Efficient Aeroelastic Analysis Method Including Inverse Design for Body Effects

Abstract

EROELASTICITY is the research field of studying theinteractionbetweenthestructuraldynamicsandaerodynamics.It deals with the complex coupled phenomena of aircraft in extremeflightconditionsinthedesignstageofaircraftdevelopment.Amongthe aeroelastic problems, flutter phenomenon is the most dangerousone. Furthermore, if the aircraft flies in the transonic range, theaerodynamiccomplexityresultingfromshockwaveoscillation,flowseparation, and so forth, dramatically increases. Therefore, theinvestigation of nonlinear aerodynamics based on computationalfluid dynamics (CFD) has become important in recent aeroelasticanalysis. An aeroelastic examination using an efficient unsteadyaerodynamic analysis with the transonic small-disturbance (TSD)equation, which has been widely recognized as one of the mostefficient CFD-based approaches, has especially strong computa-tional advantages in many different types of parametric studies,because TSD code does not require CFD grid regeneration but onlychangesinwingsurfaceslopeduetostructuralmotiononafixed-gridsystem [1]. Based on these advantages, full-span aircraft have beenstudied.Inanactiveway,thefuselageisusuallyrepresentedbyaboxwithin the embedded multigrid. Instead of the former method, theCFD-basedaeroelasticanalysisofacomplexfull-spanaircraftmodelhasbeenperformedbyYooetal.[2]assumingthattheaerodynamicsof a wing are not influenced by the body shape. This assumption ismeaningful from an aeroelastic point of view, because the main partof lift and flexibility is contributed by the wing. Nevertheless, thefuselage can distort the aerodynamic small-disturbance pressure onthewingsurface, and it is necessary to investigate the bodyeffect influtter analysis [3].Tocomputeapressureperturbationduetothefuselage,aninversedesign method is applied in this research. A typical inverse designmethodismainlyusedtoautomaticallyoptimizetheairfoilgeometrytothelevelofanadequatetargetpressure.Thereareseveralkindsofinverse design methods, such as the MGM (modified Garabedian–McFadden) method [4], defection correction method [5], spring-analogy traction method [6], free-form deformation method, and soon. Among them, the MGM method is simple and easy to adoptbecauseitusesonlyoneauxiliaryequationtoobtainthetargetairfoilshape.ThissimplicitycanbeeffectivefortheCFD-basedaeroelasticanalysis problems, which need a tremendous computing time. TheMGM method assumes that the pressure difference between targetandbaselineairfoilsisafunctionofsurfacedisplacementanditsfirstandsecondderivatives.TheMGMauxiliaryequationregardstherateof change in surface slope as a pseudotime term and iterates until itconverges to zero.Figure1showstheflowchartofinversedesignprocedure.Aswiththe other CFD analysis process, the grid is generated first. Next, thesteadyaerodynamicsareanalyzed.Thenthepressuredistributiononawingsurfaceiscomparedwiththetargetpressuredistribution.Iftheresidualtermisnotzero,allthestepsarerepeated.However,themainadvantage is in the loop. Unlike other CFD codes, the TSD-basedaeroelastic code does not require grid regeneration for every step. Itproceeds with information on surface slope variation.In this study, an efficient aeroelastic analysis method includingbody aerodynamics is introduced. First, TSD theory and aeroelasticequation are explained briefly. Next, the MGM inverse designmethodisusedtomodifytheaerodynamicforcetoincludethebodyeffect.Insequence,thevalidationoftheMGMmethodisgiven.Thenthewing-bodymodelisselectedasanumericalexample.Finally,themodified aeroelastic analysis follows.