Aerodynamics of cross-flow fans and their application to aircraft propulsion and flow control

ARTICLE IN PRESS Progress in Aerospace Sciences 45 (2009) 1–29 Contents lists available at ScienceDirect Progress in Aerospace Sciences journal home...

Download PDF

4MB Sizes 374 Downloads 408 Views

Report

Full Text

ARTICLE IN PRESS Progress in Aerospace Sciences 45 (2009) 1–29

Contents lists available at ScienceDirect

Progress in Aerospace Sciences journal homepage: www.elsevier.com/locate/paerosci

Aerodynamics of cross-ﬂow fans and their application to aircraft propulsion and ﬂow control Thong Q. Dang a,, Peter R. Bushnell b a b

Department of Mechanical & Aerospace Engineering, Syracuse University, Syracuse, NY, USA Air Management & Acoustics Engineering, Carrier Corporation, Syracuse, NY, USA

a r t i c l e in fo

abstract

Available online 6 December 2008

Cross-ﬂow fans offer unique opportunities for distributed propulsion and ﬂow control due to their potential for spanwise integration in aircraft wings. The fan may be fully or partially embedded within the wing using a variety of possible conﬁgurations. Its inlet may be used to ingest the boundary-layer ﬂow, and its high-energy exhaust ﬂow may be injected into the wake at the wing trailing edge for drag reduction or vectored thrust. Cross-ﬂow fans are high-pressure coefﬁcient machines, so they can be diametrically compact. However, their efﬁciency is fundamentally limited by unavoidable recirculation ﬂows within the impeller at all ﬂight speeds, and by additional compressibility losses at high speeds. This article reviews the fundamental aerodynamics and ﬂow regions of cross-ﬂow fans using a simple mean-line analysis to examine the basic energy transfer and loss processes. Experimental data for fans intended for aircraft application are then reviewed and compared to calculations using unsteady Navier–Stokes methods, showing the state-of-the art in ﬂow ﬁeld and performance prediction capability. Alternative prediction methods where blade action is modeled in terms of body-force or vortex elements are discussed, including challenges in handling arbitrary non-uniform, unsteady blade ﬂows for various design conﬁgurations. The article concludes with a review of cross-ﬂow fan propulsion and ﬂow control concepts that have been investigated by various researchers, and with discussions on future challenges in their application. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Airfoil Cross-ﬂow fan Flow control Propulsion Turbomachine

Contents 1. 2.

3. 4.

5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Fundamental aerodynamics of cross-ﬂow fans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1. Three ﬂow regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2. Energy transfer in region A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3. Flow in regions B and C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4. Performance analysis and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Experimental studies of cross-ﬂow fans for aviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Prediction methods for cross-ﬂow fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1. Unsteady-ﬂow methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2. Steady-ﬂow methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Aircraft concepts using cross-ﬂow fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1. Introduction

Corresponding author. Tel.: +1 315 443 4311; fax: +1 315 443 9099.

E-mail address: [email protected] (T.Q. Dang). 0376-0421/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.paerosci.2008.10.002

The cross-ﬂow fan consists of a drum-like rotor with forward curved blades, encased within housing walls as shown in Fig. 1. The inlet and outlet have rectangular cross-sections, and the key advantage of the fan in most applications is its ability to extend lengthwise, producing a uniformly distributed inﬂow and outﬂow.

ARTICLE IN PRESS 2

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Nomenclature c Di Do q Q J FB Fv p Pt Pt Ri Ro rpm S Tt Ui Uo Uj Uw UN w Ws

a b b0 z D

e f l O

absolute velocity impeller inner diameter impeller outer diameter dynamic pressure based on impeller tip speed volumetric ﬂow rate advance ratio blade body force viscous body force static pressure total pressure rotary stagnation pressure impeller inner radius impeller outer radius revolution per minute arc length measured around impeller total temperature blade speed at impeller inner radius blade speed at impeller outer radius propulsor exhaust velocity wake velocity free-stream velocity relative velocity impeller shaft power absolute ﬂow angle relative ﬂow angle blade metal angle blade stagger angle overall change ﬂow deﬂection (turning) angle fan ﬂow coefﬁcient power coefﬁcient impeller rotational speed

Therefore, the impeller length-to-diameter ratios are often large. Geometric design of the fan housing (or casing) tends to be quite varied and in some cases difﬁcult to classify and parameterize. However, the primary features can be identiﬁed as the rear wall, vortex wall (or stabilizer) and end-walls. Fig. 2 from Eck [1] gives an idea of the broad range of possible housing designs that can be used. Most housings are intended for approximately 901 ﬂow turning from inlet to outlet, however, the fan is capable of 1801 turning (casing 6) and in-line ﬂow (casing 7). The in-line design is of particular interest for aircraft applications.

Zc Zd Zp Zs Zt r c

fan adiabatic compression efﬁciency diffuser efﬁciency propulsion efﬁciency fan total-to-static efﬁciency fan total efﬁciency density pressure coefﬁcient

Subscripts 1 2 3 4 A atm B C i o r s t v

y

impeller ﬁrst stage inlet station impeller ﬁrst stage outlet station impeller second stage inlet station impeller second stage outlet station region A ambient condition region B region C inner blade station, also ideal outer blade station radial direction static total vortex (region C) circumferential direction

Others e^ r e^ y n^ ˜ o

unit vector in radial direction unit vector in circumferential direction unit vector normal to mean streamline in impeller region total pressure loss coefﬁcient

The fan rotor generally includes a large number of forward curved blades (around 35) with inner-to-outer diameter ratio of approximately 0.75. The rotor generally includes a series of partition disks and end-plates. A variety of tone noise de-phasing features may be used in the impeller design, including nonuniform blade spacing. The main parameters of the commonly used double circular arc type blades are shown in Fig. 3. Variation and optimization of impeller design and housing for airconditioning applications has been examined by many developers over decades and is relatively mature, while its use as a propulsor

Fig. 1. Main features of cross-ﬂow fans.

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 2. Sample cross-ﬂow fans from Eck [1].

Fig. 3. Double circular arc blade deﬁnition.

arrangement cited there. Mortier’s motivation was mine ventilation and his fans were used for that purpose with rotor diameters up to nearly 3 m. Shortly thereafter, axial ﬂow propeller fans came into favor and interest in the cross-ﬂow fan faded for about two decades. A reemergence occurred in the late 1920s and 1930s with a variety of patents with applications for drying grain, airconditioning, and feeding pulverized fuels (e.g. [3,4]). Despite these inventions early acceptance of the cross-ﬂow fan was limited due to relatively poor performance in relation to centrifugal fans of the time. The ﬁrst reference to use of the cross-ﬂow fan for aircraft application was provided in a 1938 lecture appropriately titled ‘‘Present and Future Problems of Airplane Propulsion,’’ by the Swiss aeronautical engineer, J. Ackeret [5]. Ackeret described a concept for boundary-layer control by means of energizing the boundary-layer ﬂow using a cross-ﬂow fan, as shown in Fig. 5, and carried out some preliminary calculations for the necessary size of the fan. The 1950s brought about signiﬁcant developments and commercialization of cross-ﬂow fans, and Coester [6] developed the ﬁrst simple vortex model for the fan internal ﬂow. Perhaps the most noteworthy early developer and researcher of cross-ﬂow fans is Bruno Eck, and his comprehensive book [1] describes their ﬂuid mechanics and controlling parameters, including the predominant eccentric vortex region which he discovered. Eck also outlines the wide range of possible vortex wall designs and their inﬂuence on fan performance. Progress and utilization of cross-ﬂow fans thereafter has been considerable, based primarily on experimental development, seeking means for stabilizing the vortex and fan performance (e.g. [1,7,8]). Simpliﬁed models of the fan were developed using potential ﬂow and mean-line analysis (e.g. [9–11]), but limited capability was achieved with those techniques. In the 1970s new initiatives were made for exploring crossﬂow fan use in aircraft propulsion and ﬂow control [12–14], but the work was stopped in the 1980s after the US Navy interest in the development of VTOL aircraft diminished. Subsequently, the use of cross-ﬂow fans in air-conditioning and air-curtains grew rapidly. Their advantages in compactness and integration with heat exchangers make them especially attractive for those applications. As a result, research and development in design and prediction for both performance and noise has occurred leading to the progression from exclusively empirical to analytical based design, particularly through the use of unsteady Reynoldsaveraged Navier–Stokes (URANS) CFD methods (see e.g. [15]). With these modern CFD methods and initiatives on unmanned aerial vehicles (UAVs) and the NASA Personal Air Vehicle program, work on aircraft concepts powered by cross-ﬂow fans has reemerged (e.g. [16–22]). The cross-ﬂow fan has unique advantages for aircraft applications because of its effectively rectangular arrangement with length adjustable to distribute along the wing span and diameter scalable to integrate with the wing thickness. Fig. 6 shows an example of how a cross-ﬂow fan can be integrated into a wing for propulsion and ﬂow control (e.g. boundary-layer ingestion and

Fig. 4. Mortier fan, taken from 1893 US patent [2].

or ﬂow control device in aircraft applications has received much less attention. The cross-ﬂow fan can be traced as a speciﬁc invention in 1891 by Paul Mortier with patent 215,662 ﬁled in France. A corresponding US Patent [2] was awarded in 1893, and Fig. 4 shows the fan

3

Fig. 5. Boundary-layer blowing fan by Ackeret [5].

ARTICLE IN PRESS 4

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 6. Cross-ﬂow fan embedded in aircraft wing proposed by Dornier [23].

wake ﬁlling), as proposed by Dornier [23] in 1962. In this case, the cross-ﬂow fan is placed inside a thick wing and distributed over the span creating a distributed propulsion system (e.g. [24,25]). Boundary-layer air from the suction and/or pressure surfaces is ingested into the fan, energized by it, and expelled downstream to produce thrust. As the fan spans over most of the wing, the exhaust ﬂow also reduces the wake deﬁcit producing a wakeﬁlling effect [26,27]. Wake ﬁlling via distributed propulsion has several beneﬁts, including improved propulsion efﬁciency, which is deﬁned as the ratio of the thrust power to the rate of production of propellant kinetic energy. To illustrate this point, consider the simpliﬁed examples of two propulsion systems shown in Fig. 7. The upper ﬁgure shows the conventional single-stream propulsion system layout where the propulsor is attached to the vehicle body via a nacelle/pylon structure, while the bottom ﬁgure shows a propulsion system placed at the rear of the body (e.g. propulsion system for naval torpedo). It is assumed that both have the same wake thickness and velocity deﬁcit of magnitude Uw. In the case of the conventional propulsion system, the air ingested into the engine has kinetic energy per unit mass of U2N/2 and the exhaust kinetic energy per unit mass is Uj2/2, with Uj4UN. In the case of the wake-ﬁlling propulsion system, the air ingested into the engine is the wake and has kinetic energy per unit mass of Uw2/2, and the exhaust kinetic energy per unit mass is U2N/2 (at the cruising condition). Neglecting the drag generated by the nacelle and pylon, the drag is the same for both cases and hence the thrust required by both propulsion systems is the same at the cruise condition. On the other hand, it is clear that the change in propellant kinetic energy through the engine is higher for the conventional propulsion system than for the wake-ﬁlling system. It can readily be shown that 2 1 þ ðU j =U 1 Þ

(1)

2 1 þ ðU w =U 1 Þ

(2)

ðZp Þconventional ¼

ðZp Þwake filling ¼

It is seen from the above relations that while the maximum propulsive efﬁciency of the conventional system approaches 1 when Uj/UN-1, the corresponding value of the wake-ﬁlling propulsion system can reach 2 when Uw/UN-0. The fact that Zp can be greater than 1 is well known to the naval industry, and the term propulsive coefﬁcient is sometimes used for Zp. Smith [27] showed that reduction of the wake distortion behind a body through ingestion of the viscous wake into an engine reduces the necessary propulsive power. Using actuator disk theory, Smith demonstrated that it is possible to achieve propulsive efﬁciencies greater than 1, the theoretical maximum for propulsion without wake ingestion. In the same light, if the engine ingests the boundary layer over the surface of a wing, the same beneﬁt can be realized by re-energizing the low momentum

Fig. 7. Conventional and wake-ﬁlling propulsion systems.

ﬂuid and expelling it out at the trailing edge to ﬁll in the wake. Even without considering boundary-layer ingestion, Ko [28] estimated that for a blended wing body aircraft with embedded propulsion, the propulsive efﬁciency could be increased from about 80% to 90% using the effect of wake ﬁlling. Finally, Kummer and Dang [20] employed CFD to demonstrate that an embedded propulsion system based on the cross-ﬂow fan can reach propulsive efﬁciency greater than 1. In addition to increased propulsive efﬁciency, embedded propulsion can potentially provide reduced noise and increased safety, since the propulsor is now buried within the structure of the aircraft (e.g. no exposed blading). Also, by eliminating the engine pylon/nacelle support structure, the aircraft parasitic drag can be reduced by 18–20%, thus improving cruise efﬁciency and range. Design of embedded propulsion systems using conventional propulsors presents many challenges. First, by embedding the engines within the wing structure, the fan size becomes restricted, and conventional axial propellers and turbofan engines incur performance penalties as their sizes are reduced. Also, embedded propulsors will inherently ingest non-uniform boundary-layer ﬂows, which tend to reduce engine performance further [29]. With cross-ﬂow fans, however, these problems are less severe as their performance is less affected by the size constraint imposed by the wing thickness, and their performance has been shown through CFD to be less sensitive to inlet ﬂow distortion. In particular, Kummer [30] showed that, using the in-line CFF housing geometry he developed, the exhaust velocity proﬁle was a weak function of the shapes of the inlet velocity proﬁle, which included uniform and boundary-layer-like proﬁles. The integration of the cross-ﬂow fan into an airfoil has also been shown to be capable of providing circulation control [21,22]. In particular, increased ﬂow ingestion into the fan by increasing its rotational speed or redirecting the exhaust ﬂow via ﬂaps (jet-ﬂap effect) can result in increased lift coefﬁcient. Sectional lift coefﬁcient on the order of 7 has been shown possible with this powered-lift device, resulting in short takeoff and landing (STOL) capability and low in-ﬂight aircraft stall speed without the use of additional high lift devices such as slotted ﬂaps or leading edge slats. The combination of circulation control and differential thrust, accomplished through fan speed and external exhaust nozzle shape, may eliminate the need for other ﬂight control surfaces. A well-known disadvantage of the cross-ﬂow fan is its low efﬁciency. However, it can compete with other propulsion technologies at the system level. The embedded cross-ﬂow fan yields lower drag relative to the conventional pylon/nacelle support structure, and as mentioned earlier, its performance is relatively insensitive to wake ingestion, making it suitable for

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

applications that require thick wings (e.g. ﬂying wing platform). Even at low angle-of-attack, the wake created by a thick airfoil can be quite large for thick wings, producing high levels of pressure drag. This renders thick wings sections impractical for most aircraft applications as the drag penalty outweighs any beneﬁts gained in lift or interior volume. This article seeks to review the basic aerodynamics of crossﬂow fans and their application in aircraft propulsion, and is organized as follows. Section 2 presents the basic ﬂuid mechanics and energy transfer processes of the fan with the aid of a simpliﬁed one-dimensional model. Performance data of crossﬂow fans speciﬁcally developed for aviation applications are reviewed in Section 3. In Section 4, prediction methods based on unsteady-ﬂow CFD methods and simpliﬁed steady-ﬂow methods are described, along with comparisons of prediction results to test data. The unsteady-ﬂow CFD results are also used to illustrate the detailed ﬂow ﬁeld of the cross-ﬂow fan, emphasizing the speciﬁc ﬂow regions. In Section 5, we review several aircraft concepts that employ the cross-ﬂow fan as a propulsor and/or ﬂow control device along with test data and computational results. Finally, concluding remarks are given in Section 6.

2. Fundamental aerodynamics of cross-ﬂow fans 2.1. Three ﬂow regions In this section, we review the basic aerodynamics and energy transfer processes in cross-ﬂow fans. We show that the ﬂow within the impeller can be classiﬁed into three distinct regions and a mean streamline analysis is used to describe the throughﬂow and loss characteristics of the fan. Computational and experimental data are presented along the way to aid in the physical description of the behavior of this unique turbomachine. The ﬂow ﬁeld of the cross-ﬂow fan is predominantly twodimensional (2D), moving perpendicular to the impeller axis. Flow enters the blade row in the radially inward direction on the upstream side, passing through the interior of the impeller, and then passes radially outward through the blading a second time. The ﬂow is characterized by the formation of an eccentric vortex that runs parallel to the rotor axis with rotation in the same direction. Fig. 8 shows an example ﬂow ﬁeld prediction based on a URANS analysis. In the ﬁgure the path-lines in the region exterior to the impeller are referenced to the stationary frame, while those on the interior are referenced to the rotating frame. Fan rotation is counter-clockwise.

Fig. 8. Cross-ﬂow fan instantaneous path-lines from URANS simulation.

5

It is important to note that the eccentric vortex develops even for an impeller in an open ﬂuid in the absence of casing walls. In such cases, as demonstrated experimentally by both Eck [1] and Yamafuji [31], the vortex leads to an adjacent through-ﬂow region. However, without casing walls the vortex and through-ﬂow tend to orbit about the fan centerline, and a vortex stabilizer wall is needed to lock the ﬂow in place. With the addition of the rear wall, a fully cased fan is created. Casing walls or not, the ﬂow pattern is sustained by the circumferentially non-uniform loading in the impeller blading that arises with one portion of the impeller advancing into the mean ﬂow and the other retreating away. The natural tendency of the fan is to produce an approximately 901 turn in the main ﬂow. A mean streamline analysis follows based on Bushnell [32] for the case of low Mach number, incompressible ﬂow. It begins with the assumption that the ﬂow within the fan can be divided into three regions that may be analyzed independently. Simple models for each region are then assembled to analyze the overall performance. This approach relies on estimations of the ﬂow region boundaries and blade cascade performance, presenting basic predictive limitations as the ﬂow tends to be strongly inﬂuenced by fan geometry and operating conditions, and in fact, the three regions are quite interactive. Nevertheless, the analysis is constructive in demonstrating the kinematics of the ﬂow and the fundamental energy transfer processes. Mean-line methods of a similar nature have been presented by other researchers (e.g. [7,11,33,34]). The three ﬂow regions can be seen in Fig. 8 and are also evident experimentally in ﬂow visualization data. Visualization using water tank rigs with Reynolds number scaling has been carried out by numerous researchers, providing key insight on the behavior of cross-ﬂow fans (e.g. [1,7,8,31,35,36]). These methods have been especially important prior to the advent of modern computational techniques. Fig. 9 shows the ﬂow patterns for a case where dye was injected so as to delineate the ﬂow regions and demonstrate their dependence on throttling, showing a marked variation in vortex size. Note that the blades are masked by an impeller end ring in the test rig. The three ﬂow regions are designated A, B and C as shown in Fig. 10. Region A represents the main through-ﬂow in the fan and is where most of the useful work is done. Two-stage action occurs as the ﬂow passes ﬁrst through the suction arc blading (ﬁrst stage) and then through the discharge arc (second stage). The ﬂow contracts as it moves across the impeller producing high velocities at the second stage. The ﬂow leaves the impeller and contracts again as it turns and squeezes around the vortex. It then expands rapidly, diffusing to the fan exit. The diffusion process may be augmented by the vortex. The combination of all these effects results in high pressure coefﬁcient capability. The action on the ﬂuid by the blades in region B resembles that of a paddle wheel, so the energy transfer is low. Region B is a necessary consequence of the cross-ﬂow phenomenon; however, it has little effect on the overall performance except with regard to its inﬂuence in determining the shape of the through-ﬂow region. Region C represents the eccentric vortex. This region consists entirely of re-circulating ﬂow, so no useful work is done there and its primary affects are energy dissipation and shaping of region A. Note that in the frame of reference of the rotating blades, the ﬂow reverses twice per revolution with blade leading edges becoming trailing edges each time, so regions B and C are fundamentally inefﬁcient, but they are also unavoidable. As noted earlier, the natural ﬂow is characterized by an approximately 901 turn in the mean ﬂow, a key consideration in relation to aircraft application in terms of efﬁcient management of the fan intake and exit ﬂows.

ARTICLE IN PRESS 6

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 9. Dye ﬂow visualization at varying non-dimensional ﬂow rates.

Rotation S1

1 2 B

A

3

Vortex wall

C

4

Flow S4

Rear wall Fig. 10. Flow regions A–C for mean-line analysis and test case fan geometry.

2.2. Energy transfer in region A Analysis of the three regions can be performed by beginning with region A, where most of the useful work is done. Flow conditions at the boundaries of this most important and efﬁcient region can then be used to deﬁne conditions for regions B and C. Fig. 11 shows the velocity diagram for the mean (mass averaged) streamline through the two stages of the impeller with terminology corresponding to Fig. 10. In the equations that follow, note that subscripts i and o refer to the inner and outer blade stations, respectively. The net ideal total pressure rise across the impeller is given by the ﬁrst and second stage total pressure rise based on the Euler compressor equation .

.

DP ti12 r ¼ U i cy2 U o cy1 and DPti34 r ¼ U o cy4 U i cy3

(3)

Flow through the ﬁrst stage is much like a 2D diffusing cascade, with a reduction in relative velocity from inlet to outlet, however, there is an increase in radial velocity component. Conversely, the second stage behaves somewhat like the blades in a forward curved centrifugal fan except the ﬂow is accelerated by contraction in the impeller interior, leading to relatively low ﬂow incidence. Flow contraction given by the ratio of suction to discharge arc lengths S1/S4 is frequently noted in the literature, yet its affect on second stage incidence and loading is often overlooked in simple models of the fan. For reference, the dotted line velocity triangles in Fig. 11 represent zero ﬂow contraction. In high-speed fans the accelerated through-ﬂow can lead to high Mach number and choking, presenting a potential limitation for high-speed aircraft application. Note that the velocity triangles

Fig. 11. Velocity diagram for region A.

make it clear that an inner blade angle near 901 is appropriate from a second stage ﬂow incidence standpoint. By inspection of the velocity triangles and assuming cy3 ¼ cy2 (conservation of angular momentum in the interior region), we can write the non-dimensional ideal total pressure rise across the two stages as

DP cti ¼ 1 ti2 12

2

rU o

! 12

2 R 2cr1 ¼2 i þ ðcot b2 þ cot a1 Þ Ro Uo

(4)

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

and

cti

34

2 R 2cr1 S1 ¼22 i cot b4 þ cot b2 Ro U o S4

(5)

Note that the arc ratio S1/S4 dictates the ﬂow contraction between the two stages, and we will see that this parameter depends strongly on casing design and varies with fan throttling conditions. The volume ﬂow coefﬁcient for region A is deﬁned

fA ¼ Q A =U o bDo ,

(6)

where b is the wheel length. Experimental data are often normalized with b as the ‘‘effective’’ wheel length, where partition and end-wall blockage lengths are subtracted from the overall span of the impeller. For an impeller of unit length the ﬂow coefﬁcient is

fA ¼ cr1 S1 =2U o Ro

(7)

Flow coefﬁcient is suitable for static fan operation; however, in forward ﬂight, it is appropriate to consider advance ratio (or tip speed ratio), parameters that will be discussed in Section 5. Further inspection of the velocity triangles leads to the relative velocities at each station (ignoring blade thickness) w1 =U o ¼ cr1 =U o sin b1 ; w2 =U o ¼ cr1 Ro =U o Ri sin b2

(8)

w3 =U o ¼ cr1 Ro S1 =U o Ri S4 sin b3 and w4 =U o ¼ cr1 S1 =U o S4 sin b4 (9) Then, using Bernoulli’s equation the ideal static pressure rise through the suction cascade in pressure coefﬁcient form is

csi ¼ ðRi =Ro Þ2 1 þ ðw1 =U o Þ2 ðw2 =U o Þ2 12

(10)

Similarly, for the discharge cascade

csi ¼ 1 ðRi =Ro Þ2 þ ðw3 =U o Þ2 ðw4 =U o Þ2

(11)

34

These equations along with the velocity triangles show a favorable static pressure rise due to change in relative velocity (outlet relative velocity less than inlet) in the ﬁrst stage and an unfavorable effect in the second stage. The opposite condition is apparent with respect to the inﬂuence of radius ratio. The ideal static-to-total pressure ratio in each stage deﬁnes their respective ideal reaction ratios. In this analysis we use cascade principals, i.e., ﬂow incidence, deﬂection (turning), deviation, and losses. Others, such as Kim et al. [34] use the slip factor approach. The blade relative inlet ﬂow angle for the suction cascade is

b1 ¼ p tan1 ½1=ððU o =cr1 Þ þ cot a1 Þ

Flow deﬂection and total pressure loss coefﬁcient for a given cascade are principally dependent upon incidence angle, with maximum deﬂection typically occurring at slightly positive incidence and minimum loss occurring near i ¼ 0. Excessive positive or negative incidence leads to separation and stall. Cascade performance generally depends upon solidity, blade angles, Reynolds number, Mach number, proﬁle geometry, inﬂow turbulence, and ﬂow unsteadiness. In cross-ﬂow fans the cascade ﬂow is circumferentially non-uniform and locally unsteady (producing dynamic lift), so determination of universal cascade data is very challenging. In this analysis, we use curves based on traditional Howell cascade data (see [37]) with adjustments made to force reasonable correlation of calculated performance with test data for a particular fan test case. The resulting cascade characteristics are shown in Fig. 12 and are intended to represent the circumferential averaged performance for both suction and discharge stages. However, it is acknowledged that the behavior should differ for the two stages. The test fan used for inferring the cascade data is shown in Fig. 10; its attributes are 80 mm diameter, 415 mm effective length, 1500 rpm operating speed, simple constant thickness (9%) blades with: b0 1 ¼ 1531, b0 2 ¼ 901 and Ri/Ro ¼ 0.75. In general, any signiﬁcant change in the blading or ﬂow regime (Reynolds number, Mach number) requires a new set of cascade data, and changes in the fan housing that produce differing blade dynamic lift response may also force the need for a new set of data. However, some extrapolation of the data is reasonable for moderate variations in parameters (such as blade angles) by suitable factoring. It should be emphasized that Fig. 12 represents a low Reynolds number case (Re only 4700 based on blade chord and wheel speed) with simple blading and spanwise losses due to partitions and end-walls (effective length only corrects the volume ﬂow). Performing the same process of cascade estimation for a high Reynolds number case with low loss proﬁles would lead to better turning and loss characteristics and improved fan performance (see [38]). Further discussion on blade cascade performance will be provided in Sections 2.4 and 4. Before proceeding downstream in region A, we brieﬂy turn our attention to the impeller interior and assume that the losses in that region can be neglected. This assumption is reasonable provided there are no interior obstructions, as it has been noted

(12)

Similarly, for the discharge cascade we have

b3 ¼ tan1 ½ðS1 =S4 Þ tan b2

(13)

Given the ﬂow angles and blade metal angles, b01 and b0 3, the air incidence angles are i1 ¼ b1b01 and i3 ¼ b0 3b3. Flow turning angles are deﬁned: e12 ¼ b1b2 and e34 ¼ b4b3, and the ﬂow deviation angles are d2 ¼ b0 2(b1e12) and d4 ¼ b0 4(b4e34). The total pressure loss coefﬁcients for each stage are then deﬁned in the traditional way, using the cascade relative inﬂow velocity ˜ 34 ¼ DP t34 12rw23 ˜ 12 ¼ DP t12 12rw21 and o o (14) The actual total pressure rise across the suction and discharge cascades are given by the ideal rise less the total pressure losses. Therefore, we can write ˜ 12 ðw1 =U o Þ2 and ct34 ¼ ct o ˜ 34 ðw3 =U o Þ2 ct12 ¼ cti o i 12

34

(15)

7

Fig. 12. Cascade deﬂection angle and loss coefﬁcient data.

ARTICLE IN PRESS 8

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

that drive shafts in the impeller interior produce signiﬁcant ﬂow disruption and loss [39]. Continuing from the second stage exit, the ﬂow contracts between the rear wall and the vortex region. It then expands rapidly and diffuses prior to discharging at the exit station. The net diffuser area ratio AR is h/S4, where h is the fan exit height. The diffuser loss, normalized by wheel speed dynamic pressure, can be expressed as qd ¼ ð1 Zd Þ ðcr4 =U o Þ2

(16)

Zd is the diffuser efﬁciency which is dependent upon casing wall design and throttling condition. If ARo1, then the diffuser becomes a subsonic nozzle and 1Zd becomes the nozzle loss coefﬁcient. Finally, if we are interested in total-to-static performance, the fan exit loss can be calculated from the exit dynamic pressure qe ¼ ðcr4 =ARU o Þ2

(17)

Now the total-to-total pressure rise from inlet to outlet of region A may be written

ctA ¼ ct12 þ ct34 qd

(18)

and the total-to-static pressure rise is

csA ¼ ctA qe

Fig. 14. Loss breakdown in region A.

(19)

The power expended to drive the impeller is related to the ideal work plus the work due to overcoming blade losses ˜ 12 ðw1 =U o Þ2 þ ci34 þ o ˜ 34 ðw3 =U o Þ2 Þ lA ¼ fA ðci12 þ o

(20)

and the total-to-total and total-to-static hydraulic efﬁciencies are

ZtA ¼ fA ctA =lA and ZsA ¼ fA csA =lA

(21)

Note that using these deﬁnitions, the correct form for the power coefﬁcient is

l ¼ W s =12rDo U 3o bfc ¼ ðQ =bDo U o ÞðDP=12rU 2o Þ

(22)

where Ws is the impeller shaft power. With this, we are now in a position to assess the performance of region A. For the test case fan geometry and ﬁxed ﬂow regions shown in Fig. 10, we calculate the ideal pressure rise and loss breakdown as shown in Figs. 13 and 14. From this it is clear that

the second stage produces most of the useful work at high ﬂow rates, whereas the ﬁrst stage is increasingly important at reduced ﬂows. It should be emphasized that the ratio of work is a strong function of S1/S4, and that this case assumes ﬁxed ﬂow regions. The affects of ﬂow region variation on performance will be discussed in more detail later. The loss breakdown in Fig. 14 shows the relative contributions of blade, diffuser and discharge losses using a constant value of 0.8 for diffuser efﬁciency (in this case AR is less than unity). Considering Fig. 14 along with the velocity diagram, it is important to note the high second stage exit velocity. The associated discharge kinetic energy can be used effectively for thrust or boundary-layer blowing in aircraft applications. However, it produces a need for energy recovery in static applications, as is apparent in the large exit loss. We will return to this test case in Section 2.4 and discuss the calculated performance in relation to test data, but ﬁrst we will consider ﬂow regions B and C. 2.3. Flow in regions B and C

Fig. 13. Ideal total pressure rise in region A.

The impeller blading in region B acts essentially like a paddle wheel, and therefore the energy transfer is relatively low and inefﬁcient. This region includes a through-ﬂow, however, its contribution is normally quite small, and from a mean-line analysis standpoint its most important features are its size and inﬂuence on region A. Referring to the URANS velocity ﬁeld data in Fig. 15, it can be seen that region B is deﬁned by the ‘‘relative eddy’’ in the blade passage by the rear wall. Immediately adjacent to the eddy the ﬂow moves through the blade passages in the rotating frame and can therefore be classiﬁed as part of region A. Through-ﬂow streamlines in region B also graze region A, with those closer to the impeller interior seeing more cascade action and those toward the rear wall seeing less. With these observations it is logical to assume that region A extends fully to the boundary of the relative eddy, making the mass ﬂow associated with region B quite small. Finally, since the ﬂow speed in B must be very nearly the same as the blade speed, the work on the ﬂuid is relatively low. As a result we neglect all aspects of region B except for its size and inﬂuence in bounding region A. It should be noted that region B may be expanded and combined as a secondary vortex in fans with speciﬁc types of rear

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

9

Fig. 15. Velocity vectors in stationary and rotating frames of reference showing delineation of regions A–C. Small-scale low-speed fan at f ¼ 1.0.

wall entrance cavities (the rear wall feature in Fig. 15 lacks the appropriate geometry to set up a secondary vortex at the conditions analyzed). Region B may interact further at low ﬂow coefﬁcients as an entrance secondary vortex (or recirculation zone) with behavior strongly dependent upon casing design [8,35,40]. As noted earlier, the overall ﬂow pattern of the cross-ﬂow fan is sustained by the circumferentially non-uniform loading in the impeller. The unsteady blade loading and casing wall interaction produce the eccentric vortex which is an unavoidable region of high loss and energy dissipation. Here, we assume that the ﬂow power associated with the vortex is proportional to the product of the cascade work in region A, the vortex kinetic energy, and the vortex volume ﬂow scale as follows: 2 cv lv c v lC cti (23) 14 Uo Ro U o where cv and lv are the characteristic vortex velocity and length scales. Note that the work term is used here since it is proportional to rotor-induced circulation. A reasonable choice for the characteristic velocity is the average of the velocities at stations 2–4, and assuming an elliptical vortex shape, the average of the major and minor radii of the vortex provides a suitable characteristic length scale. With these assumptions the vortex power can be approximated as k r c þ c3 þ c4 3 lC ¼ cti C C 2 (24) 14 Ro 3U o where kC is an adjustable factor. As noted earlier, only regions A and B contribute to the net ﬂow rate and here we neglect the through-ﬂow in region B, so f ¼ fA. We also neglect the power expended in region B so the power coefﬁcient for the whole fan is

l ¼ lA þ lC

(25)

and the fan hydraulic efﬁciencies are

Zt ¼ fct =l and Zs ¼ fcs =l

(26)

2.4. Performance analysis and discussion We conclude this part of the article by reviewing the calculated results for our test case fan and investigate the effect of vortex motion during throttling to demonstrate one of the many challenging aspects of cross-ﬂow fan analysis. Porter [35] showed that the size, strength, and position of the vortex depend on the fan operating point and housing design, greatly affecting fan

Fig. 16. Flow region boundaries for fan test case; blade geometry: bo ¼ 1531, bi ¼ 901, and Ri/Ro ¼ 0.75.

stability. Two main types of behavior occur during throttling: (1) motion and expansion of the vortex along the impeller periphery, and (2) motion into the impeller interior. Porter showed experimentally that the peripheral path produces stable performance, and fans using a simple round nose vortex wall and logarithmic spiral rear wall exhibit such characteristics. In contrast, he showed that if the vortex propagates into the interior the fan performs poorly and becomes unstable. We will explore the favorable stabilizing case using the mean-line analysis and demonstrate the need for a fully coupled analysis for cross-ﬂow fan prediction. The test fan geometry is shown in Fig. 10, and its approximate ﬂow region behavior is shown in Fig. 16 based on ﬂow visualization (Fig. 9) and other data. Condition (1) is a high ﬂow rate case where we focus our initial attention to correlate the analysis with the fan performance test data, and conditions (1)–(5) cover the range of operation f ¼ 0.35 to 1.08. Fig. 17 shows the calculated performance for the fan in relation to test data for the assumption of both constant and variable ﬂow regions. Throughout the analysis the diffuser efﬁciency is ﬁxed at 0.8 and the vortex power factor is 0.7. It can be seen that the calculated results for ﬁxed ﬂow regions (dashed lines) nicely match the test data at high ﬂow rates. In terms of pressure coefﬁcients this is a direct result of the cascade performance adjustments described in Section 2.2 (in this analysis pressure rise is entirely due to action in region A). However, the calculated power for region A alone, lA is signiﬁcantly low relative to test,

ARTICLE IN PRESS 10

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 17. Calculated performance for fan test case using ﬁxed regions (dashed lines) and variable regions (solid lines), compared to test data (symbols).

capacity. In this case, a self-regulating process occurs involving non-linear variation in vortex growth with ﬂow coefﬁcient, as well as growth of region B at condition (5). Although it is not shown here, additional growth of region B tends to occur at even lower ﬂow rates, which then tends to further unload the ﬁrst stage blading. Another observation from Fig. 17 is that the fraction of vortex power increases as the vortex grows. The vortex power ratio of approximately 33% at high ﬂow rates is in agreement with the experimental ﬁndings of Mazur and Singh [40], where vortex power was determined for a similar fan using hot-wire anemometer ﬂow ﬁeld measurements and control volume analysis. The intent of this case study is to demonstrate one of the many complex characteristics of cross-ﬂow fans. When the scope is broadened to include fan design variations, the problem becomes much more complicated. Difﬁculties arise for all models other than those that directly include all of the relevant physics, particularly the impeller–casing interaction and associated nonuniform, unsteady blade loading. While mean-line and throughﬂow models have proven to be very effective in axial and centrifugal turbomachinery, their usefulness for cross-ﬂow fans may be limited. It may be possible to characterize and correlate the fan–casing coupling effects for certain classes of designs, but such methods are not really predictive. Full prediction methods must be able to handle a wide range of casing designs including those with cavity features, multi-element vortex walls, inlet counter-swirl and fan-wing integration. Finally, the analysis must be extended to include the effects of compressibility for highspeed application. As we proceed it will become evident that any method that utilizes reduced level modeling to represent the impeller action on the ﬂuid (e.g., vortex-element or body-force methods), will face a similar need for calibration with test data, and any change in fan design may lead to differing blade performance attributes. Consequently, unsteady Navier–Stokes sliding mesh methods are now in favor for cross-ﬂow fan analysis, as they are capable of adequately representing the fundamental ﬂow physics.

3. Experimental studies of cross-ﬂow fans for aviation

Fig. 18. Calculated ﬂow mean-line incidence variation using ﬁxed parameters (dashed lines) and variable ﬂow regions (solid lines).

and vortex power dissipation must be incorporated and adjusted through the factor, kC. Consequently, overall correlation with test data for the ﬁxed ﬂow region case is accomplished by prescribing the region ﬂow boundaries and then inferring the cascade characteristics and vortex power based on the modeling framework. The intent then is to use the adjusted model to examine variations in fan operation. The calculated effect of ﬂow region variation during throttling is given by the solid lines in Fig. 17, and referring to the corresponding predicted ﬂow incidence in Fig. 18, it becomes apparent why the performance is stabilized for this type of vortex motion. In particular, contraction of the through-ﬂow leads to increased relative velocity and reduced incidence at the second stage, thereby delaying second stage stall and increasing work

In this section, we review experimental work on cross-ﬂow fans relevant to aviation. These applications are characterized by the need for in-line housing designs (e.g. casing 7 shown in Fig. 2), with operation from low-speed incompressible ﬂow to high-speed ﬂow with supersonic blade relative Mach number. The objective is to review the status of cross-ﬂow fan development for use in aviation with respect to overall performance, along with studies aimed at improving performance by varying blade and housing geometrical characteristics. With the advance of computational methods (to be discussed in Section 4), these experimental data are also suitable for CFD validation work. One of the few sets of combined global and detailed cross-ﬂow fan data for aircraft applications available in the open literature is the work of Harloff, which was reported in 1979 as a doctoral dissertation from the University of Texas at Arlington [41]. The experimental part of the work was conducted at the Vought Systems Division of LTV Aerospace Corporation under a contract from the US Naval Air Systems Command for the Multi-Bypass Ratio Propulsion System Technology Development program [12]. Harloff [41] and Harloff and Wilson [13] contended that the crossﬂow fan might be used in the ﬁeld of aviation, but it would be necessary for the fan to be capable of operating over a much wider range of air speeds, from very low-speed operation (i.e. low subsonic) all the way up to transonic, whereby shocks would begin forming within the impeller and ducting, and ﬂow choking would become a major concern. Also in the late 1970s, another

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

effort was initiated at the Lockheed-Georgia Company by Hancock [14] to explore the potential of the cross-ﬂow fan for integration into a wing to provide both propulsion and ﬂow control, although not much data are available in the open literature from this work. Consequently, only the work on the cross-ﬂow fan geometry developed by Harloff [41] will be discussed in detail in this section. Recently, a research group led by Hobson & Platzer at the Turbopropulsion Laboratory at the Naval Postgraduate School (NPS) embarked in a cross-ﬂow fan experimental and computational research program using the same geometry as Harloff and Wilson [13] as their baseline case, and they made further advancements in this area by looking at off-design operations of the same fan and small variations of the housing geometry [18,19,42–44]. The geometry of the cross-ﬂow fan housing design developed and studied by Harloff [41] and Harloff and Wilson [13] and later duplicated by the research group at NPS [18,19,42–44] is shown in Fig. 19 (fan rotation is clockwise). The cross-ﬂow fan diameter is 0.305 m (12 in), with a span of 0.038 m (1.5 in). Shown in Fig. 20 is

Fig. 19. Cross-ﬂow impeller and fan housing [44].

Fig. 20. Impeller geometry [44].

11

the impeller with a total of 30 double circular arc blades. The blade chord is around 0.046 m (1.8 in), yielding a blade aspect ratio of 0.83 and a fan inner-to-outer diameter ratio of 0.7. Note that in practice, for structural reasons, it was envisioned that low aspect ratio cross-ﬂow fans would be stacked together to any desired length. The housing contains a primary vortex cavity (PVC) within the vortex wall as shown on the left of Fig. 19, and a secondary vortex cavity (SVC) located directly opposite in the entrance rear wall area. Note that this housing geometry is signiﬁcantly different from the one shown in Fig. 10; although the concept of the three ﬂow regions is still valid, with the SVC and PVC corresponding to region B (paddle region) and region C (eccentric vortex), respectively. It was hypothesized that the addition of these cavities improved fan performance by allowing the two vortices (the primary as well as the secondary vortex) to occupy distinct spaces, resulting in a potentially larger throughﬂow region (region A). Also, the presence of the PVC could result in more stable operation of the cross-ﬂow fan by preventing the eccentric vortex from adversely affecting the size and stability of the through-ﬂow region during throttling. In the case tested by Harloff [41], the inlet used was a bell-mouth shape corresponding to an in-line design, whereas the setup at NPS used an open inlet (Fig. 21). The outlet in both cases was set at 0.117 m (4.6 in). The cross-ﬂow fan had a design pressure ratio of 1.89. Harloff [41] and Harloff and Wilson [13] reported that their housing geometry development program consisted of numerous water table tests, and several hundred housing conﬁgurations were tested in air to arrive at the ﬁnal conﬁguration shown in Fig. 19. The housing variables tested include the size of the arc lengths of the cross-ﬂow fan inlet and outlet, the arc lengths of the two cavities, and the height and shape (straight duct and duct angled upward by 111) of the exit duct. It was determined that a 1051 inlet arc, a 751 low-pressure cavity arc, a 501 high-pressure cavity arc, and a 1301 exit arc provided the highest performance for a 0.117 m (4.6 in) exit height conﬁguration. Another noteworthy ﬁnding was the drastic reduction in performance when a center shaft was present. In particular, a 0.025 m (1 in) diameter shaft reduced the adiabatic compression efﬁciency by as much as 10 points, while a 0.051 m (2 in) diameter shaft reduced the efﬁciency by as much as 25 points [41]. Their tests also included variation in blade inlet and outlet angles. The outer blade angle ranged from 1151 to 1351 (using notation in Fig. 11), while the inner blade angles ranged from 801 to 901. They also varied the number of blades from as low as 16 blades to as high as 36 blades,

Fig. 21. General layout of cross-ﬂow fan test facility at NPS [44].

ARTICLE IN PRESS 12

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

along with the blade chord which yielded a blade inner-to-outer diameter ratio between 0.7 and 0.8, and blade solidity variation between 0.83 and 1.71. Test results were reported for fan rotational speed up to 12,500 rpm, which is near or at the choking condition, with measured absolute Mach number of 1.2 at the impeller exit station. They concluded that the geometrical variables responsible for performance increase (i.e. mass ﬂow, total pressure ratio, and adiabatic compression efﬁciency) are, in order of decreasing importance, the exit height, the secondary cavity shape, the inlet arc, the exit housing shape, and the fan blade design. Next, typical overall performance curves of the cross-ﬂow fans developed in the late 1970s for aviation applications are presented. Performance curves are usually expressed in terms of the following efﬁciencies: Total efficiency :

Zt

Q ðP t;out Pt;in Þ Ws

(27)

Zc

Adiabatic compression efficiency :

ðP t;out =P t;in Þg1=g 1 ðT t;out =T t;in Þ 1 (28)

In the test data to be described shortly, the efﬁciency calculated from Eqs. (27) and (28) are based on the diffuser outlet station (e.g. station A–E in Fig. 21 for the NPS data). Hence, we note that the efﬁciency included the impeller as well as the fan housing (fan inlet and outlet diffuser). The total efﬁciency is used for industrial and commercial fan operation, while adiabatic compression efﬁciency is preferred for aviation. Fig. 22 shows typical performance curves as a function of corrected airﬂow with the fan tested by Harloff and Wilson [13], where HE is the diffuser exit height. The ﬁgure shows that adiabatic compression efﬁciency Zc above 70% was achieved with total pressure ratio as high as 1.65 at corrected rpm’s varying in the range between 8000 and 11,000. These results can also be plotted in terms of non-dimensional quantities, which show that pressure coefﬁcients up to 4.5 was achieved in the ﬂow coefﬁcient range of 1.5–2.0. In addition to global performance quantities,

detailed ﬂow ﬁeld surveys (e.g. general ﬂow ﬁeld patterns, Mach number contours, and fan inlet/outlet ﬂow conditions) were also obtained by Harloff [41] and Harloff and Wilson [13]. These results will be used for detailed CFD validations, to be discussed in Section 4. Finally, Harloff and Wilson [13] also tested a higher blade aspect ratio design with three cross-ﬂow fans each having both span and diameter of 0.305 m (12 in) stacked together, and they showed only a slight improvement in performance. As mentioned earlier, the same cross-ﬂow fan housing conﬁguration used by Harloff and Wilson [13] was also built and tested in the Turbopropulsion Laboratory at NPS. The work at NPS included not only the free-delivery condition (i.e. ambient back pressure), but also off-design performance (back pressure greater than ambient). Off-design performance data were obtained by adding an extension to the exhaust duct with a butterﬂy throttle valve shown in Fig. 21 [19,44]. One variation of the fan housing was also considered, speciﬁcally blanking off the two cavities. Fig. 23 shows plots of total pressure ratio and isentropic compression efﬁciency as a function of corrected mass ﬂow rate for rpm ranging from 2000 to 5000, taken from Yu et al. [19]. Due to facility constraints, the rpm range studied by NPS is much lower than the test conditions of Harloff and Wilson presented in Fig. 22. Also shown in the same ﬁgures are the performance curves without the butterﬂy throttle valve (denoted as open throttle), which were conﬁrmed by the authors to be comparable to those measured by Harloff [41]. Note that adiabatic compression efﬁciency values above 70% were also obtained. In addition to studying the off-design performance of this cross-ﬂow fan conﬁguration, the research group at NPS also investigated the effects of modifying the two cavities. Their results showed that when the cavities are blanked-off, a signiﬁcant gain in efﬁciency was obtained at the off-design (near stall) conditions at the expense of a small reduction in mass ﬂow rate and total pressure ratio [42]. There was no discussion on the effect of the PVC on the size and location of the eccentric vortex during throttling in Ref. [42].

Compression Efficiency, c

0.75

0.65

0.55

Symbol HE ~ cm 10.16 11.43 11.68 12.70

Total Pressure Ratio, PTout / PTin

2.0

N / Θ ~ RPM = Constant

1.8

11000 1.6 10000 9000

1.4 8000

1.2

1.0

1.25

1.5

1.75

Corrected Airflow, W Θ ~kg/sec Fig. 22. Performance results of cross-ﬂow fan studied by Harloff and Wilson [13].

Fig. 23. Performance data obtained by Yu et al. [19].

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

In the late 1970s, a similar cross-ﬂow fan research program led by Hancock was carried out at the Lockheed-Georgia Company [14]. Hancock showed that the performance of these fans varied greatly with fan and housing design, with some of the designs in the ﬁrst phase of the program having efﬁciencies as low as 40%. Fig. 24 shows the general layout of the cross-ﬂow fan housing design with the highest performance tested by Hancock in the second phase. This housing has many similarities to the one used by Harloff and Wilson [13], particularly the ‘‘initial’’ design of the PVC and SVC. Other changes made in the second phase included better impeller cascade ﬂow area distribution, along with decreasing the fan diameter ratio from 0.9 to 0.7, which is the value used by Harloff and Wilson. The fan tested by Hancock had a diameter of 0.254 m (10 in) compared to the 0.305 m (12 in) fan diameter tested by Harloff and Wilson, and the span was 0.254 m (10 in), which is signiﬁcantly longer than the baseline fan tested by Harloff and Wilson. Shown in Fig. 24 are two different designs denoted as the ‘‘initial’’ design and ‘‘modiﬁed’’ design. Hancock noted that the larger PVC delivered maximum pressure coefﬁcients at low efﬁciencies, while the smaller PVC improved efﬁciencies substantially with some reduction in output pressure. This ﬁnding is in agreement with the CFD work of Kummer [30] which will be discussed in Section 4. Shown in Fig. 25 are performance curves in the form of both total and adiabatic compression efﬁciencies as a function of ﬂow coefﬁcient. These curves showed that efﬁciencies above 80% are attained, which was a bit higher than the fan/housing design tested by Harloff and Wilson [13]. Part of the improvement may be due to the longer span tested by Hancock. Finally, Hancock noted that increasing the clearance

13

between the impeller and the cavity housing, along with rounding off the sharp cavity edges, can reduce noise signiﬁcantly. In summary, test data relevant to aero-propulsion of cross-ﬂow fans operating from low- to high-speed ﬂow regimes, show total pressure ratio as high as 1.7 with compression efﬁciencies in the range of 80%. Although these efﬁciencies are low compared to axial propellers and fans, this drawback can potentially be compensated for by cross-ﬂow fan integration for ﬂow control (separation and circulation control) and distributed propulsion (wake ﬁlling, differential lift, and vectored thrust). The literature also reveals that little experimental work has been done on the development of high-performance cross-ﬂow fans for aviation applications, including a long period of little or no activity between the late 1970s [12–14] and the late 1990s [19,42–44]. Furthermore, it is unclear as to whether the features of the fans that were used for these high-speed tests were optimized. In particular, the question arises as to whether vortex cavities are appropriate or whether other wall features may be used to attain higher efﬁciencies.

4. Prediction methods for cross-ﬂow fans Compared to conventional turbomachines used in the gas turbine industry (e.g. axial fans and centrifugal compressors), the ﬂow ﬁeld in the cross-ﬂow fan is much more complicated to predict. In particular, the impeller aerodynamics and the rather arbitrary fan housing geometries are so inter-dependent that they cannot be decoupled as is often done in conventional turbomachines where stream-surface methods (e.g., [45]) or other simpliﬁed models yield reliable predictive capability. As discussed earlier, although the ﬂow in the cross-ﬂow fan can be approximated as 2D, it is inherently unsteady since the impeller blades are subjected to strong variations in ﬂow conditions as they move through one revolution. In particular, in one revolution, each blade experiences the ﬁrst stage through-ﬂow region (region A), then the paddling region (region B), then the second stage throughﬂow region (region A), and ﬁnally the eccentric vortex region (region C). In the two stages of the through-ﬂow region the blade

Fig. 24. Housing geometry tested by Hancock [14].

Fig. 25. Best performance conﬁguration reported by Hancock [14].

Fig. 26. Vorticity contours of instantaneous ﬂow ﬁeld in a cross-ﬂow fan [15].

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

ﬂow ﬁeld can be modeled using a cascade airfoil method. However, as noted in Section 2, the ﬂow is circumferentially non-uniform and highly unsteady in the blade frame of reference. As the blade circulation varies with time, shed vorticity is present inside the impeller and in the downstream duct regions. Fig. 26 shows a snap shot of the vorticity contours in a cross-ﬂow fan predicted by an unsteady viscous ﬂow CFD method developed by Moon et al. [15]. The ﬁgure clearly shows unsteady vortical ﬂow behavior such as shedding from both ﬁrst and second stage blading. Consequently, determination of appropriate cascade data for simpliﬁed modeling is very challenging as it must include these unsteady dynamic lift effects. Another challenge is modeling of the blade ﬂow in regions B and C, where ﬂow incidence varies over 3601. As seen in Fig. 26, the ﬂow in these regions is highly rotational with large areas of ﬂow separation. In the end, any useful simpliﬁed modeling technique will depend on its ability to predict the relative size of region A as a function of casing design and throttling condition since fan performance is strongly dependent upon the through-ﬂow contraction (i.e. ratio of suction to discharge arc lengths, S1/S4), as discussed in Section 2. Finally, we note that the 2D nature of the ﬂow ﬁeld in the cross-ﬂow fan is at least partially lost when integrating into a three-dimensional (3D) wing. For example, a swept wing with variable chord would produce spanwise variations in fan inlet ﬂow conditions, and 3D ﬂow effects are introduced by wing-induced circulation and by fan end-wall effects. Prediction methods for cross-ﬂow fans vary from simpliﬁed steady-ﬂow models (e.g. [9,10,13,46–48]) to full unsteady viscous ﬂow CFD methods (e.g. [15,19,30]). In this section, we will start by describing the unsteady-ﬂow CFD methods. These techniques are shown to represent the current state-of-the-art, producing accurate ﬂow ﬁeld and performance predictions in the design operating range. We will also review validations of these predictive methods with available test data. Although there are a number of global test data sets that can be used for validation (e.g. pressure ratio and efﬁciency as a function of ﬂow coefﬁcient), detailed ﬂow ﬁeld data available in the literature are limited. One such set of data are those presented by Harloff [41] discussed in Section 3. Detailed ﬂow ﬁeld data are especially important because they can be used to identify important ﬂow features and characteristics which need to be included in the development of predictive methods. At the end of the section, we discuss simpliﬁed modeling steady-ﬂow methods in the context of the experimental and computational results to highlight the challenges for those techniques.

may be present in region A at high subsonic ﬂight speed. Moreover, the inviscid ﬂow assumption renders these methods inaccurate in regions B and C, along with the boundaries of region A where the blades encounter very large ﬂow incidence and separation. The most accurate method to capture this unsteady interaction is the unsteady ‘‘sliding mesh’’ CFD method. In this technique, the computational domain is divided into two types of zones. For the cross-ﬂow fan, a circular zone containing the impeller rotates at the impeller rotational speed, while the remaining zones exterior to the impeller are stationary. During the calculation, the impeller zone ‘‘slides’’ relative to stationary zones along the grid interface in discrete steps, and the URANS equations are solved in the moving coordinate system. At the sliding mesh interface between the rotating zone and the stationary zone, ﬂow variables and their gradients are carefully interpolated so that mass conservation and accuracy of the numerical scheme are preserved. A summary of the sliding mesh technique developed speciﬁcally for cross-ﬂow fan analysis can be found in Moon et al. [15]. In the examples to follow, all test data and calculations are for the geometry originally developed by Harloff and Wilson [13] shown in Fig. 19. These tests were carried out from low Mach number to supersonic speed near the choking condition, with maximum blade relative Mach number on the order of 2. Fig. 27 provides a sample of the CFD validation study performed by Kummer and Dang [20] using the cross-ﬂow fan geometry and

Inlet

Ω

Vought Outlet NPS 0.75

2 1.9

4.1. Unsteady-ﬂow methods

0.7

1.8 Total Pressure Ratio

As mentioned earlier, the ﬂow ﬁeld in a cross-ﬂow fan can be modeled with a 2D approximation, but the blade relative ﬂow is inherently unsteady. In the early 1990s, several researchers recognized the importance of using an unsteady-ﬂow model to describe the ﬂow ﬁeld in cross-ﬂow fans and successfully modeled the unsteady-ﬂow ﬁeld. For example, Kitagawa et al. [49] developed an inviscid, incompressible ﬂow analysis method using the discrete vortex method combined with the singularity method. The housing boundaries and blades were represented by source–vortex distributions. Shed vortices from the blades were modeled as point vortices, and the magnitude of the shed vortices were assumed to decay with time to approximate the effect of viscous diffusion. Their work showed that the general ﬂow ﬁeld in a cross-ﬂow fan can be captured by an inviscid model. In particular, the three distinct regions A, B and C described in Section 2 were captured. However, these methods are not adequate for aero-propulsion applications where shock waves

Computed

1.7 1.6

0.65

1.5 1.4

0.6

1.3 1.2

0.55

1.1 1

0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

Mass Flow Rate (lbm/s) Fig. 27. Cross-ﬂow fan CFD validation study of Kummer and Dang [20].

Compression Efficiency

14

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

test data documented by Harloff [41]. The ﬁgure shows variation of total pressure ratio and adiabatic compression efﬁciency as a function of ﬂow rate at the free-delivery condition (ambient back pressure), while fan speed is varied up to 12,500 rpm. The computed results are obtained using the commercial CFD software Fluent [50], solving the 2D compressible URANS equations using the sliding mesh method with the standard ke turbulence model and enhanced wall treatment option. The mesh size was on the order of 130,000 cells and the time step was approximately 1/20th of the blade passing period. The ﬁgure shows excellent agreement between CFD and experiment, covering the range from low speed to supersonic ﬂow near the choking condition, with choked mass ﬂow rate per unit width of approximately 1.5 kg/s (3.3 lbm/s). The results show maximum compression efﬁciency on the order of 70%. As an indication of improvement potential in this particular fan design, note that maximum compression efﬁciency on the order of 80% was demonstrated through CFD simulations by Kummer when the PVC was removed from the housing [30]. Another example comparing global performance test data to CFD results is shown in Fig. 28 from Yu et al. [19] and Yu [44]. This work was a combined experimental/CFD study performed at NPS using a duplicated cross-ﬂow fan geometry designed by Harloff and Wilson [13], and the study included off-design performance of the cross-ﬂow fan. Here, the commercial CFD software CFX was used to solve the compressible URANS equations using the sliding mesh method with the standard ke turbulence model. The mesh size was on the order of 60,000 cells and the time step was approximately 1/12th of the blade passing period. The ﬁgure shows reasonable agreement in the prediction of total pressure between computed and experimental results at various rotational speeds from open throttle to a setting near stall. However, the prediction of compression efﬁciency at low rpm was less accurate. In addition to these high-speed cases, there are a number of published studies on low-speed cross-ﬂow fans of various geometries showing excellent correlation between sliding mesh URANS predictions and experimental results. Among these are the

Fig. 28. Comparison of experimental and computed results of Yu et al. [19].

15

works of Cho and Moon [51] and Moon et al. [15], which also include aeroacoustic calculations utilizing the predicted unsteady blade and wall surface pressures to compute far-ﬁeld noise radiation based on the Ffowcs Williams–Hawkings equation and Curle’s equation, respectively. Their studies investigate the noise characteristics of the fans with uniform and non-uniform circumferential blade spacing patterns in terms of frequency modulation of blade passage tones. As an illustration of the capability of these unsteady sliding mesh CFD tools to predict the detailed ﬂow ﬁeld in a cross-ﬂow fan, a contour plot comparison of total pressure between CFD and experiment at 12,500 rpm is given in Fig. 29, taken from Kummer [30]. At the impeller rotational speed of 12,500 rpm the ﬂow ﬁeld is nearly choked, and the blade relative Mach number in the second stage through-ﬂow region is as high as 2.5. In the ﬁgure, the colored contours correspond to the computed CFD results, over which the experimental data are superimposed and are displayed as contour lines. Close agreement is seen between the CFD results and test data, especially in the through-ﬂow region. In particular, the simulations accurately predict: (1) the total pressure level achieved by the cross-ﬂow fan (up to 1.6), (2) the location and size of the eccentric vortex, and (3) the presence of a weak normal shock in the exit diffuser. Detailed ﬂow ﬁeld data comparisons give an additional level of depth to the validation of the CFD model. Fig. 30 compares the CFD results and experimental data at 12,500 rpm for absolute ﬂow angle (measured relative to the radial direction) and tangential velocity at the outer fan diameter location. The data are plotted versus angular location around the fan, measured counter-clockwise from the horizontal (as in Fig. 29). The experimental data taken from Harloff [41] was acquired by direct measurement of the ﬂow properties (e.g. pressure, velocity, temperature). Probes were placed throughout the ﬂow ﬁeld, and data were taken at discrete time intervals. The data were then time-averaged, and the mean value used in the subsequent calculations. The results show very good agreement between experiment and simulation in the through-ﬂow region. The ﬁrst stage through-ﬂow region in Fig. 30 spans the range from about 301 to 1301, and the second stage through-ﬂow lies between approximately 2201 and 3001. The only sector with signiﬁcant discrepancy is near the eccentric vortex, between about 3001 and 301. This is not surprising, since the blade ﬂow in the vortex region is highly separated, and both experiment and computation become difﬁcult. In particular, Harloff [41] stated that, ‘‘ﬂow angle measurements were less accurate near the vortex center than elsewhere due to large static pressure

Fig. 29. Total pressure contours at 12,500 rpm (DPt/patm); contours lines ¼ experimental data [41], shaded contours ¼ CFD data [30].

ARTICLE IN PRESS 16

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 31. Compression efﬁciency and radial velocity distribution at exit of 1st stage [30].

Fig. 30. Flow angle (upper) and circumferential velocity (lower) as a function of angular position at impeller inner-radius location [30].

gradients,’’ and in general probe interference can lead to experimental errors in vortex and other complex ﬂow ﬁelds. Finally, it is noted that comparisons between CFD and test data of other ﬂow quantities at different locations and fan rpm can be found in [30]. One method of quantifying local loss is to examine the local adiabatic compression efﬁciency deﬁned in Eq. (28) at the exit of the two stages. In this case, (Pt,out, Tt,out) are taken to be the local value instead of the mass-averaged exit value. Shown in Figs. 31 and 32 are CFD results of time-averaged adiabatic compression efﬁciency as a function of angular location at the exit of the ﬁrst and second stages, respectively. Note that local compression efﬁciency was computed relative to the upstream inlet conditions. Therefore, the compression efﬁciency reported in Fig. 32 after the second stage is for both stages of the fan. The data are presented for the 4000 rpm case. Upon examining Fig. 31, the most obvious result is that the compression efﬁciency in the ﬁrst stage is in the range of 90% within the main portion of the through-ﬂow region. This level of efﬁciency is as high as typical propellers, and demonstrates that the working region of the cross-ﬂow fan is very efﬁcient. Along with efﬁciency, the exit radial velocity is plotted on each ﬁgure. The large radial velocity near the 301 location is approximately where the return ﬂow from the eccentric vortex region (or PVC) meets the right-most portion of the through-ﬂow region (negative radial velocity indicates ﬂow toward the fan centerline). The

Fig. 32. Compression efﬁciency and radial velocity distributions at exit of 2nd stage [30].

analysis shows that the efﬁciency drops signiﬁcantly in this region. On the opposite side of the through-ﬂow region near the secondary cavity (or SVC) near the 1401 location, the compression efﬁciency also drops signiﬁcantly, but the ﬂow rate is relatively low there as indicated by the low radial velocity magnitude. Fig. 32 gives the distribution of compression efﬁciency at the exit of the second stage, where once again the same trend is seen. Note that positive radial velocity indicates radial outﬂow. As with the ﬁrst stage, efﬁciency on the order of 90% is attained in the through-ﬂow region, but drops off quickly approaching regions B and C. With the efﬁciency over much of the ﬁrst and second stages already in the 90% range, it is clear that only incremental improvement may be possible over the large part of the through-ﬂow region. A future goal of attaining efﬁciency higher than 90% over a larger section of region A may be possible

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

(by reducing the sizes of regions B and C). By contrast, within the through-ﬂow region immediately adjacent to regions B and C there is considerable room for performance gains, possibly through housing and blade geometry optimization. As examples, Kummer [30] has shown through CFD simulations that at the freedelivery condition: (1) decreasing the gap between the impeller and the PVC increases compression efﬁciency (however, this would lead to higher noise levels), (2) double circular arc blades are favorable compared to constant thickness circular arc blades in these high-speed machines, and (3) removal of the PVC signiﬁcantly increases compression efﬁciency but reduces ﬂow rate. However, the effects of eliminating the vortex cavity on fan stability as a function of throttling were not studied. To further investigate the work contribution of each blade, the torque input distribution was calculated from the CFD results for each blade position azimuthally. This calculation was performed by monitoring the torque on an individual blade as it traversed through one revolution. The resulting plot is shown in Fig. 33 for the 4000 rpm case [30]. For clarity, the location of the fan ﬁrst stage, second stage, PVC, and SVC are also labeled on the ﬁgure. In the ﬁgure, a negative torque corresponds to power input (compressor operation), while a positive torque corresponds to power output (turbine operation). Thus, as the blades rotate around, they act as compressor blades over most of the sections of the impeller, but they also operate as turbine blades in parts of the regions B and C. For this particular case, note that the work input in the SVC region is relatively large, along with the spatial variation in torque distribution at the boundary region between the SVC and through-ﬂow regions. Another important feature to note is the dynamic lift response of the blade. High-amplitude, high-frequency oscillations are apparent in the torque value as the blade passes through the PVC (315451) and SVC (180–2251) regions. For this case, the maximum torque in the second stage is on the order of 2.7 N-m (2 lb-ft), and the amplitude of the torque variation in these regions is on the order of 1.4 N-m (1 lb-ft). This dynamic blade loading effect is important when considering lower-order modeling methods requiring cascade data; i.e., dynamic loading effects must be implicit in data such as that shown earlier in Fig. 12. Fig. 34 shows the streamline patterns in and around the impeller region [30]. The streamlines in the impeller region are seen in the rotating frame, while the streamlines in the remaining regions are seen in the absolute frame. In the through-ﬂow region,

Fig. 33. Individual blade torque distribution at 4000 rpm [30].

17

Fig. 34. Instantaneous relative streamlines in and around impeller region [30].

Fig. 35. Outlet proﬁles at 4000 rpm (dashed line—instantaneous data, solid line—mean data) [30].

the ﬁgure shows that the impeller acts as a well-behaved cascade. In particular, the blades provide good ﬂow guidance, with low ﬂow incidence and deviation. Note that progressive incidence variation (positive and negative) and deviation occur at the boundaries of region A. Within the vortex cavity regions, large vortical/re-circulating ﬂows exist and the cascade approximation is clearly not applicable there. It should be pointed out that the vortex region in this particular fan is quite large and the fan housing does not appear to be optimal in terms of minimizing losses in regions B and C. As will be discussed in Section 4.2, simpliﬁed modeling methods must be able to represent all ﬂow regions in a coupled fashion as they all affect fan performance. Finally, it is of interest to both aero-propulsion designers and experimentalists to recognize the non-uniform ﬂow distribution at the fan exit plane. For designers, it is important to understand the details of the exhaust ﬂow and its airfoil coupling effects through viscous entrainment, separation control, and thrust generation [22]. For experimentalists, it is critical that an adequate number of measurement locations are employed to obtain accurate prediction of overall total pressure rise. For example, as noted by Yu et al. [19], additional measurement

ARTICLE IN PRESS 18

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 37. Streamline plot from Ikegami–Murata model [9].

Fig. 36. Outlet proﬁles at 8000 rpm (dashed line—instantaneous data, solid line—mean data) [30].

locations at the exit diffuser were added to the earlier work of Seaton [52] and Cheng [53] to obtain more accurate experimental results. Figs. 35 and 36 show CFD results of the total pressure ratio (denoted by PT), total temperature ratio (denoted by TT), and x-component velocity (denoted by Ux) as functions of vertical position along the diffuser exit at 4000 and 8000 rpm, respectively. In each ﬁgure, typical instantaneous proﬁles are plotted (denoted by the dashed lines) along with the time-averaged data (denoted by the solid lines). These ﬁgures clearly show that the exhaust ﬂow is highly non-uniform, and the higher total pressure region is in the middle of the exhaust duct. For this particular cross-ﬂow fan, spatial non-uniformity is much greater at 8000 than at 4000 rpm for all three values presented. In addition, the ﬂow exiting the fan also has a high swirl velocity component as a result of the forward curved blading.

4.2. Steady-ﬂow methods A variety of simpliﬁed steady-ﬂow models have been formulated for cross-ﬂow fans by a number of researchers beginning in 1959 with the work of Coester [6]. They include one-dimensional models of a similar nature to the analysis in Section 2, and 2D ﬂow ﬁeld approximations using superimposed potential ﬂows. More recently, numerical techniques have been employed using vortex-element (panel) methods, body-force methods and multi-reference frame (MRF) analysis. This section brieﬂy cites the early models and then discusses CFD-based models in more detail, emphasizing the inherent approximations in all steady-ﬂow models of the cross-ﬂow fan. The ﬁrst documented modeling of the cross-ﬂow fan was carried out by Coester [6], who developed a potential ﬂow representation for the ﬂow within the interior of the impeller with solution consisting of a single vortex or distribution of vortices on the impeller periphery. Similar analysis is described by Eck [1], to whom identiﬁcation and deﬁnition of the basic vortex ﬂow is attributed. In both cases the models were aimed at approximating the experimentally observed streamline patterns in the impeller interior and did not contain a linkage between the ﬂow ﬁeld and action of the blades. Ikegami and Murata [9] developed a model where the ﬂow ﬁeld was composed of a pair of vortices of equal strength with one located in the impeller interior and the other outside with the

same circulation and sense of rotation (not an image vortex). The fan casing was modeled as a horizontal line extending on either side of the impeller and the effect of radial and peripheral vortex motion was investigated by prescribed vortex positioning. The method calculated the stream function as shown in Fig. 37, allowing for velocity triangle analysis and blade work calculations based on local blade ﬂow ﬁeld, enabling the calculation of pressure–ﬂow curves. Ilberg and Sadeh [46] developed a similar model but included two zones. The ﬁrst consisted of a ﬂow ﬁeld described by superposition of a boundary potential function and free-vortex. The second zone represented a solid body rotation vortex core (Rankine vortex). Yamafuji [10] modeled the crossﬂow fan using a potential ﬂow vortex actuator method for a linear casing, and also produced fan curves examining variations with simple design parameters. In each of these models the impeller blades were greatly simpliﬁed and realistic fan housing geometries could not be handled. As a result, although some of these pioneering models led to better understanding of the ﬂow physics in cross-ﬂow fans, they have limited use as predictive tools as their accuracy depends primarily on how well they model the size and location of the eccentric vortex. In addition to these early potential ﬂow models, mean-line analysis was carried out by Moore [11] and Allen [33] and more recently by Bushnell [32] and Kim et al. [34]. These models attempt to capture the basic performance characteristics of the fan based on variations in suction and discharge arcs similar to the analysis in Section 2. More recent computational-based methods with realistic modeling of fan housing geometries have been developed where the ﬂow in the bladed region is modeled by a distribution of bound and trailing-vortices and by body-force ﬁelds [47,48]. Some model only the through-ﬂow region with the boundaries of regions B and C speciﬁed [13], while others attempt to model the whole ﬂow ﬁeld including resolution of the eccentric vortex [47,48]. These methods can be classiﬁed as actuator techniques and in principal encompass simpler methods based on the actuator disk and basic potential vortex approximations like those described above. Actuator methods have been used widely in the gas turbine industry to represent both stationary and rotating blade rows in multistage turbomachines (e.g. streamline curvature and through-ﬂow methods [54,55]). The key feature of these simpliﬁed models is that the discrete number of blades is replaced by a distributed bound-vortex or body-force ﬁeld, and their function is to reproduce the effects generated by the physical blades, which is to add or remove angular momentum (rcy) to or from the ﬂuid passing through the blade row. If the blades are rotating, their function is also to impart a change of total pressure and total temperature to the ﬂuid, in addition to changing the

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

ﬂuid’s angular momentum. In either case (stationary or rotating blades), the method assumes that the ﬂow is ‘‘well behaved’’ in that the ﬂuid closely follows the blade shape in the relative frame. In other words, the blades provide effective ﬂow guidance and hence ﬂow deviation is small, and a simple cascade model can be used to estimate the performance of the blades. The use of the actuator method appears to be the most promising steady-ﬂow prediction method for cross-ﬂow fan applications. However, it is much more challenging to develop such methods for cross-ﬂow fans than for conventional turbomachines in that there are three distinct regions through the impeller, with region A acting as a turbomachine ﬂow-path where a cascade model can be implemented, while regions B and C are much more challenging to model. For aero-propulsion applications, compressibility effects can become signiﬁcant and the most appropriate simpliﬁed steadyﬂow methods are CFD-based methods with a shock-capturing capability. One such method is the formulation based on solving the compressible-ﬂow Navier–Stokes equations with added source terms in the bladed region to model the presence of the blades as a distributed body-force ﬁeld [56]. This formulation can be implemented into existing CFD solvers [47,48]. To illustrate the concept, we now describe a simpliﬁed method based on a nonaxisymmetric actuator-duct approximation using the body-force ﬁeld approach [47,48]. For simplicity the ﬂow is assumed to be 2D and incompressible. Let n^ ¼ ½nr ðr; yÞe^ r þ ny ðr; yÞe^ y be the unit vector normal to the relative mean streamlines in the impeller region, or the streamlines that the average ﬂow follows as seen in the relative frame. Note that the streamlines can have different shape, depending on their radial and angular positions in the impeller region. The ﬂowtangency condition can be described as ~ n^ ¼ 0 w

(29)

~ is the relative velocity. If n^ is known, the ﬂow-tangency where w condition introduces a constraint between the radial and tangential velocity components, i.e. cy ¼ Or

nr cr ny

(30)

In Eq. (30), O is the impeller rotational speed. Note that in the case where there are an inﬁnite number of blades, then n^ is the unit vector normal to the blade camber surface (or camber line in 2D). For the case where the number of blades is ﬁnite, some ﬂow deviation exists between the blade camber surface and the streamline that the mean ﬂow follows, and this deviation must be modeled. As an example of such a model, the traditional cascade deviation model shown in Fig. 12 may be used, which states that the ﬂow deviation from the blade geometry is a function of ﬂow incidence at the blade leading-edge. With respect to the ﬂow in a cross-ﬂow fan, it is seen from Figs. 15 and 34 (taken from CFD simulations) that a large portion of the ﬂow in region A is well behaved (low ﬂow incidence and deviation), and the cascade turning and loss model is appropriate. However, as seen from these ﬁgures, the cascade model is not appropriate for regions B and C. If the blades are replaced by a body-force ﬁeld denoted by ~ FB (force per unit mass) and viscous loss modeled by a body-force ﬁeld denoted by ~ F v, then the governing equations to be solved are the continuity and momentum equations. The equations can then be written in cylindrical coordinates as follows: Continuity :

qðrcr Þ qcy þ ¼0 qr qy

(31)

" r-momentum :

r cr

19

#

qcr cy qcr c2y qp þ ¼ qr r qy r qr þ rF B;r þ rF v;r

y-momentum :

(32)

cr qðrcy Þ cy qcy 1 qp þ ¼ r qy r qr r qy

r

þ rF B;y þ rF v;y

(33)

Note that the formulation can readily be extended to compressible-ﬂow with shocks if a CFD solver with a shock-capturing capability is used (e.g. see [57]). The unknowns in the problem are the pressure ﬁeld p ¼ p(r,y) and the absolute velocity vector ~ c ¼ cr ðr; yÞe^ r þ cy ðr; yÞe^ y, along with the blade body-force ﬁeld vectors ~ F B ¼ F B;r ðr; yÞe^ r þ F B;y ðr; yÞe^ y and the viscous loss body-force ﬁeld ~ F v ¼ F v;r ðr; yÞe^ r þ F v;y ðr; yÞe^ y . As mentioned earlier, the job of the blade is to turn the ﬂow, and hence to change the ﬂuid’s angular momentum as it passes through the bladed region. The change of the ﬂuid’s angular momentum in the bladed region is the result of the blade pressure loading acting on the ﬂow. In this case, the blade bodyforce ﬁeld must satisfy the following constraint: ~ F B n^ ¼ 0

(34)

Eq. (34) states that the body-force ﬁeld must be normal to the mean streamline. This produces a constraint between the two components of the blade body-force ﬁeld, namely F B;r ¼

nr F ny B;y

(35)

The body-force ﬁeld representing loss must be in the opposite direction to the streamwise direction, which corresponds to a drag force. In general, it can be expressed as ~ w ~ F v ¼ F v ðr; yÞ w

(36)

The viscous body force and can be modeled from a loss correlation such as the loss coefﬁcient curve shown in Fig. 12. Note that Fv must be positive to represent the viscous force. The magnitude of the viscous body force can be related to the total pressure loss through Crocco’s equation, which can be shown to take on the form [58] F v ðr; yÞ ¼

~ w rðP t =rÞ w

(37)

In Eq. (37), Pt ¼ P t ðr; yÞ is the rotary stagnation pressure deﬁned as Pt ¼ Pt rOrcy

(38)

If the loss model shown in Fig. 12 is employed in Region A, then at a given y location, the overall rotary stagnation pressure loss across the cascade can be deﬁned as a function of local ﬂow incidence, and a loss model can be constructed if a streamwise (or radial) variation is assumed (e.g. linear distribution from leading edge to trailing edge). Finally, recall that in an inviscid ﬂow, Fv vanishes and Eq. (37) states that the rotary stagnation pressure is conserved along a streamline. If conventional CFD algorithms for incompressible ﬂow are used to solve ﬂuid-ﬂow problems where the body-force ﬁeld is known, e.g. the SIMPLE algorithm of Patankar and Spalding [59], then the momentum equations would be used to solve for the velocity ﬁeld while the continuity equation would be enforced to update the pressure ﬁeld. In the present problem, the blade bodyforce ﬁeld and the loss body-force ﬁeld are not known. For this 2D problem, there are seven unknowns in the problem that need to be determined, i.e. (~ c; p; ~ FB; ~ F v ). The seven equations are the three ﬂuid-dynamics equations given in Eqs. (31), (32) and (33), the

ARTICLE IN PRESS 20

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

viscous loss model given in Eq. (37), along with the ﬂow-tangency condition given in Eq. (30) and the blade body-force ﬁeld constraint given in Eq. (35). The following solution strategy can be used to compute the ﬂow ﬁeld. First, an expression for the body-force ﬁeld vector ~ F B needs to be developed. Since the ﬂowtangency condition based on a ﬂow deviation model as described in Eq. (30) must be enforced, it can be used to compute the tangential velocity cy in the bladed region. The y-component of the momentum equation given in Eq. (33) can then be used to calculate the component of the body force in the tangential direction, i.e. cr qðrcy Þ cy qcy 1 q p=r F B;y ¼ þ þ (39) F v;y r r qr r qy qy Eq. (39) states that the tangential body-force ﬁeld component FB,y must take this form in order to impart the correct amount of angular momentum to the ﬂow as it passes through the blade region. Having calculated FB,y from Eq. (39), Eq. (35) can then be used to compute FB,r, the radial component of the body-force ﬁeld. In summary, the following method can be used to iteratively calculate the ﬂow ﬁeld in the cross-ﬂow fan using the body-force method. In the bladed region where the distributed body-force ﬁelds ~ F B and ~ F v are used to represent the effects of the blades on the ﬂow ﬁeld, given an initial guess of the ﬂow ﬁeld, the unknowns (~ c; p; ~ FB; ~ F v ) in the problem can be calculated with the following procedure: (1) Update the distribution of ﬂow deviation, or the unit vector ^ yÞ, using a ﬂow deviation model. n^ ¼ nðr; (2) Update the blade body-force ﬁeld ~ F B using Eqs. (35) and (39). (3) Update the viscous loss body-force ﬁeld ~ F v using Eq. (36) given the rotary total pressure ﬁeld Pt ¼ Pt ðr; yÞ. If a loss model such as that shown in Fig. 12 is used, then the rotary total pressure ﬁeld P t ¼ P t ðr; yÞ must ﬁrst be constructed to compute the magnitude of the viscous loss body-force ﬁeld given in Eq. (37). One such model was discussed earlier ˜ in Section 2, where the total pressure loss coefﬁcient o deﬁned in Eq. (14), which is given as a function of ﬂow incidence (Fig. 12). (4) Update the radial velocity component cr by solving the radial momentum equation given in Eq. (32). (5) Update the tangential velocity component cy using the ﬂowtangency condition given in Eq. (30). (6) Update the pressure ﬁeld p using the continuity equation given in Eq. (31). The solutions to these equations are subjected to the appropriate boundary conditions. For the model presented here, it includes the inlet/outlet conditions, along with the no-slip condition along the housing geometry. Assuming that the complexity of the housing geometry can be handled numerically, e.g. by meshing the ﬂow domain and coming up with a stable and efﬁcient method to solve the equations described numerically, there are still many challenges that need to be resolved in order to turn the actuator method discussed here into a reliable predictive tool. First, as the blade moves through one revolution, it experiences region A where a cascade model can potentially be used, but it also passes through regions B and C where ﬂow incidence varies dramatically and the concept of cascade ﬂow is not appropriate. Second, in the through-ﬂow region where the ﬂow behavior can be approximated as cascade ﬂow, a ﬂow deviation model is required (e.g. the cascade curves shown in Fig. 12). In particular, this model is needed to estimate the normal vector n^ describing the local relative mean streamlines. In actuator disk/duct models used for axial and radial

turbomachines, ﬂow deviation is modeled is a function of ﬂow incidence at the leading-edge [37]. However, the ﬂow is highly unsteady in the through-ﬂow region of the cross-ﬂow fan, undergoing large and rapid changes in ﬂow incidence from one end of the through-ﬂow arc to the other. Hence, as discussed in Section 2, this type of correlation may also need to include the time history of ﬂow turning (dynamic lift model), in addition to the instantaneous ﬂow incidence. For aero-propulsion applications, this challenge is compounded by the fact that the relative ﬂow can be transonic and supersonic in the blade passage at relatively low ﬂight speed [30,41], and it is well known that shock wave location and strength can be sensitive to small changes. As an example of steady-ﬂow actuator modeling, we present some results from a body-force method developed by Combes and Marie [47]. The body-force formulation in this work was conceptually similar to the one described above, although the implementation in a ﬁnite-element RANS code was greatly simpliﬁed. In particular, a source term was added to the tangential momentum equation only (i.e. FB,y a0 while FB,r ¼ 0), and the magnitude of the tangential body force was assumed constant and was simply adjusted so that the overall ﬂow ﬁeld matched the experimental data at one ﬂow rate. Fig. 38 shows the velocity ﬁeld predicted by their body-force model on the cross-ﬂow fan tested by Mazur and Singh [40]. Although the main ﬂow features were captured by the method, i.e. the existence of the eccentric vortex and a re-circulating region at the fan inlet region, the method was not able to predict the fan performance with this crude model of the blade force. Egolf [48] reported a more reﬁned method of modeling the blade body-force ﬁelds using experimentally derived ﬂow turning schedules and a loss model. This preliminary model was able to obtain good qualitative representation of the ﬂow ﬁeld at various ﬂow coefﬁcients, however, it was not able to obtain accurate prediction of fan performance either. Given the fact that more elaborate quasi-steady turning and loss correlations could yield better results, these examples are useful in illustrating the challenges of modeling methods that represent the general action of the impeller blading. Finally, another simpliﬁed steady-ﬂow method that has been used to simulate the ﬂow in a cross-ﬂow fan is the so-called MRF method or the Frozen Rotor approach [50]. In this case, the ﬂow is divided into zones moving at different speeds relative to each other, and the steady-state Reynolds-averaged Navier–Stokes

Fig. 38. Velocity vector ﬁeld predicted by body force model [47].

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

equations are solved in the moving reference frame of the zone under consideration. At the boundaries between the adjacent zones, information from one zone is simply passed to the adjacent zone with a local reference frame transformation. Hence, the ﬂow in one zone does not take into account the relative motion of the adjacent zone. In other words, when applying the MRF method to the cross-ﬂow fan, the effect of unsteadiness on the blades is not captured. Although the MRF method has proven to be useful in some turbomachine applications with weak circumferential asymmetry, the method has been found to be unreliable in predicting the ﬂow ﬁeld in the cross-ﬂow fan. In particular, although the MRF method does predict the ﬂow ﬁeld qualitatively (i.e. the three ﬂow regions are captured), it does not predict the overall performance of the cross-ﬂow fan accurately. The MRF method does not reliably predict the size, strength, and location of the eccentric vortex. This is illustrated in Fig. 39, which gives a comparison of the predicted ﬂow ﬁeld for a cross-ﬂow fan by the authors using the MRF method and the unsteady sliding mesh method described in Section 4.1. In both cases the analysis was

21

carried out for a ﬂow coefﬁcient of f ¼ 0.82. While both methods qualitatively predict the presence of the eccentric vortex, their sizes are quite different. In addition, the MRF solution shows a large re-circulating ﬂow at the inlet and ﬂow separation in the diffuser while the unsteady sliding mesh solution does not. With respect to overall fan performance, the results obtained from the URANS simulation yields cs ¼ 1.20 and l ¼ 4.30, while the MRF simulation gives cs ¼ 0.45 and l ¼ 2.10, compared to test data of cs ¼ 1.19 and l ¼ 4.51. As the MRF method is fully viscous and the blade and housing geometries are modeled exactly, its failure to accurately predict the ﬂow ﬁeld and fan performance suggests that unsteady-ﬂow effects are vitally important and must be properly incorporated in any simpliﬁed predictive method of the cross-ﬂow fan. In summary, the ﬂow ﬁeld in a cross-ﬂow fan is rather complex because of the strong coupling between the impeller and housing, and attempts so far to develop simpliﬁed prediction methods based on the steady-ﬂow assumption have not been successful. Various studies in the literature indicate that the 2D assumption is adequate but the unsteadiness in the ﬂow ﬁeld must be properly captured, and the most reliable predictive analysis is the unsteady sliding mesh CFD method. For aero-propulsion applications where the cross-ﬂow fan is highly integrated into the airfoil, an unsteady-ﬂow simulation with time step based on the blade passing period should be performed to obtain reliable results due to the ﬂow non-uniformities leaving the impeller. These computational methods can be used effectively by aircraft designers to develop advanced integrated fan–airfoil concepts for propulsion and ﬂow control.

5. Aircraft concepts using cross-ﬂow fans

Fig. 39. Path-lines predicted using (a) unsteady sliding mesh and (b) MRF method, at ﬂow coefﬁcient, f ¼ 0.82.

The cross-ﬂow fan has unique advantages for aircraft applications with its ability to span the wing forming a natural distributed propulsion and/or ﬂow control system. For low-speed applications, the cross-ﬂow fan can be used as the sole propulsor, replacing the axial propeller. The fan can be driven by an internal combustion engine, gas generators (i.e. replacing the propeller of the turboprop engine), or electric motors. For high subsonic-speed applications, one option is to use the cross-ﬂow fan in place of the bypass axial fan in a turbofan engine [14]. The ﬁrst researcher to propose the use of the cross-ﬂow fan in aircraft applications appears to be Ackeret in 1938 [5], with the application being airfoil drag reduction. Although pressure drag is relatively small compared to viscous drag for thin airfoils, it becomes dominant for thick airfoils (maximum thickness-tochord ratio 430%). This is due to the thickening of the boundary layer as the trailing edge is approached, and hence the full theoretical free-stream dynamic pressure is not recovered. Although boundary-layer suction via slots is one candidate for pressure drag reduction suggested by Ackeret, he also considered embedding a cross-ﬂow fan inside the airfoil to provide a means to re-energize the boundary-layer ﬂuid (Fig. 5). Ackeret recognized that the cross-ﬂow fan was a natural device for this purpose because of its rectangular inlet and outlet geometry and its small size. In 1962, Dornier [23,60] proposed to use cross-ﬂow fans in aircraft for both lift augmentation and forward thrust. Fig. 6 shows the proposed layout of the cross-ﬂow fan distributed within the wing with the fan axis of rotation along the wing span. Dornier proposed that air enter the fans through openings on the suction side of the wings and leave through openings on the pressure side. He speciﬁcally mentioned that in this layout, the boundary layer on the suction side of the wing would be sucked into the fan, and therefore lift enhancement would result. He also

ARTICLE IN PRESS 22

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

suggested that the fans be used to produce thrust. Although Dornier did not show the details of the fan-casing design, he alluded to the fact that circulation control and thrust can be manipulated from the direction of the exhaust air, and the fan mass ﬂow rate can be varied by fan rotational speed and by adjusting the inlet and outlet ﬂow areas. Also discussed in the patent is a multiple fan-drive system that is intended for preventing non-symmetric thrust in case of a fan-drive or transmission failure and for multiple design-point operation. Another concept which uses the cross-ﬂow fan for propulsion alone includes the ultra-light aircraft proposed by Liang [61] in 1965 and is shown in Fig. 40, where a cross-ﬂow fan is embedded inside the fuselage of a conventional aircraft layout. In the late 1970s, active developments of cross-ﬂow fans for aero-propulsion and lift augmentation were initiated at several organizations, including the Lockheed-Georgia Company, and the Vought Systems Division of LTV Aerospace Corporation, together with the University of Texas at Arlington. Shown in Fig. 41 is an example of how cross-ﬂow fan installation in an airfoil can be implemented. This concept was developed by Vought Systems under a Navy contract [12], using the cross-ﬂow fan design of Harloff and Wilson [13] embedded in the trailing edge of a thick airfoil, with the inlet on the pressure side and exhaust on the suction side. The variable-geometry design allows for the entire fan housing to rotate as the aircraft transitions from the cruise conﬁguration, where the fan provides forward thrust, to a vectored thrust STOL condition, and vice-versa. In particular, the primary and secondary vortex cavities are rotated so that the fan

Fig. 42. General layout of aircraft with wing-mounted cross-ﬂow fans proposed by Hancock [14].

Fig. 43. Integrated cross-ﬂow fan and airfoil concepts proposed by Hancock [14].

Fig. 40. Cross-ﬂow fan installation aircraft fuselage by Liang [61].

Fig. 41. Integrated cross-ﬂow fan and airfoil concept proposed by Vought Systems Division of LTV Aerospace Corporation [12].

inﬂow and outﬂow directions are roughly 901 apart, which is the natural ﬂow direction in the cross-ﬂow fan as pointed out in Section 2. The effort at the Lockheed-Georgia company to explore the use of the cross-ﬂow fan in a propulsive wing was published by Hancock in 1980 [14]. Fig. 42 shows in some detail one example of how cross-ﬂow fans could be integrated into a wing. Because conventional transonic wings are swept and ﬂexible, a number of cross-ﬂow fans would be used and distributed along the span of the wing from root to tip, and mounted internally in the trailing edge region. These fans would be connected via universal or ﬂexcouplings at appropriate intervals and could be powered by turbines from gas generators mounted at the wing root and tip locations. In the Lockheed arrangement shown in Fig. 42, the cross-ﬂow fans can be thought of as replacing conventional turbofans to provide the bypass ratio for improved propulsion efﬁciency. Hancock noted that the boundary layer over the entire suction surface of the wing can be ingested into the fans, offering the potential of reduced drag by delaying ﬂow separation. Furthermore, the use of multiple gas generators was intended to provide some degree of safety in the case of one-engine failure and potential reduction in induced drag through favorable interference with the tip vortex. It should be pointed out, however, that the swept fan arrangement in Fig. 42 is potentially problematic as the inﬂow and outﬂow to the fan is not normal to the fan axis. Fig. 43 shows two possible sectional arrangements of cross-ﬂow fan installations in wing trailing edges, as proposed by Hancock [14]. In both cases, the inlets of the fans can be ﬂush or ram types, and they can ingest air from both the wing upper and lower surfaces. The fan exhaust can also be integrated with a Coanda-ﬂap or jet-ﬂap for circulation control.

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Recently, with the aid of CFD, Kummer and Dang [20] proposed a propulsive airfoil concept for embedding a cross-ﬂow fan into a thick wing for both lift enhancement and thrust production. The design places a cross-ﬂow fan propulsion system with a raised inlet near the trailing edge of a modiﬁed Gottingen 570 airfoil section with 34% thickness to chord ratio (Fig. 44). Note that the geometry of the raised inlet has many similarities to the original concept proposed by Ackeret shown in Fig. 5, except the fan is raised further from the airfoil surface. The raised inlet is designed to ingest and guide suction surface and free-stream ﬂow into the fan. The ﬂow is then energized by the fan and expelled at the airfoil trailing edge. Analysis was performed using the 2D URANS method discussed in Section 4.1 to simulate the complete fan–airfoil system for incompressible ﬂow at a Reynolds number based on the airfoil chord of 5 106. The results show that the jet leaving the fan

Fig. 44. Integrated cross-ﬂow fan and airfoil concept proposed by Kummer and Dang [20].

Fig. 45. Time-averaged streamlines at 401 angle-of-attack [20].

23

produces wake ﬁlling while the suction effect of the fan virtually eliminates ﬂow separation at high angles of attack, yielding very high lift coefﬁcients. Fig. 45 shows predicted streamline patterns around the propulsive airfoil at 401 angle-of-attack with the crossﬂow fan turned off and on. As expected, when the fan is off, the airfoil is fully stalled. When the fan is turned on at a ﬂow coefﬁcient of 0.5, the ﬂow is fully attached with excess thrust, and the lift coefﬁcient is on the order 6.5. A system-level analysis was also presented to examine the beneﬁts of embedded cross-ﬂow fan propulsion at the cruise condition, including a design trade-off study between propulsive efﬁciency and fan size for minimum power. For the conﬁguration shown in Fig. 44, Kummer and Dang [20] performed a fan–airfoil system analysis and showed that small propulsors beneﬁt more from boundary-layer ingestion. On the other hand, increasing fan size improves propulsive efﬁciency, but at the cost of additional skin friction drag and weight. The propulsive airfoil concept developed by Kummer and Dang [20] using CFD alone was later veriﬁed via an experimental windtunnel program by Dygert and Dang [21] and Dygert [62]. In their experiment, the airfoil chord length was 0.4 m, and the fan diameter was 0.057 m, and the tested airspeed was up to 5.9 m/s, corresponding to Reynolds number based on chord of 170,000. Data obtained in this work included static pressure distributions over the airfoil surfaces upstream of the cross-ﬂow fan, wake total pressure proﬁles 13 chord downstream of the airfoil, and ﬂow visualization images captured using a helium bubble-seeding technique. Fig. 46 shows ﬂow visualization of the propulsive airfoil at 401 angle-of-attack with the fan turned off and on, at a Reynolds number of 85,000. The upper ﬁgure shows the airfoil with the fan off, where the ﬂow is seen to be fully separated near the quarter-chord location. The bottom ﬁgure shows the same conﬁguration with the fan running at 4100 rpm, corresponding to

Fig. 46. Flow visualization of propulsive airfoil at 401 angle-of-attack with fan off (top) and fan on (bottom) [21].

ARTICLE IN PRESS 24

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 47. Pressure coefﬁcient data at level ﬂight [21]. Fig. 49. Effect of thrust vectoring on circulation of propulsive airfoil concept [63].

Fig. 48. Wake/jet total pressure proﬁle; 151 angle-of-attack [21].

an advance ratio, J ¼ UN/Uo (air speed/wheel speed) of 0.24. With the fan turned on the ﬂow is completely attached, and the time required for the fan to re-attach the ﬂow is on the order of 10 chord/UN. Pressure taps placed on the airfoil surface also conﬁrm the CFD results of Kummer and Dang [20]. Fig. 47 depicts the pressure distribution obtained from tests for two fan operating points, as well as for the case where the fan is turned off, and for the original Gottingen 570 airfoil. This ﬁgure clearly shows the ability of the cross-ﬂow fan to increase the airfoil circulation as the ﬂow coefﬁcient is decreased. In their experimental study, lift coefﬁcient on the order of 7 was attained at an advance ratio of 0.32, at 301 angle-of-attack. To demonstrate the wake-ﬁlling potential of the concept, Fig. 48 shows the measured total pressure proﬁle in the wake region one-third chord downstream of the propulsive airfoil at 151 angle-of-attack. In the ﬁgure, note that a normalized pressure of zero corresponds to free-stream total pressure. In the fan-off case, the ﬁgure shows a large wake region with a total pressure deﬁcit. As the fan rpm is increased (decreasing advance ratio), it is seen that the size of the wake region is reduced. Operating the fan between J ¼ 1.1 and 1.18 (or between f ¼ 0.55 and 0.59 in Fig. 48)

Fig. 50. AAUV model airplane of Propulsive Wing (from www.propulsivewing.com).

results in virtually ideal wake ﬁlling, along the lines of Fig. 7. Further increasing the fan’s rotational speed beyond this point results in net thrust production. Finally, the work of Dygert and Dang [21] included a CFD validation study that demonstrated the accuracy and capability of the URANS sliding mesh technique for integrated fan–airfoil analysis. Using the same propulsive airfoil wind-tunnel model studied by Dygert and Dang [21], Nguyen and Rubal [63] studied the effect of jet-ﬂap and thrust-vectoring using the rear deﬂector of the fan upper housing. Shown in Fig. 49 are experimentally measured surface static pressure distributions along the airfoil upstream of the fan. The ﬁgure shows that the lift contribution from this portion of the airfoil increases as the rear deﬂector is deployed to re-direct the exhaust jet downward (jet-ﬂap effect). A similar study was also reported where an inlet deﬂector on the fan upper housing was deployed by Nguyen and Rubal [63]. In this case, the fan mass ﬂow rate was reduced as the inlet height was reduced, which in turn had the effect of varying the lift and thrust generated by the propulsive airfoil. This experimental study suggests that fan housing inlet and exhaust deﬂectors, along with fan rpm variation, can be used to provide effective ﬂight control

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

(e.g. pitch, roll and yaw) via differential lift, differential thrust and vectored thrust. A company under the name of Propulsive Wing, LLC was formed in 2006 (www.propulsivewing.com) to commercialize the propulsive airfoil concept, and a ﬂying model airplane has been demonstrated. The model aircraft is shown in Fig. 50 as an autonomous aerial utility vehicle (AAUV). Note that the aircraft conﬁguration is basically an un-swept ﬂying wing using the propulsive airfoil cross-section shown in Fig. 44. A twin-tail is employed, most likely to counter the pitching-up moment generated by fan rotation, the high suction loading near the airfoil leading edge, and possibly the weight of the cross-ﬂow fan. As mentioned earlier, fan housing inlet and exhaust deﬂectors, along with independently driven cross-ﬂow fans on the left and right sides of the lifting body, can be used to provide effective ﬂight control for the aircraft. Few details are given about the size and performance of the AAUV, except the company claims that for the same wingspan, the lifting capability of their platform is 2–3 times, and the internal payload volume is up to 10 times, conventional UAV conﬁgurations. A concept for synergistically integrating a cross-ﬂow fan with a thick subsonic airfoil for lift augmentation and thrust production was proposed by Casparie and Dang [22] for low-speed applications and is shown in Fig. 51. The concept combines some proven aerodynamic technologies with newly developed technologies into one platform, producing highly efﬁcient aerodynamics, high lift capability, and compactness. Such arrangements offer a platform representing ‘‘Synergistic Airframe-Propulsion Interactions & Integrations’’ (SnAPII), a concept recommended by the NASA Langley Aeronautics Technical Committee as having potential for break-through beneﬁts [64]. In particular, proven aerodynamic concepts incorporated into this design include the Grifﬁth/Goldschmied airfoil concept for overall drag reduction [65], the jet-ﬂap concept for circulation control [66], and the embedded distributed propulsion concept for increased propulsion efﬁciency [24,25]. The design partially embeds a cross-ﬂow fan over the maximum thickness location of a modiﬁed 35% thick

Grifﬁth/Goldschmied airfoil equipped with a modular trailing edge ‘‘jet-ﬂap.’’ The embedded cross-ﬂow fan effectively provides a combined suction blowing effect along the wing suction surface to achieve high performance from the traditional Grifﬁth/Goldschmied airfoil. Low momentum ﬂow is ingested by the crossﬂow fan via boundary-layer inlet, energized, and expelled as a jet to re-attach the ﬂow downstream of the maximum thickness location. The newly energized ﬂow allows for aggressive rear airfoil curvature to generate static pressure thrust, as well as drag reduction by ﬁlling the wake. In addition to competitive cruise performance as a result of the concave trailing edge surface in the original Grifﬁth/Goldschmied airfoil, the trailing edge surface can be converted to a circulation control airfoil by inverting or ﬂexing it to form a convex jet-ﬂap surface. Concept feasibility was veriﬁed by URANS sliding mesh CFD simulations using the commercial software, Fluent. Flow patterns around the proposed airfoil concept, along with global performance data, are shown in Fig. 51 at 01 angle-of-attack and advance ratio of J ¼ 0.46 (f ¼ 0.23). Observe the large difference in ﬂow patterns between the cruise and STOL geometrical conﬁgurations. The cruise conﬁguration generates much larger thrust (or negative drag coefﬁcient) than the STOL conﬁguration at the expense of lift. The standard measure for comparing aerodynamic efﬁciency of 2D airfoils is the ratio of lift to drag. However, for the propulsive airfoil design presented here, the conventional lift-to-drag ratio is not meaningful because it varies greatly depending on the fan power input. Casparie and Dang [22] deﬁned the concept of an equivalent lift-to-drag ratio (L/Deq) commonly used by the powered-lift community [67] and showed that (L/Deq) on the order of 10 is achievable in the cruise condition, while (L/Deq) on the order of 20 can be reached in the STOL conﬁguration. In their deﬁnition, the equivalent drag Deq is the sum of the physical drag force on the propulsive wing, along with a drag force deﬁned as (QDPt)/UN, the ideal power required by the cross-ﬂow fan to raise the total pressure of the air stream by the amount of DPt at a ﬂow rate Q, normalized to the ﬂight speed UN.

Fig. 52. FanWing model airplane (from www.fanwing.com).

Fig. 51. Streamline patterns at cruise (top) and STOL (bottom) conﬁgurations [22].

25

Fig. 53. Aerodynamic lift generating device used in FanWing [16].

ARTICLE IN PRESS 26

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

A unique concept that has received recent publicity is the ‘‘FanWing’’ patented by Peebles [16]. Several generations of model airplanes based on the FanWing concept have ﬂown successfully. A recent version is shown in Fig. 52, and general information about the concept is available on the company web site (www.fanwing.com). In the FanWing concept shown in Fig. 53, the aerodynamic lift generating device consists of a large ‘‘unconventional’’ cross-ﬂow fan positioned in place of the leading-edge of a thick airfoil, forming a unique conﬁguration. In particular, while the lower portion of the cross-ﬂow fan is shrouded, the upper portion (adjacent to the airfoil suction side) is open to the surrounding ambient air. In other words, referring to Fig. 10, while the vortex wall is retained, the rear wall is removed. The rotational direction is such that the exposed blades move aft toward the trailing edge of the airfoil (in the counter-clockwise direction as shown in Fig. 53). One feature of the device is that the lower shrouded housing terminates with a moveable lip or ﬂap, which partially controls the eccentric vortex. The ability of the lip to control vortex size and location affects the local sectional lift and thrust. Therefore, the lip can be used as a movable ﬂap to control both lift and thrust in a 3D conﬁguration, allowing for yaw and roll controls. Several experimental programs have been carried out to demonstrate the FanWing concept, including the work of Albani and Peebles [68] at the University of Rome, and the work of Forshaw [69] and Kogler [70] at Imperial College. In the latest work of Kogler [70], both ﬂow visualization and performance data of the FanWing concept were obtained, the latter included lift and drag coefﬁcients as a function of tip-speed-ratio (TSR) at zero angle-of-attack. Here, TSR is deﬁned as the fan tip speed normalized by the free-stream velocity, hence TSR ¼ 1/J. Kogler showed that the zero drag condition is achieved at around TSR ¼ 2.7 where the lift coefﬁcient is nearly 6, although the latest geometry of the FanWing concept is considerably more efﬁcient [71]. Fig. 53 shows the pattern of the ﬂow derived from an experimental visualization study at a nominal free-stream velocity. From these results, the overall ﬂow ﬁeld within the fan has similar characteristics to conventional cross-ﬂow fans when TSR41. In particular, there is a through-ﬂow region with a signiﬁcant contraction of the stream-tube, a vortex region inside the fan, and an ‘‘exposed’’ paddling region (region B). Compared to the ﬂow in a conventional cross-ﬂow fan, however, the eccentric vortex region (region C) appears to be larger, while the throughﬂow region (region A) is smaller. An important feature is that the paddling region plays an important role in the FanWing concept

and is responsible for maintaining ﬂow attachment over the suction surface. Fig. 54 shows the predicted static pressure distribution around the FanWing obtained from URANS sliding mesh CFD calculations by Duddempudi et al. [17]. Their results show that the majority of lift comes from the fan region as a result of the suction effect along the exposed fan blades. Note that the CFD work of Duddempudi et al. [17] produced the same ﬂow pattern as shown in Fig. 53. Qualitatively, the operation of the FanWing concept appears to be as follows. As mentioned earlier, the paddling region (region B) of the exposed blades prevents ﬂow separation over the suction surface by creating a ‘‘slip’’ velocity on the surface. This results in the presence of the large suction region near the exposed blades (Fig. 54), and hence, the high lift characteristics of the device. Below the paddling region is the through-ﬂow region (region A), which produces a high-velocity jet and blowing over the airfoil. The jet has both radial and tangential velocity components; the latter depends on the amount of work acquired by the ﬂow through the fan. Therefore, proper alignment between the jet ﬂow ejection angle and the airfoil surface is necessary, which is part of the CFD study carried out by Duddempudi et al. [17]. Both the ‘‘slip’’ velocity of the exposed blades and the jet leaving the fan contribute to the ability of the ﬂow to smoothly pass through the adverse pressure gradient shown in Fig. 54. Note that the jet has components in both the lift and thrust directions. Finally, there is the eccentric vortex (region C) which plays a major role in determining the strength of the jet and therefore, the lift and drag characteristics. Another group of researchers proposed to use the cross-ﬂow fan for vertical lift operation. Gossett [18] proposed to use the cross-ﬂow fan in vertical take-off and landing (VTOL) aircraft applications. He argued that since the vertical thrust requirement is much larger than the forward ﬂight thrust requirement, and since the aircraft aerodynamic design should be optimized for forward ﬂight, the cross-ﬂow fan is a good choice to be used as a vertical thrust augmentation device as it can be easily mounted within the tube fuselage. The cross-ﬂow fan can then be turned off during the forward ﬂight phase, and the fuselageembedded cross-ﬂow fan introduces no drag penalty. Fig. 55 shows a possible layout of a combined ducted fan and cross-ﬂow fan single-seat VTOL personal air vehicle (PAV). During forward ﬂight mode, the thrust would come from the two ducted fans while lift is entirely generated by canard and horizontal tail surfaces. In the vertical ﬂight mode, the two ducted fans would rotate and become ducted lift-fans deﬂecting their exhaust in the vertical direction, while the cross-ﬂow fan would be turned on to generate additional vertical lift force. Note that the concept has some similarity to the VTOL commuter airplane developed by

Fig. 54. Static pressure distribution on FanWing [17].

Fig. 55. Airframe embedded cross-ﬂow fan for VTOL application by Gossett [18].

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

Fig. 56. Airframe embedded cross-ﬂow fan for VTOL application by Sharpe [72].

Moller (see www.moller.com) in that it also employs ducted fans for both forward and vertical thrust. However, in the concept proposed by Gossett, the forward ducted fans in Moller’s design are removed and replaced by the cross-ﬂow fan and a canard wing. Again, the argument being that the combined ducted fan and cross-ﬂow fan conﬁguration would perform more efﬁciently in the forward ﬂight mode. A similar concept was also proposed by Sharpe [72] and is shown in Fig. 56. In this case, the cross-ﬂow fans are mounted on the wing to provide vertical take-off capability, while a propeller mounted in the rear is employed for thrust. In summary, a wide range of aircraft concepts with cross-ﬂow fan propulsion and ﬂow control have been proposed and investigated to varying degrees, dating back to 1938. Many of the concepts are described only in a qualitative sense, or in some cases technical data have not been released. However, more recently a number of integrated fan–airfoil conﬁgurations have been developed using combined experimental and computational tools; the latter employ the URANS sliding mesh CFD method and allow designers to analyze these problems in detail. These computational techniques provide a basis for investigating and optimizing future designs. In exploring new designs it is worthwhile to provide a classiﬁcation of different options for fan-wing integration. This can be done by beginning with the choice of chord-wise position of the fan as forward, mid-chord or aft. The fan may then be entirely embedded within the airfoil or it may have a lateral offset toward the suction or pressure surface (e.g. Fig. 41). The inlet may be located on the suction, pressure or leading-edge surfaces, or a combination thereof (e.g. Fig. 43). The fan discharge may be located at the airfoil trailing edge, or on the suction or pressure surface, and it may be adjustable, providing vectored thrust or it may be conﬁgured in a blown-ﬂap arrangement (e.g. Fig. 51). In each of these possible arrangements, the fan may be used to provide a range of propulsion and ﬂow control capabilities. On a system level the fan diameter relative to airfoil chord and thickness are key considerations along with the advance ratio. It should also be noted that fan inlet counter-swirl tends to produce high loading in the ﬁrst stage blading and load reduction in the second stage (this can be seen by following the analysis of Section 2). Excessive levels of counter-swirl can lead to rotating stall in the ﬁrst stage [73], so depending upon the details of the fan-wing integration, the inﬂow may need to be redirected using guide vanes. So far most of the work on fan-wing integration has been of an ad hoc nature and the cruise Mach number limits have not been studied in detail. Similarly, much of the work directed at the fan itself for aircraft application has been centered on a narrow range of fan housing designs. Therefore, improved fan performance and highly effective fan-wing integration concepts may be possible through systematic study and optimization. These concepts can be

27

studied at the system level including drive and power systems (e.g., motor drives and solar power), hybrid arrangements with other propulsion devices, and the possibility of including buoyancy augmentation. Application of cross-ﬂow fans for aircraft propulsion and ﬂow control will involve many challenges including noise control, structures, drive systems, aircraft stability, and ﬂight control. These topics are outside of the scope of this article; however, we conclude this section with a brief discussion on noise. Cross-ﬂow fan noise can be classiﬁed, as with other fans, in terms of its tonal and broadband content. Tonal noise is generated by periodic ﬂow–surface interactions and occurs at the blade passage frequency and its harmonics. Broadband noise is produced by random ﬂow–surface interactions within the fan and turbulent shear ﬂow at the fan discharge (jet noise). Based on aeroacoustic sound power scaling (see e.g., [74]), jet noise will tend to be relatively weak in distributed cross-ﬂow fan-wing integrations due to low jet velocity, and ﬂow–surface interaction noise will tend to dominate. These ﬂow–surface interactions behave as dipole acoustic sources and their radiated sound power scales with the sixth power of the characteristic ﬂow velocity and the square of the source characteristic length scale. Appropriate length scales for the cross-ﬂow fan are impeller diameter and span, and the wheel tip speed is a suitable characteristic velocity, so the noise level for a particular fan design and operating condition can be scaled accordingly. The primary noise source in the cross-ﬂow fan is the unsteady aerodynamic loading due to blade–wall interaction, and this process is especially important at the vortex wall. Noise generated this way is highly tonal and much of the work in cross-ﬂow fan design for air conditioning focuses on trading off the performance beneﬁts of tight clearances with noise. As noted earlier, de-phasing techniques such as nonuniform blade spacing are used for distributing tonal noise, and aeroacoustic prediction methods have been employed [15,51] to predict the acoustic spectrum and radiation pattern. Broadband noise generation in cross-ﬂow fans is produced by blade interaction with inﬂow and boundary-layer turbulence at both stages and by blade–vortex interaction. Noise control through acoustic lining in the fan inlet and outlet ducting is feasible, and locating the fan on the suction surface is advantageous in reducing ground level noise by breaking line of sight to the fan. At present there are few data available on the noise of cross-ﬂow fans for aircraft application, however, preliminary testing noted in Ref. [12] addresses noise concerns both from an annoyance standpoint and acoustic fatigue consideration. The reference cites higher noise levels than conventional propulsors of equal power, but notes possible options for noise reduction such as adjustment of impeller-wall clearances.

6. Conclusions The purpose of this article is to review the aerodynamics of cross-ﬂow fans and their application to aircraft propulsion and ﬂow control. The discussion begins with a review of the historical development of these unique fans and their potential for spanwise integration in wings for distributed propulsion, boundary-layer control, and high lift performance. The basic nature of the fan aerodynamics is then discussed, describing the three ﬂow regions that develop in all cross-ﬂow fans (through-ﬂow, vortex, and paddle regions), and a mean-line analysis is employed to illustrate the energy transfer and loss processes. The analysis is used to demonstrate the effect of vortex motion during throttling for a fan test case, demonstrating one of the many complex interactions that occur in cross-ﬂow fans. A review of experimental studies of cross-ﬂow fans for aviation centers on work from the 1970s on

ARTICLE IN PRESS 28

T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

high-speed fans and more recent studies carried out after about two decades of inactivity. The discussion reveals that most of the work has focused on a narrow range of fan housing design developed in the original 1970s effort, and that these fans have attained total pressure ratio up to 1.7 and adiabatic compression efﬁciencies in the range of 80%. A review of cross-ﬂow fan aerodynamic prediction techniques focuses ﬁrst on 2D unsteady Navier–Stokes sliding mesh CFD methods. This relatively involved technique is shown to produce reliable performance and ﬂow ﬁeld predictions through validations with experimental data. Results of this state-of-the-art method are also used to illustrate key aspects of cross-ﬂow fan behavior, particularly the extreme unsteady ﬂow in the impeller frame of reference. Steady-ﬂow prediction methods are then reviewed beginning with the most basic potential ﬂow models and ending with discussion on actuator analysis, where blade action is represented by a bodyforce ﬁeld, and the multi-reference frame CFD technique. Current steady-ﬂow methods are shown to fall short in terms of both performance and ﬂow ﬁeld prediction, but the possibility of approximating the essential unsteady effects through quasisteady modeling is discussed. Such modeling is of special interest for 3D analysis of complete aircraft systems. Finally, the article reviews concepts for airframe integration using cross-ﬂow fans, dating back to 1938. Many of the concepts are seen to be qualitative in nature; however, recent work on fan-wing integration has become much more quantitative. Activity in this area has seen a renaissance with the emergence of CFD and interest at NASA, and two distinct cases are reported of unmanned modelscale aircraft ﬂight tests using cross-ﬂow fan propulsion and ﬂow control. We conclude the article with a summary of potential beneﬁts, limitations, and open questions in cross-ﬂow fan propulsion. The potential beneﬁts include: (1) embedded propulsion, eliminating pylon and nacelle drag; (2) distributed propulsion, enabling high propulsive efﬁciency through wake ﬁlling and potential noise reduction via low mean jet velocity; (3) boundary-layer ingestion, producing ﬂow separation control for STOL operation; (4) circulation control, producing demonstrated lift coefﬁcient on the order of 7 using powered lift and jet ﬂaps; (5) reduced ﬂight control surfaces (tail, stabilizer) by use of differential thrust, differential lift, inlet ﬂaps, jet ﬂaps, and vectored thrust to control aircraft roll, yaw and pitch; (6) hybrid systems combining the cross-ﬂow fan with other propulsion systems. The potential limitations include: (1) lower efﬁciency than existing propulsors due to inherent loss regions within the fan; (2) limited cruise speed due to ﬂow contraction and acceleration within the through-ﬂow region of the fan, producing high relative Mach number and choking; (3) pitching moment caused by fan rotation along the wing axis and unconventional aerodynamic loading distribution; (4) mechanical complexity due to coupling and drive systems needed to power the fan; (5) structures, materials, dynamics, and noise may present basic limitations for some applications. Some of the open questions include: (1) what are the cruise speed limitations for cross-ﬂow fan propulsion and what are the best ways to push the envelope? (2) What is the upper limit on efﬁciency of cross-ﬂow fans? (3) What is the optimal fan size in relation to the airfoil under various design scenarios based on system-level analysis? (4) What are the optimal fan design features for aircraft applications? All of these questions essentially relate to seeking effective aircraft conﬁgurations through utilization of cross-ﬂow fans. With renewed interest in this topic, and the advent of reliable fan performance prediction techniques, systematic studies can now be carried out to address these questions and advance this very interesting and potentially signiﬁcant technology.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

[12]

[13]

[14] [15] [16] [17]

[18]

[19]

[20] [21]

[22]

[23] [24] [25] [26] [27] [28]

[29]

[30]

[31]

[32] [33]

[34] [35] [36]

[37]

Eck B. Fans. Oxford: Pergamon Press; 1973. Mortier P. Fan or blowing apparatus. US Patent no. 507,445, 1893. Anderson EL. Unit heater and ventilator. US Patent no. 1,889,588, 1932. Buck CM. Blower. US Patent no. 2,033,273, 1936. Ackeret J. Present and future problems in airplane propulsion. Schweizer Bauzeitung 1938;112(1) (also, NACA TM no. 976). Coester R. Theoretische und experimentelle Untersuchungen an Querstromgebla¨sen, vol. 28. Zu¨rich: Mitt Inst fu¨r Aerodyn; 1959. Tramposh H. Cross-ﬂow fan. ASME Paper no. 64-WA/FE-26, 1964. Porter AM, Markland E. A study of the cross ﬂow fan. J Mech Eng Sci 1970;12(6):421–31. Ikegami H, Murata S. A study of the cross ﬂow fan: Part I, A theoretical analysis. Technology Report, Osaka University, vol. 16, no. 731, 1966. Yamafugi K. Studies on the ﬂow of cross-ﬂow impellers (2nd report, Analytical study). Bull Jpn Soc Mech Eng, December 1975;18:1425–31. Moore A. The tangential fan-analysis and design. In: Conference on fan technology and practice. London: Institute of Mechanical Engineering; 18–19 April 1972. p. 66–72. Naval Air System Command contract N00019-74-C-0434. Multi-bypass ratio propulsion system technology development, vol. I–IV. Vought Systems Division, LTV Aerospace Corporation, July 1975. Harloff GJ, Wilson DR. Cross ﬂow propulsion fan experimental development and ﬁnite element modeling. AIAA-80-0385. In: AIAA 18th Aerospace Sciences Meeting, Pasadena, 1980. Hancock JP. Test of a high efﬁciency transverse fan. AIAA-80-1243. In: AIAA/ SAE/ASME 16th joint propulsion conference, Hartford, 1980. Moon YJ, Cho Y, Nam HS. Computation of unsteady viscous ﬂow and aeroacoustic noise of cross ﬂow fans. Comput Fluids 2003;32:995–1015. Peebles P. Aerodynamic lift generating device. US Patent no. 6,527,229 B1, March 2003. See also /www.fanwing.comS. Duddempudi D, Yao Y, Edmondson D, Yao J, Curley A. Computational study of ﬂow over generic fan-wing airfoil. Aircraft Eng Aerospace Technol: Int J 2007;79(3). Gossett DH. Investigation of cross ﬂow fan propulsion for lightweight VTOL aircraft. M.S. thesis, Department of Mechanical & Aeronautical Engineering, Naval Postgraduate School, Monterey, CA, December 2000. Yu HT, Hobson G, Gannon V, Anthony J, Platzer M. Experimental investigation and numerical prediction of the performance of a cross-ﬂow fan. In: 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, 2008. Kummer JD, Dang TQ. High-lift propulsive airfoil with integrated crossﬂow fan. AIAA J Aircraft 2006;43(4) July–August. Dygert RK, Dang TQ. Experimental investigation of embedded cross-ﬂow fan for airfoil propulsion/circulation control. In: AIAA aerospace science conference, Reno, NV, AIAA Paper no. 63971, January 2007. Casparie E, Dang TQ. High lift/low drag thick subsonic Goldschmied/ Grifﬁth airfoil with integrated cross-ﬂow fan propulsion. In: International powered lift conference, London, June 2008. Dornier P. Multiple drive for aircraft having wings provided with transverse ﬂow blowers. US Patent 3,065,928, 27 November 1962. Sehra AK, Whitlow Jr. W. Propulsion and power for 21st century aviation. Prog Aerospace Sci 2004;40:199–235. Kim HD, Saunders JD. Embedded wing propulsion conceptual study. NASA TM-2003-212696, 2003. Betz A. Introduction to the theory of ﬂow machines, Section 59. ﬁrst English ed. New York: Pergamon; 1966. p. 215–7. Smith LH. Wake ingestion propulsion beneﬁt. J Propulsion Power 1993; 9(1):74–82. Ko YY. The multidisciplinary design optimization of a distributed propulsion blended-wing-body aircraft. PhD. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2003. Daggett DL, Kawai R, Friedman D. Blended wing body systems studies: boundary layer ingestion inlets with active ﬂow control. NASA/CR-2003212670, 2003. Kummer JD. Simulation of the cross-ﬂow fan and application to a propulsive airfoil concept. PhD. thesis, Department of Mechanical & Aerospace Engineering, Syracuse University, Syracuse, New York, 2006. Yamafugi K. Studies on the ﬂow of cross-ﬂow impellers (1st report, experimental study). Bull Jpn Soc Mech Eng, September 1975;18: 1018–25. Bushnell P. A mean line aerodynamic analysis for cross-ﬂow fans. Carrier Corporation Internal report, 1993. Allen DJ. The effect of rotor and casing design on cross-ﬂow fan performance. In: International conference on fan design and applications. Guilford, England, Paper no. J1, 7–9 September 1982. Kim JW, Ahn EY, Oh HW. Performance prediction of cross-ﬂow fans using mean streamline analysis. Int J Rotat Mach 2005;2005(2):112–6. Porter AM. A study of the tangential fan. PhD. thesis, The Queens University of Belfast, 1969. Tuckey PR, Holgate MJ, Clayton BR. Performance and aerodynamics of cross ﬂow fans. In: International conference on fan design and applications. Guilford, England, Paper no. J3, 7–9 September 1982. Horlock JH. Axial ﬂow compressors, ﬂuid mechanics and thermodynamics. Malabar: Krieger; 1958.

ARTICLE IN PRESS T.Q. Dang, P.R. Bushnell / Progress in Aerospace Sciences 45 (2009) 1–29

[38] Lazzarotto L, Lazzaretto A, Macor A, Martegani AD. On cross-ﬂow fan similarity: effects of casing shape. J Fluids Eng 2001;123(3):523–31. [39] Clayton BR. A review and appraisal of crossﬂow fans. Build Services Eng 1975;42:230–47. [40] Mazur J, Singh T. Momentum exchanges and energy transfers in cross ﬂow fans. ASME Paper no. 87-GT-32, 1987. [41] Harloff GJ. Cross-ﬂow fan experimental development and ﬁnite-element modeling. PhD. dissertation, University of Texas at Arlington, Arlington, TX, 1979. [42] Hobson GV, Cheng, WT, Seaton MS, Gannon AJ, Platzer MF. Experimental and computational investigation of cross-ﬂow fan propulsion for lightweight VTOL aircraft. ASME Paper GT2004-53468, 2004. [43] Schreiber CW. Effect of span variation on the performance of a cross ﬂow fan. M.S. thesis, Department of Mechanical & Aeronautical Engineering, Naval Postgraduate School, Monterey, CA, December 2006. [44] Yu HT. Experimental Investigation and numerical prediction of the performance of a cross ﬂow fan. M.S. thesis, Department of Mechanical & Aeronautical Engineering, Naval Postgraduate School, Monterey, CA, December 2006. [45] Wu CH. A general theory of three-dimensional ﬂow in subsonic and supersonic turbomachines of axial, radial, and mixed-ﬂow types. NACA TN 2604, 1952. [46] Ilberg H, Sadeh WZ. Flow theory and performance of tangential fans. Proc Inst Mech Eng 1965–1966;180:481–91. [47] Combes JF, Marie L. Numerical modeling of the ﬂow in a cross-ﬂow fan. Fluid Machinery, Proceedings of the ASME, FED-vol. 195, 1994, p. 29–34. [48] Egolf TA. Application of a body force approach for transverse fan aerodynamic performance prediction. United Technology Research Center report no. UTRC98-10, October 1998. [49] Kitagawa K, Tatsuke H, Tsujimoto Y, Yoshida Y. A numerical simulation of cross ﬂow fan. In: Proceedings of the boundary elements and ﬂuid dynamics, 1992. [50] Fluent 6.2 User’s Guide, Fluent Inc., Lebanon, NH, 2005. [51] Cho Y, Moon YJ. Blade tonal noise prediction of variable pitch cross ﬂow fans by unsteady viscous ﬂow computation. In: FAN NOISE 2003 international symposium, Senlis, September 2003. [52] Seaton MS. Performance measurements, ﬂow visualization, and numerical simulation of a cross ﬂow fan. M.S. thesis, Department of Mechanical & Aeronautical Engineering, Naval Postgraduate School, Monterey, CA, March 2003. [53] Cheng WT. Experimental and numerical analysis of a cross ﬂow fan. M.S. thesis, Department of Mechanical & Aeronautical Engineering, Naval Postgraduate School, Monterey, CA, December 2003. [54] Smith LH. The radial equilibrium equation of turbomachinery. ASME J Eng Power 1966;88:1–12.

29

[55] Marsh H. A digital computer program for the through-ﬂow ﬂuid mechanics in an arbitrary turbomachine using a matrix method. Aeronautical Research Council, R&M 3509, 1966. [56] Marble FE. Three-dimensional ﬂow in turbomachine. High speed aerodynamics and jet propulsion, vol. 10. Princeton University Press; 1964. p. 83–166, Section C. [57] Damle SV, Dang TQ, Reddy DR. Throughﬂow method for turbomachines applicable for all ﬂow regimes. ASME J Turbomach 1997;119:256–62. [58] Bosman C, Marsh H. An improved method for calculating the ﬂow in turbomachines, including a consistent loss model. J Mech Eng Sci 1974;16(1):25–31. [59] Patankar SV, Spalding DB. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic ﬂows. Int J Heat Mass Transfer 1972;15. [60] Dornier, P. Aircraft with ground effect landing gear. US Patent no. 3,082,976. 26 March 1963. [61] Laing, N. Thrust means for powering aircraft. US Patent no. 3,212,735, 19 October 1965. [62] Dygert RK. Experimental validation of embedded cross-ﬂow fan propulsive/ circulation control airfoil. M.S. thesis, Department of Mechanical & Aerospace Engineering, Syracuse University, Syracuse, NY, 2005. [63] Nguyen K, Rubal J. Circulation control of propulsive airfoil concept via exhaust nozzle geometry. Presented at the AIAA Region I northeast student conference, Boston, April 2007. [64] Yaros SF, Sexstone MG, Huebner LD, Lamar JE, McKinley RE, Torres AO, et al. Synergistic airframe–propulsion interactions and integrations. NASA/TM-1998-207644, March 1998. [65] Goldschmied FR. Thick-wing spanloader all-freighter: design concept for tomorrow’s air cargo. AIAA paper 90-3198, September 1980. Presented at the AIAA Region I northeast student conference, Boston, April 2007. [66] Neilson JN, Biggers JC. Recent progress in circulation control aerodynamics. AIAA Paper 87-0001, January 1987. [67] Jones GS. Pneumatic ﬂap performance for a 2D circulation control airfoil, steady and pulsed. NASA LaRC, NASA and ONR Flow Control Workshop, 2004. [68] Albani A, Peebles P. Span rotor: prove tecniche relazione. Universita degli Studi di Roma ‘‘La Sapienza,’’ 1997. [69] Forshaw S. Wind tunnel investigation of new ‘‘FanWing’’ design. Imperial College; 1999. [70] Kogler KU. FANWING—Experimental evaluation of a novel lift & propulsion device. MEng. thesis, Aeronautical Engineering Department, Imperial College, London, 2002. [71] Peebles P. Private communication. October 2008. [72] Sharpe TH. Lift augmentation device for aircraft. US Patent no. 4,194,707, March 1980. [73] Bushnell P. Flow stabilizer for transverse fan. US Patent no. 6,050,773, 2000. [74] Blake WK. Mechanics of ﬂow-induced sound and vibration, vols. 1–2. Boston: Academic Press; 1986.

Aerodynamics of cross-flow fans and their application to aircraft propulsion and flow control

Aerodynamics of cross-flow fans and their application to aircraft propulsion and flow control

Recommend Documents