AIAA 99-2669 Computational Investigation of Fluidic Counterflow Thrust Vectoring C.A. Hunter and K.A. Deere NASA Langley Research Center Hampton, Virginia 35th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit June 20-23, 1999 / Los Angeles, CA For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344 AIAA-99-2669 COMPUTATIONAL INVESTIGATION OF FLUIDIC COUNTERFLOW THRUST VECTORING Craig A. Hunter* and Karen A. Deere* NASA Langley Research Center Hampton, Virginia Abstract conditions, and it can extend the aircraft performance envelope by allowing operation in the post-stall regime. A computational study of fluidic counterflow thrust In addition, thrust vectoring can improve takeoff and vectoring has been conducted. Two-dimensional landing performance on short or damaged runways and numerical simulations were run using the computational aircraft carrier decks. Finally, the use of thrust fluid dynamics code PAB3D with two-equation vectoring can allow the reduction, and possibly even turbulence closure and linear Reynolds stress modeling. the elimination, of conventional aerodynamic control For validation, computational results were compared to surfaces such as horizontal and vertical tails. This experimental data obtained at the NASA Langley Jet would reduce weight, drag, and radar cross section, all Exit Test Facility. In general, computational results of which can extend an aircraft(cid:213)s range and capabilities. were in good agreement with experimental performance Some of the potential benefits of thrust vectoring are data, indicating that efficient thrust vectoring can be summarized in figure 1. obtained with low secondary flow requirements (less than 1% of the primary flow). An examination of the computational flowfield has revealed new details about Improved the generation of a countercurrent shear layer, its Improved Transonic relation to secondary suction, and its role in thrust LoCwo nStpreoeld Control HImighp rSopveeedd Control vectoring. In addition to providing new information about the physics of counterflow thrust vectoring, this Full Envelope work appears to be the first documented attempt to ee Enhanced Air-Air Performance simulate the counterflow thrust vectoring problem using udud Departure Resistance computational fluid dynamics. AltitltAit ReduScpedin D Rreacgo vaenrdy RCS High a Improved Survivability Agility Introduction Post-Stall Operation Over the past several decades, propulsion nozzle Enhanced Short Air-to-Ground research has led to the development of multi-mission TO/L Performance Roll exhaust nozzles that can provide efficient operation over a broad flight regime. In the same timeframe, Mach however, the ability to control, mix, and suppress a supersonic jet has imposed formidable challenges, and Figure 1: Potential Benefits of Thrust Vectoring remains one of the most critical elements of exhaust nozzle research to this day. The issue has become all the more imperative for future fighter aircraft that will While the benefits of thrust vectoring are attractive, it(cid:213)s rely on supersonic jet control technology for thrust implementation can be a compromise. Current thrust- vectoring, area control, and IR suppression. vectored aircraft such as the F-15 SMTD8, F-18 HARV9, X-3110, and F-22 use mechanical systems for Of the many exhaust nozzle technologies under thrust vectoring. Though effective, these systems can consideration today, studies1-7 have shown that thrust be heavy and complex, difficult to integrate, expensive vectoring is perhaps the most promising, for numerous to maintain, and aerodynamically inefficient. Figure 2 reasons. Multi-axis thrust vectoring can lead to illustrates the complexity of the vectoring system on the significant tactical advantages by increasing an F-18 HARV. With the addition of stealth requirements aircraft(cid:213)s agility and combat maneuverability. Thrust such as IR suppression and low-observable shaping, the vectoring can provide control effectiveness superior to design and integration of an efficient mechanical thrust conventional aerodynamic surfaces at some flight vectoring system becomes even more challenging. * Aerospace Engineer, Configuration Aerodynamics Branch, Copyright ' 1999 by the American Institute of Aeronautics and Aerodynamics Competency. Member AIAA. Astronautics, Inc. No copyright is asserted in the United States under Title 17, US Code. The US Government has a royalty-free license to exercise all rights under the copyright claimed herein for government purposes. All other rights are reserved by the copyright owner. 1 American Institute of Aeronautics and Astronautics In early work11,14,15, vectoring achieved with the counterflow concept was attributed to the generation of a (cid:210)countercurrent(cid:211) shear layer along the suction side of the jet. As shown in figure 4, the countercurrent shear layer has a fundamentally different character than a traditional (cid:210)coflowing(cid:211) shear layer. At sufficiently high velocity ratios U /U (in excess of —0.14), the 2 1 countercurrent shear layer transitions from convective instability to absolute instability, and there is a marked increase in the level of organized vortical and turbulent activity in the shear layer as it becomes globally self- excited. This results in enhanced mixing, even at high convective Mach numbers where compressibility typically suppresses the mixing process. Consequently, Figure 2: F-18 HARV Thrust Vectoring System a countercurrent shear layer can have a growth rate more than 50% higher than a coflowing shear layer11. The capabilities of future aircraft will depend on the development of true multi-mission (cid:210)multi-function(cid:211) exhaust systems that can provide thrust vectoring and U 2 still meet other requirements. These systems need to be simple, lightweight, and inexpensive. In light of these requirements, there is a tremendous potential to U improve aircraft system performance by replacing 1 mechanical nozzle systems with efficient fixed geometry (no moving parts) configurations that use fluidic concepts for thrust vectoring and control. The current paper presents results from a computational investigation of one such concept known as counterflow thrust vectoring. U 2 First proposed by Strykowski and Krothapali11,12 in the early 1990(cid:213)s, the counterflow thrust vectoring concept is shown in figure 3. Thrust vectoring is achieved by U 1 applying suction along one periphery of a shrouded primary jet. This creates a low pressure region along the suction collar, and causes the jet to turn. As discussed by Flamm13, this can result in effective thrust Figure 4: Countercurrent (top) and vectoring (up to 15¡) with minimal suction power and Coflowing (bottom) Shear Layers low secondary mass flow requirements (less than 1% of the primary jet mass flow). These shear layer dynamics can be used to explain the thrust vectoring achieved with a counterflow nozzle when put in the context of a 2D jet that has one SUCTION(cid:127) COLLAR countercurrent shear layer and one coflowing shear layer (i.e., figure 3). Each shear layer entrains mass SECONDARY(cid:127) from the surrounding ambient fluid, but the presence of SUCTION the suction collar inhibits this process, and causes low pressure along the collar surface. Because of the PRIMARY(cid:127) increase in organized vortical and turbulent activity in FLOW the countercurrent shear layer, it entrains more mass from the surrounding ambient fluid than the coflowing shear layer, and pressures on the counterflow side of the VISCOUS(cid:127) ENTRAINMENT collar will be lower. This, in turn, creates asymmetric pressure gradients about the nozzle centerline and draws the jet off-axis. In principle, continuous control of the vector angle can be attained because the instability level of the countercurrent shear layer Figure 3: Counterflow Thrust Vectoring Concept depends on the amount of suction applied. 2 American Institute of Aeronautics and Astronautics Though this has been the accepted explanation for the Nomenclature physics of counterflow thrust vectoring, more recent work has cast some doubt on its veracity. A control F Axial Thrust Component, lb volume analysis performed by Hunter and Wing16 F Ideal Isentropic Thrust, lb i suggested that jet vectoring would be the same H Counterflow Nozzle Primary Jet Height, in regardless of whether the secondary suction stream was counterflowing or coflowing, because both generate the k TKE per Unit Mass, ft2/s2 same momentum flux input into the nozzle system L Counterflow Nozzle Suction Collar Length, in (which is small compared to the primary jet momentum M¥ Ambient Mach Number flux). According to the analysis, the suction collar N Normal Thrust Component, lb pressure distribution is the important driver, independent of the direction of the secondary flow. In NPR Nozzle Pressure Ratio, NPR = poj/p¥ addition, recent experimental work by Flamm13, which p Static Pressure, psi was the first to accurately measure vector angle and p¥ Ambient Pressure, psi secondary flow rate, showed that vectoring was attained with both counterflowing and coflowing secondary poj Jet Total Pressure, psi streams. Finally, more recent results reported by p Upper Secondary Slot Static Pressure, psi 2 Strykowski and Krothapalli et. al.17 showed variations p Lower Secondary Slot Static Pressure, psi 3 in shear layer velocity ratio in a counterflow nozzle, Dp Secondary Slot Pressure Differential, psi ranging from U /U = —0.10 at the suction slot to —0.40 3-2 within the colla2r. 1This suggests that some regions of Dpslot Upper Secondary Slot Gage Pressure, psi the jet may support local absolute instability, but the jet R Resultant Thrust, lb, R = [ F2 + N2 ]1/2 itself may not reach levels of (cid:210)global(cid:211) absolute R/F Resultant Thrust Efficiency Ratio instability necessary for self excitation. So, there are i S* Deviatoric Mean Flow Srain Rate, 1/s unresolved questions about the detailed physics of counterflow thrust vectoring. t Time, s T¥ Ambient Temperature, ¡R The goal of the present study was to address some of T Jet Stagnation Temperature, ¡R the issues discussed above, and to make a first attempt oj at rigorous computational fluid dynamics (CFD) TKE Turbulent Kinetic Energy, lb/ft2 modeling of counterflow thrust vectoring. Several u ith Component of Mean Flow Velocity, ft/s i informal counterflow CFD studies have been attempted, U Primary Nozzle Exit Velocity, ft/s 1 unsuccessfully, but there are no known published U Upper Secondary Slot Exit Velocity, ft/s results in this area, and the resulting experience level 2 and knowledge base is lacking. So, this work appears U2/U1 Shear Layer Velocity Ratio to be the first documented attempt to simulate Æu¢u¢æ Reynolds Stress Tensor, ft2/s2 i j counterflow thrust vectoring using CFD. w Primary Nozzle Weight Flow Rate, lb/s p w Upper Secondary Slot Weight Flow Rate, lb/s In this study, a two-dimensional (2D) computational s investigation of fluidic counterflow thrust vectoring w /w Secondary to Primary Weight Flow Ratio s p was conducted using the Navier-Stokes code PAB3D x Streamwise Suction Collar Coordinate, in with two-equation k—e turbulence closure and a linear y Vertical Coordinate, in Reynolds stress model. Simulations were run at a nozzle pressure ratio (NPR) of 8, with counterflow y+ Boundary Layer Law of the Wall Coordinate suction slot pressures ranging from approximately 1 to x ith Spatial Coordinate, ft i 6 psi below ambient. For validation, computational d Thrust Vector Angle, degrees, d = tan—1(N/T) results were compared to experimental data obtained by d Ideal Thrust Vector Angle, degrees Flamm13 at the NASA Langley Jet Exit Test Facility. i d Kronecker Delta Tensor ij e Dissipation Rate of k, ft2/s3 r Primary Nozzle Exit Density, slug/ft3 1 rU2 Primary Momentum Flux per Unit Area, psi 1 1 n Kinematic Viscosity, ft2/s n Turbulent (cid:210)Eddy(cid:211) Viscosity, ft2/s t y Secondary Suction Parameter 3 American Institute of Aeronautics and Astronautics Computational Fluid Dynamics Simulation turbulence transport equations are of the standard linear form shown below, and are solved by the same The NASA Langley Reynolds-averaged Navier Stokes numerical schemes discussed above. The constants in (RANS) computational fluid dynamics (CFD) code the e equation assume their standard values of C =1.44, e1 PAB3D was used in conjunction with two-equation k-e C =1.92, s =1, and s=1.3. In this work, the turbulent e2 k e turbulence closure and a linear Reynolds stress model viscosity coefficient C was taken to be constant and m to simulate nozzle flows in this investigation. PAB3D equal to 0.09. has been well tested and documented for the simulation of aeropropulsive and aerodynamic flows involving separation, mixing, thrust vectoring, and other Dk ¶ Ø(cid:230) n (cid:246) ¶kø ¶u complicated phenomena18-22. Currently, PAB3D is = Œ(cid:231)n+ t (cid:247) œ- u¢u¢ i -e [1] ported to a number of platforms and offers a Dt ¶xj ºŒŁ skł ¶xjßœ i j ¶xj combination of good performance and low memory requirements. In addition to its advanced preprocessor which can handle complex geometries through multi- De ¶ Ø(cid:230) n (cid:246) ¶e ø e ¶u e2 block general patching, PAB3D has a runtime module = Œ(cid:231)n+ t(cid:247) œ-C u¢u¢ i -C capable of calculating aerodynamic performance on the Dt ¶xj ºŒŁ seł ¶xjßœ e1k i j ¶xj e2 k fly and a postprocessor used for follow-on analysis. [2] k2 Flow Solver and Governing Equations nt =Cm e [3] PAB3D solves the simplified Reynolds-averaged Two different types of algebraic Reynolds stress Navier-Stokes equations in conservative form, obtained models — linear and nonlinear — were initially used in by neglecting streamwise derivatives of the viscous this study. While the linear model performed well in terms. Viscous models include coupled and uncoupled preliminary work, the nonlinear models (Shi-Zhu- simplified Navier-Stokes and thin layer Navier-Stokes Lumley23 and Girimaji24) failed to produce a stable options. Roe(cid:213)s upwind scheme is used to evaluate the solution, and were not used in the final study. The explicit part of the governing equations, and van Leer(cid:213)s linear stress model is shown in equation 4, and is based scheme is used for the implicit part22. Diffusion terms on simple mixing length and eddy viscosity theories are centrally differenced, inviscid terms are upwind dating back to the 1940(cid:213)s. differenced, and two finite volume flux-splitting schemes are used to construct the convective flux tfeirrsmt-so2r2d. e rP AacBcu3rDa teis itnh itridm-oer. d eFr oarc cnuurmateer iicna ls psatacbei laitnyd, u¢iu¢j = 23kdij-2Cmke2S*ij [4] various solution limiters can be used, including min- mod, van Albeda, and Spekreijse-Venkat22. The code This model makes a simple analogy between apparent can utilize either a 2-factor or 3-factor numerical turbulent Reynolds stresses and laminar viscous scheme to solve the governing equations. stresses. It has a form that parallels the viscous stress tensor for a Newtonian fluid, in which stress is For the present study, the 2D problem was defined by j proportional to strain rate. The first term in equation 4 and k indices in a single i = constant plane (the j index represents the isotropic effect of the turbulent kinetic was oriented in the streamwise flow direction). With energy, while the second (cid:210)anisotropic(cid:211) term models the this arrangement, explicit sweeps in the i direction were linear effect of the deviatoric mean flow strain rate S*. not needed, and it was possible to solve the entire problem implicitly with each iteration (using the van No matter which model chosen — linear or nonlinear — it Leer scheme). This strategy speeds convergence and is important to realize that all current RANS gradient- reduces computational time. Based on previous based Reynolds stress models may suffer a shortcoming experience, the uncoupled simplified Navier-Stokes in simulating the dynamics of a countercurrent shear viscous option and modified Spekreijse-Venkat limiter layer. As shown in figure 5, both a countercurrent and were selected. coflowing shear layer can have the same velocity gradient ¶ u/¶y, and this gradient dominates both the Turbulence Closure mean flow strain rate and vorticity in this type of flow. From the standpoint of gradient based stress models, In simulating turbulence, transport equations for the there will be little or no distinction between coflowing turbulent kinetic energy per unit mass (k) and the and countercurrent streams, and the calculated dissipation rate of k (e) are uncoupled from the mean Reynolds stress will be virtually the same in each case. flow RANS equations and can be solved with a This is an important fact that must be taken into different time step to speed convergence. These consideration when modeling a countercurrent shear 4 American Institute of Aeronautics and Astronautics layer. The modeling of separated flows suffers from A wireframe layout of the 2D multiblock finite volume the same problem, but has received little attention due grid used in the computational simulation is presented to the fact that separated regions are usually small in figure 7. The grid contained 58 blocks totaling compared to the global aerodynamic scale of the 301,392 cells (622,956 points), and was symmetric problem at hand. Results from the present study should about the nozzle centerline. The ambient region indicate whether or not this stress model limitation surrounding the counterflow nozzle extended about 40 affects the simulation of a counterflowing jet, where the primary nozzle throat heights upstream and downstream countercurrent shear layer dominates the flow. of the primary nozzle exit, and 77 throat heights above and below the jet axis. y u Coflowing Countercurrent Figure 5: Shear Layers with the same Velocity Gradient Computational Model The 2D nozzle geometry used in this study was based on the experimental model used by Flamm13. Basic nozzle details are presented in figure 6. The primary convergent-divergent nozzle had an expansion ratio of 1.69, a design NPR of 7.82, and a fully expanded exit Mach number of 2.0 (the experimental model had a constant width of 4.5 inches and a nominal throat area of 3 square inches). Secondary flow ducts were located above and below the primary nozzle, each having a slot height approximately 41% of the primary nozzle exit height. The nozzle system was shrouded by a curved suction collar that terminated with a 27.8¡ angle at the exit nose radius. 6.329 27.8(cid:176) Figure 7: Computational Grid — Wireframe Sketch 0.459 0.667 1.125 A closeup view of the grid around the counterflow nozzle is shown in figure 8. The nozzle grid was characterized by boundary layer gridding with an 2.246 expansion ratio of about 18% and a first cell height of approximately y+= 0.5. The collar region of the nozzle was densely gridded in an attempt to capture the complicated shear layer physics of counterflow thrust 14.286 vectoring. To provide adequate simulation of vectored jet flow, the dense grid distribution extended Figure 6: Counterflow Nozzle Model Details. downstream, fanning out to cover a region Dimensions in inches. approximately –30¡ from the centerline axis. 5 American Institute of Aeronautics and Astronautics Solution Procedure and Postprocessing All solutions presented in this paper were obtained by running PAB3D on an SGI Octane workstation with a 195Mhz MIPS-R10000 CPU. To speed convergence and evaluate possible grid dependence, mesh sequencing was used to evolve solutions through coarse (1/4 resolution), medium (1/2 resolution), and fine (full resolution) grids. Local timestepping was used with global CFL numbers ranging from about 0.5 to 15. Depending on the counterflow suction pressure and complexity of flow in the nozzle, it took about 14,000 iterations and 40 hours of CPU time to obtain a fully converged solution. Convergence was judged by tracking integrated performance calculations until they settled out over at least 1000 iterations. Figure 8: Counterflow Nozzle Grid An independent postprocessor was used to compute thrust vector angle, secondary mass flow ratio, and Initial and Boundary Conditions resultant thrust efficiency by integrating pressure, mass flux, and momentum flux over a fixed control volume. The static ambient region surrounding the nozzle was The postprocessor was also used to extract flowfield defined by a subsonic inflow condition (T¥=530¡R, diagnostic data and construct schlieren-like images of p¥=14.7 psi, M¥=0.07) on the upstream face, a nozzle flow25. These images were obtained by characteristic boundary condition on the upper and calculating the density gradient and combining it with a lower faces, and a first order extrapolation outflow simulated optical (cid:210)cutoff(cid:211) effect. All images presented condition on the downstream face (flow is left to right). in this paper were generated with a root mean square The outflow condition was chosen to limit the influence average of horizontal and vertical cutoffs, and thus of the downstream far field boundary, which was show sensitivity to both streamwise and transverse relatively close to the nozzle exit. This approach was density gradients. taken in an effort to minimize the amount of grid needed to simulate the vectored jet once it left the nozzle. Control Volume Analysis Stagnation conditions were applied to the inflow duct upstream of the primary nozzle, and were chosen to In previous experimental work11-15, the upper suction match experimental conditions for T and p at an NPR slot gage pressure (cid:210)Dp (cid:211) was used as the independent oj oj slot of 8. Counterflow suction was set by applying a similar (cid:210)input(cid:211) parameter because it corresponded well with stagnation boundary condition to the left face of the secondary suction pump settings. However, this often upper secondary slot, with total pressures ranging from resulted in non-zero vector angles at Dp = 0, due to slot approximately 1 to 6 psi below ambient (p¥). The asymmetries and peculiarities in model hardware and boundary condition could accommodate inflow or suction plumbing between upper and lower slots. outflow, depending on whether the secondary stream Modeling these details (or discrepencies) would be was counterflowing or coflowing. The lower secondary difficult or impossible from a computational standpoint. slot was set to have ambient stagnation conditions. All In an effort to collapse data from numerous solid walls were treated as no-slip adiabatic surfaces. experiments, Hunter and Wing16 conducted a control volume analysis of counterflow thrust vectoring, which In order to initialize the turbulence transport equations was later adapted by Flamm13. The same analysis was and ensure the formation of a turbulent boundary layer used in the present study to develop a parameter for the in the counterflow nozzle, wall (cid:210)trip(cid:211) points were presentation of data. placed in the primary and secondary ducts. At these points, k was specified based on calculations involving Based on a simplification of Hunter and Wing(cid:213)s the mean flow velocity and vorticity and a user analysis16, the ideal thrust vector angle obtained with specified turbulence intensity ratio. A corresponding counterflow can be approximated by: value of e was calculated based on the simplifying and reasonable assumption that the production of TKE was (cid:230)p -p L(cid:246) equal to the dissipation of TKE at the trip point. Once di =tan-1Ł(cid:231) r3 U22 Hł(cid:247) [5] turbulence was established inside the nozzle, the trip 1 1 points were turned off. 6 American Institute of Aeronautics and Astronautics where p —p is the difference in static pressure between experiment, it essentially defined two different regimes 3 2 the lower and upper slots, rU2 is the primary jet of nozzle performance. As such, normal (no jet 1 1 attachment) and attached data points will be connected momentum flux per unit area, L is the suction collar by a dashed line to indicate this effect. In the length, and H is the primary jet height. See figure 9 below. Here, the numerator (p —p )L represents the experiment, jet attachment occurred at y = 0.22 for the 3 2 configuration used in this study. (cid:210)normal force(cid:211) (N) generated by the upper/lower suction slot pressure difference acting over the collar Jet attachment was also present in the computational length, and the denomenator rU2H represents the 1 1 simulation, but in this case, it resulted in unsteady flow (cid:210)axial force(cid:211) (F) generated by the momentum flux of and rendered the simulation highly unstable. This the primary jet (all forces are per unit width). So, d i phenomena will be discussed in more detail later. The represents the ideal thrust vector angle that would be main effect of attachment in the computation was to obtained given these primary and secondary pressure define an upper limit for slot suction at y = 0.43, and momentum flux inputs. beyond which stable solutions could not be obtained. Suction Slot Pressure Correlation L A correlation between the upper suction slot gage pressure Dp and the suction parameter y is shown for slot the experiment and the computational simulation in (cid:130) figure 10. Both cases have the same slope, indicating (cid:129) H good correspondence between secondary flow behavior (cid:131) in the experiment and the computational model. However, there is roughly a 0.5 psi offset in suction slot gage pressure between the two. As noted previously, this is due to peculiarities in the secondary flow plumbing in the experiment that were impossible to reproduce in the computational model. By using y as the independent variable in subsequent discussion, this Figure 9: Control Volume Analysis Definitions difference should be immaterial. It may be important, however, when comparing these results to other work. Using these results as guidance, the parameter: 10 p -p L y = 3 2 [6] rU2 H Jet Attachment 1 1 8 was selected as the independent input variable for the presentation of experimental and computational results 6 in this investigation. Slot pressures p3 and p2 were Dp obtained by a point measurement of the static pressure slot (psi) at each slot exit (on the suction collar) from both the 4 experimental data and the computational solution. The primary jet momentum flux per unit area rU2 was 1 1 estimated based on NPR from the experiment and 2 Computation integrated from the computational solution. Both Experiment methods agreed to within 0.5%. 0 0.0 0.2 0.4 0.6 0.8 Results y In the results that follow, some experimental data will Figure 10: Suction Slot Pressure Correlation Map show a jump, which occurred when the primary jet attached to the upper suction collar at higher vector angles, sealing off the suction slot. As discussed by Flamm13, this phenomena is due to the Coanda effect, in which flow tends to attach itself to a nearby solid surface. Since jet attachment was hysteretic in the 7 American Institute of Aeronautics and Astronautics Thrust Vector Angle it appears that the computational vectoring curve was (cid:210)aiming(cid:211) at this point when the onset of jet attachment Thrust vectoring results for the experiment and rendered the solution unstable. This, coupled with the computation are presented in figure 11, along with an fact that the computational simulation jumped to (cid:210)ideal(cid:211) curve based on equation 5. There is excellent attached flow at a higher value of y, indicates that the agreement between experiment and computation up to jet attachment process may be highly model- and y = 0.22 and d = 8.1¡, at which point the experimental geometry-dependent, unpredictable, and difficult to jet jumped into the attached regime. Within this low y control. Just the current results alone demonstrate a range, the data establishes a linear trend between the significant difference in the attachment characteristics suction parameter and the vector angle defined by: of a 2D computational simulation and multidimensional flow in a 2D nozzle. d=37.34y [7] Internal Performance The computational simulation continued to follow this vectoring trend out to y = 0.26 and d = 9.1¡, but then Thrust efficiency, which is the ratio of the resultant departed as it too neared jet attachment at y = 0.43 and thrust (R) to the ideal, fully expanded (cid:210)isentropic(cid:211) d = 14.2¡. primary nozzle thrust (F), is presented in figure 12. i There is relatively good qualitative agreement between 40 the two thrust efficiency curves, but the computational simulation predicted R/Fi to be about 0.5 - 0.7% higher 35 Computation throughout the range of y where the two curves Experiment Ideal overlap. This type of difference is in line with previous 30 work involving 2D simulations25, and is to be expected, since the 2D computational model does not account for 25 viscous losses on the nozzle sidewalls present in the d experiment. Putting this difference aside, both the 20 (deg) experiment and the computation show a small decrease Jet 15 Attachment in thrust efficiency, on the order of 1.5%, as the primary jet is vectored. This indicates that counterflow 10 thrust vectoring is relatively efficient, and will not cause a significant thrust penalty due to flow turning. 5 1.00 0 0.0 0.2 0.4 0.6 0.8 y 0.95 Figure 11: Thrust Vector Angle R The last five data points from the experiment show the 0.90 F Jet Attachment effect of jet attachment; with only a small increase in i secondary suction, y jumped to 0.64 and the vector angle increased to 27.4¡ (approximately the termination 0.85 angle of the suction collar) as the jet attached to the upper collar. As discussed by Flamm13, decreasing Computation suction pressure beyond this point decreased d but Experiment increased y, due to the fact that the supersonic primary 0.80 jet had sealed off the suction slot. Recovering from this 0.0 0.2 0.4 0.6 0.8 attached condition required shutting off the suction y source and decreasing primary NPR in most cases, which shows the extreme hysteretic nature of this phenomena15. Figure 12: Thrust Efficiency Comparison One final point of interest is the fact that the last In the experiment, the primary nozzle discharge attached experimental data point obtained, at y = 0.69 coefficient (the ratio of actual to ideal weight flow rate) and d = 25.6¡, falls along the vectoring trend defined by was measured to be 0.9970-0.9971 over the range of y equation 7. This may indicate an interesting connection tested. This compares favorably with the values of between the normal and attached regimes. In addition, 0.9953-0.9954 obtained from the computation. 8 American Institute of Aeronautics and Astronautics Secondary Weight Flow The ratio of secondary to primary weight flow is presented in figure 13, plotted against the suction parameter y. Here, positive values of w/w indicate s p coflow, while negative values indicate counterflow. The experiment and computation show a similar trend, with regimes of coflow and counterflow, although the two trends are shifted slightly by Dy » 0.1. Important features to note are, first, that both the experiment and computational simulation demonstrate that vectoring can be attained with coflowing and counterflowing Figure 14: y =0.01, w /w =0.0221, d =0.4¡ s p secondary streams (this detail will be revisited and clarified below). In addition, both the experiment and the computation had very low secondary weight flow rates, approximately 0.5—1% of the primary jet flow rate, for y values ranging from about 0.06 to 0.43. This confirms that counterflow thrust vectoring has minimal secondary flow requirements. 0.03 Computation Experiment 0.02 Jet Attachment Figure 15: y =0.08, w /w =0.0064, d =3.2¡ w s p s w 0.01 p Coflow 0.00 Counterflow -0.01 0.0 0.2 0.4 0.6 0.8 y Figure 13: Secondary Weight Flow Ratio Figure 16: y =0.17, ws /wp= —0.0019, d =6.2¡ Computational Schlieren Images Schlieren images, obtained by postprocessing the computational solution for sensitivity to streamwise and transverse density gradients, are presented in figures 14 through 19. These images illustrate the flowfield details 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 are present on both suction collars. As the jet was vectored, the lower separation bubble grew larger and the upper separation bubble became smaller. Figure 17: y =0.26, ws /wp= —0.0042, d =9.1¡ 9 American Institute of Aeronautics and Astronautics