NASA-CR-203258 AIAA 96-2517-CP

TWIN TAIL/DELTA CONFIGURATION BUFFET DUE TO UNSTEADY VORTEX BREAKDOWN FLOW /i/J+/- t ,-?"_' Osama A. KandiP , Essam F. Sheta 2 and Steven J. Massey 3 Aerospace Engineering Department /tl - ._ <_ - Old Dominion University, Norfolk, VA 23529-0247

ABSTRACT tices that trail aft over the top of the . The vortex entrains air over the vertical tails to The buffet response of the twin-tail configuration maintain stability of the aircraft. This combina- of the F/A-18 aircraft; a multidisciplinary prob- tion of LEX, delta wing and vertical tails leads to lem, is investigated using three sets of equations the aircraft excellent agility. However, at some on a multi-block grid structure. The first set is the flight conditions, the vortices emanating from unsteady, compressible, full Navier-Stokes equa- the highly-swept LEX of the delta wing break- tions. The second set is the coupled aeroelastic down before reaching the vertical tails which get equations for bending and torsional twin-tail re- bathed in a wake of unsteady highly-turbulent, sponses. The third set is the grid-displacement swirling flow. The vortex-breakdown flow pro- equations which are used to update the grid coor- duces unsteady, unbalanced loads on the vertical dinates due to the tail deflections. The computa- tails which in turn produce severe buffet of the tional model consists of a 7fi°-swept back, sharp ta_ls and has led to their premature fatigue failure. edged delta wing of aspect ratio of one and a swept-back F/A-18 twin-tails. The configuration Experimental investigation of the vertical is pitched at 32 ° angle of attack and the freestream tall buffet of the F/A-18 models have been con- Mach number and Reynolds number are 0.2 and ducted by several investigators such as Sellers 0.75 x 106, respectively. The problem is solved for at all., Erickson at al2., Wentz 3 and Lee and the initial flow conditions with the twin tall kept Brown 4. These experiments showed that the vor- rigid. Next, the aeroelastic equations of the tails tex produced by the LEX of the wing breaks down are turned on along with the grid-displacement ahead of the vertical tails at angles of attack of equations to solve for the uncoupled bending and 25 ° and higher and the breakdown flow produced torsional tails response due to the unsteady loads unsteady loads on the vertical tails. Rao, Puram produced by the vortex breakdown flow of the vor- and Shah s proposed two aerodynamic concepts tex cores of the delta wing. Two lateral locations for alleviating high-alpha tail buffet characteris- of the are investigated. These locations tics of the twin tail fighter configurations. Cole, are called the midspan and inboard locations. Moss and Doggett e tested a rigid, 1/6 size, full- span model of an F-18 airplane that was fitted INTRODUCTION with flexible vertical tails of two different stiff- ness. Vertical-tall buffet response results were The ability of modern combat aircraft to fiy and obtained over the range of angle of attack from maneuver at high angles of attack and at high -10 ° to +40 °, and over the range of Mach num- loading conditions is of prime importance. This bers from 0.3 to 0.95. Their results indicated that capability is achieved, for example in the F/A-18 the buffet response occurs in the first bending fighter, through the combination of the leading- mode, increases with increasing dynamic pressure edge extension (LEX) with a delta wing and the and is larger at M - 0.3 than that at a higher use of vertical tails. The LEX maintains lift at Mach number. - high angles of attack by generating a pair of vor-

i Professor, Eminent Scholar and Chair of Aerospace Engineering Dept., AIAA Associate Fellow. IPh.D. Graduate Research Assistant, Aerospace Engineering Dept., Member AIAA. 3Ph.D. Graduate Research Assistant, Aerospace Engineering Dept., Member AIAA. Copyright _)1996 by Osa.ma A. Kandil. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. An extensive experimental investigation has been conducted to study vortex-fin interaction on Kandil, Massey and Sheta 11 studied the ef- a 76 ° sharp-edged delta wing with vertical twin-fin fects of coupling and uncoupling the bending and configuration by Washburn, Jenkins and Ferman 7. torsional modes for a long computational time, The verticaltailswere placed at nine locations and the flow Reynolds number on the buffet re- behind the wing. The experimental data showed sponse, of a single rectangular tail. It has been that the aerodynamic loadsare more sensitiveto shown that the coupled response produces higher the chordwise taillocationthan itsspanwise loca- deflection than that of the uncoupled response. tion. As the tailswere moved toward the vortex Moreover, the response of the coupled case reaches core,the buffetingresponse and excitationwere periodicity faster than that of the uncoupled case. reduced. Although the taillocationdid not af- It has also been shown that the deflections of the fect the vortex core trajectories,it affectedthe low-Reynolds number case are substantially lower locationof vortex-corebreakdown. Moreover, the than that of the high Reynolds number case. investigationshowed that the presenceof a flexible tailcan affectthe unsteady pressureson the rigid In a very recent paper by Kandil, Sheta and tailon the oppositesideof the model. In a recent Massey 12, the buffet response of a single swept- study by Bean and Lees testswere performed on back vertical tMl in transonic flow at two angles a rigid 6% scale F/A-18 in a trisonic blowdown of attack (20 ° , 28 ° ) has been studied. It has been wind tunnel over a range of angle of attack and shown that the aerodynamic loads and bending- Mach number. The flight data was reduced to a torsional deflections of the tail never reached pe- non-dimensional buffet excitation parameter, for riodic response and that the loads are one order each primary mode. It was found that buffeting of magnitude lower than those of Ref. 11 of the in the torsional mode occurred at a lower angle subsonic flow. of attack and at larger levels compared to the fundamental bending mode. In this paper, we consider the buffet re- sponse of the F/A-18 twin tail. The configuration Kandil, Kandil and Massey 9 presented the consists of a 76°-swept back, sharp-edged delta first successful computational simulation of the wing and a T-extension on which the F/A-18 twin vertical tall buffet using a delta wing-vertical tall tail is attached as a cantilevers. A multi-block grid configuration. A 760 sharp-edged delta wing has is used to solve the problem for two lateral loca- been used along with a single rectangular verti- tions of the twin tail; the midspan location and cal tail which was placed aft the wing along the the inboard location. plane of geometric symmetry. The tail was al- lowed to oscillate in bending modes. The flow conditions and wing angle of attack have been se- FORMULATION lected to produce an unsteady vortex-breakdown flow. Unsteady vortex breakdown of leading-edge The formulation consists of three sets of governing vortex cores was captured, and unsteady pressure equations along with certain initial and boundary forces were obtained on the tail. These compu- conditions. The first set is the unsteady, com- tational results axe in full qualitative agreement pressible, full Navier-Stokes equations. The sec- with the experimental data of Washburn, Jenkins ond set consists of the aeroelastic equations for and Ferman _. bending and torsional modes. The third set con- sists of equations for deforming the grid according to the twin tail deflections. Next, the governing Kandil, Kandil and Massey l° extended the equations of each set along with the initial and technique used in Ref. 9 to allow the vertical tail boundary conditions are given. to oscillate in both bending and torsional modes. The total deflections and the frequencies of de- flections and loads of the coupled bending-torsion Fluid-Flow Equations: case were found to be one order of magnitude higher than those of the bending case only. Also, The conservative form of the dimensionless, un- it has been showrt that the tail oscillations change steady, compressible, full Navier-Stokes equations the vortex breakdown locations and the unsteady in terms of time-dependent, body-conformed co- aerodynamic loads on the wing and tail. ordinates _1, _2 and _3 is given by (6) = _zO El(t')'ff_z2(t"02w t) ] = 0 o_ 4 o£m o(£_), = 0;m= 1-3,s= 1-3 (1) -_ o__ o_, O0 o(o,t) = -g;(z,,t) = o (7) where The solution of Eqs. (4) and (5) are given ¢'_ = _(zl, z2, :rs,t) (2) by i 1 w(z, t) = _ _;(.-)q,(t) (s) (_ = 7[p, pu],pu2,pus, pe]t, (3) t=l M /_,, and (/_), are the _m-inviscid flux and _'-viscous and heat conduction flux, respectively. O(z,t)= _ %(z)qj(t) (9) j=]+l Details of these fluxes are given in ReL 9. where ¢i and ¢j are comparison functions Aeroelastic Equations: satisfying the free-vibration modes of bending and torsion, respectively, and qi and qj are generalized The dimensionless, linearized governing equations coordinates for bending and torsion, respectively. for the coupled bending and torsional vibrations In this paper, the number of bending modes, ], of a vertical tail that is treated as a cantilevered is six and the number of torsion modes, M -], beam are considered. The tail bending and tor- is also six. Substituting Eqs. (8) and (9) into sional deflections occur about an elastic axis that Eqs. (4) and (5) and using the Galerkin method is displaced from the inertial axis. These equa- along with integration by parts and the boundary tions for the bending deflection, w, and the twist conditions, Eqs (6) and (7), we get the following angle, 8, are given by equation for the generalized coordinates qi and qj in matrix form: o_ o_w 1 o2w t) Oz----_ EI(z)-_z2(Z,t )j + m(z)--_-(z, _ 0 qi ) 028 +m(z)zo(z)'_(z,t) = N(z,t) (4) = /_2 ;J = ]+ I,....,M (10) O-'z0 [Gj(z)O0]-_zJ - m(z)ze--_-(z,t)02w where 028

-Io(z)-_(z, t) = -Mr(z, t) (5) Mll --: M12 = M21 = riot rnzoCrCjdz (11) where z is the vertical distance from the .(to' m¢,¢idz } fixed support along the tail length, It, EI and GJ M22 = • fo' le¢,¢jdz the bending and torsional stiffness of the tail sec- tion, m the mass per unit length, Ie the mass- K rl, wI_r__C, dz 1 moment of inertia per unit length about the elastic za -- J0 _" dz-_-_ (12) ayAs, zo the distance between the elastic axis and -Lit 22 = Jo LiJ dz dz ttZ f inertia axis, N the normal force per unit length )Q1 = fro' ¢_ N dz and Mt the twisting moment per unit length. (13) The characteristic parameters for the dimension- less equations are c', a_o, p_ and c=/a_ for the Similar aeroelastic equations were devel- length, speed, density and time; where c" is the oped for sonic analysis of wing flutter by delta -chord length, a_ the freestream StrganaO 3. The numerical int.egration of Eqs. speed of sound and p_ the freestream air density. (11-13) is obtained using the trapezoidal method The geometrical and natural boundary conditions with 125 points to improve the accuracy of inte- on w and 0 are given by grations. The solution of Eq. (10), for qi;i = 1,2, .... ,I, and qJ;J = ]+1, .... ,M, is obtained us- ing the Runge-Kutta scheme. Next, w, and 0 are w(o,t) - _z (O,t) = -ff;-i_(t,,t)o2w " obtained from Eqs. (8) and (9). Grid Displacement Equations: twin tail deflections, wij,k and 0ij.k. The grid displacement equations are then used to compute Once w and 0 are obtained at the n + 1 time step, the new grid coordinztes. The metric coemcient the new grid coordinates are obtained using simple of the coordinate Jacobian matrix are updated as interpolation equations. In these equations, the .+1 and their weLl as the grid speed, _. This computational twin tail bending displacements, wij,k , cycle is repeated every time step. . displacement through the torsion angle, vi,j,_+1 k are interpolatedthrough cosinefunctions. COMPUTATIONAL APPLICATIONS AND DISCUSSION Boundary and Initial Conditions:

Boundary conditionsconsistsof conditionsforthe Twin Tail-Delta Wing Configuration: fluidflow and conditionsforthe aeroelasticbend- The twin tail-delta wing configuration consists of ing and torsionaldeflectionsof the twin tail.For a 76°-swept back, sharp-edged delta wing (aspect the fluidflow, the Riemann-invariant boundary ratio of one) and a F/A-18 twin tail. Each tail is conditionsare enforcedat the inflowand outflow of aspect ratio 1.2, a crop ratio of 0.4 and a sweep- boundaries of the computational domain. At the ba_k angle of 35 ° for the quarter-chord spanwise plane of geometric symmetry, periodicboundary line. The chord length st the root is 0.4 and at the conditionsis specifiedwith the exceptionof grid tip is 0.159, with a span length of 0.336. The tail pointson the tail.On the wing surface,the no- airfoil section is a NACA 65-A with sharp leading slipand no-penetration conditionsare enforced edge and the thickness ratio is 5% at the root and and _ -- 0. On the tallsurface,the no-slipand 3% at the tip. The dihedral angle between the no-penetrationconditionsforthe relativevelocity two tails is 40 ° . The tails are cantilevered on the components are enforced (pointson the tailsur- upper surface of a trailing-edge extension of the faceare moving). The normal pressuregradientis delta wing. The configuration is pitched at an no longerequal to zero due to the accelerationof angle of attack of 32 ° and the freestream Math the grid pointson the tallsurface.This equation number and Reynolds number are 0.2 and 0.75 x becomes _ -- -pat._, where at is the accelera- 106; respectively. tionofa pointon the tailand _ isthe unitnormal. A multi-block grid consisting of 4 blocks is Initialconditionsconsistof conditionsfor used for the solution of the problem. The first the fluidflow and conditionsfor the aeroelastic block is a O-H grid for the wing and upstream deflectionsof the twin tail. For the fluidflow, region, with 101XSOX54 grid points in the wrap theinitialconditionscorrespondto the freestream around, normal and axial directions, respectively. conditionswith no-slipand no-penetrationcondi- The second block is a H-H grid for the inboard tionson the wing and tail.For the aeroelastic region of the twin tail, with 23XSOX14 grid points deflectionsof the tail,the initialconditionsfor in the wrap around, normal and axial directions, any point on the tailare that the displacement respectively. The third block is a H-H grid for the and velocity are zero, w(z,0) = 0, _(z,0) = 0, outboard region of the twin tail, with 79XSOX14 8(z,O) = 0 and as = 0. grid points in the wrap around, normal and axis] directions, respectively. The fourth block is a O-H METHOD OF SOLUTION grid for the downstream region of the twin tail, with 101X50X24 grid points in the wrap around, The first step is to solve for the fluid flow problem normal and axial directions, respectively. Figure using the vortex-breakdown conditions and keep- 1 shows the grid topology and a blow-up of the ing the tail as a rigid beam. Navier-Stokes equa- twin tail-delta wing configuration. tions are solved using the implicit, flux-difference litting finite-volume scheme. The grid speed The configuration is investigated for two is set equal to zero in this step. This step pro- spanwise separation distance between the twin vides the flow field solution along with the pres- tail; the mid-span location for which the sepa- sure difference across the tail. The pressure dif- ration distance is 56% of the wing span and the ference is used to generate the normal force and inboard location for which the separation distance twisting moment per unit length of the tail. Next, is 33% of the wing span. the aeroelastic equations are used to obtain the Mid-span Location of Twin Tail (56% wing contours inside the region between the twin tall span): of Fig. 5 show higher pressure levels than those Initial Conditions: of the initial conditions results of Fig. 3. It is conclusively evident that the deflections of the Keeping the twin tail rigid, the unsteady, com- twin tall change the locations and shapes of the pressible, full Navier-Stokes equations are inte- vortex breakdown flow on the wing and between grated time accurately using the implicit, flux- the twin tail. difference splitting scheme of Roe with a At = 0.001 to a dimensionless time, t = 4.0. Fig- The structural responses of the twin tall ure 2 shows three-dimensional views of the to- show interesting results which are used to ex- tal pressure on the wing and twin tall surfaces, plain the fluid flow responses. These results are the vortex cores particle traces and the vortex given in Figs. 6-11 with Figs. 6, 8 and 10 for cores iso-total pressure surfaces. Figure 3 shows the right tail (as viewed in the upstream direc- the static-pressure contours and the instantaneous tion) and with Figs. 7,9 and 11 for the left tail. streamlines in a cross-flow plane which is located Figures 6 and 7 show the distributions of deflec- at z = 1.133. It is observed from Fig. 2 that tions and loads for bending and torsion responses the vortex-breakdown locations are forward of the of the right and left tails along the vertical dis- wing , about 72% of the wing chord tance z every 1000 time steps. It is observed that (consistentwith Washburn, et al results_),and the bending responses are in the first mode shape theirshape and locationsareslightlyasymmetric. while the torsion responses are combinations of Figure 3 shows that the vortex-breakdown flow the first, second and third mode shapes. More- is insidethe region between the twin tail.It is over, the maximum bending deflections are about alsoobserved that a smallvortexflowdevelopson two times those of the torsion deflections. Figure the outsidecorner of the junctureof the talland 8 and 9 show the history of the bending and tor- the trailingedge extension(consistentwith Wash- sion deflections and loads versus time of the tail burn,et al results7).The staticpressurecontours tip point and the mid point. Within the range show a lower-pressurelevelover the insidesurface of computational time (10,000 time steps = 10 of the tailthan the pressurelevelover the outside time units), the bending oscillations of the tall surface of the tail. tips are damped with an approximate mean value of w = -6X10 -4 {right tail) and +6X10 -4 (left Uncoupled Bending-Torsion Twin Tail tall). In the meantime, the torsion deflections at Response: the tip are increasing with time with the right tall showing opposite sign of deflection angles in com- Each of the tail is treated as a swept back beam parison with the left tail. Figures 10 and 11 show with dimensionless modulii of elasticity and rigid- the total deflection (bending plus torsion) distri- ity, E and G of 1.8X10 s and 0.692X10S; respec- bution along the vertical distance z every 1000 tively. The density ratio, (p/p_), of the tall time steps and the history of the root bending mo- material is taken as 32. For the present cases of ment versus time for the right and left tails. It is uncoupled bending-torsion response, the distance observed that the total deflection distributions for between the elastic axis and the inertia axis, ze, the right and left tails are of opposite sign and the in Eqs. (4) and (5) is set equal to zero. same observation is the same for the root bend- ing moments. The tails are obviously deflecting Figure 4-11 show the fluid flow and struc- toward the region between the twin tall result- tural responses of the this case. Figure 4 and 5 ing in the increase of the pressure in this region, show the three dimensional views and the cross- as has been observed in Fig. 5, and the forward flow plane views at x -- 1.133 and it = 6,000 time motion of the vortex-breakdown locations on the steps (t = 6.0) after the initial conditions. Figure wing surface. 4 shows that the vortex breakdown locations have ° moved forward of the vortex-breakdown locations Inboard Location of Twin Tail (33% wing of the initial conditions. Figure 5 shows that the span): vortex-breakdown flow is still inside the region Initial Conditions: between the twin tail, asymmetric and experienc- ing more breakdown in comparison of the initial In this case the twin tail have been moved laterally conditions results of Fig. 3. The static pressure inboard with a separation distance of 33% of the

5 wing span. The initial conditions have been ob- putational time used, both bending and torsion tained after 4,000 time steps with the twin tail deflection are showing growth with time. Figure kept rigid. Figures 12 and 13 show the three- 20 and 21 show the total deflection distribution dimensional views and the cross-flow plane views along the vertical distance z every 1000 time steps at x = 1.133. It is observed that the twin tall and the time history of the root bending moment. cut through the vorte.x-breakdown flow splitting it It is observed that the maximum total deflections into two vortical flows at each tall, with two vor- of this case is 50% lower than that of the mid-span tics] flows inside the region between the twin tail position case and similar conclusion is applicable and one vortical flow outside of each tail. The vor- to the root bending moment. tical flows inside the region are larger but weaker than those outside of the twin tail. The flow is more symmetric in comparison with that of the CONCLUDING REMARKS initial conditions of the mid-span position. The static pressures on the inside surfaces of the twin The buffet response of the twin-tall configuration tail are larger than those on the outside surfaces of the F/A-18 aircraft has been investigated com- of the twin tail. putationally using three sets of equations for the aerodynamic loads, the bending and torsional deflections and the grid displacements due to Uncoupled Bending-Torsion Twin Tail the twin tail deflections. The leading-edge vor- Response: tex breakdown flow has been generated using a Using the same aeroelastic modulii as those of the 76°-swept back sharp-edged delta wing which is mid-span case, the problem is solved for the un- pitched at 32 ° angle of attack. The twin tail is coupled bending-torsion twin-tail response. Fig- cantilevered at a trailing edge extension of the ures 14-21 show the fluid flow and structural delta wing. Two spanwise separation distances responses of the this case. Figures 14 and 15 between the twin tail are considered in this study; show the three dimensional views and the cross- the midspan location with 56% spanwise separa- flow plane views at z = 1.133 after it = 6,000 tion distance and the inboard location with 33% time steps (6 time units). It is observed that spanwise separation distance. Only, uncoupled the vortex-breakdown locations on the wing have bending-torsion response cases are considered in moved forward of the vortex-breakdown locations this study. of the initial conditions. The static pressure on the inside surfaces of the twin tail are lower than For both cases of the spanwise separation those of the outside surfaces. The vortical flow in distances, the locations of vortex breakdown of the region between the twin tall becomes stronger the wing leading-edge cores were forward of the and larger than that of the initial conditions of wing trailing edge. For the midspan location case, Fig. 13. the vortex-breakdown flow was inside the region between the twin tail. For the inboard location The structural responses of the twin tall case, the vortex-breakdown flow was split by the are given in Figs. 16-21. In Figs. 16 and 17, twin tall into a vortical flow between the twin tail it is observed that the bending deflections are in and another vortical flow outside the twin tall. In the first and second mode shapes while the tor- both cases, the vortex-breakdown location on the sional deflections are in the first, second and third wing moved forward due to the twin tail deflec- mode shapes. Here, the bending deflections show tions. For the mid-span location case, the bending positive and negative signs and so are the tor- deflections were about 50% higher than those of sion deflections. The maximum bending deflec- the inboard location case, but the torsion deflec- tions are almost 50% those of the mid-span po- tions were 50% lower than those of the inboard sition case, and the maximum torsion deflections case. For the mid-span location case the bending are 50% higher than those of the mid-span posi- deflection for each tail has the same sign; negative tion case (compare with Figs. 6 and 7). The time for the right tail and positive for the left tail. For history of the bending and torsion deflections and the inboard location case, the bending deflection loads for the twin tail tips and mid point show for each tail changed sign as the oscillations con- the same trend of lower bending deflections and tinued. The bending oscillations of the mid-span higher torsion deflections in comparison with the location case were in the first mode shape while mid-span position case. However, within the corn- those of the inboard location case were in the first and second mode shapes. The torsionaloscilla- 5. Rao, D. M., Puram, C. K. and shah, G. H., tionsforboth caseswere in the first,second and "Vortex Control forTail BuffetAlleviation thirdmode shapes. on a twin-TallFighter Configuration,"SAE Paper No. 89-2221,1989. Although many of the featuresof the ex- 6. Cole, S. R., Moss, S. W. and Dogger, R. perimentaldata of Washburn, et. al. were cap- V.,Jr.,"Some BuffetResponse Characteris- tured by this model, the resultsof the maxi- ticsof a Twin-Vertical-TailConfiguration," mum totaldeflectionsof thisstudyshows thatthe NASA TM-102749, October 1990. mid-span locationcaseproduceslargerdeflections than thoseof the inboard locationcase;opposite 7. Washburn, A. E., Jenkins, L. N. and Fer- to those of experimental data of Washburn, et. man, M. A., "Experimental Investigation al. results.However, ons has to remember that of Vortex-Fin Interaction,"AIAA 93-0050, the computational solutionis forthe uncoupled AIAA 31st ASM, Reno, NV, January 1993. bending-torsioncase.Moreover,the presenttwin- tailconfigurationisdifferentfrom that of Wash- 8. Bean, D. E. and Lee, B. H. K., "Correla- burn, et. al. In particular,our inborad location tionof Wind Tunnel and FlightTest Data case shows that the twin tailcuts through the forF/A-18 VerticalTailBuffet,"AIAA 94- vortex-breakdown flow due to itsdihedralangle, 1800-CP, 1994 while Washburn, et. al. inboard locationcase does not show.that the twin tailcuts through the 9. Kandil,O. A., Kandil,H. A. and Massey, S. vortex-breakdown flow.Washburn's inboard case J.,"Simulationof Tail BuffetUsing Delta has verticaltwin tailwith zero dihedralangle. Wing-Vertical Tall Configuration,"AIAA 93-3688-CP, AIAA Atmospheric FlightMe- ACKNOWLEDGMENT chanicsConference,Monterery, CA August 1993,pp. 566-577. This researchwork issupported under Grants No. 10. Kandil,O. A., Massey, S. J., and Kandil, NAG-I-994 and NAG-I-648 by the NASA Langly H. A.,"Computations ofVortex-Breakdown Research Center. The authorswould liketo recog- Induced Tail Buffet Undergoing Bending nizethe computationalresourcesprovided by the and TorsionalVibrations,"AIAA 94-1428- NAS facilitiesat Ames Research Center and the NASA Langley Research Center. CP, AIAA/ASME/ASCE/ASC Structural, StructuralDynamics and Material Confer- ence,SC April 1994,pp. 977-993. REFERENCES 11. Kandil, O. A., Massey, S. J. and Sheta, i. Seliers, W. L. III, Meyers, J. F. and Hepner, E. F., "StructuralDynamics/CFD Interac- T. E., "LDV Survey Over a Fighter Model tion forComputation of VerticalTail Buf- at Moderate to High Angle of Attack," SAE fet,"InternationalForum on Aeroelasticity Paper 88-1448, 1988. and StructuralDynamics, Royal Aeronauti- calSociety,Manchester, U.K., June 26-28, ° Erickson,G. E.,Hall,R. M., Banks, D. W., Del Frate,J. H., Shreiner,J. A.,Hanley, R. 1995,pp. 52.1-52.14. J. and Pulley,C. T., "ExperimentalInvesti- 12. Kandil, O. A., Sheta, E. F. and Massey, gationof the F/A-18 Vortex Flows at Sub- S. J.,"Buffet Responses of a VerticalTail sonic Through Transonic Speeds," AIAA in Vortex Breakdown Flows," AIAA 95- 89-2222,1989. 3464-CP, AIAA Atmospheric Flight Me- chanics Conference, Baltimore, MD, Aug. . Wentz, W. H., "Vortex-Fin Interactionon a ,"AIAA 87-2474,AIAA 7-9,1995,pp. 345-360. Fifth Applied Aerodynamics Conference, 13. Straganac,T. W., "A Numerical Model of Monterey, CA August 1987. Unsteady, Subsonic AeroelasticBehavior,_ NASA TechnicalMemorandum 100487, De- * Lee,B. and Brown, D., "Wind Tunnel Stud- iesof F/A-18 Tail Buffet,"AIAA 90-1432, cember 1987. 1990. ,. ,,_,,,_,. ,_ . _ , t ' ////.,,'7_/ 7" ._,'"_" ."./,',--,-"7"/_"_'- _,

Figure 1. Three-dimensional grid topology and blow-up of the wing twin-tail configuration (The tails are in Mid-span position).

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Figure 2. Three-dimensional view showing the total pressure on the surfaces,vortex-core particle traces,and vortex-core iso-totalpressure surfaces,initialconditions (Mid-span position).

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Figure 3. Initial conditions for static pressure and insta_ntaneous streaanlJnes in a cross-flow pla_e, z = 1.133 (Mid-sp_n position). I I t i

Figure 4. Three-dimensional view showing the total pressure on the surfaces,vortex-core particle traces,and vortex-core iso-totalpressure surfaces after it = 6,000 (Mid-span position).

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Figure 6. Distribution of the deflectionand load responses for an uncoupled bending-torsion case. "Right ta_l(Mid-sp_n position). Dm_umm d k_lmr l_fl_u_ _d_mu_ ,++/ ]- 0,0if t

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Midpmm Be_lml Deflecsmn & Force Hmo_, MidlPOmt Rotation ,e, Moment Hem_mj o.ooeo _ _ "-"-1 -- e

2.00E-4 g._-S

6.0_-5 1.0OE.4 M w+,Hltlv_-_ / +-_._o.., e 3._E-S -'+o0'+-"iiIV v p£j '_ O+OOEO 1. t 0._ -*_ ...... _,r-'° -1 dOOE-4 ..3.0_-6 0 200O 4OO0 80O0 _ 1'1_ _'6 n n

Figure 8. History of the deflection sad load responses for an uncoupled bending-torsion case. /tight tail (Mid-spsn position).

10 Tip Be_lial: _ A Force History Tip Roumo. & Moment Hi_ 0.00E0, 1.80E-3 w 120E-3 N 1.60E-3 -2.00E-4 /t 1.40E-3 _._./X/l \ J/l.,.- -4.00E-4 9.00E-4 N e r_'_ _ '_": I " W _ 1,_E-345.00E-4 6.00E-4 r _..__ _.._..._ _ 1,00E-3 -,B.OOE4

3.00E4 ,- T- -1.00E-3 O.OOEOo 2000 4000 8000 IJO00 100C_ n n

Midpomt Bending Deflection &' Force Hisw_ Midpom! Roca_on & Moment H|smP: . \ 3.00E-4

2.50E-4 W _t 4.00E-3 1.00E4 O._EO 200E-4 M W -3.00E-5 1.50E-4 3.00E-_ 0 f_ 3,50E-3 -1.00E-40.001E0

1.00E-4

5.00E-5 I'"o.- -9._-5 v -_ ... 1=.°°E-_ 000EO_ 2000 400O 6000 8000 10000 0 n n

Figure 9. History of the deflection and load responses for an uncoupled bending-torsion case. Left tail (Mid-span position).

Dismbulion of Lrading Edge To_d Deflecuon Rool BendingMoment o3oi

0.25 -0.00010 0.20 _.W_=_ _go12

_._14 0,10

0.05

-O.00O18 0._ .0.00060 .00o04o _.ooo2o o.o _ 0 2obo ',_ 6O0O 8OOO 1O00O Wnet n

Figure 10. Total structural deflections and root bending moment. Right tail (Mid-span position).

Dismbution of Leading Edtze Total Deflecuon RootBending Moment

0.30

0.25 0.00014 0.20 _ Mr 0.1111112 _.15

0.10 O.OOO1O

0,05 O.I

o.oo=o o.o_o,o oo_ o 200O 40OO 6O0O 8000 1OOOO Wnet n

Figure 11. Total structural deflections and root bending moment. Left tall (Mid-span position).

11 .p

_ll III

Figure 12. Three-dimensional view showing the total pressure on the surfaces, vortex-core particle traces, and vortex-core iso-total pressure surfaces, initial conditions (Inboard position).

I i

a ellis Oral

Figure 13. Initial conditions for static pressure and instantaneous streamlines in a cross-flow plane, x = 1.133 (Inboard position).

o I

Figure 14. Three-dimensional view showing the total pressure on the surfaces, vortex-i:ore particle traces, and vortex-core iso-total pressure surfaces after it = 6,000 (Inboard position).

12 _mp

o'_| 0_.14 e'rll eyl_

o'_' o'mm o_ elmo e'm, amo e_eoe e_ee6 e_eJ_ Qee_ ur_ Iooo une oe_ eew6 k oe, m

Figure 15. Snap shots of static pressure and instantaneous streamlines in a cross-flow plane, x -- 1.133 after it = 6,000 (Inboard position).

Dlsmbuuon of Bending Dcflccuon Dismbm, on of Ro_.on

O.2O

o,o °'°I t+

o.oo o._. ..0.0004 -o. o.00o2 W O

D_$mbuuon of Nomud For= Dismbuuon of Toriimul Momcm

0.30

0.25 025

020

0.10

0.10[ 0.05

0.00 00030 00060 000_0 -"_- a o. -ooo_5 .ooo_o2o oo_x) N M

Figure 16. Distribution of the deflection and load responses for an uncoupled bending-torsion case. Right ta_] (Inboard position).

13 _a_ o( Bencbns Deflecmm _ n(Roamm

o.,, "°r "__//_" 1 ::I I :"r ;#" , ,I • o.o_oo o._.o o.ooo2o "_.oo_ o._o_ o_)_ o.o004 o_

Dismbuuon of Norrmd Force Dssmbuuon of Tors)omd Moment

°'°r _s" I °"'l -__ I

• 0.00000 0.00020 -0,00040 -_. -- N M

Figure 17. Distribution of the deflection and load responses for an uncoupled bending-torsion case. Left tail (Inboard position).

Tip Bendm & Force His4mry Tip Rotation & Ncam)l Him .... 2,,BOIE-8, 2.00E.4

6.00E.4 -- e O.OOEO

0,0_[0 -2,00E-4 3.00E-4 1,1_E-5 N e M W -4.00E-4 1.0_-6 -1.OOE-4 O.00EO .,6.00E-4

-3.00E-4 .2.00E,.4 -B.OOE,,4 2.0OIE-5 O._EO -1.00E-3 -6.00E,4 -3.00E.4 t b , 0 2OO0 4ooo e0oo Ilooo 1000O 20O0 4OOO 60O0 B000 10000 n n

Midpoint Bendinl: Delleclmn & Fore HiMory Midlminl Rmabon & Mom_t H_smry

2.00E -3 • e 3.00E-5

4.00E.S. -- w i O.OOEO N 1.$0E-3 O,OOEO 2.00E-5 " .1.00E..4 1.00E -3 W -3.00E-S 0 M 0.00E0 S.00E.4 -2,00E-4 AL00E-5 N

0.00E0 -3.00E -4 -e.00E-S -2.00E-S -1.20E-4 -S.00E-4 ,.4.00E-4 •4.00E-S - -1.SOL=.4 -1.00E-3 . , , , , , , , 0 2000 4000 6000 8000 10000 0 20O0 4O00 BOO0 8000 1O00O n I'1

Figure 18. History of the deflection and load responses for an uncoupled bending-torsion case. Right t_il (Inboard position).

14 Tip _,dm$ _ & Foroe Hmory Tip Roilmon A. Mom_!! History

3.001-4 _ O.OOEO

°00'°Is/' _'-'. _,t.," q,_ V v v 1.,,o,.,

f_ 2000 4000' 0000 8000 1"2.OOE'40(X)O 0 2000 4000 6000 8000 10000 n n

Midpoint Roia.on & Momem Hi$1ory Midpoint Bending [::)¢flccuo_ & Force History . 5.00E.-4 f- .

4.00E-4 1.20E.4 0.00E0 3.00E-4 8.00E-5

2.00E-5 .5.00E-4 M 2.00E-.4 4.00E-5 N W -1.00E-3 0 0,00E0 0.00E0 \; L, 1.00E-4 -1._OE-3 0.00E0 -4.00E-5 M .,,B.00E-5 -2.00E-3 -1.00E-4 2000 4000 60OO B000 100O0 o' 'ao_' ,_o B000 8000 10000 n n

Figure 19. History of the deflection and load responses for an uncoupled bending-torsion case. Left tail (Inboard position}.

Dmnbuuon of Toial Deflection Root Bending Moment

0.30

025 0.00003 0.20 r --t--

0.O0001 0.10 0.00000

0.05 -000001

0_ OO0O10 Wnet n

Figure 20. Total structural deflections and root bending moment. Right tail (Inboard position).

DIsmbutwn of Lt.admg EdL_e Total DcfiecUon Root Bending Moment 0.00002

0.25 0.00000 0.20

0.30 '[_ Z0.15

-0.00002 o,ot t

-0.00004 .... i , 0.1_ 0.00010 0.000_0 200o 4ooo 6000 8ooo 1oo00 Wnet n

Figure 21. Total structural deflections and root bending moment. Left tail (Inboard position).

15