NASA-CR-203245

AEROSTRUCTURAL VORTICAL FLOW

INTERACTIONS WITH APPLICATIONS TO

F/A-18 AND F-117 TAIL BUFFET

Osama A. Kandil_ Steven J. Massey and Essam F. Sheta

Aerospace Engineering DepartmentOld Dominion University, Norfolk, VA 23529

HIGH-ANGLE-OF-ATTACK TECHNOLOGY CONFERENCE

NASA Langley Research Center, Hampton, VASeptember 17-191 1996

https://ntrs.nasa.gov/search.jsp?R=19970014310 2018-06-08T20:37:12+00:00Z

AEROSTRUCTURAL VORTICAL FLOW INTERACTIONS WITH

APPLICATIONS TO F/A-18 and F-117 TAIL BUFFET

Osama A. Kandil 1, Steven J. Massey 2 and Essam F. Sheta 3

Aerospace Engineering Department

Old Dominion University, Norfolk, VA 23529

SUMMARY

The buffet response of the flexible twin-tail configuration of the F/A-18 and a generic F-117 aircraft

are computationally simulated and experimentally validated. The problem is a multidisciplinary, one

which requires the sequential solution of three sets of equations on a multi-block grid structure. The

first set is the unsteady, compressible, full Navier-Stokes equations. The second set is the aeroelastic

equations for bending and torsional twin-tail responses. The third set is the grid-displacement equations

which are used to update the grid coordinates due to the tail deflections. The computational models

consist of a 76°-swept back, sharp edged delta wing of aspect ratio of one and a swept-back F/A-18 or

F-117 twin-tail. The configuration is pitched at 30 ° angle-of-attack. The problem is solved for the initial

flow conditions with the twin tails kept rigid. Next, the aeroelastic equations of the tails are turned on

along with the grid-displacement equations to solve for the bending and torsional tails responses due

to the unsteady loads produced by the vortex breakdown flow of the leading-edge vortex cores of the

delta wing. Several spanwise locations of the twin tails are investigated. The computational results arevalidated using several existing experimental data.

/

INTRODUCTION

Modern combat aircraft are designed to fly and maneuver at high angles of attack and at high

loading conditions. This is achieved, for example in the F/A-18 fighter, through the combination of aleading-edge extension (LEX) with a delta wing and the use of highly swept-back vertical tails. The

LEX maintains lift at high angles of attack by generating a pair of vortices that trail aft over the topof the aircraft. The vortex entrains air over the vertical tails to maintain stability of the aircraft. This

combination of LEX, delta wing and vertical tails leads to the aircraft excellent agility. However, at

some flight conditions, the vortices emanating from the highly-swept LEX of the delta wing breakdownbefore reaching the vertical tails which get bathed in a wake of unsteady highly-turbulent, swirling flow.The vortex-breakdown flow produces unsteady, unbalanced loads on the vertical tails which in turn

produce severe buffet of the tails and has led to their premature fatigue failure.

Experimental investigation of the vertical tail buffet of the F/A-18 models have been conducted

by several investigators such as Sellers et all., Erickson et al2., Wentz 3 and Lee and Brown 4. These

experiments showed that the vortex produced by the LEX of the wing breaks down ahead of the vertical

tails at angles of attack of 25 ° and higher and that the breakdown flow produced unsteady loads on'the

vertical tails. Cole, Moss and Doggett 5 tested a rigid, 1/6 size, full-span model of an F-18 airplane that

_vas fitted with flexible vertical tails of two different stiffness. Vertical-tail buffet response results were

obtained over the range of angle of attack from -10 ° to +40 °, and over the range of Mach numbers

from 0.3 to 0.95. Their results indicated that the buffet response occured in the first bending mode, in-

creased with increasing dynamic pressure and was larger at M = 0.3 than that at a higher Mach number.

An extensive experimental investigation has been conducted to study vortex-twin tail interac-

tion on a 76° sharp-edged delta wing with vertical twin-tail configuration by Washburn, Jenkins and

1Professor, Eminent Scholar and Dept. Chair.

2ph.D. Graduate Research Assistant.

3Ph.D. Graduate Research Assistant.

Ferman 6. The vertical twin tails were placed at nine locations behind the wing. The experimental data

showed that the aerodynamic loads are more sensitive to the chordwise tail location than its spanwise

location. As the tails were moved toward the vortex core, the buffet response and excitation were re-

duced. Although the tail location did not affect the vortex core trajectories, it affected the locationof vortex-core breakdown. Moreover, the investigation showed that the presence of a flexible tail can

affect the unsteady pressures on the rigid tail on the opposite side of the model. In a recent study by

Bean and Lee 7 tests were performed on a rigid 6% scale F/A-18 in a trisonic blowdown wind tunnel

over a range of angle of attack and Mach number. The flight data was reduced to a non-dimensional

buffet excitation parameter, for each primary mode. It was found that buffeting in the torsional mode

occurred at a lower angle of attack and at larger levels compared to the fundamental bending mode.

Tail buffet studies were also conducted on a full-scale, production model F/A:18 fighter aircraft

in the 80-by-120 foot wind tunnel at NASA Ames Research Center by Meyn and James s and Pettit,

Brown and Pendleton 9. The test matrix covered an angle of attack range of 18 ° to 50 ° and a side-slip

range of -16 ° to 16° with wind speed up to 100 Knots. The maximum speed corresponds to a Reynoldsnumber of 1.23 × 107 and a Mach number of 0.15.

Kandil, Kandil and Massey 1° presented the first successful computational simulation of the ver-

tical flexible tail buffet using a delta wing-vertical tail configuration. A 76 ° sharp-edged delta wing hasbeen used along with a single rectangular vertical tail which was placed aft the wing along the plane of

geometric symmetry. The flexible tail was allowed to oscillate in bending modes. The flow conditions

and wing angle of attack have been selected to produce an unsteady vortex-breakdown flow. Unsteady

vortex breakdown of leading-edge vortex cores was captured, and unsteady pressure forces were obtainedon the tail.

Kandil, Massey and Kandil m extended the technique used in Ref. 10 to allow the vertical tail to

oscillate in both bending and torsional modes. The total deflections and the frequencies of deflections

and loads of the coupled bending-torsion case were found to be one order of magnitude higher than

those of the bending case only. Also, it has been shown that the tail oscillations change the vortex

breakdown locations and the unsteady aerodynamic loads on the wing and tail.

Kandil, Massey and Sheta 12 studied the effects of coupling and uncoupling the bending and tor-

sional modes for a tong computational time, and the flow Reynolds number on the buffet response, of a

single rectangular flexible tail. It has been shown that the coupled response produced higher deflection

than that of the uncoupled response. Moreover, the response of the coupled case reached periodicity

faster than that of the uncoupled case. It has also been shown that the deflections of the low-Reynolds

number case were substantially lower than that of the high Reynolds number case.

In a recent paper by Kandil, Sheta and Massey 13, the buffet response of a single swept-back

vertical flexible tail in transonic flow at two angles of attack (20 ° , 28 ° ) has been studied. It has beenshown that the aerodynamic loads and bending-torsional deflections of the tail never reached periodic

response and that the loads were one order of magnitude lower than those of Ref. 12 of the subsonic flow.

In a very recent paper by the present authors 14, the buffet response of the F/A-18 twin tails were

considered. The configuration consisted of a 76°-swept back, sharp-edged delta wing and a trailing-edge-

extension on which the F/A-18 twin tails were attached as cantilevers. A multi-block grid was used

to solve the problem for two lateral locations of the twin tails; the midspan location and the inboardlocation.

In this paper, we consider computational simulation and experimental validation of the flexible

twin tail buffet of the F/A-18 and F-117 aircraft. Two multi-block grids are used in the computational

simulation. The first consists of five blocks and is used for the twin tail F/A-18 model and the second

consists of four blocks and is used for the twin tail generic F-117 model. For both models, the flexible

_wintails areallowedto oscillatein bendingandtorsionmodes.The computedresultsarecomparedwith the experimentaldataof MeynandJamess for the F/A-18 aircraft andWashburn,et. al. for thegenericF-117model.

FORMULATION

The formulation consists of three sets of governing equations along with certain initial and

boundary conditions. The first set is the unsteady, compressible, full Navier-Stokes equations. The

second set consists of the aeroelastic equations for bending and torsional modes. The third set consists

of equations for deforming the grid according to the twin tail deflections. Next, the governing equations

of each set along with the initial and boundary conditions are presented.

Fluid-Flow Equations:

The conservative form of the dimensionless, unsteady, compressible, full Navier-Stokes equationsin terms of time-dependent, body-conformed coordinates _a, _2 and (3 is given by

where

O__O_+OEm (1)Ot O_m O_s

_'_ = _m(xl, x2, x3, t) (2)

1(2 = 7[p, pul,pu2, pu3,pe] , (3)

/_m and (/_v)_ are the (m-inviscid flux and (S-viscous and heat conduction flux, respectively.

Details of these fluxes are given in Ref. 10.

Aeroelastic Equations:

The dimensionless, linearized governing equations for the coupled bending and torsional vibrations

of a vertical tail that is treated as a cantilevered beam are considered. The tail bending and torsionaldeflections occur about an elastic axis that is displaced from the inertial axis. These equations for the

bending deflection, w, and the twist angle, O, are given by

02 [ 02w ] 02w. . 020Oz 2 EI(Z)_z2 (Z,t ) + m(z)--_-(z,t)+ m(z)xo(z)-_-_(z,t) = N(z,t) (4)

0 [GJ(z)00][ J 02w" . 0200--_ -_z - m(z)x°--_ -i-(z't) - I°(z)-ot -i(z't) = -M,(z,t) (5)

where z is the vertical distance from the fixed support along the tail length, It, EI and GJ the

bending and torsional stiffness of the tail section, m the mass per unit length, Io the mass-moment of

inertia per unit length about the elastic axis, xo the distance between the elastic axis and inertia a_xis,

N the normal force per unit length and Mt the twisting moment per unit length. The characteristicparameters for the dimensionless equations are c* * *, aoo, P¢o and c*/a_o for the length, speed, density

and time; where c* is the delta wing root-chord length, a_ the freestream speed of sound and p_ thefreestream air density. The geometrical and natural boundary conditions on w and 0 are given by

w(O,t) = OW (o,t) = 02w 0 [EI(It 02w ]Oz -'O_z2 (lt't) = -_z !-_z2 (lt,t) = 0 (6)

O0

o(o,t) = -5-;z(t,, t) = o (7)

The solution of Eqs. (4) and (5) are given by

i

w(z,t) = Zi=1

(s)

M

O(z,t)= _ Cj(z)qj(t) (9)

j=i+l

where ¢_ and Cj are comparison functions satisfying the free-vibration modes of bending and

torsion, respectively, and qi and qj are generalized coordinates for bending and torsion, respectively. Inthis paper, the number of bending modes, /_, is six and the number of torsion modes, M - T is also

six. Substituting Eqs. (8) and (9) into Eqs. (4) and (5) and using the Galerkin method along withintegration by parts and the boundary conditions, Eqs (6) and (7), we get the following equation for

the generalized coordinates qi and qj in matrix form:

[ Mll M12 qi KI1 O qi )M21 M22 ] ( qj ) + [ 0 1(22 ] ( qj

where

N1 ;i= 1,2, .... ,I= -N2 ) .... ,M(10)

Mll = ]Zo'm¢r¢idz )M12 = M21 = f0h mxo¢_¢jdz

M22 = Jg* IoCsCjdz

(11)

." It dz _ d2¢i ]l_ax = fo EId_-_-zve'- dzu az a_¢

/£22 = JO (Sd dz dz az(12)

N2 = fo ¢_Mtdz(13)

Similar aeroelastic equations were developed for sonic analysis of wing flutter by Strganac 15.

The numerical integration of Eqs. (11-13) is obtained using the trapezoidal method with 125 points

to improve the accuracy of integrations. The solution of Eq. (10), for qi;i = 1,2, .... ,_T, and qj;j =

/: + 1..... , M, is obtained using the Runge-Kutta scheme. Next, w, and 8 are obtained from Eqs. (8)and (9).

Grid Displacement Equations:

Once w and 8 are obtained at the n + 1 time step, the new grid coordinates are obtained using

simple interpolation equations. In these equations, the twin tail bending displacements, w n+li,j,k, and their/_n+l

displacements through the torsion angle, _i,j,k are interpolated through cosine functions.

Boundary and Initial Conditions:

Boundary conditions consist of conditions for the fluid flow and conditions for the aeroelastic

bending and torsional deflections of the twin tails. For the fluid flow, the Riemann-invariant boundary

conditions are enforced at the inflow and outflow boundaries of the computational domain. At the plane

of geometric symmetry, periodic boundary conditions is specified with the exception of grid points on

the tail. On the wing surface, the no-slip and no-penetration conditions are enforced and 0°2n= 0. Onthe twin tail surfaces, the no-slip and no-penetration conditions for the relative velocity components are

enforced (points on the tail surface are moving). The normal pressure gradient is no longer equal to

zero due to the acceleration of the grid points on the tail surface. This equation becomes _ = -p_tt.h,where at is the acceleration of a point on the tail and h is the unit normal.

Initial conditionsconsistof conditionsfor thefluid flowandconditionsfor the aeroelasticdeflec-tionsof the twin tails. Forthe fluid flow, the initial conditionscorrespondto the freestreamconditionswith no-slipandno-penetrationconditionson the wingandtail. For the aeroelasticdeflectionsof thetail, the initial conditionsfor anypoint on the tail are that the displacementand velocityarezero,w(z,O) = 0, °_z O) = O, 8(z,O) = 0 and °°(z n_ O.Dt k ' . at\ ' _ / --_

METHOD OF SOLUTION

The first step is to solve for the fluid flow problem using the vortex-breakdown conditions and

keeping each of the twin tails as a rigid beam. Navier-Stokes e_uations are solved using the implicit,flux-difference splitting finite-volume scheme. The grid speed _ is set equal to zero in this step. Thisstep provides the flow field solution along with the pressure difference across each of the twin tails. The

pressure difference is used to generate the normal force and twisting moment per unit length of each

tail. Next, the aeroelastic equations are used to obtain the twin tall deflections, wl.j,k and _i,j,k. The

grid displacement equations are then used to compute the new grid coordinates. The metric coefficients

of the coordinate Jacobian matrix are updated as well as the grid speed, °0-_-_ . This computational cycleis repeated every time step.

COMPUTATIONAL APPLICATIONS AND DISCUSSION

Two flexible twin tail models are used in the present study. The first model consists of a twin

tail-delta wing configuration for the F/A-18 aircraft and the second model consists of a twin tail-delta

wing configuration for a generic F-117 model. The delta wing of the two configurations is a 76°-swept

back, sharp-edged delta wing of aspect ratio of one. The two configurations are pitched at a 30 ° angle ofattack. Next, the twin tails of each configuration along with its geometry, flow conditions, multi-block

grid and aeroelastic properties are given:

F/A-18 Twin Tails:

Each one of the twin tails are of aspect ratio 1.2, a crop ratio of 0.4 and a sweep-back angle of 35 °

for the quarter-chord spanwise line. The chord length at the root is 0.4 and at the tip is 0.159, with a

span length of 0.336. The tail airfoil section is a NACA 65-A with sharp leading edge and the thickness

ratio is 5% at the root and 3% at the tip. The dihedral angle between the two tails is 40 °. The spanwise

distance between the two tails is 56% of the wing span. The tails are cantilevered along the edges of atrailing-edge extension of the delta wing. The Mach number and Reynolds number (based on the wingchord length) are 0.4 and 1 x 10 6, respectively.

A multi-block grid consisting of five blocks is used for the solution of the problem. The first block

is a O-H grid for the wing and upstream region, with 101 x 50 x 54 grid points in the wrap around,

normal and axial directions, respectively. The second block is a H-H grid for the region between thetwin tails, with 23 × 30 × 12 grid points in the wrap around, normal and axial directions, respectively.

l_he third block is a H-H grid covering the region outside the twin tails, with 79 x 30 x 12 grid point_ in

the wrap around, normal and axial directions, respectively. The fourth block is a O-H grid surroundingthe second and third blocks, with 101 x 21 x 12 grid points in the wrap around, normal and axial

directions, respectively. The fifth block is a O-H grid for the downstream region of the twin tails, with

101 x 50 × 26 grid points in the wrap around, normal and axial directions, respectively. Figure 1 shows

the grid topology and a blow-up of the twin tail-delta wing configuration.

The dimensionless density and modulus of elasticity of thetwin tails are 25.5 and 1.8x10 s. The

torsional rigidity of the twin tails at the root, GJ, is 2.12 x 10-2.

Generic F-117 Twin Tails:

The twin tail-delta wing configuration consists of a 76°-swept back, sharp-edged delta wing (aspectratio of one) and dynamically scaled flexible twin tails similar to the one used by Washburn, et. al 6. The

vertical tails are oriented normal to the upper surface of the delta wing and have a centerline sweep of

53.5 °. Each tall is made of a single Aluminum spar and Balsa wood covering. The Aluminum spar has

a taper ratio of 0.3 and a constant thickness of 0.001736. The chord length at the root is 0.03889 and

at the tip is 0.011667, with a span length of 0.2223. The Aluminum spar is constructed from 6061-T6

alloy with density, p, modulii of elasticity and rigidity, E and G of 2693 kg/m 3, 6.896 × 101° N/m 2 and

2.5925 × 10 l° N/m2; respectively. The corresponding dimensionless quantities are 2198, 4.595 × 105

and 1.727 × 105; respectively. The Balsa wood covering has a taper ratio of 0.23 and aspect ratio of

1.4. The chord length at the root is 0.2527 and at the tip is 0.058, with a span length of 0.2223. The

Balsa thickness decreases gradually from 0.0211 at the tail root to 0.0111 at the tail midspan and then

constant thickness of 0.0111 is maintained to the tail tip. The tail cross section is a semi-diamond shape

with bevel angle of 20 °. The Balsa density, modulii of elasticity and rigidity, E and G, are 179.7 kg/m 3,6.896 × l0 s N/m 2 and 2.5925 × l0 s N/m2; respectively. The corresponding dimensionless quantities

are 147, 4.595 × 103 and 1.727 x 103; respectively. The tails are assumed to be magnetically suspended

and the leading edge of the tail root is positioned at x/c = 1.0, measured from the wing apex. Thefreestream Mach number and Reynolds number are 0.3 and 1.25 x 106; respectively.

A multi-block grid consisting of 4 blocks is used for the solution of the problem. The first block

is a O-H grid for the wing and upstream region, with 101 × 50 x 54 grid points in the wrap around,

normal and axial directions, respectively. The second block is a H-H grid for the inboard region of the

twin tails, with 23 × 50 x 13 grid points in the wrap around, normal and axial directions, respectively.The third block is a H-H grid for the outboard region of the twin tails, with 79 x 50 x 13 grid points

in the wrap around, normal and axial directions, respectively. The fourth block is a O-H grid for the

downstream region of the twin tails, with 101 × 50 × 25 grid points in the wrap around, normal and

axial directions, respectively. Figure 2 shows the grid topology and a blow-up of the twin tall-delta wingconfiguration.

The configuration is investigated for three spanwise positions of the twin tails; the inboard location, the

•_idspan location and the outboard location corresponding to a separation distance between the twin

tails of 33%, 56% and 78% of the wing span; respectively.

Results of the F/A-18 Configuration:

Figure 3 shows three-dimensional and top views for the initial conditions with total pressure

contours on the wing and twin tails along with the streamlines of the leading edge vortex cores. The

initial conditions are obtained after t = 10 dimensionless time units (At = 0.6 x 10-3), with the twin

tails kept rigid. It is observed that the vortex cores experience almost a symmetric breakdown on the

wing starting at about 75% chordstation. Downstream of the wing, the vortex-breakdown flow is insidethe region between the twin tails. A small vortex has also been observed on the outside corner of the

juncture of the tail and the trailing edge extension. The static pressure contours (not shown) indicatethat the static pressures on the inside surfaces of the twin tails are lower than those on the outsidesurfaces.

Figures 4-7 show the aeroelastic responses of the twin tails after t = 10 units measured from the

initial conditions solution. Figure 4 shows the bending and torsion deflection responses of the left and

right tails along the vertical distance z, every 2 time units. It is observed that the bending responses are

in the first mode shape while the torsion responses are in the first, second and third mode shapes. More-

over, the maximum bending deflections are about two times those of the torsion responses. The bending

deflections for each tail show a single sign while the torsion deflections show positive and negative signsfor each tail. Figure 5 shows the history of the bending and torsion deflections and loads versus time of

the tail tip point and mid point for the left and right tails. Periodic responses have never been reached

within the computational time of t = 20 units. Figures 6 and 7 show the histories of the root-bending-

6

momentcoefficient(C,.bm)and the pressurecoefficientson the inside(Cp_)and outside(Cpo)the tailsurfacesaswellasthe differenceof thepressuredifference(Cpi-o)versustimefor the left andright tails.

Table1 showscomparisonof the root meansquareof the presentresultsfor the twin tail-deltawing modelof the F/A-18 with the experimentaldata of Meynand Jamess and the computationalresultsof Gee,Murman and Schiff16of the productionmodelF/A-18 fighter aircraft. It shouldberecalledthat the presentmodelconsistsof a delta wing without a LEX and twin tails only, while the

results of Refs. 8 and 16 are for a full F/A-18 aircraft model.

Case

Present CFD/Structurs Results

F/A-18 Model

(Left tail)

Meyn Expiremental Data

F/A-18 aircraft

(As reported in Ref. 16)

Cpi Cpo Cpi-o Crbm

0.21 0.038 0.23 0.0252

0.28-0.3 0.14-0.16 0.34-0.37 0.0624-0.0814

Gee CFD l_esults 16 0.2 0.13 0.27 0.0182

F/A-18 aircraft

Table 1. Comparison of RMS Cp at 60% span and 45% chord, and RMS Crbm.

Results of the Generic F-117 Model:

Inboard Location of Twin Tails (33 % wing span):

The spanwise distance between the two tails is 33 % of the wing span. Figure 8 shows three-

dimensional and front views for the initial conditions with the surface total pressure contours and the

streamlines of the vortex cores. Figure 9 shows the static pressure contours and the instantaneousstreamlines in a cross flow plane at x = 1.096. The initial conditions are obtained after 10,000 time

steps, At -- 0.001, with the twin tails kept rigid. It is observed that the vortex cores experience an

almost symmetric breakdown on the wing at about the 75% chordstation. Downstream of the wing,

they are totally outside of the space between the twin tails. Smaller size vortex cores appear under the

vortex breakdown flows and at the lower edges of the twin tails. These results exactly match Washburn

observations. Figures 10 and 11 show the results for the twin tails undergoing uncoupled bending-

torsion responses after 9,600 time steps from the initial conditions. It is observed that the breakdown

shapes and locations are affected by the twin tail oscillations. The vortex breakdown is now st_ngly

asymmetric, and the vortex breakdown flows are still outside of the space between the twin tails. Theseresults conclusively show the upstream as well as the spanwise effects of the twin tail oscillations on thevortex breakdown flows.

Figures 12-14, show the distribution of deflection and load responses along the left and right tails

every 2 time units, the history of deflection and load responses versus time and the total structural

deflections and root bending moment for the left and right tails. It is observed that the bending and

torsion responses are in their first and second mode shapes. The frequencies of the bending deflections

are less than one-half those of the torsion deflections. The normal forces are out of phase of thebending deflections while the torsion moments are in phase with the torsion deflections. The total tail

responses are in first, second and third mode shapes. Periodic responses have not been reached within

the computational time covered (20,000 time steps = 10 dimensionless time units).

Midspan Location of Twin Tails (56% wing span):

The results of this case are presented in Figs. 15-21. Figures 15-18 show that the tails cut through

the vortex breakdown of the leading-edge vortex cores, which are also asymmetric. Figure 18 shows

that the bending deflections are lower than those of the inboard case while the torsional deflections are

substantially lower than those of the inboard case. Moreover, Fig. 18 shows that the bending and torsion

deflections have a single sign for the left and right tails (all are positive or all are negative). Figure

20 shows that both bending and torsion deflections are out of phase of the normal force and twisting

moment loads. The total deflections of Fig. 21 show the same trend. The root bending moments ofFig. 21 are also lower than those of the inboard case.

Outboard Location of Twin Tails (78% wing span):

Figures 22-26 show the results of this case. Figures 22 and 23 show that the space between the twin

tails include larger portion of the vortex breakdown flow of the leading-edge vortex cores, than that

of the midspan case. The vortex breakdown flow is also asymmetric. The vortical flow on the lower

outside surfaces of the twin tails is larger than any of the above two cases. Figures 24-26 show that the

bending and torsion deflections are lower than those of the midspan case. They also show that both

bending and torsion deflections are out of phase of the bending and torsional loads. The frequencies ofthe bending deflections are still smaller than those of the torsion deflections. All these observations are

in very good agreement with those of Washburn, et. al. (Ref 6). Figures 27-29 show the histories of the

lift and drag coefficients versus time for the inboard, midspan and outboard locations. It is observed

that the loss in CL is the largest for the inboard location case.

Table 2. shows a comparison of the present results of the mean root bending moment for flexible

twin tails and the lift coefficient with rigid twin tails with those of Washburn, et. al. (Ref 6), experi-mental data.

Parameter

Mean Root BendingMoment

With Flexible Tails

Lift Coefficient

With Rigid Tails

Position

Inboard

MidspanOutboard

Inboard

FTNS3D

5.62 x 10 -5

4.22 x 10 -5

3.62 x 10 -5

1.0423

WASHBURN

7.43 x 10 -5

6.05 x 10 -5

5.70 x 10-5

1.17

Midspan 1.0515 1.12Outboard 1.0674 1.17

Table (2) Validation of FTNS3D computational results with Washburn, et. al. experimental results 6.

CONCLUDING REMARKS

The buffet responses of the twin-tail configuration of the F/A-18 model and the generic F-117

model have been investigated computationally using three sets of equations for the aerodynamic loads,

the bending and torsional deflections and the grid displacements due to the twin tail deflections. The

leading-edge vortex breakdown flow has been generated using a 76°-swept back sharp-edged delta wing

which is pitched at 30 ° angle of attack. The twin tails are cantilevered at a trailing edge extension of

the delta wing for the F/A-18 model and without a trailing edge extension for the generic F-117 model.One spanwise separation distance between the twin tails is considered for the first model and three

spanwise separation distances are considered for the second model. Only, uncoupled bending-torsion

responsecasesareconsideredin this study.

The presentsimplemodelof the F/A-18 aircraft producesresultswhicharein goodagreementwith theexperimentaland computationalresultsof thefull F/A-18 aircraft.

The presentcomputationalresultsof the genericF-117modelarein very goodagreementwiththe experimentaldataof Washburn,et. al. genericmodel. It is concludedthat the inboardlocationof the twin tails producesthe largestbending-torsionloads,deflections,frequenciesand root bendingmomentswhencomparedwith the midspanandoutboardlocations.The outboardlocationproducestheleastof theseresponses.Whenthetwin tails cut throughthevortexbreakdownflow,they producestessresponsesdueto the compensatingdampingeffectproducedby theleft andrightpartsof thevortexbreakdownflowoneachtail.

Workisunderwayto upgradetheaeroelasticmodelusingfinite-elementstructuraldynamicscodesfor shellandsolidelementsof the twin tails andto addanadvancedturbulentsmodel,e.g.;k - w two

equation turbulents model. Moreover, work is underway to develop passive and active control of thetwin tail buffet problem.

ACKNOWLEDGMENT

This research work is supported under Grants No. NAG-I-994 and NAG-I-648 by the NASA

Langly Research Center. The authors would like to recognize the computational resources provided by

the NAS facilities at Ames Research Center and the NASA Langley Research Center.

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and Pulley, C. T., "Experimental Investigation of the F/A-18 Vortex Flows at Subsonic ThroughTransonic Speeds," AIAA 89-2222, 1989.

Wentz, W. H., "Vortex-Fin Interaction on a Fighter Aircraft," AIAA 87-2474, AIAA Fifth Applied

Aerodynamics Conference, Monterey, CA August 1987.

4. Lee, B. and Brown, D., "Wind Tunnel Studies of F/A-18 Tail Buffet," AIAA 90-1432, 1990.

5. Cole, S. R., Moss, S. W. and Dogget, R. V., Jr., "Some Buffet R.esponse Characteristics of a

Twin-Vertical-Tail Configuration," NASA TM-102749, October 1990.

.

.

.

.

10.

Washburn, A. E., Jenkins, L. N. and Ferman, M. A., "Experimental Investigation of Vortex-Fin

Interaction,, AIAA 93-0050, AIAA 31st ASM, Reno, NV, January 1993. ,-

Bean, D. E. and Lee, B. H. K., "Correlation of Wind Tunnel and Flight Test Data for F/A-18Vertical Tail Buffet," AIAA 94-1800-CP, 1994

Meyn, L. A. and James, K. D., "Full Scale Wind Tunnel Studies of F/A-18 Tall Buffet," AIAA

93-3519-CP , AIAA Applied Aerodynamics conference, Monterey, CA, August 9-11, 1993.

Pettit, C. L., Brown, D. L. and Pendleton, E., "Wind Tunnel Test of Full-Scale F/A-18 Twin TailBuffet: A summary of pressure and Response Measurements," AIAA-94-3476-CP, AIAA Applied

Aerodynamics conference, Colorado Springs, CO, June 1994, pp. 207-218.

Kandil, O. A., Kandil, H. A. and Massey, S. J., "Simulation of Tail Buffet Using Delta Wing-

Vertical Tail Configuration," AIAA 93-3688-CP, AIAA Atmospheric Flight Mechanics Conference,Monterery, CA August 1993, pp. 566-577.

9

11. Kandil,O. A., Massey,S. J., and Kandil, H. A., "Computations of Vortex-Breakdown

Induced Tail Buffet Undergoing Bending and Torsional Vibrations," AIAA 94-1428-CP,AIAA/ASME/ASCE/ASC Structural, Structural Dynamics and Material Conference, SC April

1994, pp. 977-993.

12. Kandil, O. A., Massey, S. J. and Sheta, E. F., "Structural Dynamics/CFD Interaction for Com-

putation of Vertical Tail Buffet," International Forum on Aeroelasticity and Structural Dynamics,

Royal Aeronautical Society, Manchester, U.K., June 26-28, 1995, pp. 52.1-52.14. Also published

in Royal Aeronautical Journal, August/September 1996, pp. 297-303.

13. Kandil, 0. A., Sheta, E. F. and Massey, S. J., "Buffet Responses of a Vertical Tail in Vortex

Breakdown Flows," AIAA 95-3464-CP, AIAA Atmospheric Flight Mechanics Conference, Balti-

more, MD, August 7-9, 1995, pp. 345-360.

14. Kandil, O. A., Sheta, E. F. and Massey, S. J., "Twin Tail/Delta Wing Configuration Buffet Due

to Unsteady Vortex Breakdown Flow," AIAA 96-2517-CP, 14th AIAA Applied Aerodynamics

Conference, New orleans, LA, June 18-20, 1996, pp. 1136-1150.

15. Straganac, T. W., "A Numerical Model of Unsteady, Subsonic Aeroelastic Behavior," NASATechnical Memorandum 100487, December 1987.

16. Gee, k., Murman, S. C. and Schiff, L. S., "Computational Analysis of F/A-18 Tail Buffet," AIAA95-3440-CP, Atmospheric Flight Mechanics Conference, Baltimore, MD, August 1995, pp. 151-162.

10

Figure1: Three-dimensionalgrid topologyof the twin tail-deltawingconfiguration(Midspan),F/A-18model.

Figure2: Three-dimensionalgrid topologyof the twin tail-deltawingconfiguration(Midspan),F 117Genericmodel.

Figure3: Three-dimensionaland top viewsof surfacepressureandvortex-coresstreamlinesfor a rigidtail, t = 10, At = 0.0006.

11

Bending Dmtnbotion Hiztofy

W

Fo_l Dismbu_on _or/

oo -o_ .o_o -OOLO o_ ooso

N

Rotlt_ D.mi_ut k:,q History

Z °'2

0.1

U

0+3 1+

M

(a) Left tail

ii?N++.Z

" .o.oo1_o -o_o .oJ_o_ o.ooeoo

W

Force D_nbut_ HtJ_o_

o'o -oolo o_ oolo oo_o oo_-

N

RoudJon Owlrib_oq HZltO_

+:;Z

o.o,.<mo,.¢mm";'omoommoo_ oo_, do,,I+

momen_ D.itntxMion Hlltory

M

(b) Right tail

Figure 4: Distribution of the deflection and load responses for an uncoupled bending-torsion case.

Moo = 0.4, a = 30°, Re = 1.00x106, (Midspan position).

Z.100% Bzr_lng Oizplacemer_ & Force vs T_me

<!" +: ..... o.om+ooo_ :'_ _: _ _ i ._ _ : ::

oo_oo s 1o ts 0o010

T

Z. 100% Rotlt ion & Mom4w_ vl T_,al

i!i i: " i _ oo_o_

-o._olo -4.oo0o_-6

o _ lO IS

T

Z.50% Rolllkm & Momlnl vl Tm+ll

o.__

o.o_ _ -0o0o10

-o.oo_ • : _ ,.o+og_

-0O(O4 ' -0_0_O_O M

Z..50% Be_di_ 9 Di_lac4ml_nt & Force vs Time

_ O+Ol4

oooo_ :! oo1_

:r OOlO N eW

o_oo_

o_

Z. 100"X, 8m:lt)g D_olaceen*m & Fome ,_ "nm_

o.o¢oo ,, . .o_omo

-+-::--++ : ,. '. ;,;' ' ' " ' _ " /_ .o_ols

-00_ ..... :. / ,

W..o.omo ! _ : : ,.o_e N e

o s lo ts

T

°'_ t __ w + -O.O04

++!++++rot++++(b) Right tail(a) Left tail

Z. 100% _otat_ & kkx'n_ vZ _m*

.....[.-:t.--,;i_ • :'+ ._,-+-+Lr.+.+..i+", , ++++_,+o_,

o.oo_o_:l : ,: :, ,.: .-;: _' ,. ,_f,H_wooe-_:'_

'/:: ii _!."_:'..i i"'_ ,.0_,_+o.ooos i' : : _ o_oo£ "oM

o._ -I._-Is

o s lo IS

T

o.oolo ,, . _ • 1

, .¢:..u :: : : i:: _{ +: !. : :., o,_o

• :':; *, .; , :: :: ::

; i :!'_: 'i:" i I °_°M

,o.¢_1o

T

Figure 5: History of the deflection and load responses for an uncoupled bending-torsion case. Mooa = 30 °, Re = 1.00xl0 _, (Midspan position).

o.1_

C_o.1111

o+1_0

o s lo is

"°2° Cp _'_

= 0.4,

Figure 6: History of root-bending moment coefficient and surface pressure coefficients for an uncoupled

bending-torsion case. Moo = 0.4, _ = 30 °, R+ = 1.00xl06. Left tail (Midspan position).

12

C_

cv

,'0 i'*1

_ o_ Prluum (l_out. m_.,t) vs Non_lmemmc_t "nine It 45% C_xd. 60_ $toan

o.oo[ cp.

-o=o

-o.4o

-oJo

-o_o

.i.oo

o s Io 16

Figure 7: History of root-bending moment coefficient and surface pressure coefficients for an uncoupled

bending-torsion case. Moo = 0.4, _ = 30 °, R_ = 1.00xl06. Right tail (Midspan position).

Figure 8: Three-dimensional and front views showing the total pressure on the surfaces, and the vortex-

core streamlines. Initial conditions (Inboard position).

\

\

o o1_1_

N O?IS

M 0.711

L 0?06

K 0.7O2

• a O_a

q O._d

H of,_

Q om

E o.s_

o o.s'rJ

C o._

0 o._t5

2 o._7

Figure 9: Initial conditions for static pressure and instantaneous streamlines in a cross-flow plane,

x = 1.096 (Inboard position).

13

5

!0

.,,-4

0

t_O_

°,.-_

0

o_

_o=0

o_ 0

J

0

0

_30

c_

0

c_°

._ 0

u3

• .i11111tlii

.itii!]ll|l

]

.illillllli

.llii!lllli

_4444_4tH_

i

.sllillllliH44H4tH_

.lllliliill

.iilil_llil

1444444tH+

.lllii|l!li

H H444t_tH_ H44H_tH+O ._

.__ _ _ _ _ _ _ o

0

0

0

_o

0

0

0,--" 0

-_::_

r.-,

00 ,-_

°_

s_

I,OOE,_

400E-3

ooo_

4 ooE-,1

.1=oE-2

.i 6OE.2

o.oo_o

-I .COE-_

-2 _£-3

W-3._-3

-4 _£-3

Tip B_m8 L_n_uon & Fort= Hii_oly

J: ,i a, IL

' '_' " '" o_c

.I._E.1

n

Midp,Olnl Bendin 8 DclW_a_ & Fore Histo_

Tip Ro_tion & bf_t Hir.l_

4O0O _ _2o0o 16_oo 2.o_oo

Midpoint [_oul_ _ & Moo_nt I_

Z.OOE-S _.ooE.2

M

O.o02o 4.o_-_

o._

o1_-3 1._E-1

:i/!i iiii ,j ,i.... ,'.' _ : ', _ '_" _oo_ s -2 w

.l: 11 11 S I 1_0E-4

•_ OOE-3 I JOOE_

-- _ i _ _ -7 O0_n O00eO40OO _ 12OOO Ie¢_0 2OOOO 4OOO eO00 nX_O_ lao_

n

(a) Left tail

•np I_=_dia g Dei_c_ & Fort.'= Hi_ Tip I_o_11_i & M_t Hi_

j

-- w ^_ ,_o_ _ ' _ s.oo_-s=.oo_._ l[--:-- M ,,

fl I r I ' _I N

:_ ' ' _._ .1.,_., ' ' i i " -,_,

n

Midp_nt g©_d_, s De nec_ & Rxce H/SlC_

• _. • , • 7.ooE-_ -i,soE-1

--:--- " , , _ _, _.oo_

' ,/ i'_ i ' '_ -,_-,

4000 eO00 n 1_ooo 1_o1_ _c_oo

n

M_dpcln( Roe_aoa & M_'nt

(b) Right tail

Figure 13: History of the deflection and load responses for an uncoupled bending-torsion case. Moo =

0.3, c_ = 30 °, Re = 1.25x106, (Inboard position).

l)i_ bu_ of L_ding ]_d_ze Tot, I DeP._.'I_ n 0.0¢_0 ,Root Bcn_lin_ Moment . Die,bunion of Lea_nl_ Edlte To_l Deikcaon Roo[ Be.rKSng Morne_

o_.o o_o e_-s

4_oE-S _.. -S

o,o _. o.,o --4.ooE.._

.4_.so_ o._

oc_ ° °°E°o 44_o aooo 1_eo leO_O _ooooo soo _o1_oo -ooosco o o.ooeoo o.oIo_O oole_o o1_,ooo

Wned n Wn_ n

(a) Left tail (b) Right tail

Figure 14: Total structural deflections and root bending moment for an uncoupled bending-torsion case.

Moo = 0.3, (_ = 30 °, Re = 1.25x106, (Inboard position).

To,It

e._l eJ;s e._l e.?s e.m

Figure 15: Three-dimensionai and front views showing the total pressure on the surfaces, and the

vortex-core streamlines. Initial conditions (Midspan position).

15

o

0

u

0

c_

t_

u_

t_

_r3

o.O"_

0

•-" ,._°_

o

0

o

_o

_a0o

°,,,_

o _:_,.=

_ ooooooooooo o©oao oooo

Z /o

"_;

o

,e-..4

II

o

0

0

""4 0

u _

o_

r_ u

_8

D1_bc_ of kn_ng Delloe_o_ Du ,ril_uo_ e¢ R_ Di_uee of BesdiR s _ D_buzi_ of Ro_mo_

o, o; = .... : 7o.,o _1-_- -- o.,o _ _.. o.,o o.,o

oO6 O.OS O J06 0._

000 -OnO'JO0 -00_00 -0 O. 0010 O.e_O 0.000 0.040 O.OSO 00_00" 0.0O400 0.00600 0.0_00 0._ -0.0_ -0000 _0_0 -0010W e W

D_mbu_on of Noc_r_l Fore Di_bu_ of Tomoeal M_nl

°: 7[ °"1°

.- - . , :__N

(a) Left tail

D/mlbubon of Normal F_ DiJ_buu_ orTom_il Moment

z _ _-

oos o.o6

N M

(b) Right tail

Figure 19:

M_ = 0.3, a = 30 °, R_ = 1.25x106, (Midspan position).

: _ : :_ :i' ,._N . • _ ! _' ' _ : ' U" _ W _' _: ' _ '_ N _._

.... ' , ; , _ _ _ _ o_o ]_ _ ,4._•_ OOE_ =.OOE-_ :; !I ' .4ooE4

Mld_n[ ,__nding [_ef'u_c_ & ]Q_ Hi_Ol_ Mid r,,t]ln1!_0¢11110Q,_ Monl_nl Hixlm'_ Midpo_l ]Bem_l( Dc ['Jec_ou _k _ Hillfory

w :i"! ! ' _ii,_,_!','_ ' ...... ' , , ,-;_ooE-3 ', _ I ' N = Z _00E-'3 WgOE < ,JOE4

_°°e-_t,v V 1! , , , 1.=,,o_ a_-*

o ,,,ooo _oo n _z,o_ lscoo 2_oo o _ _ooo n12O_ t(_o zo_o _°°E's o._=c *,ooo ao_o n I,z_o 1_o

Distribution of the deflection and load responses for an uncoupled bending-torsion case.

(a) Left tail

Tip Rotadon & Momcat Hilm_• , ! . l.¢os-e

' I --e

4ooo K_O 12¢oo _s¢oo 2¢ooon

Midpoiat RoUdoo & M_n<nt l_;to,_o.ooe0 .

-t._E4

*._-2 -t.lOE4

(b) Right tail

Figure 20: History of the deflection and load responses for an uncoupled bending-torsion case. Moo =

0.3, a = 30 °, Re = 1.25x106, (Midspan position).

l_m_U_ orL,_lln_ Edge Total D_o_. ..s OmZ._ ,R°°t Bending Moment ,

<I.SOE-S

Mr

Z S .4 ¢OE-S

olo .4,soe,_

o_

-sl_t[-s

ooo o ,coo ,_o ,2ooo i_ooWn_ n

(a) Left tail

Figure 21: Total structural deflections and root bending moment for an uncoupled bending-torsion case.Moo = 0.3, a = 30 °, Re = 1.25x106, (Midspan position).

17

10

_ m_ o

1!

o _

• .i111111111 .i1111!IIII

i;;;;iiiill i _

/

J

>_

0

0

¢',1

_z

_ >

0

,-_ _-. .t11111IIii .i111111111

.._ t4444t44H_ t4444t@_

=N !

_ o _

M .IIIIIIIIII

,2, t4444t4ttt+0 ._

.illillltlit444H@_

Ot:::h_---

_ o

o _

_°

_ o II

°,-_4_

_g

_ e

Tip B_din s Dcnu_c_ & Fo(_ HJuory Tip Roumm & M_nmmHi_

o,ommII---'_", ,', s.ooee ,,,', ,_ I _ I 1.ooe.,.

°°ee°N:_ ,,_1 tl , p, 'I I ; _o.ooeo,,++++++++....,, +..+._.+ + ' ' .,.,' -,.ore-, oooc-o ,i '._",.e.ooE,a -+1_4

-I oom.z ,! _ j -2_oE,+

o .meo tmoon l+Oeo _eeeo _o_ o ,moo _oo _2ooo le,ooo =<moo

Mi+Jl+,,mnl B+_m,_ l_l'_mm _c_ H+,mr.s Midpmnt m+.mmm m Mtm_.l HlllOr/

°-I]' +I ....-- il ,_ _; ++E32.OOE.2 ...... u :,,..6.00_4 - - - + ' ,',

-_.OOE-+ _ +t t ',, ,j,' , ,, -_me-+. J: mJw _'I, ',

-,_-_ _ _ _ ' _ _I_ ' N e _ ,'', : ' ' ', U .:_.3 _otm._

•2 (mE._ _ ' +'

4.0oE-a .

•= soE+_ -2.SOE-I

0 4000 e¢O0n 12000 16000 20g_O 0 40_ _ hi2000 iS000 20000

(a) Left tail

Tip BcadmBDeneceoe& FomeI_l_'y

1_4E.a ' _ I I.cx_4• * 't I

h -- N ; _, J' o.ee¢-oec_-_ I , II c¢_.,+

w h _ i4 '.,:! ,, ' ' omeo ""=e'=4._+s , ,L , _ ,,,_ . b _ N

p,, , :, ,_ ,,+, . .=_o_.=

i_ , ,' , +.... .+,_.+n

M_dp_ntB©e,dJn8 I)elkm:_ & Fmc= H_r.mxy

t " 'lil"t .... °+.... t "! it '_/_it i ....I+I?+,i' IlVl ......

"1.OOE+ I_OE+ +_o_

S.O_E_ l.ooE_

II ,,', _I ! ',"+

:+ +i_ :}I

2L +-+l=Oe_ lemoon

Midp_nl RotJ_ & Moment II11¢+ol2,

_o ,<m .,_o ,=oo mooo

(b) Right tail

Figure 25: History of the deflection and load responses for an uncoupled bending-torsion case. Mo_ =0.3, a = 30 °, Re = 1.25x106, (Outboard position).

I_tribuu_ of L_ing Edtte Total D¢llecmn Root Bendin_ Moment Dil_be*io= or1..=_ ng EdtteTotal Dcftecsio_ Root Bcn_ng Mome_

o+o _ .. ..+,_++ ,l+eoE-s

____=

7 °:+ .-- .+_.+

,l.ooE.s

M+"

o.to _ 40¢1+ o.1o = s

ooo -+OOE_ _ :t,lt,OE.e

_ n _ n

(a) Left tail (b) Right tail

Figure 26: Total structural deflections and root bending moment for an uncoupled bending-torsion case.

Moo = 0.3, a = 30 °, Re = 1.25x106, (Outboard position).

1.10

CL

1.05

History of Lift Coefficient

+

1.00 -+

0.90

.... i . , , , I _ _ , , i .... I .... i

0 4000 8000 12000 16000 20000

n

History of Drag Coefficient

0.640

0.600

0.580 f V V _)

0.560 I

0540 L ................

0 4000 8000 12000

n

i ,

, , , I , , ,

16000

I

20000

Figure 27: Hisotory of the forces on the wing/twin-tail configuration. M_o = 0.3, a = 30 °, Re =1.25x106, (Inboard position).

19 ¸

..a ..... J .... n .... i .... i ....

°_,_ _

d d d cir..)

ID

8_

O

8 _¢,D U_

d d

...... _8

O

°_"_ 1 O

i ',o0 0 0 0 0 0

°_2_ ° o o o,._ • ,._ _ ,._ ,._

II

o

II

0

II

o

t,-i

q=;

o

..-q

°,-q

O

o o

o _

._

o

Oc..)

C..)

O

_ 8

r , , i , oo O o O o

d _ d d d d

oo

II

ooC,O

II

0

II

8

o

b.0r4=

o

O

O O O O

_ q q q

0

°o _ oo o_

0 0

._

O