. .

‘ 1 L

‘L

L

AIAA 93-3058

Unsteady Navier-Stokes Simulation of the Canard-Wing-Body Ramp Motion

Eugene L. Tu NASA Ames Research Center Moffett Field, CA

S h igeru Obayas h i MCAT Institute Moffett Field, CA

Guru P. Guruswamy NASA Ames Research Center Moffett Field, CA

AlAA 24th Fluid Dynamics Conference July 6-9, 1993 / Orlando, FL

For pennbsbn to copy or repubiiah, contact the American Institute of Aeronautics and AmOnautlW 370 LEnfant Promenade, S.W., Washington, D.C. 20024

v UNSTEADY NAVIER-STOKES SIMULATION OF THE

CANARD-WING-BODY RAMP MOTION

Eugene L. Tu,' Shigeru Obayasbit and Guru P. Guruswamyt NASA Ames Research Center Moffett Field. California 94035

Abstract

A time-accurate thin-layer Navier-Stokes simula- tion of the unsteady flowfield is performed for a typ- ical canard-wing-body configuration undergoing ramp motions. The computations are made at a transonic Mach number of 0.90 and for ramp angles from 0 to 15 degrees. Accuracy is determined by comparisons with steady-state experimental data and with spatial and time-step refinement studies. During the ramp. motion, the computational results show improved dy- namic lift performance and a strong canard-wing inter- action for the canard-on configuration. Formation of the canard leading-edge vortex is inhibited in the early stages of the ramp motion. An analysis performed on the transient flowfield after the ramp motion ends shows that the canard vortex rapidly gains strength and vortex breakdown eventually occurs. These char- acteristics of the canard vortex have significant iuflu-

v ences on wing performance,

Introduction

The use of canards in advanced aircraft for con- trol and improved aerodynamic performance in both cruise and maneuver conditions is a topic of continued research. In addition to providing maneuver control and trim, the influence of canarda on wing aerody- namics can often result in increased maximumlift and decreased trim drag. There are also unique dynamic performance characteristics for canard-configured air- craft coupled with the capability of present-day auto- matic control systems. The reduced or even negative

* Research Scientist, Member AIAA t Senior Research Scientist, MCAT Institute, Se-

t Research Scientist, AIAA Associate Fellow nior Member AIAA

Copyright 01993 b y the American Insti- tute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States un- der T i t l e 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Govern- mental purposes. All other rights are reserved

W by the copyright owner.

static stability of canard configurations can lead to improved aircraft agility and maneuverability.

Several examples of the use of canards for stability and control are currently available. The X-31 aircraft uses a long-coupled canard for pitch control' while the SAAB JAS 39 Gripeu uses a short- (or close) coupled canard in maneuvering, cruise and even landing roll- out conditions.2 The close-coupled canard of the X- 29 forward-swept aircraft is integrated into the active control system and is used to maintain control of this inherently unstable aircraft3

In the three examples given above and, indeed, in most canard-configured aircraft, the main benefits of canards are realized during maneuver or other dy- namic conditions. Therefore, the detailed study of ca- nards as primary control surfaces requires the accurate prediction of the unsteady aerodynamics of such con- figurations. For closecoupled canards, the unsteady aerodynamic performance associated with the canard- wing interaction is of particular interest.

At moderate angles of attack, canards or wings with sharp leading edges exhibit flow separation at the leading edge due to the adverse pressure gradi- ent on the leeward side. In general, the flow structure of highly swept or delta canard-wing Configurations is characterized by a canard downwash, which modifies the wing flowfield, and an interaction between the ca- nard and wing vortex systems. The inboard wing flow- field is often dominated by the canard downwash and the outboard is affected by the subsequent change in wing leading-edge vortex formation and the canard- wing vortex interaction. Further details of the flow features of steady canard-wing-body aerodynamics are given in Ref. 4.

In general, the characteristics ofstatic canard con- figurations are adequately reprksented by steady-state aerodynamics. At higher angles of attack, some of the conditions that may result in unsteady aerodynam- ics include large regions of separated flow and vortex breakdown. However, for a configuration undergoing unsteady motion, the dynamic effects can be quite sig- nificant. In particular, the downwash of the canard and the interaction between the canard and wing vor- tices can exhibit highly nou-linear unsteady aerody- namic characteristics.

The use of canards for improved cruise perfor- mance has been supported by both experimental (e.g.

1

Refs. 5-9) and computational studies (e.g. Refs. 1C- 12) that investigated the steady-state aerodynamics of typical canard configurations. Many of these studies examined the effects of canard size, position and de- flection angle on the canard-wing aerodynamic inter- action. An unsteady experimental study by Boydenls determined the dynamic stability and response char- acteristics of typical canard configurations and showed potential benefits in maneuverability and agility with the use of canards.

Computationalfluid dynamics (CFD) has become a valuable tool for understanding the complex three- dimensional flow physics of canard configurations. A number of studies based on conformal mapping, lin- ear and nonlinear vortex lattice methods, the tran- sonic small perturbation (TSP) equation, and Euler equations have been performed for steady canard-wing aerodynamics and are listed in Ref. 4. However, very limited computational work has been performed to study the details of the unsteady canard-wing-body flowfield using the Navier-Stokes equations, which are required to model viscous effects accurately.

Numerous studies on typical airfoil and wings (e.g. Refs. 1416) have demonstrated the potential of using well-behaved and predictable unsteady aerodynamics for enhanced performance during maneuver. A r e cent Navier-Stokes s im~la t ion '~ has been performed to investigate the unsteady aerodynamics of a wing- body configuration undergoing ramp motions. Refer- ence 17 demonstrated significant dynamic effects on wing-body aerodynamic loads. Previous ~ t u d i e s ~ " ~ ~ ' ~ have successfully solved the Navier-Stokes equations to investigate steady-state canard-wing-body aerody- namics, including the effects of canard deflection and vertical position. Accuracy was demonstrated by fa- vorable comparisons with experimental surface pres- sure, force and moment data. A grid refinement study was also performed that further improved the compar- isons with experiment.

In the present study, the thin-layer Navier-Stokes equations are solved for the unsteady flow about a highly-swept canard-wing-body configuration under- going ramp (pitch-up) motions. Emphasis is placed on understanding the complex unsteady flowfield at vary- ing pitch rates and flow conditions. In addition to sur- face pressures, forces, and moments, a detailed anal- ysis of the unsteady canard-wing vortex structure is performed. Both grid and time-step refinement studies are conducted to verify adequate spatial and temporal accuracy of the current method.

Computational Modeling ' W

Numerical Procedure

The NASA Ames ENSAERO code is used to solve the unsteady thin-layer Navier-Stokes equations. ENSAERO has the capability to simultaneously in- tegrate the Navier-Stokes equations coupled with the modal structural equations of motion and has been recently demonstrated for steady, unsteady and aero& Iastic a p p ~ i c a t i o n s . ' ~ ~ ~ ~ - ~ ~ Si nce the current study is restricted to rigid-body motions, the modal structural equations are not solved.

The current version of ENSAERO includes both a central-difference scheme,z3 which is identical to that used in the Tkansonic Navier-Stokes (TNS) and a streamwise upwind numerical scheme." Both schemes have been found to be accurate for the current geometry and flow conditions. In order to compare current results directly with earlier steady- state canard-wing-body computations: the eentral- difference scheme is utilized in this study. The central- difference scheme in ENSAERO is first-order accurate in time and second-order accurate in space.

The Baldwin-Lomax algebraic eddy-viscosity modelz5 is used to provide turbulence closure. Due to the vortex-dominated flow structures of the highly swept sharp-leading-edge canard and wing, a mod- ification to the original Baldwin-Lomax formula- tion is required. For this study, the Degani-Schiff modification?' as originally developed for crossflow- type separations, is employed. It is noted that with present-day CFD technology, higher-order eddy- viscosity models could easily be utilized and are readily available within the ENSAERO code. However, with the lack of significant non-equilibrium or streamwise separation effects at the moderate angles of attack be- ing investigated, the benefits for the current study of such higher-order models do not justify the increased commtational costs.

All results in this study were computed on either a CRAY-YMP or CRAY C90 a t NASA Am- Research Center. The average performance of ENSAERO on a single CRAY-YMP processor is 160 MFLOPS and 12 psec per iteration per grid point. A typical unsteady ramp case that was started from a converged steady- state solution (up to 4,000 iterations for convergence) required an additional 6,000 time steps to complete the nrescribed motion.

Geometry Modeling and Grid Generation

The geometry in this study is based on the wind- tunnel model used by Gloss and Washburns and is -

2

illustrated in Fig. 1. A variant of this model was also used by Boydenls to study the dynamic response char- acteristicn of a canard configuration. The same geom- etry was used in the previous steady-state numerical study4 and in the unsteady wing-body (canard-off) study." In the original wind-tunnel model, fairings were used to facilitate a vertical-offset canard. These fairings, which account for slight asymmetries in the experimental results, are omitted in the current com- putational modeling. The sting used for wind-tunnel mounting is modeled by extending the body, with its appropriate nc-slip boundary condition, to the down- stream boundary.

Using the S3D surface geometry and grid gen- eration code,2' the canard, wing, and body compo. nent surface geometries are modeled from their origi- nal analytical definitions. The 3DGRAPEZs program is then used to generate the singlezone canard-wing- body flowfield grid. The overall H-0 topology grid is given in Fig. 2. An expanded view of the flow- field grid near the body is also shown. The resul6- ing grid for the canard-wing-body configuration con- tains 4,625 points (half-model) on the surface, and approximately 470,000 points in the flowfield. This same grid was used extensively in previous steady- state computations4 and provided accurate results up to moderate angles of attack. A grid refinement study that increases the total number of flowfield points to 1.7 million is aLS0 performed. Since the current com- putations are performed in the transonic regime, the flowfield grid is extended upstream and downstream by approximately eight wing root-chord lengths, and in the radial direction by six wing-span lengths.

u

w

Results and Discussion

Results are presented to validate the current methodology and provide analyses of the unsteady canard-wing-body flowfield. All steady and unsteady results are computed at M, = 0.90 and a Reynolds number based on the mean aerodynamic chord of the wing (Ree) of 1.52 million. Comparisons between com- puted results and experimental data6 are made to val- idate the accurate prediction of the steady flowfield. Convergence of the unsteady flowfield is verified using both spatial and timestep refinement studies. Pre- vious s t ~ d i e s ~ ' ~ ~ ~ * ~ ~ have demonstrated accurate un- steady flowfield predictions using ENSAERO on wing- body, flexible wings, and wing with control surface ge- ometries.

Steady-State Flowfield

v The span stations on the inboard of the wing are

significantly influenced by the presence of the canard. Figure 3 shows the effect of the canard on the wing flowfield at 45% span for a M 4'. For the canard-off case, the suction peak on the upper surface indicates the presence of a leading-edge vortex. At this static angle of attack, the canard-on results show that the wing leading-edge vortex is inhibited by the canard at this inner station. This effect of the canard on the wing leading-edge vortex is directly attributed to the canard downwash. At higher angles of attack, the C-

nard weakens the wing vortex and delays wing vortex breakdown!

Effect of Canard on Unsteady Loads

The effect of the canard on the unsteady aero. dynamic loads associated with pitch-up ramp motion are presented in this section. All unsteady canard- wing-body results are computed for a from 0' to ei- ther 12.83' or 15' and for non-dimensional pitch rates (defined hy A = &E/U,) of 0.05 and 0.10. Ramp mo. tions are started from converged steady-state solutions at an initial angle of attack (ai) and held at the final angle (a,) for afked length of time. The pitch axis of the ramp motion and the pitching moment results are taken from the model c.g. location shown in Fig. 1.

A typical ramp motion from ai = 0' to at = 15O is illustrated in Fig. 4. In order to directly compare un- steady results at different pitch rates and steady-state results, time (t) is given in degrees. During the ramp motion (OD 5 t 5 15') a and t are equal (a = t). How- ever, fo r t > 15", a is held constant at 15' (a = 15" or a!). Consequently, the ramp motion has an im- pulsive start and stop which significantly influence the unsteady results. (Note that the conversion to phys ical time can be easily obtained using the definition A = drE/U, and replacing & with Atrad/Atrcc).

Computed time histories of lift, drag and pitch- ing moments for the configuration, with and without canard, undergoing a ramp motion (pitch rate, A = 0.10) are illustrated in Fig. 5. Computational and ex- perimental steady-state results are also given for the corresponding angles of attack. The lift curves of Fig. 5 show a significant lift increase for the unsteady canard- on case. Early in the motion (1 < 4"), the unsteady canard-on lift is slightly lower than the canard-off lift due to the effects of the virtual m a s of the fluid and the pitch rate of the configuration. Since the entire ca- nard is forward of the pitch axis, there is an initial loss of lift on the canard at the start of the ramp motion (2 = 0'). As the ramp motion continues, the canard- on case exhibits increased lift over both the canard-off and steady-state canard-on cases.

The timehitories of drag coefficients show that at

3

a given instantaneous angle of attack, there is higher drag for the canard-on case. However, by replotting the drag results of Fig. 5 in drag polar form, Fig. 6 shows that the unsteady canard-on case exhibits im- proved dynamic lift-t-drag performance at the higher angles of attack.

The pitching moments given in Fig. 5 also illus- trate the significant influence of the fluid virtual m a s at the beginning (1 = Oo) and end (t = 15') of the ramp motion. The virtual mam acts to counter the acceleration of the body and, therefore, causes a rapid nwe-down pitching moment at t = 0' and a nose-up moment at t = 15". Beyond t = 15', the lift, drag and pitching moment values converge toward the steady- state (I = 15' result.

The effect of pitch rate on lift for the canard-on case is given in Fig. 7 for A = 0.10 and 0.05. Note that since comparisons are made at instantaneous angles of attack during the ramp motion ( t in deg.), the physical time (t in sec.) between the two pitch rates differ by a factor of two. Figure 7 shows that the lift of the canard configuration is increased at the higher pitch rate throughout the ramp motion. Further into the ramp motion (t > IOo), the pitch rate and total lift are approximately proportional at given angles of attack.

Analysis of Unsteady Loads

Better insight into the dynamic loads produced by the ramp motion can be attained by examining the separate component regions of the geometry. The canard region consists of the canard and the body forward of the wing leading-edge root location (fore- body). The wing region consists of the wing and the remaining aft-body (not including the sting).

Time histories of the canard and wing region lift contributions for the A = 0.05 ramp motion are il- lustrated in Fig. 8. Computed steady-state lift coeffi- cients are also given for reference. By definition, the total configuration lift is the sum of the canard and wing region lift. The effects of the fluid virtual mass are evident at both ( ~ j = 0' and (11 = 15'. Due to the relative locations of the canard and wing to the pitch axis, there is an initial increase in wing region lift and a decrease in canard region lift at ai = 0'. These trends are then reversed at (11 = 15'.

Figure 8 shows that, in comparison to the steady- state results, there is a net loss of lift for the canard throughout the ramp motion. The increased lift for the total configuration during the ramp motion is due to the large increase in the lift of the wing. Although the canard-wing flowfield is highly non-linear and com- plex in nature, it can be quite useful to qualitatively describe the effects of the unsteady motion in terms

of simplified linear theory. In the linear theory, the lift of the wing OF canard can be written a the sum of the static lift (CL,~), the lift due to pitch or q u b sistatic lift (CL.q), and the unsteady lift ( C ~ ~ c k ) . The terms C L ~ , C L ~ and CL& are the stability derivatives (aC~/aa)o , (aCL/aq)o and (BCL/B&)O, respectively; q is the angular velocity of the Configuration about the pitch axis. The notation ()o indicates that par- tial derivatives are evaluated asuming the disturbance quantities are zero. Note that for the ramp motion, q

For the wing, the lift contribution due to pitch is represented in the C L ~ and C L ~ t e rm. The loss of canard lift is primarily due to the canard location forward of the pitch axis which, if described by lin- ear stability theory, causea a large negative contribu- tion to CL,,,,,, from the CL*q term for high pitch rates. The directions of the induced velocities due to pitch are given schematically in Fig. 8 as well. After the ramp motion stops (1 > 15O), the wing region lift contribution converges to the steady-state result much more slowly than the canard region lift. Results shown in the following section indicate that the canard-wing vortex interaction is a significant factor in this phe- nomenon.

= a.

Spatial and Temporal Convergence U

To confirm the convergence and accuracy of the unsteady computations, time-step and grid refine- ments are performed for the A = 0.05 ramp case pre- sented above in Figs. 7 and 8. Figures 9 and 10 show the effect of time-step size (At in deg.) on the unsteady lift curves near t = 0' and t = 15O, respectively, for the component regions of the geometry. In all previous computations presented in this study, At = 0.0025° was used. From Fig. 9, it is clear that with decreasing time-step size, the time-accurate solutions converge quickly. In fact, even when using a larger step size, the lift curves compare favorably for t > 0.lo. Fig- ure 10 shows that, after the ramp motion has stopped, the transient solution is adequately converged in time using At = 0.0025'.

Spatial accuracy is demonstrated in Fig. 11 by the favorable comparison between baseline and refined grid solutions of component lift curves. The refined grid contains over 1.7 million points in the flowfield and was used extensively in Ref. 4 for the steady-state study. Figure 11 shows that, with the refined grid, slightly higher lift coefficients are predicted due to the improved resolution of the canard and wing leading- edge vortices. The remaining analyses of the unsteady canard-wing vortex interaction are performed using the refined grid.

v

FXect of Canard on Unsteady Vortex Interaction v

An analysis of the canard-wing vortex interaction provides further understanding of the complex flow- field that produces the unsteady load characteristics shown earlier. Computations are performed for the canard-wing-body configuration undergoing a ramp motion of mi = O.OOo to uj = 12.83' and at a pitch rate of A = 0.05. Comparisons are also made with the corresponding steady-state results.

The steady and unsteady ramp motion results are summarized in Figs. 12 and 13, respectively, which show instantaneous streamlines released on the upper surfaces of the canard and wing. Positions A,, B, and C,, as indicated in Fig. 12, correspond to steady-state u = 4.2lo,8.55O and 12.83', respectively. Similarly, during the ramp motion (Fig. 13), positions A, B and C correspond to instantaneous a = 4.21°, 8.55' and 12.83'. The ramp motion stops at CY, = 12.83' and the configuration is held fixed for all remaining time (t > 12.63'). Time-accurate transient results are givcn fort > 12.83' at instances D, E and F. The (1 vs. time plot given in Fig. 13 illustrates the relative instances of the ramp motion (A - F). Corresponding upper surface pressure contours for the steady and unsteady cases are given in Fig. 14 for the same instances during the ramp motion as in Figs. 12 and 13 (A, - C. and

A comparison between the steady and unsteady results of Figs. 12-14 shows significant differences in the characteristics of the canard and wing vortices dur- ing the early portibn of the ramp motion. Steady and unsteady case total pressure contours at a crossflow plane of z/E = 3.6, as measured from the body nose, are given in Fig. 15 for these same angles of attack. As observed in Figs. 13, 14 and 15b, a delay in canard vortex formation occurs for the unsteady case which correlates with the loss of lift due to the pitching mo- tion (Fig. 8). For the steady case, Fig. 15a shows the presence of the convected canard vortex. Differences between the steady and unsteady wing vortices are also noted in Fig. 15. During the ramp motion, the increased strength of the wing vortex contributes to the increased lift of the wing portion observed earlier in Fig. 8.

For the current ramp motion, as the configuration reaches u,, the motion stops. Fig. 13 shows the form& tion of the canard vortex and, at later times, evidence of canard vortex breakdown. Total pressure contours in Fig. 16 illustrate the transient vortical flowfield of the canard (z/E = 2.0) and wing (z/E = 3.6) once the ramp motion has stopped. The development of the canard vortex, which was inhibited during the early

\c/ ramp motion, is clearly observed. The canard vor-

L' A - C, respectively).

tex convects downstream and the changes in canard lift and downwash influence the characteristics of the wing vortex. As time increases from instances D to F (Fig. 16), the canard-wing flowfield approaches the steady-state results illustrated earlier in Fig: 15a.

Although the canard vortex forms rapidly once the ramp motion has stopped, Fig. 16 shows that the increasing strength of the canard vortex, its suhse quent convection downstream, and its interaction with the wing vortex occur more slowly. As also observed earlier in Fig. 8, it is evident that the time scale is con- siderably larger for the wing than the canard to reach a relatively steady-state condition. Although some un- steadiness remains in the flow due to the breakdown of the canard vortex, the time-accurate results indicate a relatively stable flowfield for large time (t >> 12.83').

Concluding Remarks

The capability of canard-wing aerodynamic aual- ysis has been extended to account for unsteady mo- tion and flowfields. The time-accurate Navier-Stokes equations are solved for a coplanar canard-wing-body Configuration undergoing ramp motions. Since ex- perimental data were available only for the steady- state cases, a spatial and time-step refinement study was conducted to verify the convergence of the un- steady computations. To further understand the p r e dicted unsteady loads, an analysis of the unsteady canard-wing-body aerodynamics with emphasis on the canard-wing vortex interaction was performed.

Computations with and without the canard showed increased dynamic lift and improved lift-to- drag ratios for the canard-on configuration. Results also indicated the strong influence of the relative p~ sitioning of the canard and wing to the pitch axis. For the canard located forward of the pitch axis, the ramp motion at high pitch rates decreases the effec- tive angle of attadc of the canard and delays the for- mation of the canard vortex. However, as angle of attack increases and the ramp motion ends, the ca- nard vortex and its interaction with the wing develops rapidly. As time increases, the configuration flowfield approaches a relatively steady solution. The accurate predictions of the unsteady flowfield during this tran- sient period have led to an improved understanding of timeaccurate canard-wing aerodynamics.

References

Yeh, D.T., George, M.W., Clever, W.C., Tam, C.K. and Woan, C.J., "Numerical Study of the X-31 High Angle-of-Attack Flow Characteristics," AIAA Paper 91-1630, June 1991.

5

’ Modin, K.E. and Clareus, U., “Aerodynamic De- sign Evolution of the SAAB JAS 39 Gripen Air- craft,” AIAA Paper 91-3195, September 1991. Kehoe, M.W., Bjarke, L.J. and Laurie, E.J., “An In-Flight Interaction of the X-29A Canard and Flight Control System,” NASA TM 101718, April 1990. Tu, E.L., “Navier-Stokes Simulation of a Close-Coupled Canard-Wing-Body Configura- tion,” Journal of Aircraft, Vol. 29, No. 5, September-October 1992, pp. 830.838. Gloss, B.B. and Washburn, K.E., ‘Load Distrihu- tion on a Close-Coupled Wing Canard at Tran- sonic Speeds,” Journal of Aircraft, Vol. 15, No. 4,1978, pp.234239. ‘ Er-El, J. and Seginer, A,, ”Vortex Trajectc- ries and Breakdown on Wing-Canard Coufigura- tions,” Journal of Aircraft, Vol. 22, No. 8, August 1985, pp. 641-648. ’ Calarese, W., Vortex Interaction on a Canard- Wing Configuration,” Air Force Wright Aeronau- tical Laboratories AFWAL-TR-8&3100, October 1986. Oelker, H. and Bummel, D., “Investigations on the Vorticity Sheets of a Close-Coupled Delta- Canard Configuration,” Journol of Aircraft, Vol. 26, No. 7, July 1989, pp. 657-666. Erickson, G.E., Schreiner, J.A. and Rogers, L.W., ‘Canard-Wing Vortex Interaction at Subsonic Through Supersonic Speeds,” AIAA Paper 90- 2814, August 20-22,1990,

lo Agrell, N., “Transonic Aerodynamic Compnta- tions for a Canard Configuration,” AIAA Paper 842158, August 1984. Bandyopadhyay, G., “Low Speed Aerodynam- ics of Canard Configurations,” The Aeronautical Journal, Vol. 93, No. 921, January 1989.

I’ Longo, J.M.A. and Das, A., UNumerical Sim- ulatioa of Vortical Flows Over Close-Coupled Canard-Wing Configuration,” AIAA Paper 90- 3003-CP, August 1990.

l3 Boyden, R.P., “Subsonic Dynamic Stability Char- acteristics of Two Close-Coupled Canard-Wing Configurations,” NASA TP 1291, October 1978.

l4 McLaughlin, T., Robinson, M. and Luttges, M., “Aerodynamic Foundation for Use of Unsteady Aerodynamic Effects in Flight Control,” AIAA Paper 93-0188, January 1993.

“ Rediniotis, O.K., Klute, S.M., Hoang, N.T. and Telionis, D.P., “Pitch Up Motions of Delta Wings,” AIAA Paper 92-0278, January 1992.

l6 Hoang, N.T., Rediniotis, O.K. and Telionis, D.P., “3-D LDV Measurements Over a Delta Wing in Pitch-Up Motion,” AIAA Paper 93-0185, January

1993. l7 Obayashi, S., Guruswamy, G.P. and Tu, E.L.,

“Unsteady Navier-Stokes Computations on a Wing-Body Configuration in Ramp Motions,” AIAA Paper 91-2865, August 1991. Tu, E.L., “Effect of Canard Deflection on Close-Coupled Canard-Wing-Body Aerodynam- ies,” AIAA Paper 92-2602, June 1992.

l9 Tu, E.L., “Effect of Canard Position on the Longitudinal Aerodynamic Characteristics of a CloseCoupled Canard-Wing-Body Configura- tion,” AIAA Paper 92-4632, August 1992. Guruswamy, G.P., “Navier-Stokes Cornputations on Swept-Tapered Wings, Including Flexibility,” Journal of Aircraft, Vol. 29, No. 4, July-August

Obayashi, S., Guruswamy, G.P., and Goorjian, P.M., “Streamwise Upwind Algorithm for Com- puting Unsteady Transonic Flows Past Oscillating Wings,” AIAA Journal, Vol. 29, No. 10, October 1991, pp. 1668-1677. ’’ Obayashi, S. and Guruswamy, G.P., “Unsteady Shock-Vortex Interaction on a Flexible Delta Wing,” Journal of Aircraft, Vol. 29, No. 5, September-October 1992, pp. 790-798.

23 Beam, R. and Warming, R.F., “An Implicit Finite-Difference Algorithm for Hyperbolic Syc tems in Conservative-Law Form,” Journal of Comp. Physics, Vol. 22, September 1976, pp. 87-110.

24 Holst, T.L., Kaynak, U., Gundy, K.L., Thomas, S.D. and Flores, J., “Numerkal Solution of Tran- sonic Wing Flows Using an Euler/Navier-Stokes Zonal Approach,” Journal of Arrcrafl, Vol. 24, No. 1, January 1987, pp. 17-24.

” Baldwin, B.S. and Lomax, H., “Thin Layer A p proximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper 78-257, January 1978.

26 Degani, D. and Schiff, L.B., “ComputationofTur- bulent Supersonic Flows Around Pointed Bodies Having Crossflow Separation,” Journal of Com- putational Physics, 66, 1986, pp. 173-196.

” Luh, R.C., Pierce, L. and Yip, D., “Interactive Surface Grid Generation,” AIAA Paper 91-0796, January 1991.

’* Sorenson, R.L., “The SDGRAPE Book: Theory, Users’ Manual, Examples,” NASA TM 102224, July 1989.

29 Obayashi, S. and Guruswamy, G.P., “Navier- Stokes Computations for Oscillating Control Sur- faces,” AIAA Paper 92-4431, August 1992.

L/

1992, pp. 588-597.

W

6

PlTCH AXIS

2.54 2.54

c-- 47.04 - -59.14 * I

(Dlmnslons In centlrneters)

ClMrd wne AR I 4.12 AR I 2.5 Clrcular arc

=1483cm 123.31 cm .Itloll .ec(iom s = Z E E . ~ crn2 (exposed) s S10322M2 muclmurn thlckneu Root chord I 17.92 crn Roo1 chord 29.80 crn

Root.& l?p.4% np chord = 359 cm np chord D 6 . n M

Fv. 1 Canard-wing-body geometry (Configuration pitch axia shown).

Fig. 2 Canard-wing-body flowfield grid topology and baseline grid reaolution near the oonfiguration.

s-

Fig. 3 Comparison of computational and experimental steady wing surface pressures for the configuration with and without canard. M, = 0 . 9 0 , ~ ~ w 4",Res = 1.52million.

o 1 4 .I .I 1.0 X E

U 0 5 10 15 20 25 30

an fd.0.l Fq. 4 Schematic of unsteady ramp motion from 0' to 15..

7

COMPVTATION EXPERIMENT

Canard-On Canard-011

- UNSTEADY:A-O.tO _ _ _ _ _ _

SRAW -- Canard-On 0

.0.6+ I

I I I I

0 5 10 15 20 25 3 0 time (dog)

-0.8 / , I i

0 5 10 15 20 25 30 time (a&)

Fig. 5 Effect of canard on unsteady aerodynamic loads during ramp motion. A = 0.10,oi = Oo,af = 15'.

COMPUTATIONS EXPERIMENT

C l n M . M 1 - camman

UNSTEAOtA -0.10 _ _ _ _ _ _ STEADY - C.rarn-3"

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 CO

Fig. 6 Drag polar of the canard-wing-body eonfigura- tion undergoing ramp motion. A = 0.10, ai = 0', a, = 15".

- UNSTEADYA- 0.10 ------UNSTEADY A -0.05

SlEADY -

0 5 10 1 5 20 25 30 U N (d.p.1

Fig. 7 Effect of pitch rate on canard-wing-body lift. ai = OO,a, = 15'.

8

W

h e Step. Ai (dag) 0.00167

, -0.00250 -- - 0.00500

_____.

-0.2-1 0 5 10 1 5 20 25

Fig. 8 Comparison of steady and unsteady component lift curves for the canard configuration. A = 0 . 0 5 , ~ r i = O ~ , a ~ = 15'.

AI (dog): also Aa - - -0.01000 - 0.00500 0.00250 - - - 0.00125 -

0.15 L I I

I I I I 1

-0.15- 0 0.1 0.2 0.3 0.4 0.5

tim- tw1 Fig. 9 Effect of tirne-step size on the unsteady com- ponent lift curves near the beginning of the ramp mc- tion, ai. A = 0.05, ai = O", at = 15".

W

time (d~g]

Fig. 10 Effect of time-step size on the unsteady com- ponent lift curves near the end of the ramp motion, UJ. A = 0.05,ai = O ' , a j = 15".

Relined Grid Baseline Grid

1

_. _--___ 1.2 I.

T0t.l Ut

~~~:~~~ 0.4 1 0.2

0

-0.2 mu6 P- Lm

10 15 20 25 0 5 Ilm fd.0.I

Fig. 11 Effect of grid refinement on the unsteady corn- ponent lift curves. A = 0.05,ai = OD, a! = 15'.

9

STEADY-STATE UNSTEADY 6

--'

::. ........... ::::: ....................

C, ) 12.83 deg

Fig. 12 Upper surface streamlines for the steady-state canard-wing-body configuration at various angles of attack.

L.-,-, A ) 4.27 deg; t = 4.27 deg

v D ) 12.83 deg; t = 14.0 deg

20 Uns1.ady Ramp Motlon

/- E ) 12.83 deg; t = t8.0deg

....................... 0 5 10 I5 20 25 F ) 12.83 deg; t = 20.0 d q

lime (dep.)

Fig. 13 Upper surface instantaneous streamlines at various times for the canard-wing-body configu- ration undergoing unsteady ramp motion. A = 0.05, ai = O', a, = 12.83".

10

.I

, . STEADYSTATE UNSTEADY

W

Low pressure region (L) A ) 4.27 deg; t = 4.27 deg

B ) 8.55 deg; t E 8.55 deg

C ) 12.83 deg; t = 12.83 deg

Fig. 14 Upper surface pressure contours at various angle of attack and times for the steady and unsteady canard-wing-body configuration. A = 0.05,~~; = O",aj = 12.83' (for unsteady ramp motion).

!

wing Pdmary vortex (W) v

J 4.27deg -..- J 4.27deg

+ .A-3.6

J 8.55deg J a.55deg

J 1283deg 12.83deg

a) STEADYSTATE b) UNSTEADY RAMP MOWN U Fig. 15 Comparison of c r d o w total pressure con-

rd Primary Vortex (C) Iff-3.6

a) 1- 14.0 (deg): Position D

- _ - _ -..

- - _ _ - _ - _ - _ - _

- _ - _ - _

- _ - _ - - - - _ - - - _

c) I I 20.0 (dag); Posltfon F

Fig. 16 Crossflow total Dresure contoura for the tran- to& between the steady and unsteady cases at var-

(unsteady case).

- sient flow after the ramp motion has ended. A = 0.05,oi = On, aj = 12.83'.

ious angles of attack. A = 0.05,oi = Oo,uj = 12.83' 11