[American Institute of Aeronautics and Astronautics 39th AIAA/ASME/ASCE/AHS/ASC Structures,...

Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc.

A98-25311AIAA-98-2071

APPLICATION OF THE TRANSPIRATION METHOD FOR AEROSERVOELASTICPREDICTION USING CFD

Cole H. Stephens* and Andrew S. Arena, Jr.*Oklahoma State University

School of Mechanical and Aerospace EngineeringStillwater, OK

andKajal K. Gupta*

NASA Dryden Flight Research CenterEdwards, CA

Abstract

Research presented in this paper illustrates theimplementation of the transpiration boundary conditionin steady and unsteady aeroelastic and aeroservoelasticsimulations. For two reference cases, the AGARD445.6 wing and the BACT wing with a finite-span flap,application of the transpiration method hasdemonstrated the effectiveness of applying thetranspiration boundary condition at a variety of Machnumbers on configurations of practical interest.Additionally, the effectiveness of the transpirationmethod is demonstrated by its ability to model largescale continuous and discontinuous surface deflectionswithout the computational expense of re-meshing ateach CFD time-step.

Nomenclature

CFD Computational Fluid DynamicsM Mach NumberASE AeroservoelasticityCP Pressure Coefficienta Angle of Attack (deg)5 Control Surface Deflection (deg)q Generalized Displacement<t Modal Displacement MatrixT| Generalized Displacement Vector

Introduction

In the simulation of an aircraft's aeroelasticand aeroservoelastic characteristics, it is the time-marched CFD solution that requires the overwhelmingproportion of CPU time. Dowell states that thecomputational time required is on the order of P*TF

* Graduate Research Assistant, Student MemberAIAAf Assistant Professor, Department of Mechanical andAerospace Engineering, Senior Member AIAA.J Aerospace Engineer, Member AIAA.

Copyright © 1998 by Cole H. Stephens. Published bythe American Institute of Aeronautics andAstronautics, Inc. with permission.

where P is the number of parameter combinationsrequired and TF is the time required for a simultaneousfluid-structure time-marching calculation to complete atransient.1 Even with continued improvements in flowalgorithms and processor speeds, the computationaldemands generated by complicated three-dimensionalconfigurations overwhelm the processors ability todevelop a timely solution. These demands are furtheramplified when a modification of the existingcomputational grid is necessary. An expeditious ASEsimulation is even more unrealizable when the entirecomputational grid must be modified at each CFD time-step to account for structural and/or control surfacedeflections.

An idea, first developed by Lighthill, hasproven to be an effective tool for reducing the timerequired for unsteady aerodynamic calculations2.Lighthill used a method of equivalent sources tosimulate changes in airfoil thickness. Instead ofthickening the actual airfoil, an equivalent surfacedistribution of sources is used to simulate the boundarylayer. This is done by modifying the normal velocityjust outside the boundary layer to include additionaloutflow due to the boundary layer. The technique isalso often used for boundary layer patching withinviscid flow techniques. Also more recently, thetechnique has been used to simulate surfacedeformations in full potential solution techniques, inaddition to steady and unsteady rigid-body applicationswith Euler codes3-'0.

Transpiration offers the advantage of beingfast and relatively simple to implement. If, by someother means, the change in normal is known, then thischange can be correlated to an appropriate change insurface normal on a CFD mesh and implementeddirectly on the existing grid.

An additional benefit of the transpirationmethod for boundary condition modeling is inaeroservoelastic problems. In such problems, it is oftennecessary to account for unsteady control surfacedeflections in the coupled CFD/Structural Dynamicssimulation. These types of boundary conditions areproblematic for unsteady CFD flow solvers due to the

3092American Institute of Aeronautics and Astronautics


very close proximity of control surface edges toadjacent parts of the airframe. Representing theseadjacent surfaces in many cases would require contactbetween opposing surfaces of the mesh which iscomputationally intractable.

The objective of the current study is toinvestigate the use of the transpiration boundarycondition approach when applied to steady andunsteady aeroelastic and aeroservoelastic problemsusing an Euler solver with unstructured meshes.Results for two different test cases address the extent towhich the method may be used for geometries ofpractical interest.

MethodologyComputational analysis for the study was

performed using the STARS codes developed at theNASA Dryden Flight Research Center11. STARS is anhighly integrated, finite-element based code formultidisciplinary analysis of flight vehicles includingstatic and dynamic structural analysis, computationalfluid dynamics, heat transfer, and aeroservoelasticitycapabilities. All computations are performed onmeshes consisting of unstructured tetrahedra.

In the present investigation, the transpirationboundary condition is utilized to simulate: staticdeformations, structural deformations during flutter,and control surface deflections. Structural calculationsare performed using the finite element technique withmodal superposition. Aeroelastic simulations are thenperformed through a coupling of a dynamics solverusing the modal vectors, and the Euler aerodynamicsolver. Additionally, static aeroelastic and controlsurface calculations were performed in which thesimulated body deformation was compared with resultsobtained by deforming the actual structure and re-meshing the computational domain.

The actual surface deformations for the steadyflow comparisons were accomplished by displacementof the surface tetrahedra through modal superposition14.Each surface node qoW is displaced by the superpositionof the nodal vectors each multiplied by a generalizeddisplacement:

Qnew = Qoid + Aqwhere Aq(i) is determined by

Aq = Or|where O is the modal displacement matrix and r| is thegeneralized displacement vector.

Control surface deflections are a result of amanual calculation of nodal displacements. For thetranspiration study, the uniform change in normal dueto a flap deflection is incorporated onto an existingCFD surface mesh. Constructing the actual deflectedgrid required knowledge of flap-wing intersectionpoints and a total reconstruction of the CFD geometry.

Once the surface mesh has been deflected, theentire computational domain is re-meshed and the Eulersolution is performed for comparison with thetranspiration method.

The transpiration method is, quite simply, ameans by which to trick the flow solver into seeingsome sort of deflection in the mesh that is not actuallythere. If a change in surface normal is known, from astructural dynamics solver for example, then thischange in normal could be applied directly to theexisting CFD grid through a slight modification of theexisting surface normals. The CFD solver has alreadycalculated surface normals at each CFD node based onan average of the surrounding tetrahedra. Withtranspiration, the nodes affected by a surface deflectionsimply require a modification of its existing surfacenormal. Even though the surface is not actuallydeflected, all the flow solver sees is the normal at thatparticular nodal location, it does not matter what thatnormal is.

ResultsTwo representative test cases that have

successfully implemented the transpiration boundarycondition are presented. Test cases were chosen tohighlight the effectiveness of the transpiration methodeven on relatively large surface deflections.

The first example is the AGARD wing. In thiscase, the transpiration boundary condition was used tocouple the structural deformations from the dynamicssolver to the Euler flow solver. Steady aeroelasticcalculations were accomplished through arbitrarygeneralized displacements of all mode shapes.Unsteady aeroelastic simulations were performedthrough a coupling of the dynamics solver using themodal vectors and the Euler aerodynamics solver.

The second case is the BACT wing with afinite span flap. In this case, steady aerodynamiccalculations are performed for a relatively large 10° flapdeflection at transonic Mach numbers. Comparisonsare made between solutions for the actual flapdeflection and the simulated flap deflection usingtranspiration.AGARD 445.6

The AGARD wing is a standard aeroelastictest configuration which has been investigated in theLangley Transonic Dynamics tunnel15. The wing has a45° quarter chord sweep angle, aspect ratio of 1.65 anda taper ratio of 0.66. The airfoil cross-section is aNACA 65A004. Figure 1 is a planform view of theAGARD wing and the unstructured finite element CFDmesh generated in STARS.

Characteristic structural mode shapes werecalculated using a structural dynamics routine inSTARS on a solids mesh. These mode shapes included



first bending and first torsion. The superposition ofthese mode shapes provides the basis for the aeroelasticsimulation. Application of the transpiration boundarycondition on the surface of the wing allows the whig todynamically deform at each intermediate CFD time stepwithout modification to the surface or computationaldomain.

Figure 1: AGARD Test Wing Geometry andSurface Discretization

Figure 2: Transpiration Surface Mesh

Figure 2 and Figure 3 show the transpirationsurface mesh and the corresponding deflected mesh.Transpiration was applied to the mesh in Figure 2 tosimulate the actual deflection shown in Figure 3. Thesteady finite-element Euler flow solver in STARS isused to solve for the aerodynamic pressures forcomparison of the actual and simulated structuraldeformation.

Figure 4 is an example of pressure contours onthe surface of the AGARD wing. Along the span of thewhig, sections marked A, B, and C show cut-planesalong which pressure contours are plotted.

Figure 3: Deflected Surface Mesh

Figure 4: Pressure Contours at Mach 0.99

Figure 5, Figure 6, and Figure 7 are the resultingpressure distributions at cuts through the wing atlocations indicated hi Figure 4.

A Actually Deflected

9 Transpiration

Figure 5: Pressure Distribution at Section A




• Transpiration

Figure 6: Pressure Distribution at Section B


• Transpiration

Figure 7: Pressure Distribution at Section C

Application of the transpiration method hadlittle effect on the ability to predict flutter.Experimental flutter data was obtained at the LangleyTransonic Dynamics tunnel and compared to flutterpredictions using STARS. Figure 8 is a plot of flutterspeed index vs. Mach number and illustrates STARSability to predict flutter, even to the point of capturingthe transonic dip.

•3i o**B ComputedA Experiment

M»ch Number (M)

Figure 8: AGARD Wing Flutter Prediction andComparison With Experiment

Results presented thus far highlight theeffectiveness of the transpiration method when appliedto larger scale, continuous structural deflections.Substantial difficulties arise when discontinuousstructural deformations are to be modeled withcontemporary mesh-deforming techniques. An obviousexample is the deployment of a flap on a wing. Suchdeflections disrupt the continuity of the wing surfaceand introduce surfaces that are essentially non-existentwhen the control surface is in its stowed position.Modeling these narrow gaps between control surfacesand the opposite wing surfaces introduces aconcentrated region in which the flow solution isadversely affected due to the scale of the gap in relationto the rest of the wing.

The following example investigates theefficacy of the transpiration method when applied tolocally large, discontinuous surface deflections such asthose experienced in the deflection of a control surface.BACT Wing With 10° Flap Deflection

The BACT, Benchmark Active ControlsTechnology, wing is part of the Benchmark ModelsProgram (BMP) at the NASA Langley ResearchCenter13. The BMP program includes a series ofmodels which were used to study different aeroelasticphenomena and to validate computational fluiddynamics codes.

The BACT wing has a rectangular planformwith a NACA 0012 cross-section. The wings chord andspan are 16 and 32 inches respectively. The trailingedge control surface is 25% of the chord, 30% of thetotal span of the wing, and is centered about the model60% span station. Figure 9 shows a picture of theactual BACT wing used at Langley.

Figure 9: BACT Model

The wing also included 2 spoilers, one on the upper andlower surface of the wing in locations noted in Figure 9.For the present study, only the trailing edge controlsurface was modeled, the upper and lower spoilers werenot.



Representative pressure plots were obtained atMach numbers ranging from high-subsonic (Mach0.77) and transonic (Mach 0.82) at an a of 0°. The 10°flap deflection was chosen to highlight the effectivenessof the transpiration method for large control surfacedefections.

Figure 10 shows the surface mesh generated inSTARS for the actual 10° flap deflection. Figure 11shows an end-on view to more clearly show the extentof the flap deflection.

computational grid. With transpiration, the flapdeflection can be modified at each time step withouthaving to modify the existing surface or computationaldomain. Shown in Figure 12 is an example of the typeof mesh shearing that would have to take place within amoving mesh algorithm. In cases such as the BACTwing, the element stretching that occurs with mesh-deforming techniques would produce highly stretched,ill-conditioned tetrahedra in a place that actually shouldreceive additional mesh refinement.

Figure 10: Surface Mesh for Actual 10° FlapDeflection

Figure 11: Profile of 10° Flap Deflection

The difficulty in modifying the mesh in Figure10 is apparent when one looks at the varyingintersection points along the control surface and thesurface of the wing. Any slight modification in flapdeflection angle requires that the entire geometry in thevicinity of the wing be re-calculated and re-meshed.This is, of course, time consuming.

Mesh deforming techniques are another meansby which structural deflections are modeled.Deforming the mesh in an area where the surface goesfrom a smooth-continuous surface to a discontinuoussurface leads to poor element structure. In the BACTcase, however, the severe mesh shearing that wouldoccur between the flap and the wing surfaces wouldlend itself to a poorly constructed mesh. Additionally,when a flap is deflected, there are new surfaces thatwould be exposed due to the displacement of the flap.The difficulty in modeling this sort of behavior ismagnified with the desire of implementing a controlalgorithm to control aeroservoelastic flutter.

Transpiration is the most amiable alternative tore-defining the CFD surface mesh and resulting

Figure 12: Mesh Shearing Example

With the transpiration method, all one needs todo is modify the generalized displacement by constant.Since there is no mesh modification necessary, thetransition from one flap deflection angle to another isessentially instantaneous. Figure 13 and Figure 14show the surface mesh used for the transpirationstudies. Note that Figure 14 clearly shows that thetranspiration mesh has no actual deflection.

Figure 13: Surface Mesh for Simulated FlapDeflection



Figure 14: Profile of 10° Simulated Flap

The differences between the meshes for the actual andsimulated flap deflections are kept at a minimum toeliminate any differences due to grid refinement.

Pressure contours on the surface of the wingare given in Figure 15 and Figure 16. These pressurecontours are the result of the steady Euler solution atMach 0.77, cc=0°, and 8=10°. The difficulty indifferentiating the two figures indicates the successfulapplication of the transpiration boundary condition for alarge surface deflection. Figure 15 shows the pressurecontours for the case of an actual flap deflection.Figure 16 shows the pressure contours on the mesh inFigure 13 with a simulated flap deflection.

Figure 15: Surface Contours for 10° FlapDeflection at Mach 0.77 and a=0°

Figure 16: Surface Contours for 10° SimulatedFlap Deflection at Mach 0.77 and ct=0°

A qualitative comparison between Figure 15and Figure 16 clearly shows the excellent agreementbetween the solutions. Slight differences exist but arenot entirely due to the application of the transpirationboundary condition.

Convergence rates for these two cases wereslightly different due to the difficulties associated withsolutions in the transonic regime. Solutions appeared tobe converging towards one-another , but are slightlydifferent. Results have shown that extending thesolution to exact agreement quickly reaches a point ofdiminishing returns.

Quantitative results are presented in the formof chord-wise pressure distributions at the wings 60%span. A chord-wise plane through this sectioncorresponds to the mid-span of the flap. Figure 17shows the superposition of the chord-wise pressuredistributions.

.*****-».#«••• • t . •«

f

A STARS—10" Flap Deflection

• Transpiration—10" Simulated Flap

Figure 17: Actual and Simulated Flap PressureDistributions at Mach 0.77, cc=0°, and 8=10°

Except for the slight difference in peak CP atthe beginning of the flap, the actual and simulated flapshow excellent agreement. Notice that Figure 17 doesnot clearly depict the existence of anything other than aweak transonic shock.

Figure 18: 3-D Pressure^Contours; at0° a, Mach0.82,10° Flap Deflection



Another solution run at the same flapdeflection and angle of attack, but at Mach 0.82 doeshave a very distinctive transonic shock.

Figure 18 and Figure 19 show a three-dimensional pressure distribution along the wing andthe surrounding flow-field. This particular view allowsthe visualization of the complete three dimensionalflow field and conveys a plethora of both qualitativeand quantitative data. Again, excellent agreement isnoted between the actually deflected mesh and the meshmodified through transpiration.

Figure 19: 3-D Pressure Contours at 0° a, Mach0.82,10° Simulated Flap Deflection

.1* :>*

A STARS—10° Flap Deflection

• Transpiration—10° Simululed Flap

Figure 20: Actual and Simulated Flap PressureDistributions at Mach 0.82, a=0°, and 8=10°

Figure 20 is again a superposition of chord-wise pressure distributions at the mid-span of the flap.As was experienced with the Mach 0.77 case, the mostsignificant difference was again at the beginning of theflap. Even with this large flap deflection, thetranspiration method shows to be a viable tool in theanalysis of control surface deflections for a varied range

of Mach numbers. As noted by Fisher and Arena, thereliability of the transpiration method was expected todiminish as the relative nodal displacements grew14.The BACT wing, with its relatively large flapdeflection, expands the possible operating envelope forwhich the transpiration method is applicable.

Concluding RemarksThe purpose of the current study was to

highlight the effectiveness of the transpiration methodfor aeroelastic and aeroservoelastic simulations in orderto realize significant time savings. As has been shown,the transpiration method can be a valuable tool incoupled structural dynamics and CFD solutions whererelatively large, continuous or discontinuous surfacedeformations are experienced.

The simplicity, ease of implementation, andversatility of the transpiration boundary condition makeit an attractive, time-saving alternative torediscretization or deforming mesh techniques.

Research in progress will use the transpirationmethod to simulate control surface deformations in afull unsteady aeroservoelastic simulation. Controlleddeflection of a flap during aerodynamic flutter usestranspiration for control surface deflections as a meansfor flutter suppression.

AcknowledgementsFunds for the support of this study have been

allocated through the NASA-Ames UniversityConsortium Office, under Interchange Number NCC2-5105, and Oklahoma State University.

References

1. Dowell E.H., Crawley, E.F., Curtiss, Jr., H.C.,Peters, D.A., Scanlan, R.H., and Sisto, F., "AModern Course in Aeroelasticity", 3rd edition,Klewer Academic Publishers, 1995.

2. Lighthill, M.J., "On Displacement Thickness,"Journal of Fluid Mechanics, Vol. 4, Part 4, Jan.1958, pp. 383-392.

3. Sankar, N.L., Malone, J.B., and Tassa, Y., "AnImplicit Conservative Algorithm for Steady andUnsteady Three-Dimensional Transonic PotentialFlows," AIAA Paper 81-1016, June 1981.

4. Malone, J.B., Sankar, L.N., and Sotomayer,W.A., "Unsteady Aerodynamic Modeling of aFighter Wing in Transonic Flow," AIAA Paper 84-1566, AIAA 17th Fluid Dynamics, PlasmaDynamics, and Lasers Conference, Snowmass, CO,June 25-27, 1984.



5. Malone, J.B., and Sankar, L.N., "UnsteadyFull Potential Calculations for Complex Wing-Body Configurations," AIAA Paper 85-4062.

6. Sankar, N.L., Ruo, S.Y., and Malone, J.B.,"Aplication of Surface Transpiration inComputational Aerodynamics," AIAA Paper 86-0511, AIAA 24th Aerospace Sciences Meeting,Reno, NV, January 6-9, 1986.

7. Sankar, N.L., Malone, J.B., and Schuster, D.,"Euler Solutions for Transonic Flow Past a FighterWing," Journal of Aircraft, Vol. 24, No. 1, Jan.1987, pp. 10-16.

8. Ruo, S.Y., and Sankar, N.L., "EulerCalculations for Wing-Alone Configurations,"Journal of Aircraft, Vol. 25, No. 5, May 1988, pp.436-441.

9. Bharadvaj, Bala, K., "Computation of Steadyand Unsteady Control Surface Loads in TransonicFlow," AIAA Paper 90-0935.

10. Raj, P. and Harris, B., "Using SurfaceTranspiration with an Euler Method for Cost-effective Aerodynamic Analysis," AIAA 93-3506,August, 1993.

11. Gupta, K.K., "STARS - An IntegratedGeneral-Purpose Finite Element Structural,Aeroelastic, and Aeroservoelastic AnalysisComputer Program," NASA TM-4795, May, 1997.

12. Scott, R.C., Hoadley, S.T. Wiesman, C.D. andDurham, M.H., "The Benchmark Active ControlsTechnology Model Aerodynamic Data," AIAAPaper 97-0829, 35th Aerospace Sciences Meetingand Exhibit, Reno, NV, 1997.

13. Rivera, J.A., Jr., Dansberry, B.E., Bennett,R.M., Durham, M.H., and Silva, W.A., "NACA0012 Benchmark Model Experimental FlutterResults With Unsteady Pressure Distributions.NASA TM-107581, March 1992.

14. Fisher, C.F., and Arena, Jr., A.S., "On theTranspiration Method for Efficient AeroelasticAnalysis Using an Euler Solver," AIAA 96-3436,August 1996.

15. Yates, E.G., Jr., Land, N.S., and Foughner,J.T., Jr., "Measured and Calculated Subsonic andTransonic Flutter Characteristics of a 45°Sweptback Wing Planform in Air and Freon-12 inthe Langley Transonic Dynamics Tunnel," NASATND-1616, March 1963.

16. Arena, Jr., A.S., Voelker, L.S. and Gupta,K.K., "Applications of Time-Marched FiniteElement Euler Solutions for AeroelasticPrediction," 10th International Conference on FiniteElements in Fluids, Tucson, AZ, January 5-8,1998.


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