AlAA 90-0435 Static Aeroelastic Analysis of Fighter Aircraft Using a Three-Dimensional Navier-Stokes Algorithm D. Schuster Georgia Tech. Atlanta, GA J. Vadyak Lockheed Aerospace Systems Co. Marietta, GA E. Atta Lockheed Aerospace Systems Co. Valencia, CA

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28th Aerospace Sciences Meeting January 8-1 1, 1990/Reno, Nevada

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W STATIC AEROELASTIC ANALYSIS OF FICIITER AIRCRAFI’USKG A ll IREE-DlhlENSIONAl. NAVIFR-STOKES AI.GORm IJI

David M. Schuster* Georgia Tech Research Institute

Atlanta, Georgia

Joseph Vadyak** Lockheed Aeronautical Systems Company

Marietta, Georgia

EssamAtta*** h k l i c c d Aeronsuticsl Sywmr Compnny

V.dcncia, C;rliionri&

ABSTRACT

INTRODUCTION

A great deal of emphasis is being placed on the development of accurate computational methods for the aeroelastic analysis of aircraft operating at extrcme flight conditions. This capability is especially needed for the analysis of maneuvering fighter aircraft.

Modem fighters are increasingly called upon to operate at exueme flight conditions involving high lift coefficients and high transonic Mach numbers. In order to achieve and sustain flight in this rcgime, the wing is forced to operate in a highly transonic flow whcre, inevitably, strong shock wavcs and separated flow exist. In addition, acrodynarnicists have been forced to utilize fluid dyn:miic phenomena like vortex flow, so as to enhance wing performance at these conditions. These aerodynamic design techniques often lead to localized high loads, so that only sinall portions of the wing are generating the overall lift, while the remaining portions are not heavily loaded. An accurate zieroelnstic analysis tcchnique is required to aid in identifying thcsc arcas so that the wing structure can be efficicntly designcd

In addition to the basic aermlastic analysis probicm, there is a need for this type of technology from an aerodynaniic/stnictural design standpoint. The development of composite technology lias ni:tdc the aeroelastic tailoring of lifting surfaces feasible.

W * Reseuch Engineer, Mcmber A M ** Senior Scientist, Member AIAA *** Scientist, Member AIAA

This is especially applicable to maneuvering fighter aircraft where high loads can be used to deflect the lifting surface into a shape which will be aerodynamically favorable. Thus, if loads in this flight rcgime could be accurately predicted, alternative wing deflection and twist distributions could be numerically evaluated. Ultimately the structure could be tdored to deflect to a selected, aerodynamically efficient, shape under maneuver loading.

Finally, it is becoming apparent that one of the most significant side-effects of fighters operating under maneuvering conditions is the reduction in service life of tail surfaces due to fatigue. This fatigue is caused by buffet resulting from the bursting of strake and wing vortices. Burst vortices generally produce a highly unsteady flow which ultimately fatigues tail sections, especially the vertical fins of twin-tailed fighters. This problem requires an analysis capability applicable to unsteady, viscous dominated flows.

Unfortunately, the geometric and computational complexity of coupled aerodynamiclstmctural analysis has forced engineers to rely on simplified aerodynamics to solve aeroelastic problems Programs like XTRAN3S of Reference 1 and CAP-TSD of Reference 2 utilize Transonic Small Disturbance aerodynamics to model static and dynamic aeroelastic problems. While thesc methods are somewhat effective for problems involving relatively weak shock waves and attached flow, they simply cannot be applied to problems like a maneuvering fighter, where viscous effects dominate the flow, Also, these programs are resuictcd to analysis of only simplified models of aircraft geometries. Modern fighter designs often rely on the aerodynamic interaction of the wing, fuselage and sometimes, a leading edge strake to achieve the desired aerodynamic performance. Accurate prediction of the flowfields for thesc types of vehicles requires an accurate geometic model.

Researchers have realized for quite some time that effective analysis of these types of problems requires the development and application of three-dimensional Navier-Stokes technology. This is evidenced by the comments of the authors of References 3 and 4. Until recently however, numerical algorithms, modeling methods and computer facilities capable of solving the Navier-Stokes equations for complex problems have not been available. This trend is rapidly changing due to developments like zonal grid generation methods and new supercomputer hard ware.

For the past decade, Lockheed has been heavily involved in the development and application of Navier-Stokes solvers to realistic aircraft problems. This effort began with the development of a two-dimensional program for airfoils 526 and has steadily progressed to the development of a three-dimensional program applicable to realistic aircraft configurations 7.8. Reference 9 describes an application of this program to a generic fighter geomehy operating at high incidence involving a burst vortex. The favorable comparison of these calculations with experimental laser velocimeter data demonstrates the utility of this program for complex, viscous dominated flows.

This paper describes the further application of this technology to the computation of flowfields about flexible fighter aircraft operating at extreme flight conditions. The developed method uses the Lockheed EuleriNavier-Stokes Three-Dimensional (ENS3D) aerodynamic method in conjunction with a zonal grid generation scheme and a linear structural model. The method has k e n programmed for both static and dynamic analysis, but to this point, only the static analysis option has been tested. Turbulence characteristics for the program are supplied by the Baldwin-Lomax algebraic turbulence model of Reference IO.

GRTD GENERATION METHOD

A zonal H-grid topology has k e n chosen to model complete aircraft configurations for use in the aeroelastic method. The grid generation method is closely patterned after that descrikd in Reference 11 and is capable of modeling configurations consisting of combinations of wing, fusclagc. canard, horizontal r:il. and venical tail. At the present time, the program only models vertical tails located in the plane of symmetry of the aircraft.

Thc method, known as the Complete Aircraft Mesh Program (CAMP) uses a hybrid algebraic/parabolic/elliptic grid generation scheme to generate grids in two-dimensional sections, which are subsequently stacked and algebraically sheared to develop the full three-dimensional grid. The parabolic scheme used in the program is that of Noack and Anderson of Reference 12.

Tlie zonal H-grid topology for a typical wing/fuselage grid is shown in Figure 1. Basically CAMP breaks the configuration up into a wing zone and a fuselage zone. Each of these zones is eventually subdivided into upper and lower zones. The wing zone contains a11 of the horizontal lifting surfaces. Therefore, the wing, canard and hotiwntal tail are all modeled in the wing zone. The fuselage zone contains !he fuselage and venical tail.

The details surrounding the actual generation of the grid are describcd in Referencc 11 and will not be repeated here. It should be mentioned however, that the program has been written for batch execution with a modular input fonnat so that different aircraft componcnts can be readily added or deleted. The scheme is extremely efficient, especially since the addition of thc parabolic grid generation scheme, which was not included in the original program. Gencration of a four zone, 318,000 grid point wingJfuselage grid requires only eleven seconds on a Cray X/MP-24.

AEROELASTIC METHOD

The acroclastic nicthod is centered around Lockhecd's three- dimensional EulerNavier-Stokes method, ENS3D. This program solves the three-dimensional Reynolds averaged Wavier-Stokes equations for compressible flow. The method, described in References 7 , s and 9, uses an implicit time- stepping algorithm to advance the solution. The equations are written in strong conservation form for general curvilinear coordinates. The algorithm can be run in a time accurate mode by using a fixed time step, or in a steady state mode using a

Figure I . %on;il 11-Grid '~opologiy.

spatially varying time step. All computations presented here were run using the steady state option. Turbulence characteristics are generated using the standard Baldwin-l.omax algebraic turbulence model.

The method uses one of two models to calculate the structural deflections. Both of these models result in the solution of a matix equation of the form:

[Mllq) + [Dllql + [Kllql = (Fl

whcre IM1 is a mass matrix. ID1 is a damoine matrix and IKI is

and the second time derivative of the deflection respectively {F] is a force vector of the form,

where, IF 1 is the aerodynamic force vector calculated by ENS3D and IFI) is the inertial force vector determined from tlic flight condition (i.e. "g" loeding).

All of the cases presentcd in this paper are static with no incrtial loading. Therefore, the time derivative terms and the inertial force term are identically zero and the problem reduces to:

A

Eithcr a structural influence coefficient model or a mode shape

W

W

model can he used to generate the structural deflections. For the influence coefficient model, [Kl is simply the stiffness influence coefficient matrix, while {q) is the vector of structural deflections at the influence coefficient locations. In this case (FA] is computed by lumping the calculated aerodynamic forces at thc IoCations of the stiffness influence coefficicnts.

The mode shape model on the other hand assumes a dcflcction of thc form,

- where ( w] is the vector of physical deflections, [@I is a matrix whosc columns are the deflection modes and ( q ) is a vector of multipliers for the mode shapes. For this case, the matrix [Kl is the generalized stiffness mamx given by:

where, [k] is the stiffness influence coefficient mamx and [FICl is the mamx of mode shapes interpolated at the locations of the structural influence cncfficients.

Similarly, {FA) is now the generalized force vector given by,

where, [@,IT is the transpose of the matrix of mode shapes interpolated at the aerodynamic points and I fA) is the vector of aerodynamic loads calculated by ENS3D.

The choice of the structural model is a trade-off between computer time/storage requirements versus ease of imple. mentation. Basically, while easier to implement for most cases, the influence coefficient model can require as much as an order of magnitude more points to accurately describe the stmcture as compared to the mode shape model which may only require three or four modes. This will result in a greater storage requirement and more computer tirne to solve the si~uctitral equations. However, mode shapes are not always readily available and the time and storage required for the stntctural analysis, even using the influence coefficient model, is minimal when compared to the aerodynamic analysis. It has been our experience that the influence coefficient model tends to give more reliable results and is generally worth the cxtra computer storage and execution time.

An imporrant issue which ultimately influences the accuracy of the aerodynamic solution is the method used to updatc the g i d to account for the suucturd dcflcction. The procedure developed for this method is a simple algcbraic shearing which preserves the initial quality of the grid, Figure 2 will be used to describe the grid update method. First, it is assumed that all smctural deflections are restricted to the Y-direction as defined i n the figure. Thc basic idca is to update the grid so that points ncar the aeroelastic surface move with the surface, while points near the upper and lower boundaries do not move significantly. 'lhis is accomplished by computing a normalized arc-length distribution for each grid line connecting the aeroelastic surface to the top or bottom boundary. The deflection of each grid point along R given line is computed according to the following fonnula:

,-,.

AYK=AYAE (1 - S K l S w x )

..J where, AYAE is the deflection at the aernclastic surface. SK is the arc-length along the grid line at point K and Smx is the

t -X

Figure 2. Grid Dcflcction Method

total arc-length for the grid line. Grid points ahead of and behind the aeroelastic surface are updated according to the deflection of the leading and trailing edge of the surface respectively. Points beyond the tip are handled similarly.

While this is an extremely simple method for updating the grid, it is also very effective. The procedure tends to maintain the quality of the initial grid, especially near the aeroelastic surface where resolution of the boundary layer is impon;int. The method guarantees that grid lines will not cross as long as the sulface is not deflected past the upper or lower boundary of the grid. It also ensures that if the original grid was smooth, and the deflection distribution is smooth, then the deflected grid will he smooth.

ANALYSIS RESULTS

3

Figure 3. Planform View o f Acroelasti(:ally Tailored Fighrer Wing'Body.

Figure 4. Surface Grid for the Aeroelustically Tailored Fighter WingjBdy

a V

M=0.9 I cr=9.00

10,000 ft. Alt. ?7=0.45

4 Yiti!: Aloiie Rigid I /Body 1;lexiblc

Mz0.9 cr=9.00

~t Wing Aloile Rigid 0 n Wing/Body 1;lexiblc

Experinvat (Rcl'. 13)

0

Distributions for the Aeroekistically Tailored Figlitcr.

0

0

d: 0

/r

'4

Experiinent(Ref. 13)

b .n 0.2 A -

N.

2r Figurc 6. (Continued).

M=0.9 2 I

10,000 ft. Alt.

N 3 I A + Wing Alonc Rigid

0 u Win@cdy Flexible 0 Experiment (Ref. 13)

0 I

": 0 I

a 0

x

d: 0

2 Figure 6. (Continued)

For rcicrcncc. l.igurc 7 compares the rigid wing lxdy pressures with the flrxiblc w i n g h x i y prrssures and expenmental data at the hO? sp:m station. As expected for the w3rh-out uing, the 3Jdilii)ri o1 flexibility to the 3n;ilyGs tends to rcduer the suction IctcI i m r ihc wing leading edge. and louerr thc pressure on the Iowcr urfke. Both of thcse trends are indicative of a decresjc 111 the mgle of atovk, which is what is expected for R w a h - o u t wing under these conditions

Figurc X S~IOWS a f ront vicw of a section of the deflected wingh(dy grid This figure is prcnentcd for [no reasons. First. it 5hows the cffwrivcncss of the grid update procedur.:

-

'9 M=0.9 I a=9.00 3

10,000 ft. All.

N * I 0 0 WinglBody Flexible

A t WinglBody Rigid

0 Experiment (Ref. 13)

2 I

2 TFigure 7. Comparison ofwingmody Flexible and W i n o o d y Rigid Pressures for thc Aeroelastically Tailorcd Fighter.

' ' ' ' 1 ' ' Figure 8. Front View ofDeflected Wing and Grid.

employed in the aeroelastic analysis. This grid has been deflected over a thousand times (once every time step) and there has been no visible degradation to the grid over this period. The grid is still well clustered near the wing surface and it appears to be smooth everywhere. The second reason is to illustrate the extent to which this wing has flexed. The original wing was flat, Le. no leading edge deflection and no twist. The experimental data indicates a front spar deflection of 3 inches at the wing tip and ENS3D predicts a deflection of 2.8 inches at this station. The wing semi-span for the model was approximately 22 inches and as can be seen, the deflection for this case is significant.

A comparison of the computed and experimental wing twist dismbutions is shown in Figure 9. Once again, excellent agreement with the experimental data is obtained. ENS3D predicts the wing twist within 0.1 degrees over virtually the entire wing semi-span. We found this quite remarkable since the shuctural model consisted of only four chordwise and seven spanwise stations.

5

z , M=0.9 u=9.00

10,000 ft. Alt.

. ,, , ~~~~, ~~~ , , - ~ ~ ~ ~ ~ . , '1 -~-O.l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 9 .,, Span Station w ,/,,

9 '? 0 p:'

Figure 9. Wing Twist Disuibution Complrison for the Acroclastically Tailored Fighter.

CONCLUSION

A three-dimensional Navier-Stokes solver has been coupled with a linear smctural model and a zonal grid generation scheme to provide aeroelastic analyses of aircraft operating at extreme flight conditions. The method has been tested on an aeroelastically tailored wingjbody configuration representative of modern fighter aircraft. Flow conditions for these tests are typical of those experienced by fighter aircraft operating in a 9g maneuver. The developed method compares very well with experimentally measured data both from a fluid dynamics and smctural deflection standpoint. The analyses demonstrate the effec- tiveness of the numerical solution of the Navier-Stokes equations in solving these types of problems. In addition, the importance of an accurate geometric model for effective analysis at these flight conditions is also demonstrated. Turbulence modeling has been shown to delay the prediction 0: upper surface flow separation, but this does not have a significant impact on the overall analysis results.

ACKNOWLEDGEMENT

This effort has been sponsored by AFWAL Contract F33615- 87-C-3209 "Flight Loads Prediction Methods for Fighter Aircraft." The authors would like to express their appreciation to Mr. Elijah Turner and Mr. Larry Huttsell of WRDC/FIB for their continuous suppon throughout this program. They would also like to thank Dr. John Malone of NASA Langley Research Center for his insight and ideas which aided in the development of this method.

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4.

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