computational investigation of fluidic counterflow thrust ... · the more imperative for future...

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AIAA 99-2669

Computational Investigation ofFluidic Counterflow Thrust VectoringC.A. Hunter and K.A. DeereNASA Langley Research CenterHampton, Virginia

https://ntrs.nasa.gov/search.jsp?R=20040086850 2020-05-13T22:19:18+00:00Z

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American Institute of Aeronautics and Astronautics

COMPUTATIONAL INVESTIGATION OF FLUIDIC COUNTERFLOW THRUST VECTORING

Craig A. Hunter* and Karen A. Deere*NASA Langley Research Center

Hampton, Virginia

Abstract

A computational study of fluidic counterflow thrustvectoring has been conducted. Two-dimensionalnumerical simulations were run using the computationalfluid dynamics code PAB3D with two-equationturbulence closure and linear Reynolds stress modeling.For validation, computational results were compared toexperimental data obtained at the NASA Langley JetExit Test Facility. In general, computational resultswere in good agreement with experimental performancedata, indicating that efficient thrust vectoring can beobtained with low secondary flow requirements (lessthan 1% of the primary flow). An examination of thecomputational flowfield has revealed new details aboutthe generation of a countercurrent shear layer, itsrelation to secondary suction, and its role in thrustvectoring. In addition to providing new informationabout the physics of counterflow thrust vectoring, thiswork appears to be the first documented attempt tosimulate the counterflow thrust vectoring problem usingcomputational fluid dynamics.

Introduction

Over the past several decades, propulsion nozzleresearch has led to the development of multi-missionexhaust nozzles that can provide efficient operationover a broad flight regime. In the same timeframe,however, the ability to control, mix, and suppress asupersonic jet has imposed formidable challenges, andremains one of the most critical elements of exhaustnozzle research to this day. The issue has become allthe more imperative for future fighter aircraft that willrely on supersonic jet control technology for thrustvectoring, area control, and IR suppression.

Of the many exhaust nozzle technologies underconsideration today, studies1-7 have shown that thrustvectoring is perhaps the most promising, for numerousreasons. Multi-axis thrust vectoring can lead tosignificant tactical advantages by increasing anaircraftÕs agility and combat maneuverability. Thrustvectoring can provide control effectiveness superior toconventional aerodynamic surfaces at some flight

conditions, and it can extend the aircraft performanceenvelope by allowing operation in the post-stall regime.In addition, thrust vectoring can improve takeoff andlanding performance on short or damaged runways andaircraft carrier decks. Finally, the use of thrustvectoring can allow the reduction, and possibly eventhe elimination, of conventional aerodynamic controlsurfaces such as horizontal and vertical tails. Thiswould reduce weight, drag, and radar cross section, allof which can extend an aircraftÕs range and capabilities.Some of the potential benefits of thrust vectoring aresummarized in figure 1.

Figure 1: Potential Benefits of Thrust Vectoring

While the benefits of thrust vectoring are attractive, itÕsimplementation can be a compromise. Current thrust-vectored aircraft such as the F-15 SMTD8, F-18HARV9, X-3110, and F-22 use mechanical systems forthrust vectoring. Though effective, these systems canbe heavy and complex, difficult to integrate, expensiveto maintain, and aerodynamically inefficient. Figure 2illustrates the complexity of the vectoring system on theF-18 HARV. With the addition of stealth requirementssuch as IR suppression and low-observable shaping, thedesign and integration of an efficient mechanical thrustvectoring system becomes even more challenging.

AIAA-99-2669

* Aerospace Engineer, Configuration Aerodynamics Branch, Aerodynamics Competency. Member AIAA.

Copyright © 1999 by the American Institute of Aeronautics andAstronautics, Inc. No copyright is asserted in the United States underTitle 17, US Code. The US Government has a royalty-free license toexercise all rights under the copyright claimed herein for governmentpurposes. All other rights are reserved by the copyright owner.

Alt

itude

Mach

ImprovedTransonicControl

High aAgility

Post-StallOperation

ShortTO/LRoll

EnhancedAir-to-GroundPerformance

ImprovedLow Speed

ControlImproved

High SpeedControl

Full EnvelopeEnhanced Air-Air Performance

Departure ResistanceSpin Recovery

Reduced Drag and RCSImproved Survivability

Alti

tude

2


Figure 2: F-18 HARV Thrust Vectoring System

The capabilities of future aircraft will depend on thedevelopment of true multi-mission Òmulti-functionÓexhaust systems that can provide thrust vectoring andstill meet other requirements. These systems need to besimple, lightweight, and inexpensive. In light of theserequirements, there is a tremendous potential toimprove aircraft system performance by replacingmechanical nozzle systems with efficient fixedgeometry (no moving parts) configurations that usefluidic concepts for thrust vectoring and control. Thecurrent paper presents results from a computationalinvestigation of one such concept known ascounterflow thrust vectoring.

First proposed by Strykowski and Krothapali11,12 in theearly 1990Õs, the counterflow thrust vectoring conceptis shown in figure 3. Thrust vectoring is achieved byapplying suction along one periphery of a shroudedprimary jet. This creates a low pressure region alongthe suction collar, and causes the jet to turn. Asdiscussed by Flamm13, this can result in effective thrustvectoring (up to 15¡) with minimal suction power andlow secondary mass flow requirements (less than 1% ofthe primary jet mass flow).

SECONDARY�SUCTION

PRIMARY�FLOW

VISCOUS�ENTRAINMENT

SUCTION�COLLAR

Figure 3: Counterflow Thrust Vectoring Concept

In early work11,14,15, vectoring achieved with thecounterflow concept was attributed to the generation ofa ÒcountercurrentÓ shear layer along the suction side ofthe jet. As shown in figure 4, the countercurrent shearlayer has a fundamentally different character than atraditional ÒcoflowingÓ shear layer. At sufficiently highvelocity ratios U2/ U 1 (in excess of Ð0.14), thecountercurrent shear layer transitions from convectiveinstability to absolute instability, and there is a markedincrease in the level of organized vortical and turbulentactivity in the shear layer as it becomes globally self-excited. This results in enhanced mixing, even at highconvective Mach numbers where compressibilitytypically suppresses the mixing process. Consequently,a countercurrent shear layer can have a growth ratemore than 50% higher than a coflowing shear layer11.

U2

U1

U2

U1

Figure 4: Countercurrent (top) andCoflowing (bottom) Shear Layers

These shear layer dynamics can be used to explain thethrust vectoring achieved with a counterflow nozzlewhen put in the context of a 2D jet that has onecountercurrent shear layer and one coflowing shearlayer (i.e., figure 3). Each shear layer entrains massfrom the surrounding ambient fluid, but the presence ofthe suction collar inhibits this process, and causes lowpressure along the collar surface. Because of theincrease in organized vortical and turbulent activity inthe countercurrent shear layer, it entrains more massfrom the surrounding ambient fluid than the coflowingshear layer, and pressures on the counterflow side of thecollar will be lower. This, in turn, creates asymmetricpressure gradients about the nozzle centerline anddraws the jet off-axis. In principle, continuous controlof the vector angle can be attained because theinstability level of the countercurrent shear layerdepends on the amount of suction applied.

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Though this has been the accepted explanation for thephysics of counterflow thrust vectoring, more recentwork has cast some doubt on its veracity. A controlvolume analysis performed by Hunter and Wing1 6

suggested that jet vectoring would be the sameregardless of whether the secondary suction stream wascounterflowing or coflowing, because both generate thesame momentum flux input into the nozzle system(which is small compared to the primary jet momentumflux). According to the analysis, the suction collarpressure distribution is the important driver,independent of the direction of the secondary flow. Inaddition, recent experimental work by Flamm13, whichwas the first to accurately measure vector angle andsecondary flow rate, showed that vectoring was attainedwith both counterflowing and coflowing secondarystreams. Finally, more recent results reported byStrykowski and Krothapalli et. al.17 showed variationsin shear layer velocity ratio in a counterflow nozzle,ranging from U2/U1 = Ð0.10 at the suction slot to Ð0.40within the collar. This suggests that some regions ofthe jet may support local absolute instability, but the jetitself may not reach levels of ÒglobalÓ absoluteinstability necessary for self excitation. So, there areunresolved questions about the detailed physics ofcounterflow thrust vectoring.

The goal of the present study was to address some ofthe issues discussed above, and to make a first attemptat rigorous computational fluid dynamics (CFD)modeling of counterflow thrust vectoring. Severalinformal counterflow CFD studies have been attempted,unsuccessfully, but there are no known publishedresults in this area, and the resulting experience leveland knowledge base is lacking. So, this work appearsto be the first documented attempt to simulatecounterflow thrust vectoring using CFD.

In this study, a two-dimensional (2D) computationalinvestigation of fluidic counterflow thrust vectoringwas conducted using the Navier-Stokes code PAB3Dwith two-equation kÐe turbulence closure and a linearReynolds stress model. Simulations were run at anozzle pressure ratio (NPR) of 8, with counterflowsuction slot pressures ranging from approximately 1 to6 psi below ambient. For validation, computationalresults were compared to experimental data obtained byFlamm13 at the NASA Langley Jet Exit Test Facility.

Nomenclature

F Axial Thrust Component, lbFi Ideal Isentropic Thrust, lbH Counterflow Nozzle Primary Jet Height, ink TKE per Unit Mass, ft2/s2

L Counterflow Nozzle Suction Collar Length, inM¥ Ambient Mach NumberN Normal Thrust Component, lbNPR Nozzle Pressure Ratio, NPR = poj/p¥

p Static Pressure, psip¥ Ambient Pressure, psipoj Jet Total Pressure, psip2 Upper Secondary Slot Static Pressure, psip3 Lower Secondary Slot Static Pressure, psiDp3-2 Secondary Slot Pressure Differential, psiDpslot Upper Secondary Slot Gage Pressure, psiR Resultant Thrust, lb, R = [ F2 + N2 ]1/2

R/Fi Resultant Thrust Efficiency RatioS* Deviatoric Mean Flow Srain Rate, 1/st Time, sT¥ Ambient Temperature, ¡RToj Jet Stagnation Temperature, ¡RTKE Turbulent Kinetic Energy, lb/ft2

ui ith Component of Mean Flow Velocity, ft/sU1 Primary Nozzle Exit Velocity, ft/sU2 Upper Secondary Slot Exit Velocity, ft/sU2/U1 Shear Layer Velocity Ratioá ¢ ¢u ui j ñ Reynolds Stress Tensor, ft2/s2

wp Primary Nozzle Weight Flow Rate, lb/sws Upper Secondary Slot Weight Flow Rate, lb/sws /wp Secondary to Primary Weight Flow Ratiox Streamwise Suction Collar Coordinate, iny Vertical Coordinate, iny+ Boundary Layer Law of the Wall Coordinatexi ith Spatial Coordinate, ftd Thrust Vector Angle, degrees, d = tanÐ1(N/T)di Ideal Thrust Vector Angle, degreesdij Kronecker Delta Tensore Dissipation Rate of k, ft2/s3

r1 Primary Nozzle Exit Density, slug/ft3

r1 12U Primary Momentum Flux per Unit Area, psi

n Kinematic Viscosity, ft2/snt Turbulent ÒEddyÓ Viscosity, ft2/sy Secondary Suction Parameter

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Computational Fluid Dynamics Simulation

The NASA Langley Reynolds-averaged Navier Stokes(RANS) computational fluid dynamics (CFD) codePAB3D was used in conjunction with two-equation k-eturbulence closure and a linear Reynolds stress modelto simulate nozzle flows in this investigation. PAB3Dhas been well tested and documented for the simulationof aeropropulsive and aerodynamic flows involvingseparation, mixing, thrust vectoring, and othercomplicated phenomena18-22. Currently, PAB3D isported to a number of platforms and offers acombination of good performance and low memoryrequirements. In addition to its advanced preprocessorwhich can handle complex geometries through multi-block general patching, PAB3D has a runtime modulecapable of calculating aerodynamic performance on thefly and a postprocessor used for follow-on analysis.

Flow Solver and Governing Equations

PAB3D solves the simplified Reynolds-averagedNavier-Stokes equations in conservative form, obtainedby neglecting streamwise derivatives of the viscousterms. Viscous models include coupled and uncoupledsimplified Navier-Stokes and thin layer Navier-Stokesoptions. RoeÕs upwind scheme is used to evaluate theexplicit part of the governing equations, and van LeerÕsscheme is used for the implicit part22. Diffusion termsare centrally differenced, inviscid terms are upwinddifferenced, and two finite volume flux-splittingschemes are used to construct the convective fluxterms22. PAB3D is third-order accurate in space andfirst-order accurate in time. For numerical stability,various solution limiters can be used, including min-mod, van Albeda, and Spekreijse-Venkat22. The codecan utilize either a 2-factor or 3-factor numericalscheme to solve the governing equations.

For the present study, the 2D problem was defined by jand k indices in a single i = constant plane (the j indexwas oriented in the streamwise flow direction). Withthis arrangement, explicit sweeps in the i direction werenot needed, and it was possible to solve the entireproblem implicitly with each iteration (using the vanLeer scheme). This strategy speeds convergence andreduces computational time. Based on previousexperience, the uncoupled simplified Navier-Stokesviscous option and modified Spekreijse-Venkat limiterwere selected.

Turbulence Closure

In simulating turbulence, transport equations for theturbulent kinetic energy per unit mass (k) and thedissipation rate of k (e) are uncoupled from the meanflow RANS equations and can be solved with adifferent time step to speed convergence. These

turbulence transport equations are of the standard linearform shown below, and are solved by the samenumerical schemes discussed above. The constants inthe e equation assume their standard values of Ce1=1.44,Ce2=1.92, sk=1, and se=1.3. In this work, the turbulentviscosity coefficient Cm was taken to be constant andequal to 0.09.

DkDt x

kx

u uuxj

t

k ji j

i

j

= +æ

èç

ö

ø÷

é

ëêê

ù

ûúú

- ¢ ¢ -¶

¶n

ns

¶¶

¶¶

e [1]

DDt x x

Cku u

ux

Ckj

t

ji j

i

j

e ¶¶

nns

¶e¶

e ¶¶

e

ee e= +

æ

èç

ö

ø÷

é

ëêê

ù

ûúú

- ¢ ¢ -1 2

2

[2]

n

emt Ck

=2

[3]

Two different types of algebraic Reynolds stressmodels Ð linear and nonlinear Ð were initially used inthis study. While the linear model performed well inpreliminary work, the nonlinear models (Shi-Zhu-Lumley23 and Girimaji24) failed to produce a stablesolution, and were not used in the final study. Thelinear stress model is shown in equation 4, and is basedon simple mixing length and eddy viscosity theoriesdating back to the 1940Õs.

¢ ¢ = -u u k C

kSi j ij ij

23

22d

em * [4]

This model makes a simple analogy between apparentturbulent Reynolds stresses and laminar viscousstresses. It has a form that parallels the viscous stresstensor for a Newtonian fluid, in which stress isproportional to strain rate. The first term in equation 4represents the isotropic effect of the turbulent kineticenergy, while the second ÒanisotropicÓ term models thelinear effect of the deviatoric mean flow strain rate S*.

No matter which model chosen Ð linear or nonlinear Ð itis important to realize that all current RANS gradient-based Reynolds stress models may suffer a shortcomingin simulating the dynamics of a countercurrent shearlayer. As shown in figure 5, both a countercurrent andcoflowing shear layer can have the same velocitygradient ¶ ¶u y/ , and this gradient dominates both themean flow strain rate and vorticity in this type of flow.From the standpoint of gradient based stress models,there will be little or no distinction between coflowingand countercurrent streams, and the calculatedReynolds stress will be virtually the same in each case.This is an important fact that must be taken intoconsideration when modeling a countercurrent shear

5


layer. The modeling of separated flows suffers fromthe same problem, but has received little attention dueto the fact that separated regions are usually smallcompared to the global aerodynamic scale of theproblem at hand. Results from the present study shouldindicate whether or not this stress model limitationaffects the simulation of a counterflowing jet, where thecountercurrent shear layer dominates the flow.

Coflowing Countercurrent

y

u

Figure 5: Shear Layers with the same Velocity Gradient

Computational Model

The 2D nozzle geometry used in this study was basedon the experimental model used by Flamm13. Basicnozzle details are presented in figure 6. The primaryconvergent-divergent nozzle had an expansion ratio of1.69, a design NPR of 7.82, and a fully expanded exitMach number of 2.0 (the experimental model had aconstant width of 4.5 inches and a nominal throat areaof 3 square inches). Secondary flow ducts were locatedabove and below the primary nozzle, each having a slotheight approximately 41% of the primary nozzle exitheight. The nozzle system was shrouded by a curvedsuction collar that terminated with a 27.8¡ angle at theexit nose radius.

14.286

0.667

0.4591.125

2.246

6.329

27.8°

Figure 6: Counterflow Nozzle Model Details.Dimensions in inches.

A wireframe layout of the 2D multiblock finite volumegrid used in the computational simulation is presentedin figure 7. The grid contained 58 blocks totaling301,392 cells (622,956 points), and was symmetricabout the nozzle centerline. The ambient regionsurrounding the counterflow nozzle extended about 40primary nozzle throat heights upstream and downstreamof the primary nozzle exit, and 77 throat heights aboveand below the jet axis.

Figure 7: Computational Grid Ð Wireframe Sketch

A closeup view of the grid around the counterflownozzle is shown in figure 8. The nozzle grid wascharacterized by boundary layer gridding with anexpansion ratio of about 18% and a first cell height ofapproximately y+= 0.5. The collar region of the nozzlewas densely gridded in an attempt to capture thecomplicated shear layer physics of counterflow thrustvectoring. To provide adequate simulation of vectoredjet flow, the dense grid distribution extendeddownstream, fanning out to cover a regionapproximately ±30¡ from the centerline axis.

6


Figure 8: Counterflow Nozzle Grid

Initial and Boundary Conditions

The static ambient region surrounding the nozzle wasdefined by a subsonic inflow condition (T¥=530¡R,p¥=14.7 psi, M¥ =0.07) on the upstream face, acharacteristic boundary condition on the upper andlower faces, and a first order extrapolation outflowcondition on the downstream face (flow is left to right).The outflow condition was chosen to limit the influenceof the downstream far field boundary, which wasrelatively close to the nozzle exit. This approach wastaken in an effort to minimize the amount of gridneeded to simulate the vectored jet once it left thenozzle.

Stagnation conditions were applied to the inflow ductupstream of the primary nozzle, and were chosen tomatch experimental conditions for Toj and poj at an NPRof 8. Counterflow suction was set by applying a similarstagnation boundary condition to the left face of theupper secondary slot, with total pressures ranging fromapproximately 1 to 6 psi below ambient (p¥). Theboundary condition could accommodate inflow oroutflow, depending on whether the secondary streamwas counterflowing or coflowing. The lower secondaryslot was set to have ambient stagnation conditions. Allsolid walls were treated as no-slip adiabatic surfaces.

In order to initialize the turbulence transport equationsand ensure the formation of a turbulent boundary layerin the counterflow nozzle, wall ÒtripÓ points wereplaced in the primary and secondary ducts. At thesepoints, k was specified based on calculations involvingthe mean flow velocity and vorticity and a userspecified turbulence intensity ratio. A correspondingvalue of e was calculated based on the simplifying andreasonable assumption that the production of TKE wasequal to the dissipation of TKE at the trip point. Onceturbulence was established inside the nozzle, the trippoints were turned off.

Solution Procedure and Postprocessing

All solutions presented in this paper were obtained byrunning PAB3D on an SGI Octane workstation with a195Mhz MIPS-R10000 CPU. To speed convergenceand evaluate possible grid dependence, meshsequencing was used to evolve solutions through coarse(1/4 resolution), medium (1/2 resolution), and fine (fullresolution) grids. Local timestepping was used withglobal CFL numbers ranging from about 0.5 to 15.Depending on the counterflow suction pressure andcomplexity of flow in the nozzle, it took about 14,000iterations and 40 hours of CPU time to obtain a fullyconverged solution. Convergence was judged bytracking integrated performance calculations until theysettled out over at least 1000 iterations.

An independent postprocessor was used to computethrust vector angle, secondary mass flow ratio, andresultant thrust efficiency by integrating pressure, massflux, and momentum flux over a fixed control volume.The postprocessor was also used to extract flowfielddiagnostic data and construct schlieren-like images ofnozzle flow25. These images were obtained bycalculating the density gradient and combining it with asimulated optical ÒcutoffÓ effect. All images presentedin this paper were generated with a root mean squareaverage of horizontal and vertical cutoffs, and thusshow sensitivity to both streamwise and transversedensity gradients.

Control Volume Analysis

In previous experimental work11-15, the upper suctionslot gage pressure ÒDpslotÓ was used as the independentÒinputÓ parameter because it corresponded well withsecondary suction pump settings. However, this oftenresulted in non-zero vector angles at Dpslot = 0, due toasymmetries and peculiarities in model hardware andsuction plumbing between upper and lower slots.Modeling these details (or discrepencies) would bedifficult or impossible from a computational standpoint.In an effort to collapse data from numerousexperiments, Hunter and Wing16 conducted a controlvolume analysis of counterflow thrust vectoring, whichwas later adapted by Flamm13. The same analysis wasused in the present study to develop a parameter for thepresentation of data.

Based on a simplification of Hunter and WingÕsanalysis16, the ideal thrust vector angle obtained withcounterflow can be approximated by:

d

ri

p p

U

LH

=-æ

èç

ö

ø÷

-tan 1 3 2

1 12

[5]

7


where p3Ðp2 is the difference in static pressure betweenthe lower and upper slots, r1 1

2U is the primary jetmomentum flux per unit area, L is the suction collarlength, and H is the primary jet height. See figure 9below. Here, the numerator (p3Ðp2)L represents theÒnormal forceÓ (N) generated by the upper/lowersuction slot pressure difference acting over the collarlength, and the denomenator r1 1

2U H represents theÒaxial forceÓ (F) generated by the momentum flux ofthe primary jet (all forces are per unit width). So, d i

represents the ideal thrust vector angle that would beobtained given these primary and secondary pressureand momentum flux inputs.

H

L

�

�

�

Figure 9: Control Volume Analysis Definitions

Using these results as guidance, the parameter:

y

r=

-p p

U

LH

3 2

1 12

[6]

was selected as the independent input variable for thepresentation of experimental and computational resultsin this investigation. Slot pressures p3 and p2 wereobtained by a point measurement of the static pressureat each slot exit (on the suction collar) from both theexperimental data and the computational solution. Theprimary jet momentum flux per unit area r1 1

2U wasestimated based on NPR from the experiment andintegrated from the computational solution. Bothmethods agreed to within 0.5%.

Results

In the results that follow, some experimental data willshow a jump, which occurred when the primary jetattached to the upper suction collar at higher vectorangles, sealing off the suction slot. As discussed byFlamm13, this phenomena is due to the Coanda effect, inwhich flow tends to attach itself to a nearby solidsurface. Since jet attachment was hysteretic in the

experiment, it essentially defined two different regimesof nozzle performance. As such, normal (no jetattachment) and attached data points will be connectedby a dashed line to indicate this effect. In theexperiment, jet attachment occurred at y = 0.22 for theconfiguration used in this study.

Jet attachment was also present in the computationalsimulation, but in this case, it resulted in unsteady flowand rendered the simulation highly unstable. Thisphenomena will be discussed in more detail later. Themain effect of attachment in the computation was todefine an upper limit for slot suction at y = 0.43,beyond which stable solutions could not be obtained.

Suction Slot Pressure Correlation

A correlation between the upper suction slot gagepressure Dpslot and the suction parameter y is shown forthe experiment and the computational simulation infigure 10. Both cases have the same slope, indicatinggood correspondence between secondary flow behaviorin the experiment and the computational model.However, there is roughly a 0.5 psi offset in suction slotgage pressure between the two. As noted previously,this is due to peculiarities in the secondary flowplumbing in the experiment that were impossible toreproduce in the computational model. By using y asthe independent variable in subsequent discussion, thisdifference should be immaterial. It may be important,however, when comparing these results to other work.

0

2

4

6

8

10

0.0 0.2 0.4 0.6 0.8

ComputationExperiment

y

Jet Attachment

(psi) Dpslot

Figure 10: Suction Slot Pressure Correlation Map

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Thrust Vector Angle

Thrust vectoring results for the experiment andcomputation are presented in figure 11, along with anÒidealÓ curve based on equation 5. There is excellentagreement between experiment and computation up toy = 0.22 and d = 8.1¡, at which point the experimentaljet jumped into the attached regime. Within this low yrange, the data establishes a linear trend between thesuction parameter and the vector angle defined by:

d y= 37 34. [7]

The computational simulation continued to follow thisvectoring trend out to y = 0.26 and d = 9.1¡, but thendeparted as it too neared jet attachment at y = 0.43 andd = 14.2¡.

0

5

10

15

20

25

30

35

40

0.0 0.2 0.4 0.6 0.8

ComputationExperimentIdeal

y

d

JetAttachment

(deg)

Figure 11: Thrust Vector Angle

The last five data points from the experiment show theeffect of jet attachment; with only a small increase insecondary suction, y jumped to 0.64 and the vectorangle increased to 27.4¡ (approximately the terminationangle of the suction collar) as the jet attached to theupper collar. As discussed by Flamm13, decreasingsuction pressure beyond this point decreased d butincreased y, due to the fact that the supersonic primaryjet had sealed off the suction slot. Recovering from thisattached condition required shutting off the suctionsource and decreasing primary NPR in most cases,which shows the extreme hysteretic nature of thisphenomena15.

One final point of interest is the fact that the lastattached experimental data point obtained, at y = 0.69and d = 25.6¡, falls along the vectoring trend defined byequation 7. This may indicate an interesting connectionbetween the normal and attached regimes. In addition,

it appears that the computational vectoring curve wasÒaimingÓ at this point when the onset of jet attachmentrendered the solution unstable. This, coupled with thefact that the computational simulation jumped toattached flow at a higher value of y, indicates that thejet attachment process may be highly model- andgeometry-dependent, unpredictable, and difficult tocontrol. Just the current results alone demonstrate asignificant difference in the attachment characteristicsof a 2D computational simulation and multidimensionalflow in a 2D nozzle.

Internal Performance

Thrust efficiency, which is the ratio of the resultantthrust (R) to the ideal, fully expanded ÒisentropicÓprimary nozzle thrust (Fi), is presented in figure 12.There is relatively good qualitative agreement betweenthe two thrust efficiency curves, but the computationalsimulation predicted R/Fi to be about 0.5 - 0.7% higherthroughout the range of y where the two curvesoverlap. This type of difference is in line with previouswork involving 2D simulations25, and is to be expected,since the 2D computational model does not account forviscous losses on the nozzle sidewalls present in theexperiment. Putting this difference aside, both theexperiment and the computation show a small decreasein thrust efficiency, on the order of 1.5%, as theprimary jet is vectored. This indicates that counterflowthrust vectoring is relatively efficient, and will notcause a significant thrust penalty due to flow turning.

0.80

0.85

0.90

0.95

1.00

0.0 0.2 0.4 0.6 0.8


y

Jet Attachment

RFi

Figure 12: Thrust Efficiency Comparison

In the experiment, the primary nozzle dischargecoefficient (the ratio of actual to ideal weight flow rate)was measured to be 0.9970-0.9971 over the range of ytested. This compares favorably with the values of0.9953-0.9954 obtained from the computation.

9


Secondary Weight Flow

The ratio of secondary to primary weight flow ispresented in figure 13, plotted against the suctionparameter y. Here, positive values of ws/wp indicatecoflow, while negative values indicate counterflow.The experiment and computation show a similar trend,with regimes of coflow and counterflow, although thetwo trends are shifted slightly by Dy » 0.1. Importantfeatures to note are, first, that both the experiment andcomputational simulation demonstrate that vectoringcan be attained with coflowing and counterflowingsecondary streams (this detail will be revisited andclarified below). In addition, both the experiment andthe computation had very low secondary weight flowrates, approximately 0.5Ð1% of the primary jet flowrate, for y values ranging from about 0.06 to 0.43. Thisconfirms that counterflow thrust vectoring has minimalsecondary flow requirements.

-0.01

0.00

0.01

0.02

0.03

0.0 0.2 0.4 0.6 0.8


y

Jet Attachment

wws

p

Coflow

Counterflow

Figure 13: Secondary Weight Flow Ratio

Computational Schlieren Images

Schlieren images, obtained by postprocessing thecomputational solution for sensitivity to streamwise andtransverse density gradients, are presented in figures 14through 19. These images illustrate the flowfielddetails corresponding to the normal (no jet attachment)regime of nozzle operation for 0.01 £ y £ 0.43.Overall, the computational solutions look well behaved,with good resolution of the primary jet shock structure.In all the flowfield images, separation bubbles arepresent on both suction collars. As the jet wasvectored, the lower separation bubble grew larger andthe upper separation bubble became smaller.

Figure 14: y =0.01, ws /wp=0.0221, d =0.4¡

Figure 15: y =0.08, ws /wp=0.0064, d =3.2¡

Figure 16: y =0.17, ws /wp= Ð0.0019, d =6.2¡

Figure 17: y =0.26, ws /wp= Ð0.0042, d =9.1¡

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Figure 18: y = 0.34, ws /wp= Ð0.0036, d =11.5¡

Figure 19: y =0.43, ws /wp=0.0004, d =14.3¡

The schlieren images also show the behavior of thesecondary flow. In figures 14 and 15, the secondarystream was coflowing, and there is little activity in theupper suction slot. That changed with the onset ofcounterflow in figures 16, 17, and 18. In these images,there is significant flow activity in the upper secondaryduct, likely due to the fact that secondary suction wasentraining ambient flow through the nozzle collar. Theflow activity subsided with the return back to coflow infigure 19.

Upper Suction Collar Pressures

Normalized gage pressures along the upper suctioncollar are presented in figure 20. Experimentalcenterline (open symbols) and sideline (closed symbols)data are shown for 0.06 £ y £ 0.22, and computationalresults are given for 0.01 £ y £ 0.26. Note that x/L = 0at the suction slot exit and x/L = 1 at the end of thesuction collar. Though direct comparison at a commonvalue of y is not possible, there is good qualitativecorrespondance between the experimental centerlinedata and computational results, with similar featuresand some overlap. In particular, a comparison ofexperimental centerline data for y = 0.10 withcomputational results for y = 0.08 shows excellentagreement.

In comparing computational results with centerlineexperimental data, there are minor differences in thenature of the pressure distributions near the end of thesuction collar, from x/L = 0.8 to 1.0. This is likely dueto differences in separated flow behavior between the

2D simulation and 3D flow in the experimental nozzle.Comparing centerline and sideline experimental datashows that flow inside the nozzle was in fact 3D at thehigher values of y. As discussed by Hunter25, this sortof discrepancy between a 2D computational simulationand 3D flow inside a 2D nozzle is typical whenseparation occurs.

CFD

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.0 0.2 0.4 0.6 0.8 1.0x/L

p pp- ¥

¥

SL CL Experimenty = 0.0556y = 0.1029y = 0.1529y = 0.2180

y = 0.0111

y = 0.0830

y = 0.1688

y = 0.2613CFD

CFD

CFD

Figure 20: Top Collar Pressure Distributions

Internal Flow Details

In an effort to better understand the physics of thecounterflow thrust vectoring process, the internalflowfield of the counterflow nozzle will be looked at inmore detail. In the discussion that follows, twocomputational cases will be examined:

Case y ws/wp d1 0.08 0.0064 3.2¡2 0.26 Ð 0.0042 9.1¡

Note that case 1 had a coflowing secondary stream,while case 2 had a counterflowing secondary stream.

Normalized streamwise velocity contours for case 1(coflowing) are shown in Figure 21, where u velocitiesare normalized by the primary jet exit velocity U1. Inthe jet shear layer region, these contours effectivelyrepresent the shear layer velocity ratio U2/U1. Positivevalues of U2/U1 indicate forward flow, while negativevalues indicate reverse (countercurrent) flow. In theupper collar region, U2/U1 varied from 0.05 at thesecondary slot exit (confirming that the secondarystream was coflowing) to a maximum negative value ofÐ0.15 midway down the collar, and then back down toÐ0.10 near the collar exit. Further downstream, U2/U1

returned to positive values outside the nozzle. Thoughthere was no suction in the lower slot (it was open toambient pressure), similar behavior occurred in theseparated lower collar region.

11


0.05

0.05 0.00

–0.10

0.00

–0.0

5–0.15

0.00 0.05

0.05

–0.05 0.050.00

0.05

0.00

–0.10–0.05

–0.15–0.10–0.15 0.00

–0.05 0.000.05

Figure 21: Normalized Velocity Contours, Case 1

Streamlines for case 1 are presented in Figure 22, andclearly show the pattern of flow in the upper collarregion. External freestream flow entered the nozzle,separated around the collar nose, and then traveledupstream along the collar surface, generating a largeregion of reverse flow. This ended just downstream ofthe suction slot exit, as the external reverse flow metthe forward flowing secondary stream and turned backto flow parallel with the primary jet. A stagnationregion is visible about one slot height downstream ofthe upper slot exit, where the primary, secondary, andreverse flows met. Flow in the lower collar regionexhibited similar behavior, though the lower secondarystream penetrated further out before mixing with theprimary jet and separated flow on the lower collar.

Figure 22: Streamlines, Case 1

Normalized streamwise velocity contours for case 2(counterflowing) are shown in figure 23. Thesecontours are similar to case 1, with a few notabledifferences. First, flow at the upper secondary slot exithad a negative velocity ratio of U2/U1 = Ð0.05,indicating that the secondary stream was indeedcounterflowing. In addition, the maximum negative

velocity ratio in the upper collar region was Ð0.25,larger than case 1. This indicates the presence of astronger reverse flow in case 2.

0.05

0.05

0.05 0.05 0.00–0.05

0.00 0.05

0.00

0.00

–0.15

–0.0

5

–0.10

0.05

–0.15 0.00

0.00–0.10

–0.10

0.00

–0.15–0.05

–0.05 –0.25

Figure 23: Normalized Velocity Contours, Case 2

Case 2 streamlines are shown in figure 24. As withvelocity contours, these are similar to case 1, but thereis a major difference near the upper secondary slot.Here, the external reverse flow split into two streams;one turned to coflow downstream with the primary jet,and the other continued upstream into the secondaryduct. The division between these two flows can be seenjust inside the secondary duct, where a stagnation pointformed on the lower surface, short of the exit. Thisdiffers significantly from case 1, where three flows metoutside the secondary slot.

Figure 24: Streamlines, Case 2

Together, all of these observations lead to severalimportant conclusions. First, a countercurrent shearlayer was generated in both cases, though it was limitedin extent and existed only within the suction collar. Inthe collar region, reverse velocity ratios were largeenough (less than Ð0.14) to support local absoluteinstability, but the jet itself did not reach levels of

12


global absolute instability necessary for self excitation.This agrees with results reported by Strykowski andKrothapalli et. al.17.

In addition, though the integrated secondary weightflow for case 1 was positive (coflowing), it is clear thatthere was enough suction to establish a countercurrentshear layer within the suction collar, even if it waslimited in extent. This may help to explain theexperimental results obtained by Flamm1 3, whoobtained vectoring with a coflowing secondary stream,but concluded that a countercurrent shear layer was notgenerated. Based on computational results, it appearsthat the net weight flow rate of the secondary streammay be a poor indication of the state of the jet shearlayer. Results from the present study indicate that acountercurrent shear layer can be generated with acoflowing or counterflowing secondary stream. Assuch, the distinction between a counterflowingsecondary stream and a countercurrent shear layerneeds to be made clear.

Finally, even though the focus has been on the uppercollar region, it is interesting to note that flow in theseparated lower collar region of both cases 1 and 2 issomewhat similar to the upper collar flow of case 1(low suction coflowing secondary stream). Thissuggests that flow in the upper collar region may notspecifically be related to the generation of acountercurrent shear layer, but in fact, may just be aresult of separation and its associated reverse flow(present on the lower collar). The fact that there was avery small region of ÒcountercurrentÓ flow in bothcases 1 and 2 indicates that the vectoring achieved withthe counterflow concept may not be related to thecountercurrent shear layer at all. It may simply be aresult of asymmetric separation control in a ductednozzle, where the secondary suction merely serves tomodify the separation region and provide a measure ofcontrol over thrust vector angle.

Concluding Remarks

A computational study of fluidic counterflow thrustvectoring has been conducted. Two-dimensionalnumerical simulations were run using the computationalfluid dynamics code PAB3D with two-equationturbulence closure and linear Reynolds stress modeling.For validation, computational results were compared toexperimental data obtained by Flamm13 at the NASALangley Jet Exit Test Facility. Specific conclusionsfrom this work are as follows:

1. In general, computational results were in goodagreement with experimentally measured vector angle,internal performance, and secondary flow rate,indicating that efficient thrust vectoring (less than 1.5%thrust efficiency penalty) can be obtained with low

secondary flow requirements (less than 1% of theprimary flow). In addition, internal suction collarpressures from the computational simulation showedfavorable comparison to experimental pressures.

2. Though RANS gradient-based Reynolds Stressmodels make little or no distinction between coflowingand countercurrent shear layer velocity gradients, thislimitation did not appear to be a shortcoming in thecurrent study, at least from the standpoint of integratedperformance parameters and nozzle internal pressures.

3. Differences in jet attachment behavior between theexperiment and computation indicate that the jetattachment process may be highly model- andgeometry-dependent, unpredictable, and difficult tocontrol. The current results demonstrate a significantdifference between the attachment characteristics of a2D computational simulation and multidimensionalflow in a 2D nozzle.

4. An examination of the computational flowfield fortwo cases, one with a coflowing secondary stream andone with a counterflowing secondary stream, revealednew details about the generation of a countercurrentshear layer and its relation to secondary suction. Inboth cases, a countercurrent shear layer was generated,though it was limited in extent and existed only withinthe suction collar. In the collar region, reverse velocityratios were large enough to support local absoluteinstability, but the jet itself did not reach levels ofglobal absolute instability necessary for self excitation.This agrees with results reported by Strykowski andKrothapalli et. al.17.

5. Based on computational results, it appears that thenet weight flow rate of the secondary stream may be aninaccurate indication of the state of the jet shear layer.Results from the present study indicate that acountercurrent shear layer can be generated with acoflowing or counterflowing secondary stream. Assuch, the distinction between a counterflowingsecondary stream and a countercurrent shear layerneeds to be made clear.

6. Results from this study suggest that flow in the uppercollar region is not specifically related to the generationof a countercurrent shear layer, but in fact, may just bethe result of separation and its associated reverse flow.Combined with the fact that there was a very smallregion of ÒcountercurrentÓ flow observed in thecomputational simulation, this indicates that thevectoring achieved with the counterflow concept maynot be related to the countercurrent shear layer at all. Itmay simply be a result of asymmetric separationcontrol, where secondary suction merely serves tomodify the separation region in the nozzle and providea measure of control over thrust vector angle.

13


References

1. Bitten, R. and Selmon, J. ÒOperational benefits ofThrust Vector Control (TVC)Ó. High-Angle-of-Attack Technology, Volume I. J.R. Chambers,W.P. Gilbert, and L.T. Nguyen, eds.NASA CP-3149, Part 2, 1992.

2. Herbst, W. B. ÒFuture Fighter TechnologiesÓ.Journal of Aircraft, vol. 17, no. 8. August 1980.

3. Herrick, P. W. ÒPropulsion Influences on AirCombatÓ. AIAA-85-1457, July 1985.

4. Nguyen, L.T.n and Gilbert, W.P. ÒImpact ofEmerging Technologies on Future Combat AircraftAgilityÓ. AIAA-90-1304, May 1990.

5. Herrick, P. W. ÒAir Combat Payoffs ofVectoring/Reversing Exhaust NozzlesÓ.AIAA-88-3239, July 1988.

6. Costes, P. ÒInvestigation of Thrust Vectoring andPost-Stall Capability in Air CombatÓ.AIAA-88-4160-CP, 1988.

7. Capone, F. J. ÒThe Nonaxisymmetric Nozzle - It isfor RealÓ. AIAA-79-1810, August 1979.

8. Bursey, R. and Dickinson, R. ÒFlight Test Resultsof the F-15 SMTD Thrust Vectoring/ThrustReversing Exhaust NozzleÓ.AIAA-90-1906, July 1990.

9. Regenie, V., Gatlin, D., Kempel, R., Matheny, N.ÒThe F-18 High Alpha Research Vehicle: A HighAngle-of-Attack Testbed AircraftÓ.NASA TM-104253, 1992.

10. Knox, F., and Scellenger, H. ÒX-31 Flight TestUpdateÓ. AIAA-92-1035, February 1992.

11. Strykowski, P. J., and Krothapalli, A. ÒTheCountercurrent Mixing Layer: Strategies for Shear-Layer ControlÓ. AIAA 93-3260, July 1993.

12. Strykowski, P. J., Krothapalli, A., and Wishart, D.ÒEnhancement of Mixing in High-Speed HeatedJets Using a Counterflow Nozzle,Ó AIAA JournalVolume 31, number 11. November 1993.

13. Flamm, J.D. ÒExperimental Study of a NozzleUsing Fluidic Counterflow Thrust VectoringÓ.AIAA 98-3255, July 1998.

14. Van Der Veer, Michael R. ÒCounterflow ThrustVectoring of a Subsonic Rectangular JetÓ.M. S. Thesis, University of Minnesota, 1995.

15. Schmid, Geoffrey F. ÒDesign and Optimization ofa Counterflow Thrust Vectoring SystemÓ.M. S. Thesis, University of Minnesota, 1996.

16. Hunter, C. and Wing, D. ÒCounterflow ThrustVectoring: Control Volume Similarity AnalysisÓ.NASA Langley Research Center White Paper,August 1995.

17. Strykowski, P. J., Krothapalli, A., and Forliti, D. J.ÒCounterflow Thrust Vectoring of SupersonicJetsÓ. AIAA 96-0115, January 1996.

18. Pao, S.P., and Abdol-Hamid, K.S. ÒNumericalSimulation of Jet Aerodynamics Using a ThreeDimensional Navier Stokes Method (PAB3D)Ó.NASA TP-3596, September 1996.

19. Abdol-Hamid, K.S. ÒImplementation of AlgebraicStress Models in a General 3-D Navier-StokesMethod (PAB3D)Ó. NASA CR-4702, December1995.

21. Abdol-Hamid, K.S., Lakshmanan, B., and Carlson,J.R. ÒApplication of the Navier-Stokes CodePAB3D with k-e Turbulence Models to attachedand Separated FlowsÓ. NASA TP-3480, January1995.

22. Carlson, J.R. ÒHigh Reynolds Number Analysis ofFlat Plate and Separated Afterbody Flow UsingNon-Linear Turbulence ModelsÓ. AIAA 96-2544,July 1996.

23. Shih, T.H., Zhu, J., and Lumley, J.L. ÒA NewReynolds Stress Algebraic Equation ModelÓ.NASA TM-106644, August 1994.

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25. Hunter, C.A. ÒExperimental, Theoretical, andComputational Investigation of Separated NozzleFlowsÓ. AIAA 98-3107, July 1998.

computational investigation of fluidic counterflow thrust ... · the more imperative for future...

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