configuration (Fig. 11c). The INV can be only detected by a weak local vorticity peak. The roll-up process is therefore already close to completion where most of the free circulation is fed to the remaining trailing vortex, here further denoted as OFV–ONV. In contrast, the TAK configuration shows for

the most downstream plane (x*¼4.5; t*¼0.105) that the WTV and OFV–ONV are clearly separated, i.e. being far from merging (Fig. 11f). Furthermore, the peak vorticity assigned to the INV is three times larger with respect to the E403 case. The HTV is now also influenced by the induction of the main vortex resulting in a counter-clockwise movement. The shift in downward and outboard direction is accompanied by a significant reduction in peak vorticity. For the TAK configuration, Fig. 12 highlights the development of the wake vortex system in the extended near field presenting the axial vorticity distributions for all measured cross flow planes. The downstream development of the peak vorticity levels xmax of the main vortices is summarized in Fig. 13a. The near field (t* o0.03) shows the largest gradients in peak vorticity reduction because turbulence intensities are high (cf. Fig. 9). During the rollup process the positive axial vorticity peaks for WTV and INV are reduced to almost zero up to t*E0.18 because vortictiy is transferred to the developing main vortex (OFV–ONV). Also, the negative vorticity peak of the HTV tends to zero up to t* E0.18, reflecting its dissipation. The reduction in peak vorticity for the OFV/ONV is compensated by vorticity feeding through merging of the OFV with the ONV and of the WTV with the main vortex (OFV–ONV). Therefore, the OFV–ONV peak vorticity stabilizes downstream at a certain level, given here by xmax, OFV–ONV, E403 E14. Reaching a nearly constant peak vorticity level points out that the formation of the remaining trailing vortex is almost completed. Besides these results, further data for the OFV–ONV peak vorticity levels are included obtained from five-hole probe measurements conducted in the German–Dutch wind tunnel facility DNW-LLF at UN ¼60 m/s [75]. Regarding the whole downstream development there is a very good agreement between TUM-AER data and the DNW reference values.

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.3

0.3

E403–Baseline

0.2

0.1 0

z*

z*

0 -0.1

HTV

WFV -2.1

OFV-ONV 27

-0.3

-0.4 -0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

E403–Baseline WTV 19.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

WTV 47.5

0.2

0.1

0.1

0

0

-0.1

-0.1 z*

z*

INV 24

WFV 1.3

0.3

0.2

-0.2 OFV-ONV 24

-0.3

OFV-ONV 29.4

ξ – levels

-0.2 -0.3

HTV -16

-0.4 INV 6

-0.5 -0.6

-0.5 -0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

HTV -23.3

INV 12.6

TAK–Baseline 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

y*

y* 0.4

0.4 0.3

OFV-ONV 14

0.2 0.1

0.1 0

0

-0.1

-0.1 WTV 1.4

-0.2

z*

z*

WTV 46

0.3

E403–Baseline

0.2

-0.2

-0.3

-0.3

-0.4

-0.4

-0.5 -0.6

OFV-ONV 27

0.4

0.4

-0.4

HTV -59

-0.3

INV 11.5

-0.4

0.3

-0.1 -0.2

-0.2

-0.5

WTV 53

TAK–Baseline

0.2

WTV 35

0.1

101

INV 0.6

HTV -1.8

INV 1.9

-0.6 -0.7

-0.8

-0.8

y*

HTV -3.6

-0.5

-0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

OFV-ONV 25.2

TAK–Baseline 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

Fig. 11. Field distributions of non-dimensional axial vorticity x for reference configurations 1 (E403 model) and 2 (TAK model) measured at various downstream positions xn ¼ 1.0, 2.0 and 5.56 (E403), and 4.5 (TAK): (a) E403: xn ¼1.00, tn ¼ 0.031, (b) E403: xn ¼ 2.00, tn ¼0.062, (c) E403: xn ¼ 5.56, tn ¼ 0.173, (d) TAK: xn ¼1.00, tn ¼ 0.023, (e) TAK: xn ¼2.00, tn ¼0.047 and (f) TAK: xn ¼ 4.50, tn ¼ 0.105.

The wing vortex sheet integrates the boundary layer of the wing upper and lower sides, resulting in flowfield areas of retarded axial flow. At x* ¼0.37, minima in axial velocity of 0.65 UN are found in the region of the WFV while axial velocity levels of about 0.8 UN characterize the outboard wake vortex shear layer. The centers of the dominant vortices, namely WTV, OFV, ONV, INV, WFV and HTV exhibit local minima in axial core velocities. From the downstream relocation of these velcocity

minima the roll-up process with the merging of the single vortices can also be analyzed as shown before based on the axial vorticity fields. In Fig. 13b, the axial velocity deficits ðU1 umin Þ=U1 taken at the core areas of the main vortex (OFV; OFV–ONV) and the WTV are plotted as function of x* and t*, respectively. The velocity deficits in the near field reach typically levels of 25% and decrease in the extended near field to levels of about 10  8%. For the main vortex (OFV–ONV), a value of about 8% remains while for the WTV

102

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

y*

x* x* = 0.37 z* x* = 1.00 WTV

HTV

OFV INV

x* = 2.00

ONV

WTV HTV

OFV–ONV INV

x* = 3.00 WTV OFV–ONV x* = 4.00

HTV

INV ξ–levels

WTV OFV–ONV

HTV

INV

x* = 4.50

Roll-up process: Rotation (counter clock-wise) and merging of dominant near field vortices to form the final rolled-up trailing vortex

Fig. 12. Development of the non-dimensional axial vorticity fields x in the extended near field region for reference configuration 2 (TAK model).

the deficit reduces to approximately 2.5% as a result of merging with the main vortex. The axial velocity deficit attributed to the core of the remaining trailing vortex corresponds to a value of about 30% of the maximum cross flow velocities. Consequently, it means a considerable difference against a purely two-dimensional modeling of the wake vortex system where only cross flow velocities are taken into accout. Vortex trajectories and core radius: Fig. 14a illustrates the trajectories of the main vortex (OFV, OFV–ONV) and the wing tip vortex (WTV) for the E403 configuration as a function of the nondimensional coordinates of the cross flow plane, y* and z*. The distance between these vortices is shown as function of the streamwise coordinates x* and t* in Fig. 14b for both the E403 and the TAK models. The vortex trajectories demonstrate the counter-clockwise movement of the WTV around the main vortex. The latter moves first outboard and then inboard approaching the center of the free circulation. Its spanwise position is y*OFV, E403 ¼0.718 at x* ¼5.56. The distance between the WTV and the main vortex decreases up to t* ¼0.02 to the same extent for the E403 and for the TAK configuration (Fig. 14b). The reduction in vortex distance continues in case of the E403 model when progressing further downstream. It reflects the

merging of WTV and main vortex which starts at t* 40.05. However, for the TAK model the distance between the WTV and the main vortex increases for t* 40.05 so that merging will take place much further downstream. Half the distance between the maxima of the vortex induced circumferential velocities defines the viscous core radius rc (Fig. 4). Here, the radius rc is presented in non-dimensional form referring to the wing half span, rc/(b/2) (Fig. 15). The downstream development of this relative radius is given for the main vortex (denoted as OFV, Fig. 15a) and the WTV (Fig. 15b) as function of x* and t*, respectively. The expansion of the viscous core radius with increase in downstream distance shows a very similar course for both reference configurations. Within a time scale of t*¼0.02 up to t*¼0.2 the size of the core radius is doubled indicating a growth rate of d(rc/b)/dtn E0.11. Referring to the growth rate of the Lamb– Oseen vortex model for viscous flows (see Appendix), drc2 =dt ¼ 4bn  8:5  105 (m2/s), the vortex core turbulence leads to a much larger increase in the core size. Based on the measured values this increase is calculated as drc2 =dt  4:5  103 (m2/s), so the following relation can be derived:

Drc2 ¼ 4bnð1 þðnt =nÞÞt0 Dt ;

nt  88n;

b ¼ 1:25643:

ð14Þ

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

103

Fig. 13. Downstream development of axial peak vorticity and axial velocity deficit for reference configuration 1 (E403 model): (a) non-dimensional vorticity maxima xmax of several dominant near field vortices as function of xn and tn, respectively and (b) axial velocity deficit (UN  u% min)/UN of wing tip vortex (WTV) and main vortex (OFV–ONV).

Consequently, the expansion of the squared viscous core radius with time, Drc2 =Dt, due to turbulence (eddy viscosity nt) is larger by a factor of 50 than the increase in vortex core size caused by fluid viscosity only. A similar trend can be detected for the increase in the viscous core radius of the wing tip vortex before its core becomes strongly stretched when merging with the main vortex starts. It is found that the viscous core radius of the fully developed trailing vortex is typically about 3 4% of the wing span. Turbulence intensities and Reynolds stresses: The roll-up process and the merging of dominant vortices is further indicated by the areas of increased turbulence intensities (Fig. 16). Contour plots of the turbulence intensities associated with the vertical velocity fluctuations are presented for the TAK configuration for all measured cross flow planes in Fig. 17. As in the near field, and also in the extended near field, the centers of the dominant vortices are characterized by local turbulence maxima. Depending on the considered single vortex and the stage of the roll-up process the turbulence peak levels are in the range of 7 14%. The roll-up process of the vortex sheets is highlighted by the spiral arrangement of regions of increased turbulence intensity (Tuz ¼1C2.5%) around the zone of the turbulence peak of each dominant vortex. Maximum levels of the vertical turbulence intensities, Tuz,max, taken in the core region of dominant vortices, are presented for the E403 configuration as function of x* and t* in Fig. 18. Progressing downstream the peak levels for the WTV and INV decrease significantly because of merging with the main vortex. The

turbulence maximum of the main vortex diminishes much less reaching a nearly constant level of Tuz,max E8% at t*¼0.18. This trend is also detected for the turbulent shear stresses (Fig. 19). Similar to the near field, the dominant vortices are characterized by two pairs of local shear stress maxima of opposite sign. Depending on of these vortices the related peak values  the concentration  vuwu max =U 2  are in the range of 0.00060.003. 1 Two-scale vortex model: An analytical or semi-analytical model for the vortex induced velocities is of high value for stability analysis and real-time simulations. Here, a modified two-scale model is used to reproduce the measured velocity profiles [82]. The two-scale characteristics (rc,rv) are clearly depicted using a logarithmic scale for the radial expansion of the vortex core (Fig. 20). Therefore, the vortex induced velocity field can be divided into three areas starting at the vortex center and progressing outward: (i) an inner vortex core, dominated strongly by viscosity and defined by the viscous core radius rc, (ii) the rotational core, where there is a gradual change in the dominance of viscous and convective forces, quantified by the vorticity radius rv and (iii) an outer region where the induced velocities can be approximately represented by inviscid flow modeling due to a potential vortex. The circumferential velocity of the two-scale vortex model yields

Vy ¼

G0

"

r2

2pr ðR4cv rv4 þ r 4 Þð1 þ n=4Þ ðrv4 þ r 4 Þð1n=4Þ

# ;

Rcv ¼

rc rv

ð15Þ

104

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

flow plane (x* ¼5.56, t* ¼0.173) resulting in rc ¼0.032b, rv ¼0.1b and n ¼0.45 for the E403 main vortex. Using these values to calculate the vertical velocity profile w=U1 ¼ f ðr=ðb=2ÞÞ, the twoscale vortex model represents nearly exactly the actual velocity distribution (Fig. 21).

0.4 WTVE403

0.3

OFVE403

3.5. Major findings

0.1

The wake vortex system of (four-engine) large transport aircraft in approach configuration is characterized by the following features:

z*

0.2

0

Initial position

Merging

 The near field includes typically six main vortices, namely

-0.1

-0.2

Initial position

-0.3 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 y*

1



0.5

dOFV-WTV/(b/2)

0.4

0.3

 0.2

E403

0.1

TAK

0

0

0.05

0.1 τ*

0.15

0.2

Fig. 14. Trajectories and distances of main and wing tip vortices for the roll-up process: (a) trajectories of wing tip vortex (WTV) and main vortex (OFV–ONV) (counter clockwise rotation) mapped in the yn–zn-plane for reference configuration 1 (E403 model) and (b) relative distance dOFV–WTV/(b/2) between main vortex (OFV–ONV) and wing tip vortex (WTV) as function of tn for reference configurations 1 (E403 model) and 2 (TAK model).

The maximum induced velocity exists at the station of the viscous core radius r¼ rc: " # G0 R1n cv Vy ¼ ð16Þ 2prc ð2Þ1 þ4 n ð1 þ R4 Þ1n 4



the wing tip vortex (WTV), the outboard flap vortex (OTV), the outer and inner engine nacelle vortices (ONV and INV), the wing–fuselage vortex (WFV) and the horizontal tailplane vortex (HTV). While WTV, OFV, ONV and INV exhibit the same sense of rotation, an opposite sense of rotation is attributed to the WFV and HTV. The counter-rotating WFV results from the change in the circulation gradient at the wing–fuselage junction. The HTV with its opposite sense of rotation is due to the negative lift produced by the horizontal tailplane for trimmed flight. In the extended near field the position and strength of the vortices change progressively because of the wake roll-up process and vortex merging. The neighboured OFV and ONV merges quickly constituting the main vortex OFV–ONV for t*E0.04. This main vortex acts as the roll-up center because its position is close to the center of the free circulation (s¼b0/bE0.76). Merging of the WTV with the OFV–ONV starts at t*40.05 and is completed at t*E0.2–0.22 while the overall roll-up process is finished at t*E0.25–0.3. The investigated reference configurations show an advanced roll-up process for the higher lift coefficient of CL ¼1.76 while for the lift coefficient of CL ¼ 1.44 the wing tip vortex is still clearly separated from the main vortex system. The core regions of the main near field vortices are characterized by axial vorticity peaks and considerable axial velocity deficits. The vortex core structure reveals maximum turbulence intensities and a ‘‘quadrupel structure’’ of Reynolds shear stress peaks. Progressing downstream the levels of these peak values change due to vortex merging and diffusion. The main vortices show non-dimensional axial vorticity maxima of xmax,E403 E14 (t* ¼0.173) and xmax,TAK E25 (t*¼ 0.105). The magnitudes of the corresponding cross flow velocities Vy max are in the range of 15–25% of the freestream velocity UN. The non-dimensional axial velocity deficits ðU1 umin Þ=U1 stabilize at values of about 8% in the extended near field. The turbulence intensities for the rolled-up main vortex reach levels of Tumax E8–9%. The increase of the vortex core radius in the extended near field caused by turbulence and vortex merging is 50 times larger than the one given by the Lamb–Oseen vortex model for viscous flow. The cross flow velocity profiles of the main vortex can be approximated using a modified two-scale vortex model providing a smooth profile based on the length scales of viscous core radius rc and vorticity radius (external core radius) rv. Characteristic dimensions of the vortex core radii are found to be for the viscous core radius rc ¼ 0.03b 0.04b and for the external core radius rv ¼0.10b  0.12b.

cv

The peak axial vorticity is given by

omax ¼

G0

R1n rc2 cv

p

4. Unsteady effects ð17Þ

The two-scale model parameters are determined from the measured velocity fields at the most downstream located cross

This chapter concentrates on important unsteady phenomena associated with the wake vortex development. Specific instability mechanisms are of particular relevance for both the wake vortex

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.1

105

0.1 E403 OFV TAK OFV

E403 OFV TAK OFV 0.08

0.06

0.06 rc / (b/2)

rc / (b/2)

0.08

0.04

0.04

0.02

0.02

0

0

1

2

3

4

5

0

6

0

0.05

0.1

0.15

0.2

0.15

0.2

τ*

x* 0.1

0.1 E403 WTV TAK WTV

E403 WTV TAK WTV

0.06

0.06 rc / (b/2)

0.08

rc / (b/2)

0.08

0.04

0.04

0.02

0.02

0

0 0

1

2

3

4

5

x*

6

0

0.05

0.1 τ*

Fig. 15. Development of the relative viscous core radius of the main vortex (OFV–ONV) and the wing tip vortex (WTV) in the extended near field region for the reference configurations 1 (E403 model) and 2 (TAK model): (a) relative viscous core radius rc/(b/2) of the main vortex (OFV–ONV) as function of xn and tn and (b) relative viscous core radius rc/(b/2) of the wing tip vortex (WTV) as function of xn and tn.

evolution in the near field and the further development in the far field [11,82]. Section 4.1 is devoted to the merging process of co-rotating vortices determining the interaction of the main single vortices during the roll-up process. Section 4.2 deals with inherent instability mechanisms for developed wake vortex systems consisting of two or four trailing vortices. Finally, Section 4.3 includes a summary of the major findings. 4.1. Vortex merging Following the formation of the wing vortex sheet and the main vortices in the near field, the roll-up process dominates the wake

vortex evolution in the extended near field due to the selfinduction of the vortex sheet and embedded main vortices, cf. Section. 3.4. In the course of this process adjacent vortices merge until one rolled-up trailing vortex is formed for the left and right parts of the wing (Fig. 2).

4.1.1. Principle experiment The merging of co-rotating vortices has been investigated by Meunier and Leweke conducting a basic experiment to study the interaction of vortices of nearly the same strength in a water tank [98] (Fig. 22). Corresponding DNS calculations have been carried

106

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.3 E403 Baseline 0.2 WTV

z*

0.1 ONV

HTV

0

WFV

-0.1 -0.2

OFV INV

-0.3 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

1

1.1

Tuz–levels

0.4 E403 Baseline

0.3 0.3

0.2

E403 Baseline

0.2

WTV

0.1 z*

0

z*

0

WFV

-0.1

HTV

HTV

-0.4

-0.4

-0.5

INV 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

1

-0.6

1.1

INV 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

1

1.1

0.4

0.4 E403 Baseline

0.3

E403 Baseline

0.3

OFV ONV

0.2

0.2

WTV

0.1

0.1

0

0

OFV ONV

-0.1

-0.1 z*

z*

-0.1

-0.3

-0.3

-0.2

-0.2 WTV

-0.3

-0.3

-0.4

HTV

-0.4

-0.5

-0.5

HTV

-0.6 INV

-0.6 -0.7

OFV ONV

-0.2 OFV ONV

-0.2

-0.5

WTV

0.1

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

INV

-0.7 1

1.1

-0.8

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

1

1.1

Fig. 16. Field distributions of the vertical turbulence intensity Tuz for the reference configuration 1 (E403 model) at xn ¼ 0.37, 1.0, 2.0, 3.0 and 5.56: (a) xn ¼ 0.37, tn ¼ 0.012, (b) xn ¼1.00, tn ¼0.031, (c) xn ¼2.00, tn ¼0.062, (d) xn ¼ 3.00, tn ¼ 0.093 and (e) xn ¼ 5.56, tn ¼0.173.

out by Laporte and Darracq [89]. The results show that different mechanisms determine vortex merging at low and high Reynolds numbers. For low Reynolds numbers, ReG ¼ 500–2000, merging takes place as a quasi two-dimensional, laminar process which can be characterized by three stages: Firstly, the vortices rotate around each other due to the mutually induced velocities. The vortex sheets start to deform elliptically during these rotations because of the radial shear. The viscous core radius increases accordingly approximately to the growth rate given by the Lamb–

Oseen vortex model [122], Drc2 ¼ 4bnDt (cf. lower line in Fig. 25). Secondly, two vorticity layers are formed at the outer sides of the vortices when the ratio of core radius to vortex distance reaches a certain critical value, namely RV,crit ¼rc/dE0.29. The two vorticity layers spread out in radial direction wrapping around the vortices. At the same time the distance between the vortex cores decreases significantly within a third of the initial rotation period. The two core areas merge to form a common vortex core. Thirdly, the vorticity layers roll up around the common center leading to a

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

107

Fig. 17. Downstream development of the cross flow patterns of vertical turbulence intensity Tuz for reference configuration 2 (TAK model).

E403 Baseline - X* = 5.56

Region of strained WTV OFV merging with WTV

0.002

0.00107 0.001 0.0008 0

-0.001

-0.0006

-0.0008

-0.6 -0.4

-0.002

-0.2 Fig. 18. Peak values of the vertical turbulence intensities Tuz,max in the core region of dominant vortices as function of xn and tn, respectively, for reference configuration 1 (E403 model).

nearly axisymmetric final vortex. Here, merging is mainly a convective process. The square of the viscous core radius of the merged vortex based on the initial vortex distance, (rc/d)2 is about two times larger than that of the initial vortices (Fig. 25). At higher Reynolds numbers, ReG 42000, the characteristic time of the viscous phase before merging becomes long enough that a three-dimensional instability develops. It reveals itself as a sinusoidal displacement of the trajectories of the vortices while they rotate around each other and their centers approach each other (Fig. 22). The interaction between the vorticity of one vortex and the induced strain of the opposite vortex results in a flowfield with elliptical streamlines giving rise to this cooperative, short wave elliptical instability, see Section 4.2. The perturbations of both vortices are in phase and the corresponding amplitudes grow exponentially within a certain time interval. Starting from the locations of the largest deformation, fluid layers of the one vortex wraps around the other and vice versa creating periodically

z*

0 0.2

1

0.8

0.6 y*

0.4

0.2

0

2 Fig. 19. Field distributions of non-dimensional turbulent shear stresses vuwu=U1 at xn ¼5.56 (tn ¼ 0.173) for reference configuration 1 (E403 model).

overlapping structures. The corresponding vortex stretching leads to the formation of secondary vortices that are orientated perpendicular relative to the primary vortex trajectories (Fig. 25). Compared to the quasi two-dimensional case at low Reynolds numbers, the three-dimensional instability developing at high Reynolds numbers accelerates the merging process because the interaction of the secondary and primary vortex structures transforms the initial core flows more quickly to a common vortex core. The merged vortex is therefore characterized by increased turbulence and a larger core radius. The square of the normalized viscous core radius (rc/d)2 increases by a factor of 3–3.5 with respect to the value before merging. In comparison to the case without instability, an enlargement of the core radius by 22–32% can be stated (Fig. 25).

108

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.8

0.2 E403 OFV

0.18

Two-scale model

0.16

0.4

0.14

0.2 w/U∞

0.12 w/U∞

Measured profile GemessenerVerlauf

0.6

0

0.1 -0.2 0.08 -0.4 0.06 -0.6

0.04

rv

0.02

-0.8 -0.5

rc

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

r / (b/2) 10

-2

10

-1

10

0

r / (b/2)

Fig. 21. Comparison of radial profiles of vertical velocity between measured and smooth two-scale vortex model for the main vortex OFV–ONV of the reference configuration 1 (E403 model) at xn ¼ 5.56 and tn ¼0.173.

Fig. 20. Radial profile of vertical velocity w /UN for the main vortex OFV–ONV of the reference configuration 1 (E403 model) at xn ¼5.56 and tn ¼ 0.173.

The critical ratio of the viscous core radius to vortex distance for vortex merging triggered by the elliptical instability is given by RV,crit ¼

rc ¼ 0:225 70:025 d

ð18Þ

The following ranges of characteristic values can be derived from the relevant basic research including wave number ka,Vrc, wavelength lV and amplification rate sV. For the wavelength lV normalized with the wing span b, a ratio of viscous core radius to wing span of rc/b¼0.03–0.05 is taken: ka,V rc ¼ 1:925 70:175;

lV ¼

lV

lV

rC

¼ 3:3 7 0:3 ðbÞ;

s s ¼ V ¼ 1:6 70:2; er  V

b

2p ðaÞ; ka,V

¼ 0:135 7 0:045 ðcÞ ;

er ¼

G 2pd2

ð19Þ

OFV (xOFV,E403 E 17) has rotated clockwise halfway around the stronger ONV (xONV,E403 E55) with respect to the positions of vortex formation (Fig. 23a). The value of the normalized core radius of rc/d¼0.36 indicates that merging is on-going. At xn ¼1.0, only one center of maximum turbulence intensity exists pointing out that merging of OFV and ONV is far advanced. The final roll-up of the spiral vortex sheets, depicted here by local turbulence maxima, finishes the merging process. Therefore, the merging sequence of the main vortices embedded in the wing vortex sheet corresponds to the mechanisms found in the principle experiment, even if additionally interactions with a variety of other small scale vortices exist. The characteristic time for vortex merging tV is given by tV ¼ N trev ;

trev ¼

ð2pdÞ2 ; G1 þ G2

N ¼ 12

ð20Þ

ðdÞ

4.1.2. Present investigations Regarding a detailed aircraft configuration, the merging of corotating vortices has been investigated mainly for the interaction of outboard flap vortex (OFV) and outboard nacelle vortex (ONV) and wing tip vortex (WTV) and main vortex (OFV–ONV) in the extended near field for the E403 model. The corresponding vortex Reynolds numbers are in the range of ReG ¼(0.6–1.8)  106 depending on the considered vortices. These high Reynolds numbers indicate that vortex merging is accompanied by an elliptic instability. The 3D merging criterion is proven herein by analyzing the values of rc/d given in Fig. 23, which includes contour plots of the distributions of vertical turbulence intensity. These plots concentrate on the regions of OFV and ONV, and WTV and OFV–ONV, where vortex merging takes place. Absolute turbulence maxima are attributed to the vortex core areas while local turbulence maxima are assigned to vortex sheets. The merging of outboard flap and nacelle vortices, OFV and ONV starts immediately after their formation because the critical value RV,crit is already large due to the small distance between these vortices. At xn ¼0.37, the OFV is located below the ONV, so that the weaker

Using d E0.04b, G1 ¼ GONV E0.36G0, G2 ¼ GOFV E0.11G0 and N ¼1, it follows trev E0.12 s. The investigations of Bristol et al. [13] and Chen et al. [14] carried out on a principle model in a towing tank document also that merging takes place within one revolution of the weaker vortex around the stronger vortex triggered by a cooperative three-dimensional instability. The merging of the wing tip vortex (WTV) and the main vortex (OFV–ONV; here also denoted as OFV alone) is illustrated in Fig. 23b. The analysis of the downstream development of the vortex distance between main vortex and wing tip vortex based on the wing half span dOFV–WTV/(b/2), of the relative viscous core radius rc/(b/2) and of the ratio rc/d can be taken from Fig. 24. The ratio of rc/d reaches the critical value of RV,crit E0.2 for the onset of vortex merging at a non-dimensional time of t* E0.06. The gray shaded area in Fig. 24b highlights the range of RV,crit defined by Eq. (18). The merging process itself starts at t* E0.1. During this process the core radius of the stronger vortex (OFV–ONV) increases only slightly, while the distance between WTV and OFV–ONV becomes strongly reduced due to the roll up of the vorticity sheets. This development is indicated by the turbulence intensities shown in Fig. 23b. At t* E0.17, the weaker WTV has

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Γ2

Γ1

rc1

109

w2 d

w1

rc2

Γ 1 , Γ2 : rc1 , rc2 : d: ReΓ :

Circulation Viscous core radii Distance of vortex cores Reynolds number (based on circulation)

Co-operative elliptical instability

Before merging

During merging

Co-operative elliptical instability Fig. 22. Main parameters, basic experiment and direct numerical simulation (DNS) for merging of co-rotating vortices: (a) main parameters for merging of co-rotating vortices, (b) basic experiment of Meunier and Leweke [98] and Leweke et al. [92]; ReG E ¼4500 and (c) vorticity development based on DNS representing basic experiment [92,89]; ReG ¼5000.

turned around the stronger main vortex by approximately 2701, so that merging will be completed at t* E0.2–0.22. The findings from this study for the relative viscous core radius (rc/d)2 are presented in Fig. 25, considering the eddy viscosity nt in the viscous time scale: ð4n Dt t0 Þ=d2 ; nn ¼ n(1+ nt/n); cf. Eq. (14). It is documented that the predicted trend in the expansion of (rc/d)2 is confirmed by the results obtained for the detailed aircraft configuration. As mentioned in Section 3.4 for the TAK model, the ratio of the viscous core radius of the main vortex to the distance between the main vortex and the wing tip vortex does not follow the trend of the E403 configuration at t* 40.05 but reveals an opposite behaviour (Fig. 24b). The reason is that in case of the TAK model first the merging of the main vortex with the relatively strong inboard nacelle vortex (INV) takes place (see Fig. 12), before the merging of the main vortex and the wing tip vortex will start.

4.2. Instabilities The wake vortex development is siginificantly influenced by inherent instability mechanisms in the form of centrifugal and mainly cooperative instabilities. 4.2.1. Basics Rayleigh criterion: The Rayleigh criterion states that stability is obtained for a rotating, inviscid fluid, the axial, radial and azimuthal velocity components of which are Vx ¼0, Vr ¼0 and Vy ¼Vy(r), if the circulation increases monotonically with the radius r [122]: dG2 dðrVy Þ2 ¼ 40 dr dr

ð21Þ

Initial disturbances: The development of an instability requires temporal and spatial disturbances, superimposed on the mean

110

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Tuz Vortex sheets

0.110 0.105 0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

rc / d =0.36

Tuz 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

ONV OFV

ONV

OFV

x* = 0.37

x * = 1 .0

0.100 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000

Vortex WTV sheets

OFVONV rc / d = 0.23

x* = 3.00 x* = 5.56 Vortex sheets

WTV

Tuz

OFVONV

OFVONV WTV

x* = 4.00

rc / d = 0.26

Fig. 23. Merging of dominant near field vortices during the roll-up process documented by turbulence intensity fields Tuz for reference configuration 1 (E403 model): (a) merging of outboard flap vortex (OFV) and outboard nacelle vortex (ONV) and (b) merging of main vortex (OFV–ONV) and wing tip vortex (WTV).

(steady) flowfield of a single vortex or a vortex system [90,91]. The analytical description introduces Kelvin waves propagating along the vortex [82]. The corresponding initial disturbances associated with velocity and pressure fluctuations, Vux ,Vur ,Vuy , and p0 , can be written as ^ iðka x þ myotÞ ðVux ,Vur ,Vuy ,puÞ ¼ ðV^ x , V^ r , V^ y , pÞe

ð22Þ

The axial wave number ka ¼2p/l, the azimuthal wave number m and the angular frequency o ¼2pf determine the disturbance characteristics. The frequencies o related to a discrete spectrum ^ represent the are the eigenvalues; the components ðV^ x , V^ r , V^ y , pÞ eigenvector. The mode shape of the disturbances depends on m comprising an axially symmetric shape for m¼0, a helical shape for m¼ 71 (bending mode) and a multiple helix form for 9m941 (Fig. 26). In particular, a deformation of the vortex axis occurs for m¼ 71, so that the disturbance velocities at the station of the vortex axis (r ¼0) do not vanish. Analytical expressions for the Lamb–Oseen vortex are given in Ref. [82]. Wavelengths: The instability mechanisms include both long and short wave phenomena where the following ranges are used for classification: (1) Long wave instability (LW) (‘‘Crow instability’’): l/b0 42p

(2) Medium wave instability (MW) (‘‘Crouch instability’’): 2p 4 l/b0 4 p/2 (3) Short wave instability (SW) (‘‘Widnall instability’’): p/24 l/b0 4 p/4 (4) Ultra-short wave instability (USW; vortex merging): l/d o p/4 4.2.2. Long wave instabilities The mutual induction of the trailing vortices on each other leads to the evolution of cooperative instabilities. They result from the radial deformation induced by the neighbouring vortex and the superposition of three-dimensional disturbances when there is a resonance between deformation field and disturbance modes [122]. Radial deformation: The trailing vortices constitute a counterrotating vortex pair of approximately equal strength,  G1 ¼ G2 ¼ G0 (Fig. 3). The induced downward velocity at the vortex centers, having a spanwise distance of Dy¼b0 ¼ sb and a vertical distance of Dz ¼0, is w1 ¼w2 ¼ G0/(2pb0) (Eq. (6)). The corresponding (outer) radial deformation (shear rate) er at the vortex centers is then given by

er ¼

G0 2pb20

ð23Þ

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

τ*

τ* 0.5

0

0.0311 0.0622 0.0933 0.1244 0.1555

0

0.0311 0.0622 0.0933 0.1244 0.1555

0.14

0.45

WTV OFV

0.12

0.4 0.35

0.1

0.3

rc / (b/2)

dOFV-WTV / (b/2)

111

0.25 0.2 0.15

0.08 0.06 0.04

0.1 0.02

0.05 0

0

1

2

3 x*

4

5

0

6

0

1

2

3 x*

4

5

6

τ* 0.5

0

0.0311 0.0622 0.0933 0.1244 0.1555

0.5

OFV

E403 OFV TAK OFV 0.4

rc / dOFV-WTV

rc / dOFV-WTV

0.4

0.3

0.2

0.3

0.2

0.1

0.1

0

0 0

1

2

3 x*

4

5

6

0

0.05

0.1 τ*

0.15

0.2

Fig. 24. Characteristic quantities of vortex merging of main vortex (OFV) and wing tip vortex (WTV) for the two reference configurations (conf. 1: E403 model, conf. 2: TAK model): (a) relative distance dOFV–WTV/(b/2) between main vortex (OFV) and wing tip vortex (WTV) and relative viscous core radius rc/(b/2) of main and wing tip vortex as function of xn and tn, respectively, and (b) ratio of viscous core radius of main vortex to the distance between main vortex and wingtip vortex rc/dOFV–WTV as function of xn and tn, respectively, for reference configuration 1(E403 model, left) and configurations 1 and 2 (E403 model and TAK model, right).

Considering a coordinate system for the cross flow plane moving downward with the sinking vortex pair, circular streamlines exist within the vortex cores, but outside the cores the streamlines are deformed elliptical. When taking into account only vortex ‘‘1’’ with its downward movement according to the velocity w1, a stagnation point is present at the center of vortex ‘‘2’’. The same induction arises from vortex ‘‘2’’ on vortex ‘‘1’’. The stagnation flows lead to a radial deformation of each vortex or vortex core. The axes of maximum deformation correspond with the locations of vanishing pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi circumferential velocity Vy ¼ v2 þ w2 ¼ 0. For a counter-rotating vortex pair, the inclination angle of these axes relative to the y-axis, here the horizontal line corresponding to the lateral direction, yields sffiffiffiffiffiffiffiffiffiffi! G2 ð24Þ y0 ¼ arccos 7 2G1 For the special case of counter-rotating vortices of equal strength (  G1 ¼ G2), the inclination angle is y0 ¼ 7451. The radial deformation for viscous vortex cores of finite size is caused, on the one hand, by the induction of the neighbouring

vortex, and on the other hand, by the deformation of the vortex core flow itself. Including viscous effects (represented e.g. by the Lamb–Oseen vortex model) the radial deformation may be enlarged by a factor of about 2.5 [122]. Initial disturbance: A sinusoidal initial disturbance triggering the formation of a cooperative instability results from the superposition of two Kelvin waves A and B, if they move in opposite direction (mA ¼  mB), are of helical shape (9mA9 ¼ 9mB9¼1) and stationary (oA ¼ oB), and have the same axial wave numbers (ka,A ¼ka,B). This elliptic instability develops along the planes of maximum radial deformation given by Eq. (24). If further Kelvin waves are present, the wave numbers of which are different from ka,A but fulfill the other conditions, more cooperative elliptic instabilities of different wavelengths may also occur [12,89]. In the following, the long wave instability of a trailing vortex pair is considered as analyzed first by Crow. Shape, wavelength and growth rate: The linear stability analysis conducted by Crow is documented in Refs. [28,29]. Results of the corresponding wind tunnel tests can be taken from [39]. Disturbances, e.g. due to the turbulent atmosphere, initiates the

112

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Γ2

Γ1

rc1

w2 d r c2

w1

0.3 Vortex merging with instability

0.25

Vortex merging without instability

z y

(rc / d)2

0.2

0.15 ~x2 0.1

~ x 3 – 3.5

0.05

Present investigations

rc/d = 0.2 0 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 (4ν*Δτ*t*0)/d

0.1

2

Fig. 25. Scaling of the relative viscous core radius (rc/d)2 for merging of co-rotating vortices without and with elliptical instability as a function of the non-dimensional time parameter 4nnDtn t0 =d2 .

distance between the two vortex trajectories. 9rðtÞ9  es t ;

3 

Db0 ðtÞ ¼ Db^ 0 esCrow t ¼ Db^ 0 esCrow t ¼ Db^ 0 esCrow ðp=ð4sÞÞ 



m=0

t

ð25Þ

s ¼ m = ±1

m = ±2 Fig. 26. Schematic representation of the structure of Kelvin waves.

development of this instability [127]. The Crow instability reveals itself by contrails6 in the atmosphere, indicating sinusoidal deflections of the vortex trajectories (Fig. 27a). These disturbances develop along the planes with maximum radial deformation, i.e. in the planes inclined at y0 ¼ 7451 against the horizontal. The stability analysis basically provides both a symmetric mode and an antimetric mode. However, only the symmetric disturbance leads to a strong interaction between the two trailing vortices. The projection of the trajectory deflections of the two trailing vortices on the x–yplane shows the symmetric behaviour with respect to the x-axis (Fig. 27b) and the projection on the x–z-plane documents that they are in phase. With increase in time and distance, the increase in deflection amplitude Db0 (Fig. 27b) grows exponentially with the amplification rate sCrow, thus reducing significantly the lateral

2pb20 s 2p 2 ¼s ¼s b G0 ReG n 0 er

Upon contact of the two trailing vortices, there is an exchange of vorticity of opposite sign over the plane of symmetry, so that the vortex tubes break up and form vortex rings,7 which dissolve faster in smaller structures and finally decay. The contact of the vortex tubes is expected at a value of BZ0.85 in the growth of the related lateral distance. BðtÞ ¼

Db0 ðtÞ

ð27Þ

b0

The growth rate sCrow , wave length lCrow and inclination angle y0 depend on the ratio of vortex core radius rc to the vortex distance b0 and on the axial velocity Vx. For Vx ¼0, the dependencies of the Crow instability parameters are plotted as function of rc/b0 in Fig. 28. The following relations give the ranges for wave number ka,Crowb0, related wavelength lCrow/b0 and amplification rate sCrow determined for y0 ¼4517151and b0/b¼ p/4: ka,Crow b0 ¼ 0:706570:0785;

lCrow ¼

lCrow

lCrow

b0

¼ 9:0 7 1:0 ðbÞ;

sCrow ¼ 0:82570:025; 6 The pressure drop in the vortex core and jet-vortex interaction leads to condensation of water vapor and formation of ice crystals, respectively, over suitable nucleation sites, like soot particles and sulfur aerosols, emitted by aircraft engines.

ð26Þ

b

2p ðaÞ; ka,Crow

¼ 7:068670:7854 ðcÞ;

tCrow ¼

1

sCrow

ð28Þ

¼ 1:21 ðdÞ:

7 But also the strongly bended vortex segments may cause a certain danger for an encountering aircraft if the flight path runs accordingly.

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

113

t0

t0 + 17 s

t0 + 57 s

t0 + 76 s

t0 + 102 s

t0 + 120 s

y

b0 + Δb0 b0 λCrow

x

z

θ0 = + 45°

x z

z

θ0 = – 45°

r y y

x

¨ Fig. 27. Topology of the long wave Crow instability: (a) wake vortex development of B747 aircraft (courtesy K. Hunecke) and (b) schematic representation.

The time scale tCrow related to the growth rate sCrow is given for an elliptical circulation distribution by tCrow ¼

1

sCrow

¼ 9:38

Lb0 Lb ¼ 7:37 CL U1 CL U1

ð29Þ

This time scale is at least five times larger than the time scale associated with the roll-up process, troll-up ¼ t*t* E0.25(p3/4) (Lb0)/(CLUN). 4.2.3. Medium wave instabilities–four-vortex systems Medium wave instabilities are especially of relevance in the case of vortex systems including two pairs of co- or counterrotating vortices. The-four vortex systems considered here consist of a dominant wake vortex pair (main vortices) and an accompaning vortex pair of lesser strength (minor vortices) located inboard. Referring only to a half of the full cross flow plane, two cases are regarded, namely the inboard relative to the main vortices are either co- or counter-rotating (Fig. 29). A

combination with co-rotating vortices is for example the couple of wing tip vortex (WTV) and outboard flap vortex (OFV). A counterrotating vortex pair results from the combination of wing tip vortex (WTV) and inner flap edge vortex (IFV) or horizontal tail plane vortex (HTV) and wing main trailing vortex. The analytical relations assume that the vortex centers are initially arranged on a horizontal line and the corresponding vortices from each pair are of the same strength. The circulation 9GH9 is attributed to the main vortices and the distance between the main vortices is bH, while the circulation of the inboard minor vortices is 9GN9 and their spacing is bN (Fig. 29). The parameters RG and Rb denote the ratios of circulations and lateral distances: RG ¼

GN ðaÞ; GH

Rb ¼

bN o 1 ðbÞ: bH

Co-rotating: 0 oRG o1 ; Counter-rotating: –1oRG o0.

ð30Þ

114

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

The total circulation in the case of multiple vortex systems results from the sum of the individual circulation parts Gi, with

G¼

N X

Gi ðaÞ;

G ¼ GH þ GN ðbÞ:

ð31Þ

i¼1

The lateral center of the free circulation is given by   bH GH þ bN GN 1þ Rb RG b~ 0 ¼ ¼ bH : GH þ GN 1 þ RG

ð32Þ

Eq. (32) shows that for a four-vortex system, where main and inboard minor vortices are co-rotating (RG 40), the free circulation center of the vortex system relative to the main vortex position is located inboard (b~ 0 obH ), while for a fourvortex system with counter-rotating main and inboard vortices (RG o0), the free circulation center is located outboard (b~ 0 4 bH ). The time and length scales, t4WS and x4WS, respectively, assigned to the induction of a four-vortex system are

G

¼

2pb2H

GH

  1 þ Rb RG ðaÞ; 1 þRG

x4WS t4WS U1 ¼ ðbÞ b b

0.9

0.85

12

90

11

75

10

60

σ*Crow

θ0 = 48° (Crow [28]) 9

σ* 0.8

0.75

8

λ/b0

0

0.1

0.2

ð33Þ

45

15

6

0

¼ 1:54:0 ðaÞ;

sCrouch,S ¼ 1:3 ðcÞ; lCrouch,A b

rc /b0 Fig. 28. Parameters of Crow instability: Relative growth rate sCrow , relative wavelength lCrow/b0 and inclination angle y0 of wave propagation plane as function of relative viscous core radius rc/b0.

–ΓH

lCrouch,S b~ 0

30

7

0.3

θ0

2 2pb~ 0

λCrow /b0

t4WS ¼

The parameters RG and Rb are used to classify co- and counterrotating four-vortex systems with respect to a divergent or periodical behaviour in the movement of the minor relative to the main vortices [36] (Fig. 30). The first case means a vertical displacement of the two vortex pairs in opposite direction, thus moving away from each other. The second case refers to a periodical movement of the inboard minor vortices around the main vortices during the downward movement. The divergent behaviour is present for ranges of RG and Rb indicated by the gray shaded areas in Fig. 30, while a periodical movement is found for ranges of RG and Rb corresponding to the non-shaded areas. The limits between these areas are marked by the bold lines. The combinations of RG and Rb of several numerical and experimental studies are added to Fig. 30 and highlighted by the corresponding symbols. A four-vortex system with co-rotating vortices: Investigations on the instabilities and the temporal development of four-vortex systems with neighbouring co-rotating vortices have been performed by Crouch [25]. Two symmetrical and two antimetric forms characterize the instabilities of such vortex systems. The occuring long wave instabilities reflect the Crow instability due to the mutual induction of the main vortices while medium wave instabilities arise from the interaction between the inboard minor and neighbouring main vortices. The relevant distance between main and minor vortices is given by d¼(bH–bN)/2. The following values are determined for the wavelength and maximum growth rate for the symmetrical (index S) and the antimetric form (index A), where the wavelengths include a relatively wide range (b~ 0 =b ¼ p=4Þ:

(–)/+ΓN

lCrouch,S b

lCrouch,A b~ 0

¼ 1:183:14 ðbÞ;

¼ 1:56:0 ðdÞ;

sCrouch,A ¼ 1:6 ðfÞ

¼ 1:184:71 ðeÞ;

The instabilities developing on the pair of minor vortices can evoke a rise in the amplitudes of the long wave instability by a factor of 10 over a distance of 30 wing spans, thus leading to a shortening in the evolution of wake vortex decay. A four-vortex system with counter-rotating vortices: Also, combinations of an inboard minor and outboard main vortex with opposite

(+)/–ΓN

+ΓH

bH bN rcN

rcH

z

y Fig. 29. Parameters of a four-vortex system.

Circulation of main vortex/inboard minor vortex GH; GN; 9GN9 o9GH9 Distances between main vortices/inboard minor vortices bH; bN Core radii of main vortices/inboard minor vortices rCH; rCN Circulation ratio / distance ratio RG ¼ GN/GH o9719; Rb ¼bN/bH o1

ð34Þ

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

sense of rotation are studied. In particular, this vortex interference is aimed to reduce significantly the time or the distance, respectively, from which the main vortex trajectory deflection is large enough that the fast decay of the trailing vortex system begins. The relationship for the limiting curve between the areas of divergent and periodic behaviour of minor and main vortices with opposite sense of rotation, –1oRG o0, is given by (Fig. 30) R3b þ 3RG R2b þ 3Rb þ RG ¼ 0 ðaÞ;

R3b þ3Rb ðbÞ 3R2b þ 1

RG ¼

ð35Þ

1 Divergent

0.8 0.6

R = N / H

0.4 Co-rotating

0.2 0

Ortega et al. [102,103], Ortega and Savas [104], Stuff [128] and Durston et al. [38] analyzed the development of four-vortex systems in towing tank experiments using generic (aircraft) models. A fast decay of the main vortex pair is documented due to an interaction with the counter-rotating inboard vortex pair. It is further shown that the resulting reduction in the induced rolling moment over a distance of 30 wing spans is up to 50%. The smoke visualization and flowfield data of Fig. 32 illustrate the strong sinusoidal deflection of the trajectories of the inboard minor vortices leading to the formation of vortex loops wrapping around the main vortex. On contact of the minor vortices with the main vortices the interaction of vorticity of opposite sign causes a bursting of the main vortex along with a break of the vortex tubes resulting in the formation of small scale vortical structures. These interactions have been also investigated numerically, e.g. by Rennich and Lele [110], Fabre and Jacquin [44], Fabre et al. [47] and Stumpf [129] using low- and highfidelity methods (Fig. 31). The wavelengths attributed to the interaction of inboard minor and main vortices are ka,4WS b~ 0  0:8 ðaÞ;

l4,WS b~ 0

 2:5p ðbÞ

ð36Þ

Periodic

-0.2 -0.4 -0.6

Steady Counter rotating

-0.8 -1

115

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Rb = bN /bH Crouch [25]

Stumpf [129]

Rennich und Lele [110] Fabre und Jacquin [44]

Coustols et al. [23]

Fabre und Jacquin [47]

Ortega et al. [102,103]

Fig. 30. Circulation ratio RG as function of distance ratio Rb of inboard minor and main vortices for a four-vortex system (Donaldson–Bilanin diagram [36]).

The evaluation of the results shows very high amplification rates. An optimal growth parameter Gopt can be determined which refers to the maximum of the amplification rates for all wave numbers and initial conditions [47]. The trends for Gopt are indicated in the diagram representing RG as a function of Rb (Fig. 33). For the area attributed to the divergent movement of inboard and main vortices very high growth rates are associated with ultra-short wave instabilities, which develop on the inboard minor vortices. Since the inboard vortices remove relatively quickly from the sinking main vortex pair the latter is nearly not influenced by the instabilities developing on the inboard vortices. The contour lines of Gopt are almost parallel to the ordinate within the area related to the periodical movement of the inboard vortices around the main vortices referring to circulation ratios of RG o–0.2 and spacing ratios of Rb 40.3. High amplification rates are thus established, on the one hand, for large spacing ratios and, on the other hand, at the boundary curve indicating a stationary behaviour (cf. Fig. 30). Regarding the case

~ x / b0 = 30

~ x / b0 = 0

τ=0

~ x / b0 = 10

τ = 0.7

~ x / b0 = 20

τ = 1.76

Fig. 31. Numerical simulations of four-vortex system instabilities based on counter-rotating main and inboard minor vortices. (a) Fabre und Jacquin [47]: linear vortex filament method; RG ¼ –0.3, Rb ¼0.3 and (b) Stumpf [129]: LES; RG ¼ –0.35, Rb ¼ 0.35.

116

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

of RG ¼–0.3 and Rb Z 0.3, which are treated numerically in [47] (CL ¼1.53, L ¼10; Fig. 31), an amplification rate of Gopt E5700 is obtained at a downstream position of x=b~ 0 ¼ 30. Comparing this amplification rate with those of the Crow and Crouch type instabilities, it is larger by a factor of about 2600 and 570, respectively. However, further detailed investigations with regard to realistic aircraft configurations must show, whether by such interactions the time up to the onset of wake vortex decay can be really significantly reduced. The aim is a reduction in the induced rolling moment of about 50% with respect to the case without interference at comparable downstream distances. Considering a real transport aircraft in approach configuration, the four-vortex wake may be due to horizontal tailplane vortex (HTV) and wing main vortex. Circulation ratios needed for the

development of ‘‘optimal perturbations’’, as indicated by the dotted circle in Fig. 33, contradict the requirements on longitudinal stability margins and center of gravity ranges. Creating a substantial downforce on an aerodynamic surface (e.g. horizontal tail plane) aimed to alleviate the vortex wake is strictly limited because of lift penalties and trim drag. The corresponding high static margins are fully impractical for typical transport aircraft [38].

4.2.4. Short wave instabilities In addition to the long and medium wave instabilities, short and ultra-short wave instabilities also develop enhancing, for example, the process of vortex merging as shown in Section 4.1. According to the actual conditions long and short wave instabilities occur

wing

tail plane

U

Smoke visualization of starboard vortex pair

UU 8

HTV

HTV

WTV

WTV

x* = 1.0 x* = 4.0 x* = 8.0

Main vortex

Inboard vortex

x* = 12.0 x* = 16.0 Vorticity contours

~ ~ 2.5 π b0

x* = 20.0 x* = 24.0

x* = 36.0

x* = 48.0

Fig. 32. TUM-AER wind tunnel experiments of four-vortex system instabilities based on counter-rotating main and inboard vortices shed at a generic four-vortex aircraft model (DLR F13 configuration).

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

together and interact with each other [131,89]. The short wave instability is also known as Widnall instability [132,136,137]. The description of this type of instability depends on the detailed vortex core structure. Therefore, besides the knowledge of the viscous core radius rc information about the velocity and vorticity distribution in the core region is needed [45,46]. The Widnall instability is also developing along the planes associated with maximum radial deformation of the vortex core, i.e. along the planes inclined by y0 ¼ 7451against the horizontal one (Fig. 34). The projection of the trajectory deflections on the x–y-plane shows an in-phase behaviour, while the projection on the x–z-plane indicates a phase shift of 1801. The values for wave number ka,Wrc, wavelength lWidnall and amplification rate sWidnall are listed below: ka,W rc ¼ 2:26 70:2; lWidnall ¼

lWidnall rc

lWidnall b0

2p ðaÞ; ka,W

¼ 2:8027 0:248 ðbÞ;

lWidnall

¼ 0:1267 0:029 ðcÞ;

b

¼ 0:1 70:023 ðdÞ;

sWidnall ¼ 0:95 70:3 ðeÞ

ð37Þ

0 Periodic

Divergent

The values of lWidnall/b and lWidnall/b0 are based on rc/b¼ 0.03–0.04 and b0/b¼ p/4. The amplifcation rates are larger than those of the Crow instability, but the short wave instability is amplified only at a relative distance of rc/d 40.2 [45,89] . This corresponds to the result for the elliptical instability associated with vortex merging at higher Reynolds numbers (ReG 42000). Regarding values of rc/d o0.2, alternating cycles of excitation and attenuation exist from which no marked amplification can arise. 4.2.5. Present investigations The occurrence of the explained types of instabilities is proven for the E403 reference configuration analyzing the flowfields of the main vortex and the wing tip vortex for the most downstream located measurement plane (x* ¼5.56, t* ¼0173). The instabilities are associated with significant quasi-periodic fluctuations in the time-dependent velocity components. The related amplitudes indicate the development stage. For the present analysis, the power spectral densities of the axial velocity fluctuations in dimensionless form, SN u0 , are used (cf. Eq. (11)). The identification of characteristic spectral peaks within the frequency bands assigned to the instabilities informs about their type and intensity [9]. The characteristic frequency parameter is the reduced frequency k based on the freestream velocity UN and the wing half span b/2:

-0.1 k¼

-0.2

SW

opt

R

G SW -0.3

MW opt

~10

4

-0.4 opt

-0.5

G

USW opt

G -0.6 0.1

opt

G

10

~10

~10

f ðb=2Þ b ¼ ðaÞ; U1 2l

f¼

U1

l

ðbÞ

ð38Þ

The main vortex and the wing tip vortex represent a combination of co-rotating neighboured vortices for the considered cross flow plane. Therefore, the analysis concentrates on the Crow and Crouch type instability and the short wave elliptic instability associated with vortex merging. Applying Eq. (38), the corresponding reduced frequencies result as ratios of wing span b and vortex spacing b0 and b~ 0 , respectively, based on the wavelengths defined by Eqs. 28, 34 and 19. The characteristic ranges of the reduced frequencies related to long wave (LW), medium wave (MW) and (ultra-) short wave ((U) SW) instabilities are then given by

3

~10

G

117

5

3

>10

Crow instability (LW):

0.2

0.3

0.4

0.5 kCrow ¼ 0:056 7 0:006

Rb

b ðaÞ; b0

kCrow ¼ 0:08 7 0:01,

b0 ¼ 0:70:8 ðbÞ b

Fig. 33. Optimal growth rates Gopt of the instabilities of a four-vortex system with counter-rotating neighboured vortices; cf. [47].

ð39Þ

y

λWidnall

b0

x

z

θ0 = + 45°

x z

θ0 = – 45°

z

r y

x Fig. 34. Topology of short wave Widnall instability.

y

118

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Crouch instability (MW): kCrouch ¼ 0:21 7 0:12

b ðaÞ; b~ 0

kCrouch ¼ 0:547 0:28,

b~ 0 ¼ 0:40:8 ðbÞ b

ð40Þ

Vortex merging elliptic instability (USW): kV ¼ 4:2 71:4

ð41Þ

x*

These ranges are shown in the diagrams of the power spectral density distributions, which are plotted for a typical station within the regions of main vortex (OFV–ONV) and wing tip vortex (WTV).

0.4 0.3 OFV-ONV 0.2 14 0.1 0 -0.1 WTV -0.2 1.4 -0.3 -0.4 -0.5 INV HTV 0.6 -0.6 - 1.8 -0.7 -0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Ordinates and abscissa are each scaled logarithmically. The spectra exhibit certain moderate amplitude peaks present in the frequency ranges associated with the instability mechanisms. Spectral peaks are detected for the OFV–ONV at frequencies of fE7, 13, 31 and 59 Hz and for the WTV at fE7, 16, 37 and 77 Hz. The corresponding reduced dominant frequencies kd1–kd4 are listed in the table of Fig. 35. The reduced frequency of kd1 ¼0.36 is about four times the value of kCrow E0.09 (Eq. (39)). The Crow type instability propagates approximately with the freestream velocity UN. Assuming a vortex spacing in the range of b0/bE0.7–p/4, a characteristic length of xCrow ¼ UNtCrow ¼(5.22–7.37)Lb/CL results from Eq. (29). Referring to the geometric and aerodynamic data of Tables 2 and 3, the characteristic length and time scales are calculated to be

Non-dimensional axial vorticity distribution ξ for reference configuration 1 (E403) at x* = 5.56

OFV– ONV

y*

 −5 / 3  −8 / 3 N u'

S

k WTV

 −5 / 3

SuN'

 −8 / 3

k

OFV– ONV

WTV

kd1

0.36

0.38

kd2

0.65

0.84

kd3

1.62

1.92

kd4

3.08

4.04

k Fig. 35. Power spectral densities of the axial velocity fluctuations obtained in the region of main vortex (OFV–ONV) and wing tip vortex (WTV) for reference configuration 1 (E403 model) at xn ¼ 5.56.

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

xCrow/bE33 and t*Crow/t*E7, respectively. This means that in the extended near field only the very first stage of the development of the Crow type instability can be detected. However, since the trailing vortices are very concentrated and the vortex flowfield shows high velocity gradients already small trajectory displacements may cause pronounced oscillations in the velocity signal. The reduced frequencies kd2 and kd3 can be attributed to the reduced frequency range linked to the Crouch type instability. Here, spectral peaks occur mainly for the wing tip vortex. Considering the short wavelength range, amplitude peaks are present at kd4,OFV–ONV ¼3.08 and kd4,WTV ¼4.04 associated with the elliptic instability of vortex merging. It refers here to the merging process of wing tip and main vortex. The spectral range for frequencies of k410 (f4200 Hz) is characterized by the typical drop of  5/3 related to turbulent energy spectra while this decrease amplifies for k430 to 8 /3.

119

4.3. Major findings The following parameters can be derived from the analysis of vortex merging and inherent instabilities of the trailing vortex system:

 The merging of co-rotating vortices starts at a critical ratio



of viscous core radius to vortex distance of rc/d¼ 0.20–0.25. Vortex merging is linked to a cooperative elliptic instability for vortex Reynolds numbers of ReG 4104. The corresponding wavelength related to the viscous core radius is lV/ rc ¼3.0–3.6. Specific instability mechanisms are assigned to the wake vortex system associated with the following wavelength ranges (long wave (LW) instability: l/b0 42p; medium wave

Vorticity peak of the main vortex OFV–ONV of reference configuration 1 (E403; x* = 5.56)

OFV– ONV

Su ' f Meandering: Random fluctuations of vortex core at high Reynolds numbers (ReΓ > 103)

u '2

Vorticity contour lines 2.5 2

f lμ U∞

–

+

1.5 1

WTV

z

0.5 0 -0.5 -1 -1.5 -2

+

–

-2.5 -2.5 -2 -1.5 -1 -0.5

0

0.5

1

1.5

2

y

Schematic representation: Contour lines of turbulent shear stress distribution v' w' for fluctuations of vortex center; cf. Fig. 19.

2.5

Su ' f u '2

f lμ U∞ Fig. 36. Spectral distributions of the axial velocity fluctuations of the main vortex (OFV–ONV) and the wing tip vortex (WTV) for reference configuration 1 (E403 model) at xn ¼ 5.56.

120



C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

(MW) instability: 2p 4 l/b0 4 p/2; shortwave/ultra-short wave (SW/USW) instability: l/b0 o p/2). The dominant long wave instability is known as the Crow instability, featuring a relative wavelength of lCrow/b¼ 7.068670.7854. A medium wave instability, named Crouch instability, may appear in the case of four-vortex systems with co-rotating neighboured vortices, the characteristic wavelength of which is lCrouch =b~ 0 ¼ 1:56:0. Specific short wave instabilities occur at wavelengths lWidnall/ b¼0.1 70.023. Characteristic reduced frequencies are derived to detect the wake vortex inherent instabilities on the basis of power spectral densities of the velocity fluctuations. The reduced frequencies are calculated with the wing half span (b/2) and the freestream velocity UN resulting in the following values: Crow instability: kCrow ¼0.0870.01 Crouch instability: kCrouch ¼0.5470.28 Elliptical instability of vortex merging: kV ¼4.2 71.4.

 The core of the main trailing vortex exhibits irregular fluctuations. They constitute random oscillations of the vortex center around a middle position known as vortex meandering [34,82]. These fluctuations show small amplitudes and are of broadband type so that there is no characteristic frequency assigned (Fig. 36) [11]. These fluctuations arising from the unsteady flow due to the aircraft turbulent boundary layer and

local flow separation are fed into the aircraft wake during the roll-up process, also linked to the turbulence in the core areas of the dominant vortices (see schematic of v0 w0 -distribution in Fig. 36).

5. Wake vortex alleviation Following the characterization of the trailing vortex system and the analysis of inherent instability mechanisms, this chapter is dedicated to possible measures aimed to reduce the wake vortex hazard in terms of diminishing the induced rolling moment on a follower aircraft. Already in the seventies, a number of configurational means were considered and investigated in model and flight tests to weaken the trailing vortex system or to achieve an earlier breakup. Many of the actions undertaken, such as mounting perturbation elements at the wing tip (‘‘Spines’’; ‘‘Cross blades’’) or wing tip blowing in axial or vertical direction, were not considered successful [37]. A reduction of the induced rolling moment was achieved by deflected spoilers and special flap settings, where partly a strong interference of multiple wake vortices took place [20,21,24]. Strategies to minimize the wake vortex hazard can be divided primarily into two categories [52]. On the one hand, the objective is a low vorticity vortex (LVV) design, which reduces the wake

Dispersion of vorticity field associated with reduction in peak vorticity level Larger core size

Reduced circumferential velocities

Alleviation of induced rolling moment

Ortega et al. [102]:

Crow instability:

Principle experiment of four vortex system interference – vortex trajectories visualization in towing tank: Main vortex pair

Turbulent

Interfering i/b vortex pair

diffusion 1

 / 0

Rapid decay

T *Q D V

T*

t*

Strong excitation of the main vortex decay due to the interaction of counter-rotating inboard (i/b) minor vortices

Fig. 37. Wake vortex alleviation means: (a) low vorticity vortex (LVV) and (b) quickly decaying vortex (QDV): excitation of inherent cooperative three-dimensional instabilities.

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

near field, a smaller induced rolling moment than a wing with a standard flap setting. Different measures can also be attributed to the QDV approach. Because a multiple vortex system shows instabilities that can grow more rapidly, cf. Section 4.2.3, passive devices aim to promote these kinds of instabilities through the deliberate production of single vortices in addition to those coming from the wing tip and the flap edge [44,82]. The production of additional distinct vortices can also be achieved by differential flap setting. The efficiency of these concepts depends on the persistence of such additional vortex pairs, which is determined by configurational details of the aircraft. Especially, active devices are considered as a possible powerful mean to amplify wake vortex instabilities [27].

vortex hazard by enhancing the dispersion of the vorticity field. It is aimed on the generation of wake vortices with larger core size and smaller swirl velocities at the core radius after roll-up is completed (Fig. 37a). Consequently, the induced rolling moment is diminished. On the other hand, the focus is on a quickly decaying vortex (QDV). An enhanced wake vortex decay may be achieved by promoting three-dimensional instabilities by means of passive or active devices [26,55,56]. Particularly, the growth rates of the long wave instability have to be increased significantly (Fig. 37b), e.g. by the interaction of multiple vortex systems or active excitation. A variety of configurative measures is tested for the implementation of these concepts. Considering the LVV strategy, (modified) wing control surfaces, such as spoilers or flap edge elements, are used to create zones of highly turbulent flow aimed to expand the core size of the trailing vortices [23]. Also, a modified wing load distribution may minimize the induced rolling moment for a following aircraft [40,67]. The alteration of the circulation distribution of the wake generating wing can be obtained using, e.g. differential flap or spoiler settings. It has been shown that a wing with an outboard partially deflected flap and an inboard fully deflected flap produces, at least in the extended

Left delta spoiler

5.1. Passive means Viscous and convective mechanisms are used to spread the vorticity field of the trailing vortex over a wider spatial area, reducing peak values in axial vorticity and circumferential velocities. The radial transport of vorticity and thus the expansion of the vortex core is supported by the increase in the turbulence

Right delta spoiler

Double delta spoiler

Outboard flap Outboard engine nacelle

~ 65° cDS = 0.053 b/2

~ 25°

sDS = 0.024 b/2 cDS

sDS

Outboard Engine Pylon Pylon Extension Fairing (PEF)

Pylon extension fairing

Outboard flap

Outboard engine nacelle

121

cOF = 0.056 b/2

U

sOF = 0.371 b/2

E403 „Flap plate“

sOF/4

cOF/2 Fig. 38. Delta spoiler and flap plate elements for wake vortex alleviation: (a) delta spoiler devices and (b) flap plate device.

122

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

swept leading-edge or both edges swept (Fig. 38). They are denoted as ‘‘right’’, ‘‘left’’ and ‘‘double’’ delta spoiler. The leadingedge sweep is 651; the relative incidence is 251. Dimensions and mounting locations are shown in Fig. 38a. Leading-edge vortices are shed at the side of the delta device facing the wing. Regarding a delta wing planform with 651 leading-edge sweep at an incidence of 251, vortex bursting occurs approximately at 45% of the root chord [7]. The concentrated region of highly turbulent flow due to the burst leading-edge vortices along with the turbulent wake emanating from the spoiler trailing-edge affects the merging area of OFV and ONV aimed to enlarge the radial vorticity distribution. Fig. 38b shows further the geometry and position for a triangular element attached to the outboard flap trailing-edge, denoted as ‘‘flap plate’’. Here, the focus is on the interference of the OFV with the concentrated vortex shed at the

intensity for the rolling up vortex sheet and/or in the formation area of concentrated single vortices. Flap edge and spoiler elements are applied to produce turbulent wakes enhancing the turbulent mixing in specific regions of the wake vortex near field [1,24,105]. Wing fins have been considered as well [114,124].

5.1.1. Spoiler elements Here, delta shaped spoiler elements are used to create a highly turbulent flow in the regions of outboard flap vortex (OFV) shedding and merging of the OFV and outboard nacelle vortex (ONV). These vortices contribute mainly to the formation of the final trailing vortex (cf. Section 3.4). According to the design of ¨ Hunecke [75], three variants of delta type elements are investigated, namely spoilers with right swept leading-edge, left

0.3

0.3

E403 Baseline

0.2

0.2 WTV

0

ONV

HTV WFV

-0.2

WFV

0.4 E403 Baseline

0.3 0.2

WTV

-0.2

OFV ONV

-0.1 -0.2

-0.3

-0.3 HTV

-0.4

-0.5

Tuz– levels

HTV

-0.5 INV

-0.6

-0.6 -0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

E403 Baseline OFV ONV

z*

z*

WTV

0 z*

z*

OFV ONV

-0.1

0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

E403 Double delta device

0.1

0

-0.7

INV

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

0.1

-0.4

OFV

-0.3

0.4 0.2

HTV

-0.2

OFV INV

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

0.3

ONV

0 -0.1

-0.1

-0.3

WTV

0.1 z*

z*

0.1

E403 Double delta device

WTV

HTV

INV

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

INV

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

E403 Double delta device OFV ONV

WTV

HTV INV

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

Fig. 39. Field distributions of the vertical turbulence intensity Tuz for the E403 reference and E403 double delta spoiler configuration at xn ¼ 0.37, 3.0 and 5.56: (a) baseline: xn ¼ 0.37, tn ¼0.012, (b) baseline: xn ¼3.00, tn ¼ 0.093, (c) baseline: xn ¼5.56, tn ¼0.173, (d) double delta spoiler: xn ¼0.37, (e) double delta spoiler: xn ¼ 3.00 and (f) double delta spoiler: xn ¼ 5.56.

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

flap plate inboard edge, which is counter-rotating with respect to the OFV. The wing facing narrow side of the spoiler elements blocks the near surface flow to a lesser extent relative to a standard spoiler of constant span width. Therefore, the drop in the spanwise circulation distribution is lower compared to that of a standard spoiler. The reduction in local camber caused by the deployed spoiler shifts the lift polar only slightly to lower levels, with little noticeable effect on the maximum lift coefficient. The maximum reduction in DCL0 is given for the double delta spoiler with –2.9% [8]. Maintaining the approach lift coefficient for trimmed flight (cf. Table 3) requires therefore in the case of the double swept delta spoiler a raise in the angle of attack of Da E0.31. The arrangement of the spoiler elements with respect to a technical implementation is linked to the location of the outboard pylon extension fairing. The influence of the delta spoiler elements on the vorticity and tubulence intensity fields is discussed for the E403 configuration. Comparing the turbulence intensity fields for the baseline and double delta spoiler configuration highlights the concentrated region of increased velocity fluctuations in the near field caused by the deflected spoiler (x* ¼0.37: 0.45oy* o0.55; –0.15oz* o –0.05; Fig. 39a and d). The extension of this turbulent zone, Dy/ bE Dz/b E0.04–0.05, is approximatley twice the effective span of

123

the spoiler elements (0.025b) derived from the viscous core size of the trailing vortex (rc/b E0.03; cf. Section 3.4). The spoiler induced turbulent zone affects mainly the evolution of the OFV and ONV while the roll-up process enhances the dispersion of the turbulent region. Consequently, the adjacent wing vortex sheet reveals higher turbulence intensity levels too. The expanded turbulent vortex core areas persist also further downstream (Fig. 39b, c, e and f ). The comparison of the axial vorticity fields of the baseline configuration and the configurations with deflected delta spoilers confirms that the OFV vorticity field is radially distributed due to turbulent mixing accompanied by a reduction in peak vorticity levels. During merging of OFV and ONV the vorticity area becomes further enlarged and peak vorticity levels decrease significantly. The peak values of the non-dimensional axial vorticity xmax of OFV and OFV–ONV are plotted as function of the streamwise coordinates x* and t* in Fig. 40. It is shown that a substantial reduction in the axial vorticity maximum occurs from t* E0.01 up to t* E0.1 (x*¼ 3.0). At t* ¼0173, the turbulent wake evoked by the right, left and double delta spoilers leads to a reduction in axial peak vorticity of Dxmax ¼–21%, –36% and –52%, respectively. The alleviation in peak vorticity by a factor of two clearly points out the possible potential of this measure. Fig. 40 includes also the result for the flap plate device indicating a decrease in xmax up to

− 52 %

Right delta spoiler

Left delta spoiler

Double delta spoiler

Fig. 40. Non-dimensional axial peak vorticity levels xmax of the main vortex (OFV–ONV) for the E403 reference and the E403 delta spoiler configurations as function of xn and tn, respectively.

124

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Double delta spoiler

0.2 0.15 0.1

Left delta spoiler w / U∞

0.05 0 -0.05

Right delta spoiler

-0.1 Baseline Right delta device Left delta device Double delta device

-0.15 -0.2 -0.4 -0.3 -0.2 -0.1

0 0.1 r / (b/2)

0.2

0.3

0.4

1

0.12 0.1

Baseline Right delta device Left delta device Double delta device

0.8

0.6 G*

rc / (b/2)

0.08 0.06

0.4 0.04

Baseline Right delta device Left delta device Double delta device

0.02 0

0

1

2

3

4

5

x*

0.2

6

0 0

0.05

0.1

0.15

0.2

0.25

0.3

r / (b/2)

Fig. 41. Radial velocity profiles, viscous core radii and radial circulation distributions of the main vortex for the E403 reference and the E403 delta spoiler configurations: (a) radial velocity profiles w/UN of the main vortex (OFV–ONV) for the E403 reference (baseline) and the E403 delta spoiler configurations at xn ¼ 5.56 and (b) relative viscous core radius rc/(b/2) as function of xn and radial course of non-dimensional circulation Gn at xn ¼ 5.56 of the main vortex (OFV–ONV) for the E403 reference and the E403 delta spoiler configurations.

t* E0.1 due to the interaction of the neighboured flap plate vortex and OFV having the opposite sense of rotation. But after merging, the flat plate xmax reaches again the baseline level at t* ¼0.173. Besides the analysis of axial peak vorticities the vortex induced cross flow velocities and the vortex core radius are evaluated. The radial profiles of the time-averaged vertical velocities w=U1 of the delta spoiler configurations exhibit lower velocity maxima relative to the baseline configuration at x* ¼5.56, t*¼ 0.173, while the locations of the velocity maxima are shifted outboard (Fig. 41a). For the three delta spoiler configurations, i.e. right, left and double delta device, the decrease in the maxima of the vertical velocities relative to the reference value of wmax =U1  0:16 is Dwmax =U1 ¼–10%, –25% and –33%, respectively. The radial displacement of the velocity maxima indicate that the viscous core radius rc is significantly enlarged at x* ¼3.0 as a result of the turbulence fed into the core area. This increase in rc reaches relative to the reference case values of 32%, 38% and 47% (right delta device: rc/b¼0.045, left delta device: rc/b ¼0.047 and double delta device: rc/b¼0.050, respectively; Fig. 41b). Thus, the vortex core expansion described by Eq. (14) corresponds to an

eddy viscosity level of nt E250n, which is about three times as high compared to the baseline case. The radial circulation parameter shows for the delta spoiler configurations at r/(b/2)40.15 a deviation from the course of the reference case, which is due to the lower gradient dG/dr as a result of the vorticity re-distribution (Eq. (5); Fig. 41b). At r/(b/2)E0.24 there is a difference between the reference and the delta spoiler configurations of DG*¼ 0.05–0.075. The enlargement of the vortex core radius associated with the decrease of the velocity maxima leads to the desired reduction in the induced rolling moment coefficient Cl,f (Fig. 42). The calculation of the rolling moment coefficient is based on a follower aircraft (index f) characterized by bf/b¼0.2, Lf ¼7.5, CLa,f ¼2p and Uf ¼UN. The maximum of the induced rolling moment coefficient, Cl,f,max ¼9–0.21919 exists in the area of the main vortex (OFV–ONV). Depending on the type of delta device this maximum is reduced by 12.0% (right delta device), 22.3% (left delta device) and 28.4% (double delta device), respectively. Additional towing tank experiments have proven that the enlargement of the vortex core radius accompanied with the

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.4

0.4 Cl,f,max = |− 0.2191|

0.3 0.2

0.2

0.1

0.1

0

0

-0.1 OFV– ONV

-0.2 -0.3

-0.2 -0.3 -0.4

-0.5

-0.5

-0.6

-0.6

-0.7 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Cl,f,max = |− 0.1929|

-0.1

-0.4

0

E403 Right delta device

0.3

z*

z*

125

-0.7

1

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

y* 0.4

0.4 E403 Left delta device

0.3 0.2

E403 Double delta device

0.3

Cl,f,max = |− 0.1569|

0.2

Cl,f,max = |− 0.1703|

0.1

0.1

0

0

-0.1

-0.1

z*

z*

1

y*

-0.2

-0.2

-0.3

-0.3

-0.4

-0.4

-0.5

-0.5

-0.6

-0.6

-0.7

-0.7 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

y*

1

y*

-0.30 -0.28 -0.26 -0.24 -0.22 -0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 -0.00 0.02

0.04

0.06

0.08

0.10

Levels of induced rolling moment coefficient, Cl,f Fig. 42. Field distributions of the induced rolling moment coefficient Cl,f for the E403 reference and the E403 delta spoiler configurations at xn ¼ 5.56. (a) Baseline: xn ¼ 5.56, tn ¼ 0.173, (b) right delta spoiler: xn ¼5.56, (c) left delta spoiler: xn ¼5.56 and (d) double delta spoiler: xn ¼ 5.56.

lower maxima in circumferential velocity holds also for the far field and thus the reduction in the induced rolling moment [75].

5.1.2. Differential flap setting The second passive measure concentrates on influencing the wake by deploying the inboard and outboard trailing-edge flaps at different angles, called differential flap setting (DFS). Several studies concentrate on DFS as a possible mean to alleviate the induced rolling moment [2,23,124]. Increasing the number of dominant near field vortices raises also the number of merging processes throughout the roll-up process, thus enlarging the main vortex core and reducing peak cross flow velocities. Here, the TAK baseline or reference configuration 2 features an inboard flap setting of ZIF ¼261 and an outboard flap setting of ZOF ¼261 referring to approach flight (Table 2). In addition, the effects on the wake vortex evolution and development caused by an inboard loading with a flap setting of ZIF ¼321/ZOF ¼81 (DFS 32/8) and an outboard loading of ZIF ¼81/ZOF ¼321 (DFS 8/32) are investigated.

Keeping the lift coefficient constant (CL ¼1.44, Table 3) requires in both cases an increase of the angle of attack, namely from a ¼7.01 (baseline) to 8.31 (inboard loading) and to 9.21 (outboard loading). First, the effects of the inboard loading (DFS 32/8) on the wake vortex evolution are discussed. The corresponding dominant vortices are marked in Fig. 43. The comparison of the axial vorticity fields between the baseline case and the configuration with inboard loading shows that a weaker outboard flap vortex (OFV) is present because of the less deflected outboard trailingedge flap (xOFV,Baseline ¼27, xOFV,DFS-32/8 ¼11, Fig. 43). Also, an outboard flap inboard vortex (OFIV) is shed at the inner side edge of the outboard flap. The OFIV is not as strong as the OFV and its sense of rotation is opposite to that of the OFV. A further dominant vortex is the inboard flap vortex (IFV) emanating from the flow separating along the outer side edge of the more deflected inboard trailing-edge flap. The IFV is located near the INV, which is displaced upward and slightly inboard relative to the baseline case. Consequently, the positions of ONV and OFV are changed too. Further downstream, the development of the vortex

126

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

Outboard Flap

Inboard Flap

8° 32° Inboard Loading 0.4 0.3

0.4 Baseline

0.2

WTV, 55 HTV, -64

ONV, 68

-0.1

HTV, -91

0

INV, 49

-0.2 INV, 56

-0.3

OFV 11

-0.1

OFV, 27

-0.2

-0.4

WTV, 45

0.1 z*

z*

0.1 0

DFS 3 2 / 8

0.3

0.2

IFV, 10

-0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

-0.4

ONV, 62

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y* U

Inboard

–levels

Loading INV

ONV 8°

32° OFIV

IF V

OFV

WTV

Fig. 43. Field distributions of the non-dimensional axial vorticity x for the TAK reference and TAK DFS 32/8 configuration at xn ¼ 0.37 and DFS 32/8 vortex topology (axial peak vorticity levels are added to vortex labels).

wake is characterized by the merging processes, on the one hand, of INV and IFV, and on the other hand, of OFV and ONV. After completion of these merging processes, the wake consists of a four-vortex system rolling up progressively. At x* ¼4.5, t* ¼0.105, the merging of OFV–ONV and WTV is already in progress (Fig. 45a and b). Two regions of concentrated vorticity of opposite sign, namely inboard flap vortex (IFV; xIFV,DFS-8/32 ¼13) and outboard flap inboard vortex (OFIV: xOFIV,DFS-8/32 ¼–6.5), can be clearly identified in the axial vorticity plot for the configuration with outboard loading (DFS 8/32) at x*¼0.37 (Fig. 44). At this station, the INV is already dissolved due to the strong interference with the OFIV. Compared to the baseline and inboard loading cases, the wake of the outboard loading configuration behaves differently in the near field. The IFV is orbiting clockwise around the vortex resulting from merging of OFIV and HTV, then it dissipates. Conversely, the whole wake rotates counter-clockwise during its roll-up process (cf. Section 3.4). The ONV and OFV start immediately to merge, while the latter exhibits a quite low vorticity peak in spite of the high deflection angle of the outboard flap. This weaker OFV is due to a large portion of separated flow on the strongly deflected outboard flap. At x*¼4.5, a threevortex wake is formed, where the WTV and the OFV–ONV begin to merge. The peak vorticity of the OFV–ONV system is only slightly reduced, whereas it is significantly decreased for the WTV (Fig. 45c). Relative to the reference case, both DFS configurations are

characterized by an advanced merging and roll-up process between OFV–ONV and WTV. The maximum value of the induced rolling moment coefficient, Cl,f,max ¼9–0.2969, has been found for the baseline configuration in the region of the OFV–ONV system. Both DFS configurations exhibit lower rolling moment coefficient maxima (Fig. 46): Cl,f,max ¼9–0.1549 near the WTV for the inboard loading case (here the OFV–ONV is stretched and wrapped around the stronger WTV due to the merging process), and Cl,f,max ¼9–0.1669C9–0.1679 for the outboard loading configuration in the areas near the WTV and the OFV–ONV, respectively. These values indicate a reduction in the maximum induced rolling moment coefficient relative to the baseline case of about 48% and 44%, respectively. After completion of the roll-up process and stabilization of the remaining trailing vortex, this alleviation may appear less strong. It is further shown that applying DFS a multiple vortex system with counter-rotating neighboured vortices of appropriate circulation ratio, which persists long enough for developed medium wave instabilities (cf. Section 4.2.3), is hardly achieveable.

5.2. Active means In the mid 1970s, theoretical and experimental studies dealt with the influence of sinusoidally moving flaps on the wake

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

127

Outboard Flap

Inboard Flap

8°

32° Outboard Loading

0.4 0.3

0.4 Baseline

HTV, -64 ONV, 68

-0.1

0

HTV, -50 ONV, 83

-0.1

OFV, 27

-0.2

OFV, 16

-0.2

INV, 56

-0.3

WTV, 42

0.1 z*

z*

0.2

WTV, 55

0.1 0

DFS 8 / 3 2

0.3

0.2

IFV, 13

-0.3

-0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

-0.4

OFIV, -6. 5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

Outboard

ξ−levels

U

Loading INV 8°

ONV 32°

IFV OFIV

OFV

WTV

Fig. 44. Field distributions of the non-dimensional axial vorticity x for the TAK reference and TAK DFS 8/32 configuration at xn ¼0.37 and DFS 8/32 vortex topology (axial peak vorticity levels are added to vortex labels).

vortex behaviour and predicted a reduction in the wake lifespan by a factor of three [36]. In the last years, such means were carefully investigated again. 5.2.1. Control surfaces An active system was proposed by Crouch et al. [26,27] based on periodic oscillations of control surfaces, for example, ailerons and flaperons. The perturbations influence the vortex wake to trigger inherent instabilities which, after sufficient amplification, may cause an earlier breakup of the trailing vortices into vortex rings resulting in a rapid decay. The investigations concentrate on towing tank experiments using models of generic wing configurations. The oscillating devices include inner and outer ailerons [27], trailing-edge flaps [36] and winglet flaps [10]. Depending on the streamwise distance the wake vortex hazard diminishes, quantified, for example, by the maximum induced rolling moment or vorticity distribution. Other means, such as separation control by zero massflux blowing slots at flap edges [55] and active Gurney flaps [56] are also under consideration. Further, commanded roll oscillations for shifting periodically the free circulation centroid to trigger and amplify the Crow instability has been tested as well [115]. 5.2.2. Winglet flaps Measurements have been performed with both symmetrically and asymmetrically oscillating winglet flaps on a 1:32 scaled half model on a typical large transport aircraft (Fig. 47) [10]. The model has a half span of 1.242 m (aspect ratio L ¼8.0; taper ratio l ¼0.21),

a wing mean aerodyanimic chord of lm ¼0.362 m and a fuselage length of 2.119 m. Again, a high-lift approach configuration is studied with the inboard and midboard slats set at 26.51 and the outboard slat set at 30.01. The inboard and outboard flaps are deployed to 26.01 and the ailerons (inboard and outboard) to 51. The horizontal tail plane is set to –101 according to trimmed flight. The large winglet is equipped with lower and upper moveable trailingedge flaps, the deflections of which are statically or dynamically up to d ¼ 7201. The flaps can be moved in phase (symmetrical case) or with 1801 phase shift (asymmetrical case), where the winglet flaps are deflected in opposite directions. The maximum oscillation frequency is up to 100 Hz. Here, maximum flap deflections of d ¼ 7201 at oscillation frequencies of fA ¼1–40 Hz are investigated. The latter corresponds to reduced frequencies of kA ¼fA(b/2)/UN ¼0.05–1.987. Based on freestream velocity and wing half span the reduced frequency k serves as a non-dimensional frequency parameter (Eq. (38)), and it is also used as a similarity parameter to transfer values between smallscale and full-scale conditions. The frequency range of kA E0.05–2 is chosen to cover the frequencies of dominant wake instabilities, namely, those of the Crow [28] and Crouch [25] type. Related reduced frequencies are kCrow ¼ 0.08–0.1 (long wave; Eq. (40)) and kCrouch ¼0.12 0.6 (medium wave; Eq. (41)). The maximum flap deflection angle of 201 is chosen for two reasons. On the one hand, the magnitude of the flap induced velocities at a certain frequency has to be large enough to amplify the initial disturbance level in the rolled-up vortex accelerating the development of long to medium wave instabilities responsible for wake vortex decay. On the other

128

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.1

OFV-

0

ONV,

As proven in Fig. 48 for x* ¼0.37 and x* ¼5.56, the spectral peaks associated with the oscillation frequency kA are mostly much larger than the corresponding values of the baseline configuration (oscillation off). Consequently, the relative difference between these values is of interest, which is given, for example, for the lateral velocity fluctuations by

-0.1

25.2

DSvu ¼ ðSNvuosc SNvu,Baseline Þ=SNvu,Baseline ¼ ðSNvu ðk,kA ÞSNvu ðk,kA ¼ 0ÞÞ=SNvu ðk,kA ¼ 0Þ

Baseline

0.4 0.3

z*

0.2

WTV, 46

ð42Þ

-0.2 -0.3 -0.4 -0.5 -0.6 -0.7

HTV, -3.6

INV, 1.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y* DFS 32/8

z*

0.4 0.3

WTV,

0.2

32.2

0.1

OFV-

0

ONV,

-0.1

3

-0.2 -0.3 -0.4

INV-

-0.5

IF V ,

-0.6

6.2

-0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y* DFS 8/32

0.4 0.3 0.2 0.1

WTV, 31.1 OFV-

z*

0

ONV,

-0.1

22

-0.2 -0.3 -0.4 -0.5 -0.6 -0.7

HTV+IFV, -0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 y*

Fig. 45. Vortex topology (non-dimensional axial vorticity distributions) for the TAK reference and TAK DFS 32/8 and TAK DFS 8/32 configurations at xn ¼ 4.50 (axial peak vorticity levels are added to vortex labels): (a) baseline, (b) DFS 32/8 and (c) DFS 8/32.

hand, the maximum deflection angles at full-scale frequencies are limited by the performance of real aircraft actuator systems. Here, the velocities induced by the oscillating winglet flaps are on the order of 25% with respect to the freestream velocity. They are aimed to increase the axial, lateral and vertical velocity fluctuations at the frequencies of long wave instabilities in the rolled-up (main) vortex by at least a factor of 3–5. Therefore, the most downstream located cross flow plane at x*¼5.6 is inspected and results are compared with those obtained without flap oscillations (baseline).

As expected, local maxima along a diagonal line, here indicated by values larger than 2, are found (Fig. 49). This diagonal trace reflects a synchronous forcing of desired disturbances by introducing frequency dependent velocity fluctuations. In addition, vertical traces of peaks in the spectral differences are detected, for example, at reduced frequencies of kE0.1 and kE0.3, reflecting also narrowband concentrations of turbulent kinetic energy. These peaks along vertical lines indicate an increase of the velocity fluctuations at specific frequencies independent of the specific forcing frequency, that is, the effect of a receptive mechanism to asynchronous forcing. The presence of instability mechanisms propagating along the vortex wake in streamwise direction can lead to a relevant distortion of the trailing vortex pair, accelerating its decay and dispersion, cf. Section 4.2. The wavelength of the Crow type instability obtained by linear stability analysis is approximately lCrow E8b0, Eq. (28). The quantity b0 is the lateral distance of the vortex pair, with b0 ¼0.76b–0.78b for the present case [8]. Thus, the wavelength corresponds to a reduced frequency of kCrow E0.08, Eq. (39). Velocity fluctuations caused by turbulence or fed actively into the vortex wake represent inhomogeneous forcing terms with respect to stability theory. The influence of turbulence on wake vortex life spans was investigated, e.g. by Crow and Bate [29]. Regarding linear stability theory the velocity perturbation at the core of the trailing vortex is then composed by the component due to mutual induction and the component related to superimposed fluctuations. Introducing such fluctuations at the frequency of the inherent instability may significantly reduce the time for vortex linking. Rapid wake decay will then start within a shorter trailing distance compared to the nonperturbed case. The reduced frequency of kE0.1, related to the first vertical line of local spectral maxima in Fig. 49, is close to the value of kCrow. It indicates that the development of the Crow type instability is also accelerated to a certain extent by asynchronous forcing. The vorticity pattern taken at x*¼ 5.6 shows that for some cases two vortex pairs are still present consisting of the weak winglet vortex (WLV) and the main vortex (merged OFV/ONV/ WTV). Further instabilities are related to the case of two vortex pairs with co-rotating neighboured vortices, see ‘‘Crouch instability’’ Section 4.2.3. The related instabilities include a symmetrical mode corresponding to the long wave Crow instability, but also additional symmetric and anti-metric modes of medium wave lenghts are present. The growth rate can be twice that of the Crow instability and transient growth of the long wave instability can amplify an initial disturbance by a factor of 10. For the Crouch instability, the reduced frequency range is kCrouch E0.25–0.8, Eq. (40). The vertical line of the local spectral maxima at kE0.3, observed in Fig. 49 for the lateral velocity fluctuations, falls within this frequency range. It indicates that the development of such instabilities can also be provoked by introducing controlled disturbances. In summary, the oscillation of the winglet flaps leads to a concentration of turbulent kinetic energy in the frequency range of dominant inherent instabilities for both, symmetrical and asymmetrical flap deflections. Although the oscillations with asymmetrically deflected flaps show lower amplifications in

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

129

0.4 WTV

0.3 0.2 Cl,f = |− 0.2279|

0.1

z*

0 OFV– ONV

-0.1 -0.2 -0.3 -0.4

Cl,f = |− 0.2958|

-0.5 TAK Baseline

-0.6 -0.7 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

0.4

0.4 WTV

0.3

0.2

0.1

0.1

Cl,f,max = |− 0.1541 |

0

0

-0.1

-0.1

z*

z*

WTV

0.3

0.2

-0.2

Cl,f = |− 0.1655 |

-0.3

Cl,f = |− 0.1374 |

-0.4

-0.4

INV/ IFV+

-0.5

-0.5

-0.6

-0.6

TAK DFS 32/8 0

OFV– ONV

Cl,f,max = |− 0.1670 |

-0.2

-0.3

-0.7

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

1

-0.7

TAK DFS 8/32 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y*

-0.30 -0.28 -0.26 -0.24 -0.22 -0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 -0.00 0.02

0.04

0.06

0.08

1

0.10

Levels of induced rolling moment coefficient, Cl,f Fig. 46. Field distributions of the induced rolling moment coefficient Cl,f for the TAK reference and the TAK DFS 32/8 and TAK DFS 8/32 configurations at xn ¼4.50: (a) baseline: xn ¼ 4.50, tn ¼ 0.105, (b) DFS 32/8: xn ¼4.50 and (c) DFS 8/32: xn ¼ 4.50.

comparison to the symmetrical case, it is still favorable as the overall lift and side force as well as the pitching moment are fairly constant over the oscillation period.

6. Conclusions An overview on wake vortex research including early studies, integrated national and European programs, model and flight tests, numerical investigations and fundamental physical aspects and alleviation strategies has been presented. In particular, characteristic quantities for wake vortex analysis including typical length and time scales as well as turbulence quantities are shown. The discussion and analysis concentrate on detailed results on the near field wake vortex properties associated with large transport aircraft in approach configuration. In context of the far field development instability mechanisms are explained along with their relevance for wake vortex decay. Parameters are given for short wave instabilities related to vortex merging and long and medium wave instabilities for wakes consisting of a twoand four-vortex system, respectively. Finally, studies on wake

vortex alleviation are shown including spoiler elements, differential flap setting and oscillating winglet flaps. The following features characterize the trailing vortex system in the near field (x/br0.5, t* r0.01):

 Four-engine large transport aircraft in approach configuration generates heterogeneous vortex systems where concentrated single vortices are embedded in the vortex sheet emanating from the wing trailing-edge. Progressing from the wing tip to the wing root, the dominant single vortices typically are: the wing tip vortex, the outboard flap vortex, the outboard and inboard nacelle vortices and the wing fuselage vortex. The latter shows an opposite sense of rotation with respect to the other dominant wing vortices due to a change in the circulation gradient at the wing fuselage junction. A further dominant vortex is the horizontal tail plane vortex. It is also counter-rotating with respect to the wing tip vortex because of the negative lift produced by the horizontal tail at trimmed flight. In addition, concentrated vortices of smaller scale are shed, for example, at nacelle strakes, and are further due to flow separation at slat horns, flap track fairings, etc.

130

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

0.013 b

Upper flap ηWA = ± 20°

38.4°

48.0 ° 0.067 b

Lower flap ηWI = ± 20° Motor housing 0.037 b

Configuration data: b ηIS ηMS ηOS

= = = =

2.484 m 26.5° 26.5° 30.0°

; Λ = 8.0 ; ; ; ;

ηIF ηOF

= =

26.0° 26.0°

; ξI = 5.0° ; ; ξO = 5.0° ;

ε

=

–10.0°;

Relµ α

= =

0.5 ×106 ; 6.5° ; CL = 1.43

Fig. 47. Winglet with active devices for wake vortex alleviation tested on a large transport aircraft configuration: (a) winglet with actively controlled lower and upper flap elements; fA,max ¼100 Hz and (b) half model of a four-engine large transport aircraft fitted with large winglet featuring trailing-edge flaps.

 The dominant single vortices can be detected by local maxima in the (dimensionless) axial vorticity distributions (xmax ¼ 30–70), minima in the related axial velocities ððU1 umin Þ= U1  0:25Þ and maxima in turbulence intensities (Tumax E 9–12%). The deficit in the axial velocity is related to the wing boundary layer contributing to the vortex sheet shed at the wing trailing-edge. Changes in gradients and curvatures of the velocity profiles associated with the wing vortex sheet and the three-dimensional turbulent boundary layer result in local turbulence maxima corresponding to the core areas of the dominant single vortices.



For the extended near field (0.5 ox/br10, 0.01 o t* r0.2), the wake vortex characteristics are as follows:

 The wake vortex development is determined by the roll-up process and the merging of adjacent dominant vortices. Outboard flap vortex and outboard nacelle vortex merge until t* E0.04 constituting the so-called main vortex, the position of which is linked to the center of the free circulation (b0 E 0.7b–0.8b). The merging of the main vortex with the (weaker) wing tip vortex is completed up to t* E0.2, where the wing tip vortex has rotated typically once around the main vortex. The entire roll-up process is finished up to t*E0.25–0.3.





For the present Reynolds numbers of ReG 4104, the merging of co-rotating vortices starts at a critical ratio of viscous vortex core diameter to vortex distance of rc/d¼0.2–25. The development of a short wave cooperative elliptic instability speeds up the merging process and contributes to the enlargement of the core radius of the resulting vortex. The main trailing vortex shows maximum circumferential velocities of about 15–25% of the freestream velocity associated with axial vorticity maxima of xmax E15–25. The related axial velocity deficit stabilizes downstream at levels of 8%. The turbulence intensities in the core region of the main vortex reach local maxima of approximately Tumax E8–9%. The turbulence levels of the surrounding wing vortex sheet are Tu E1–2%, while the area of the plane of symmetry with an expanded shear layer region exhibits turbulence levels of Tu E2–4%. Throughout the roll-up process, the viscous core radius of the main vortex increases in size due to turbulence and merging processes. This expansion, defined by the growth rate Drc2 =Dt, is 50 times larger than the one given by fluid viscosity only. The typical length scales are for the inner/viscous core radius rc ¼0.03b–0.04b and for the outer/vortcity radius rv ¼0.1b–0.12b. For the wake vortex systems considered here, the maximum induced rolling moment coefficient related to a follower

C. Breitsamter / Progress in Aerospace Sciences 47 (2011) 89–134

131

2 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Sv’

kA

1.5

1

0.5

0

0

Crow instability

0.5

1

1.5 k

2

2.5

3

Crouch instability

2

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Sv’

kA

1.5

1

0.5

0

0

0.5

1

1.5 k

2

2.5

3

Fig. 49. Distribution of the relative differences in power spectral densities DSv0 (k;kA) between the baseline case and the cases with oscillating winglet flaps obtained for the region of the main vortex of a large transport aircraft configuration at xn ¼ 5.56: (a) oscillation with 01 phase shift—symmetrical deflection and (b) oscillation with 1801 phase shift—unsymmetrical deflection. Fig. 48. Power spectral densities of the axial velocity fluctuations SN u obtained in the region of the main vortex at (a) xn ¼ 0.37 and (b) xn ¼5.56 for various reduced excitation frequencies kA.

aircraft, with a wing span of 20% of the leading aircraft and a lift slope of 2p, is in the range of Cl,f,max ¼0.30–0.22 at stations of t* E0.11–0.17.

During the interaction of the wake vortices, long, medium and short wave instabilities develop. For classification and analysis, characteristic reduced frequencies based on freestream velocity and wing half span are assigned. Considering the dominant long wave instability, well-known as the Crow instability (lCrow/ b0 E8.0), the corresponding reduced frequency is kCrow ¼ 0.087 0.01. Regarding four-vortex systems with co-rotating main and minor vortices, medium wave instabilities occur, known as Crouch instabilities (lCrouch =b~ 0 ¼ 1:56:0), the amplification rate of which can be twice that of the Crow instability. The reduced frequency range is kCrouch ¼0.5470.28. The turbulent merging of co-rotating vortices is accompanied by a short wave elliptic instability (lV/rc ¼3.0–3.6). The corresponding reduced frequency range is kV ¼4.271.4.

Based on the wake vortex characteristics obtained for the reference configurations, both passive and active means for wake vortex alleviation have been studied. These means include delta type spoiler devices, differential flap setting (DFS) featuring inboard and outboard loadings and a large winglet equipped with lower and upper flaps which provide harmonic oscillations at given frequencies and amplitudes. The main results are as follows:

 Specifically designed spoilers of delta type planform are deployed to create a zone of highly turbulent flow in the area of the outboard flap vortex, also influencing the region of the free circulation center. During the roll-up process with the merger of the outboard flap and outboard nacelle vortices, the highly turbulent flow is fed into the core region of the main trailing vortex. Relative to the reference case (no spoiler deflection), a marked dispersion of the vorticity field is achieved up to t* E0.1, resulting in a reduction in axial peak vorticity. A significant expansion of the viscous core by 50–90% occurs accompanied by a reduction in maximum induced velocities of about 50% and in the maximum induced rolling moment of about 30%. The use of the delta type spoilers affects only slightly the overall flight performance.

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 The differential setting of inboard and outboard trailing-



edge flaps results in an inboard or outboard wing loading. Typically, the angle of attack must be increased to keep the lift coefficient at the level of the reference case. Differential flap setting is associated with the shedding of additional vortices, namely at the outboard side edge of the inboard flap and the inboard side edge of the outboard flap. These vortices are counter-rotating to each other while their respective strengths depend on the flap deployment angle. They influence the sequence of vortex merging in the extended near field, so that the persistence of a multiple vortex system is supported over a larger distance downstream. An inboard loading leads to a main vortex of less strength and enhances its merging with the wing tip vortex. The reduction in the maximum induced rolling moment is up to 48%. The outboard loading results in a vortex topology similar to the reference case. Due to the interaction of the additional vortices a reduction in the maximum induced rolling moment of about 44% is achieved. Periodic variations of the spanwise load distribution by means of oscillating control surfaces such as ailerons and/or spoilers may significantly amplify the excitation of inherent instabilities. The forcing frequency is adapted to the wave number associated with the highest amplification rate of the considered instabilities. It has been demonstrated in model studies that by such means the time up to contact of the trailing vortices could be halved with the subsequent exchange of circulation via the symmetry plane and the beginning of wake vortex decay. In the present case, the potential of a large winglet with two integrated trailing-edge flaps has been investigated. Harmonic oscillations of the two flaps with 1801 phase shift ensure the temporal stability of the overall aerodynamic coefficients. Regarding flowfield stations at the main vortex at t* E0.16 (x/b¼5.6), the results document an increase by a factor of 2–5 in the power spectral densities of the velocity fluctuations at reduced frequencies corresponding to the Crow and Crouch type instabilities. This increase in spectral energy significantly raises the excitation level attributed to the inherent instabilities triggering an increase in their amplification.

A final evaluation of the considered wake vortex alleviation means can only be obtained performing flight tests. Within the European technical platform AWIATOR, spoiler deflection (standard outboard spoiler), differential flap setting and oscillating ailerons have been investigated using the A340 test aircraft to evaluate the potential of such means. Here, atmospheric turbulence is of great importance, which could markedly overlay the effects obtained by configuration measures. Additional studies are needed to further develop and provide solutions taking the aircraft system as a whole into account.

Appendix. Lamb–Oseen vortex model The Lamb–Oseen vortex model is the basic vortex model taking viscosity into account. The model describes a twodimensional flow characterized by circular streamlines around the axis or vortex center. The vorticity o ¼ ox is a function of radial distance r and time t. It results as an exact solution of the Navier–Stokes equations based on the initial condition o(r,0) ¼ G0d(x)d(y). Hence, the Navier–Stokes equations reduce to a single equation for the vorticity: @o ¼ nr2 o @t

ð43Þ

The exact solution including (axial) vorticity and (circumferential/tangential) velocity is i 2 G G h 2 ox ¼ 0 eðr =4ntÞ ðaÞ; Vy ¼ 0 1eðr =4ntÞ ðbÞ ð44Þ 4pnt 2pr The relation for the viscous vortex core radius rc represents the temporal development of the vortex core structure due to viscous diffusion: 2 rc2 ðtÞ ¼ rc,0 þ 4bnðtt0 Þ ðaÞ;

drc2 ¼ 4bn ðbÞ dt

ð45Þ

Hence, the axial, radial and circumferential velocity components associated with a cylindrical coordinate system can be written as   2 r G0 1eb rc ðcÞ Vx ¼ 0 ðaÞ; Vr ¼ 0 ðbÞ; Vy ¼ 2pr With dVy/dr¼0 at r ¼rc, the parameter b is calculated to be

b ¼1.25643. The axial vorticity ox and the circulation parameter G (Eq. (5)) and dG/dr then yield

ox ðrÞ ¼

G0

prc2

2

bebðr=rc Þ ðaÞ;

2 dG r ¼ 2b 2 ebðr=rc Þ ðcÞ dr rc

2

GðrÞ ¼ 1ebðr=rc Þ ðbÞ; ð46Þ

The velocity gradient is the largest at the vortex center where the radial profile of the circumferential velocity represents a solid body rotation reflecting the influence of viscosity. The maximum (axial) vorticity ox,max ¼ bG0 =ðprc2 Þ is linked to the vortex center, r¼ 0, while the maximum circumferential velocity Vy,max ¼ G0 =ð2prc Þð1eb Þ is reached at the radial position given by the viscous core radius, r¼ rc. Long time periods are needed to alter the vorticity distribution at large distances due to viscosity. The circulation far from the axis is time independent according to Kelvin’s theorem. The circulation attributed to the vortex core is G(rc) ¼ G0(1–e–1.25643)¼0.716G0, which is about 72% of the total circulation. Typically, real trailing vortices show lower values [126]. The Lamb–Oseen vortex model serves as a reference case analyzing the influence of viscosity on the trailing vortex characteristics. References [1] Bellastrada C, Breitsamter C. Large transport aircraft wake affected by vortex devices. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, NNFM, vol. 87. Springer Verlag; 2004. p. 1–9. [2] Bellastrada C, Breitsamter C. Effect of differential flap settings on the wake vortex evolution of large transport aircraft. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, NNFM, vol. 92. Springer Verlag; 2006. p. 25–32. [3] Bellastrada C, Breitsamter C, Laschka, B. Analysis of turbulent wake vortex behind a large transport aircraft in landing configuration. In: Jahrbuch der ¨ Luft- und Raumfahrt–Lilienthal-Oberth e.V., Deutschen Gesellschaft fur Hamburg, September 17–20, DGLR-2001-178; 2001. ¨ Angewandte [4] Betz A. Das Verhalten von Wirbelsystemen. Zeitschrift fur Mathematik und Mechanik 1932;XII(3):164–74. [5] Bilanin AJ, Donaldson CduP. .Estimation of velocities and roll-up in aircraft vortex wakes. AIAA Journal of Aircraft 1975;12(7):578–85. [6] Bilanin AJ, Teske ME, Williamson GG. Vortex interactions and decay in aircraft wakes. AIAA Journal 1977;15(2):250–60. ¨ [7] Breitsamter C. Turbulente Stromungsstrukturen an Flugzeugkonfiguratio¨ nen mit Vorderkantenwirbeln. Dissertation, Technische Universitat ¨ Munchen, Herbert Utz Verlag Wissenschaft (Aerodynamik); 1997. ISBN 3-89675-201-4. [8] Breitsamter C. Nachlaufwirbelsysteme großer Transportflugzeuge— Experimentelle Charakterisierung und Beeinflussung. Habilitationsschrift, ¨ Munchen, ¨ Technische Universitat Herbert Utz Verlag Wissenschaft (Aerodynamik); 2007. ISBN 3-8316-0713-6. [9] Breitsamter C. Aerodynamic active control for fin buffet load alleviation. AIAA Journal of Aircraft 2005;42(5):1252–63.

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