5th Flow Control Conference

3D e�ects in a supersonic rectangular jet vectored by

ow separation control, a numerical and experimental

study

V. Jaunet� D. Aymer� E. Collin� J.P. Bonnet� A. Lebedev� C. Fourment�

The vectorization of a supersonic rectangular jet by ow separation control is inves-tigated with the help of non intrusive measurement techniques and Reynolds AverageNavier-Stokes numerical computations. The combination of the two types of results isused in order to understand the structure of the ow, the separated region and thus thevectorization mechanism. It is shown that three dimensionality has strong e�ect on thee�ciency of the system.

Nomenclature

� = tan�1 Fy

Fxthrust vector angle

qinj

Q uidic injection rate

Fy longitudinal thrust componentFy vertical thrust componentQ primary mass ow rateqinj mass ow rate of the injectoru� adimensionnalized streamwise velocityv� adimensionnalized vertical velocityx� = x

h adimensionnalized streamwise distancey� = y

h adimensionnalized vertical distancez� = z

h adimensionnalized transverse distance

e subscript refering to subsonic ow conditionsinj subscript refering injection conditionsj subscript refering jet exit conditions

I. Introduction

A fundamental issue regarding the performance of military aircrafts is manoeuvrability. One emergingtechnology, thrust vectoring, seems to be a very e�cient way to improve aircraft’s motion abilities whileo�ering the possibility of reducing wet surfaces that cause drag and radar signature.Thrust vectoring occurs when the forces on the aircraft engine are unbalanced, leading to a torque whichgives the aircraft means of changing direction rapidly. The �rst generation of thrust vectoring nozzles de- ects the engine exhaust through mechanical actuators. Due to the severe conditions at the engine exhaust,component design happens to be complex, inducing weight increase along with production and maintenancecosts. Thus an alternative solution is the use of small secondary air streams to vector the primary jet. Suchtechniques are expected to reduce nozzle weight up to 80% and maintenance costs up to 50%1 from themechanical ones.A great variety of uidic thrust vectoring techniques has been developed. Secondary injection thrust vec-toring2,3 was the �rst uidic method to be proposed. It consists in using a cross ow jet blowing into the

�PPRIME Institute, CNRS - University of Poitiers - ENSMA, UPR 3346Copyright c 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

5th Flow Control Conference28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-4976

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

supersonic primary jet creating a shock wave inducing asymmetry in the ow �eld and unbalanced lateralforces on the nozzle. Di�erent techniques have been recently explored to avoid the loss of thrust due to thepresence of shock waves in the nozzle. Suction and injection in conjunction with Coanda e�ect can be usedto manipulate the primary jet without shock wave4{6 but this techniques need the addition of an exhaustcollar. The throat skewing technique introduced by Miller et al.3 and later modi�ed by Deere1 and Flamet al.7 manipulates the jet subsonically by the use of a particular shaped convergent-divergent-convergentnozzle equipped with injection slots at the upstream throat.Because of the need of uidic actuators to alter wall pressure distributions, isolated cross ow jets have beenintensively studied for both subsonic8 and supersonic ows.9,10 These studies showed a complex network ofseparated and reattached ows and, in most cases the creation of a counter-rotating vortex pair convectedby the ow. More recently attention has been paid to the e�ects of vertical con�nement on rectangular jetin subsonic cross ow11 showing a link between the span of the slot and the three dimensionality of the ow.Ahmed et al12 shows that this three dimensionality no more exists when the slot spans the entire width ofthe ow except in the near wall region.In order to provide yaw control of an aircraft powered by a high mixing (i.e. rectangular with an aspectratio of 5:1) supersonic nozzle, we equiped the nozzle smallest dimension with short divergents located justbefore the exhaust section. When passing through the expansion fan, the boundary layer turbulence levelis attempted to be signi�cantly reduced13 so that it can separate more easily. A secondary ow injectionlocated at the middle of one divergent is used to control the boundary layer separation. Moreover, as thedivergents at the exit are symmetric, the pressure di�erence between the two opposite sides of the nozzle isthen ampli�ed by the separation.Because of the aspect ratio of the nozzle, the cross ow jet used is this study is strongly con�ned in thespanwise direction so that sidewall e�ects cannot be neglected. Thus we propose in this paper to analyse,with the help of non-intrusive measurements combined with numerical computations, the structure of the ow and more precisely the structure of the controlled separated region.The �rst part of this paper is devoted to the experimental device and the ow conditions. The second partprovides the description of the unmanipulated ow. The third part is devoted to the vectored jet and thevectorization mechanism. Finally, conclusion is given on the three dimensional e�ects on vectorization.

II. Experimental device and Numerical characteristics

A. Wind tunnel

The wind-tunnel Fig.: 1 (a) is equipped with a rectangular cross section nozzle having an aspect ratio of5 : 1 (its smallest dimension is 30 mm) blowing into a 500 mm wide square-shaped subsonic test section. Thetwo short sides of the nozzle end with a 10 � angle and 30 mm long divergent (Figure : 1 (b)). Furthermore,a thin cross ow jet is implanted in one of the divergents and spans the whole width of the nozzle. Thethickness of the slot is 0:5 mm and the cross ow jet blows out upstream with an angle of 45 � with the axisof the nozzle.

(a) (b) (c)

Figure 1: (a) S150HP facility, (b) the actuator, (c) exhaust section of the nozzle and chosen coordinatesystem

A Cartesian coordinate system fx, y, zg is chosen with its origin located at the center of the exhaustsection of the main jet and with the x-axis along the streamwise direction and the y-axis and z-axis along

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

the long and short dimensions of the nozzle (Figure : 1 (c)).

Distances are nondimensionalized by the width of the nozzle and noted x�; y� and z�. Flow speedmagnitude in nondimensionalized with respect to the jet exit ow speed uj and the external ow speed ue

such as :

u� =u� ue

uj � ue, v� =

v

uj � ue

B. Flow characteristics

The Reynolds number of the jet based on the mean axial velocity (380 m:s�1) and on the hydraulic diameterof the exhaust section is equal to 3:3 � 106. Stagnation pressure is chosen equal to 3:7 bar, which is theminimum pressure needed to avoid natural detachment before the end of the nozzle. It is maintainedconstant by an hydraulic valve and kept at its nominal value within variations of �0:05 bar. Stagnationtemperature is measured during all the experimentations. It can vary from 250 K up to 260 K from oneexperiment to another (depending mainly on the atmospheric conditions and tank pressure). The jet speedis thus controlled with a 2 % accuracy.Several uidic injection rate qinj

Q are tested from 0 to 1:62 % . The 0:78 % uidic injection rate, correspondingto an injection stagnation pressure of 7:5 bar, is chosen for this study.

C. Computational characteristics

The computations are conducted using a commercial code (@Fluent) solving the stationnary Reynolds Aver-age Navier-Stokes equations in �nite volume formulation and second order accuracy in space. The Spalart-Allmaras turbulence model is used because of its e�ciency in predicting separated ows14 and supersoniccross ow jets.15

Two and three dimensional are performed in order to highlight three dimensional behaviour of the jet.The computational domain corresponds to a supersonic rectangular nozzle surrounded by a rectangularsubsonic tunnel. The two dimensional is reduced to the plane of symetry z� = 0.

The supersonic nozzle ow has been simpli�ed

Figure 2: Mesh of the 3D domain used of computations

using a slightly diverging 0:66 � rectangular channelwhose length is equivalent to the distance betweenthe beginning of the divergent and the throat ofthe real nozzle. Notice that the real nozzle hasbeen built with this slight divergence in its rect-angular part to compensate the boundary layer in-crease of thickness. The injection slot is representedby a surface which can be either a wall or an inletboundary. The subsonic ow inlet surface is situ-ated at x� = �3 distance to the nozzle lips consid-ered enough to generate a boundary layer equivalentto the experimental one. The exit section is situ-ated at a distance x� = 23:3. This distance has beenconsidered after several tests to be enough to pre-vent approximate constant downstream conditionto in uence the part of the ow to be investigated.which is enough to allow the exhaust supersonic jetto mix with the subsonic ow on a su�cient dis-tance to get accurate results in the same volume asmeasurements. The mesh is re�ned near the wallsso that the �rst point located at y+ nearly equal to1. The injection region is also re�ned in order to

take account on its small dimension compared to the nozzle. A sketch of the domain is given �gure 2.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

The boundary conditions are set up to �t with the experiment : at the supersonic inlet Mj = 1:45,Ptj = 3:7 bar and Ttj = 260 K ; at the subsonic inlet : Me = 0:2, Pte = 1:0 bar and Tte =290 K. And theoutlet pressure is imposed using a static pressure slightly lower than the subsonic static pressure inlet. Theinjection is set with a sonic condition : Minj = 1:0, Ptinj = 7:5 bar and Ttinj = 260 K.

III. Results and Discussions

A. Structure of the unmaniputaled ow

Particle image velocimetry (PIV) is performed in the fx; yg plane in order to have quantitative informationon the ow. The ow is seeded with SiO2 particles and 200 pairs of images are taken for each con�guration.The PIV device consists of a 1376 � 1040 pixel CD camera equipped with a 28 mm objective and two 190mJ Nd-YAG laser cavities. A 5 �s time between each laser pulse is selected. it corresponds to a particledisplacement of 7 pixels in the supersonic part of the ow. Image processing is conducted with the LaVisionsoftware, and spurious vectors are corrected using a Gappy POD procedure based on the algorithm proposedby Murray and Ukeiley .16

A comparison of computational results against experimental one is given on �gure 3. Firstly, one can noticethat the 2D computation does not agree with the experimental results. The adaptation shock strengh isunderestimated leading to misprediction of the jet growth. On the contrary the 3D calculation gives a goodagreement with the PIV measurement, this tends to indicate that the jet behaviour is fully three dimensionaleven in the natural case.

-4

-2

0

2

4

y*

x*=0.40x*=0.74

x*=1.08x*=1.42

x*=1.76x*=2.10

x*=2.44x*=2.80

0.0

0.4

0.8

1.2

x*=3.14

-4

-2

0

2

4

y*

x*=0.40x*=0.74

x*=1.08x*=1.42

x*=1.76x*=2.10

x*=2.44x*=2.80

0.0

0.4

0.8

1.2

x*=3.14

Figure 3: Pro�les of mean longitudinal velocity component u�,(top) 2D calculation against PIV , (bottom)3D calculations against PIV. (PIV have been plotted with symetry)

The �gure 4 represents the structure of the jet. Iso-surfaces of absolute values of the pressure gradientcolored by its sign are plotted on the upper part of the domain and slices of iso-contours of Mach number arepresented on the bottom of the �gure. It is relevant that the shock structure is totally three dimensionnal.The upper expansion caused by the divergent leads to a overexpanded jet so that shock waves are attachedto the lips of the nozzle. In the middle of the nozzle one can see that the jet expands in the transversedirection. This shows that the jet is both under and over expanded along its perimeter.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

Figure 4: Structure of the unmanipulated jet. Iso-surfaces of the pressure gradient colored by its sign andiso-contours of Mach number

The addition of the actuator on the exit of nozzle have lead to complex three dimensional ow that hasto taken into account in both computations and experiments in order to avoid misinterpretation of results.

B. Structure of the vectored jet

Once vectored the jet shows a new shock spacing organization presented on the shclieren photograph on�gure 5. A shock wave exiting in the middle of the nozzle appears in the ow. This shock wave results fromthe uidic injection and its origin can be located in front of the actuator. The two adaptation shock wavesare still present in the ow but their crossing point position has mowed up compared to the natural case. Infact the main features of the jet have signi�cantly been moved up by the injection.

(a) (b)

Figure 5: Schlieren photographs of the natural case (a), and the vectored case qinj=Q = 0:78 (b) , a fx; ygplane view of the ow.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

Figure 6 shows vertical mean velocity �eld obtained by PIV. Schematic adaptation shock waves are alsoprinted in order to give a more comprehensive view of the ow. Observation of these results gives a clue inunderstanding on how the jet is vectored. The increase of vertical velocity component is obtained thanksto the presence of the injection shock wave, what is visible in the lower part of the �gure. Nevertheless, asin the unmanipulated case the 3D behaviour of the jet cannot be neglected here, so that the vectorizationmechanism are certainely linked to what occurs in the transverse direction.

x*

y*

2 4 6-4

-2

0

2

4

V*

0.160.130.100.070.040.01

-0.02-0.05-0.08-0.11-0.14-0.17

x*y*

2 4 6-4

-2

0

2

4

(a) (b)

Figure 6: Mean vertical velocity �leds in the natural case (a) and the vectored case qinj=Q = 0:78 (b) , afx; yg plane view of the ow. Black lines represent the position of the adaption and injection shock waves

A two component Laser Doppler Velocimetry (LDV) measurements are performed using Dantec BSAFlow in the mixing layer downstream of the actuator at x� = 1. The ow was seeded with same particlesas for the PIV and 50000 samples are taken for each measurement point, so that the second order statisticsare converged up to 0.5 %.The results are presented on �gure 7. One interesting result visible on this �gure is related to the shape ofthe controlled mixing layer that can now be visualized in a plane perpendicular to the ow. As the injectionoccurs in the whole width of the nozzle, one may have expected the jet to be displaced vertically in onepiece. But these results show that the behaviour of the vectored jet is more complex : the mixing layerbends around the centerline of the jet and its increased thickness observed with the schlieren photograph isjust due to spatial integration along the optical path.Furthermore, even if the vertical velocity component has been increased in the major part of the measuredsection, a region of negative vertical velocity remains in the jet. Contrary to what can be interpreted fromthe PIV measurement, the vectorization of the jet is not only due to the presence of the injection shockwave. The mean behaviour of the vectored ow observed here, might be a consequence of the separation ofthe boundary layer behaviour. This implies that the ow inside the nozzle and the separation mechanismhas to be known to give an appropriate vectorization scenario.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

z*

y*

0 0.2 0.4 0.6-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

u*

0.950.890.820.760.690.630.560.500.440.370.310.240.180.110.05

z*

y*

0 0.2 0.4 0.6-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

v*

0.050.030.01

-0.01-0.03-0.05-0.07-0.08-0.10-0.12-0.14-0.16-0.18-0.20-0.22

Figure 7: Mean velocity �elds of vectored case qinj=Q = 0:78. Measurements are taken at x� = 1, in afy; zgin the bottom mixing layer.

C. Geometry of the separated region

As no measurement can be made in the nozzle, a numerical calculation is performed in order to assess onthe geometry of the separated region.

1. Comparison between CFD and experimental results

The �gure 8 shows comparisons between nondimensionalized mean vertical and longitudinal velocity pro�lesextracted from PIV measurements and CFD computations at several x� locations downstream of the nozzlefor qinj=Q = 0:78 %. It shows that a great agreement is obtained between the two results. The location ofthe injection and adaptation shocks are well reproduced and the velocities are in the same order for the tworesults. The main di�erences are visible on the �rst pro�les in the mixing layers. This is due to di�cultiesin seeding the ow in the wake of the nozzle lips so that experimental results are probably biased.

-4

-2

0

2

4

y*

x*=0.40x*=0.74

x*=1.08x*=1.42

x*=1.76x*=2.10

x*=2.44x*=2.80

0.0

0.4

0.8

1.2

x*=3.14

Figure 8: Pro�les of mean longitudinal velocity component u�, 3D calculations against PIV.

Moreover, as the calculation are performed to assess on the separation region, a comparison betweenoil ow visualization and computational wall streamlines in the separated region is given on �gure 9. Itshows again a good agreement between the two results, so that numerical results can be interpreted withcon�dence.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

(a) (b)

Figure 9: (a) Oil ow visualisation, (b) computed wall streamlines, for qinj=Q = 0:78

2. Detachment structure

When a cross ow jet blows in a supersonic ow, it is attempted to make the incoming boundary layerseparate, inducing a shock wave in the supersonic part of the ow.9,10 In most of the sudies, the cross owjet does not span the entire nozzle, this way the main ow can go round creating a horse-shoe vortex. Here,the injection slot is located through the whole width of the nozzle so the e�ect of transverse con�nementchanges completely the behaviour of the separation. The external ow cannot go round and due to thepresence of the side wall boundary layers, the secondary jet penetration cannot be uniform. These e�ectsof con�nement combined with the fact that the secondary jet blows out at 45 � leads to a speci�c separatedmean behaviour that can be seen on �gure 9. A rotating region is visible whose diameter is about half thewidth of the nozzle which means that the detachment is three dimensional. A three dimensional view ofthe separated region can be seen on �gure10, it shows that the detachment has a saddle like shape alongthe width of the nozzle. These has direct e�ect on the vectorization because the main ow undergoes acompression on longitudinal direction and on the transverse one, followed then by expansion on these twodirections. This is illustrated on �gure 10(b), where it can be seen that the Mach number of the ow re-increases just after the separated region. This complex movement at the exit section is the cause of thenegative mean vertical velocity region observed with LDV.

W*

0.100.070.040.01

-0.01-0.04-0.07-0.10

Mach

1.601.371.140.910.690.460.230.00

(a) (b)

Figure 10: Detachment structure, (a) streamlines colored by transverse velocity, (b) streamlines colored byMach number

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

IV. On the vectorization e�ciency

Vectorization e�ciency is di�cult to obtain experimentally because of the absence of strain sensors, thusonly an estimation of the thrust vector angle is possible. Computations can be used to calculate the thrustvector angle with more accuracy.

Thrust vector angle corresponds to the angle formed by the vertical and horizontal components of thee�ort on the nozzle :

� = tan�1

�Fy

Fx

�= tan�1

R�E

p+ �UV d�R�E

p+ �U2d�

!,

with �E the exhaust section of the nozzle. The estimated thrust vector angle from the PIV measurementsis obtained through :

� � tan�1

R�eUV d�R

�eU2d�

!.

Calculating � this way, implies strong assumptions : in uence of p is neglected, and � is assumedconstant. Thrust vector angles estimated with PIV measurement and calculated with the numerical resultsare represented on �gure 11.Comparing PIV approximation and 3D computational results it is obvious that the assumptions made bycalculating � from the PIV leads to an overestimation of the thrust vector angle. In the two dimensional casethe thrust vectoring the thrust vector angle calculated is highly over-estimated, which once again proovesthe need of taking into account the entire three dimensional behaviour the jet.Nevertheless, the system proposed in this study leads to relative e�cient vectorization with near 4 � of thrustvectoring with only 1:25 % of uidic injection rate.

qinj/Q (%)

α(°)

0 0.25 0.5 0.75 1 1.25 1.5 1.75 20

1

2

3

4

5

Figure 11: Thrust vector angle � function of uidic injection rate. N Estimated from PIV measurements, �Computation 3D, � Computation 2D

V. Conclusion and perspectives

A combination of experimental and numerical results was used to study the vectorization of a supersonicrectangular jet by boundary layer separation control on the smallest side of the nozzle. It has been shownthat an e�cient angle of thrust vectoring can be obtained even vectored by actuator located in the smallestside.It has been shown that the modi�cations of the nozzle proposed to accomplish thrust vectoring have a strongimpact on the structure of the unmanipulated jet. Its shock wave network is completely disorganized bythe fact of being unregularly expanded along its perimeter. It has also been shown that the transversecon�nement of the secondary jet is of great importance in the way the boundary layer separates and on thevectorization e�ciency.

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American Institute of Aeronautics and Astronautics Paper AIAA-2010-4976

Furthermore, only one uidic injection rate con�guration has been investigated in this paper. Experimentalobservations show that increasing injection pressure provokes di�erent bahviours of the separated regionwhich have to be investigated.

Acknowledgments

Part of this work has been supported by the R�egion Poitou-Charentes and the French Ministry of Defense(Through a PEA program of the DGA/SPA�e).

References

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2Wu, C., \A Computational Study of Secondary Injection Thrust Vector Control," AIAA 95-1787 , 1995.3Miller, D., Yagle, P., and Hamstra, J. W., \Fluidic throat skewing for thrust vectoring in �xed geomtery Nozzles," AIAA

Paper 1999-365 , 1999.4Strykowski, P. and Krothapalli, A., \The countercurrent mixing layer : strategies for shear layer control," AIAA 93-3260 ,

1993.5Strykowski, P. and Krothapalli, A., \Enhancement of mixing in high-speed heated jet using a counter ow nozzle," AIAA

Journal Vol. 31, number 11 , 1993.6Santos, M., Experimental study on counter ow thrust vectoring of a gaz turbine engine, Ph.D. thesis, Florida State

University, 2005.7Flamm, J. D., Deere, K., Mason, L., Berrier, B. L., and Johnson, S., \Experimental Study of an axisymmetric Dual

Throat Fluidic Thrust vectoring Nozzle for Supersonic Aircraft Application," AIAA paper 2006-3701 , 2006.8Weaston, R. and Thames, F., \Properties of aspect-ratio-4.0 rectangular jets in a subsonic cross ow," J. Aircrafts, Vol. 16,

1979, pp. 701{707.9Spaid, F., A study of secondary injection gases in supersonic ow , Ph.D. thesis, California institute of technology, 1964.

10Ben-Yakar, A., Experimental investigation of mixing and ignition of transverse jets in supersonic cross ows, Ph.D.thesis, 2000.

11Plesniak, M. W. and Cusano, D. M., \Scalar mixing in a con�ned rectangular jet in cross ow," J. Fluid Mech., Vol. 524,2005, pp. 1{45.

12Ahmed, K., Moody, J., and Forliti, D., \The e�ect of slot jet size on the con�ned transverse slot jet," Exp. in Fluids,Vol. 45, 2008, pp. 13{26.

13Dussauge, J.-P. and Gaviglio, J., \The rapid expansion of a supersonic turbulent ow : role of bulk dilation," Journal ofFluid Mechanics, Vol. 174, 1987, pp. 81{112.

14Al-Dulaimy, F. M. A. and Cousin, R., \A CFD Assesment to transonic ow around a RAE-2822 airfoil," Research Reportsfrom guest scientists in the faculties 07 and 09 in the academic year 2004/2005 , 2005.

15Kovar, A. and Sch�ulein, E., \Comparison of expermental and numerical invesitgation on a jet in a supersonic cross- ow,"The Aeronautical Journal , 2006, pp. 353{360.

16Murray, N. and Ukeiley, L., \An application of Gappy POD," Exp. Fluids, 42:79-91 , 2007.

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