Computational Aeroelasticity

7/24/2019 Computational Aeroelasticity

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JOURNAL OFAIRCRAFTVol. 40, No. 5, SeptemberOctober 2003

Computational Aeroelasticity: Success, Progress, Challenge

David M. Schuster

NASA Langley Research Center, Hampton, Virginia 23681

D. D. Liu

Arizona State University, Tempe, Arizona 85287and

Lawrence J. Huttsell

U.S. Air Force Research Laboratory, WrightPatterson Air Force Base, Ohio 45433

Introduction

N EARLY 70 years ago, Theodorsen1 published a now famous

report outlining, in detail, an analytical method by which theutter characteristics of airfoils with two or three degrees of free-dom could be theoretically calculated. This development laid thegroundwork for what has become a rich area of research in theoret-ical aeroelasticity.

Recently, the term computational aeroelasticity (CAE) has beencoined,and thetermgenerallyisusedto referto thecouplingofhigh-level computational uid dynamics (CFD) methods to structuraldynamics tools to perform aeroelasticanalysis. However, given thelargebody of researchthathas led us to this point,it is inappropriateto constrain the denition of CAE in this fashion.

Dr. David Schuster is the Technical Lead for the Theoretical Aeroelasticity Group within the Aeroelasticity

Branch (AB) a t NASA Langley Research Center (LaRC). He received his B.S. degree in aerospace engineeringfrom the University of Cincinnati, and his M.S. and Ph.D. degrees from the Georgia Institute of Technology.After a career of nearly 20 years in industry and academia, Dr. Schuster joined NASA Langley in 1997, where

he is responsible for the development and application of advanced computational aeroelasticity and unsteadyaerodynamics methods. He also provides analysis support and participates in aeroelastic testing in the LaRC

Transonic Dynamics Tunnel. Dr. Schusters previous experience includes computational methods developmentand applicationsat Lockheed Martin Aeronautical Systems and the Georgia Tech Research Institute. His researchhas included analysisof high-lift systems, the NationalAerospace Plane, HighSpeed Civil Transport, Abrupt Wing

Stall, X-43 aeroelasticity, and the a pplication of NavierStokes aeroelastic methods to the design a nd analysis ofhigh-performance and transport aircraft.

Danny D.Liu holdsa Ph.D. in aeronauticsand astronautics from theUniversity of Southampton,U.K., an M.S.in

aerospace engineering from Georgia Institute of Technology, and a B.S. in mechanical engineering from National

Taiwan University. Dr. Liu has been a Professor at Arizona State University in the Mechanical and Aerospace

Engineering Department since 1982. He is a lso the founder and the president o f ZONA Technology, Inc. Dr. Liu

is an author/co-author of over 90 technical papers and reports, mostly in unsteady aerodynamics, aeroelasticity,

and structural dynamics of ight vehicles. He is a Fellow of AIAA.

Lawrence Huttsell is the Aeroelasticity Team Leader in the Design and Analysis Methods Branch, StructuresDivision, Air Vehicles Directorate, Air Force Research Laboratory at WrightPatterson AFB, Ohio. He received aB.S.in mechanical engineering from theUniversity of Louisville in 1967 and an M.S.in aeronautical and astronau-

tical engineering from the Ohio State University in 1972.He has considerable experience in unsteady aerodynamic,aeroelasticity, and aeroservoelasticity. He has led several national and international programs: unsteady pressuremeasurementp rograms with the Netherlands, activeutter suppression wind tunnel tests (Germany,France, Eng-

land, & Israel) and a USAF/German ight test demonstration, and a joint AF/NASA NASP government workpackage for panel utter. He has served on Executive Independent Review Teams and consulted on system prob-lems in the area of unsteady aerodynamics,aeroelasticity, buffet, and aeroservoelasticity.He is currently leadingan

in-houseteam forcomputationalaeroelasticity.He has over70 publications,eight of which arein archival journals.

He is an Associate Fellow of AIAA.

Presented as Paper 2003-1725 at the AIAA Dynamics Specialists Conference, Norfolk, VA, 07 April 2003; received 16 April 2003; revision received 12 May2003; accepted for publication 13 May 2003. This material is declared a work of the U.S. Government and is not subject to copyright protection in the UnitedStates. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright ClearanceCenter, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/03 $ 10.00 in correspondence with the CCC.

This article asserts a much broader denition of the term, one inwhichCAE encompassesalllevelsof aeroelasticanalysis.Aeroelas-tic tools based on both linear unsteadyaerodynamicsand nonlinearCFD methods have been developed and successfully applied. Werefer to both of these methodologies as components of CAE. Like-wisestructuralmodelingas simple as beamtheory to state-of-the-artnite element modeling (FEM) have been incorporated into aeroe-lastic tools, and these techniquesshould also be included under theCAE heading.

It is not the intention of this article to provide an exhaustivehistory of the development and application of CAE over the past70 years. Rather, the subject will be examined in the context oftwo primary themes: 1) aeroelastic problems requiring theoretical

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844 SCHUSTER, LIU, AND HUTTSELL

investigation and 2) strategies and techniques attacking theseproblems.

The discussionwill be brokeninto threedistinctcategories.Prob-lems that are relatively well understood and associated CAE toolsthat are viewed as mature and accepted for these types of problemswill be discussed as the successes of CAE. Emerging, less under-stoodaeroelasticproblemswhere CAE has beenappliedon a limitedbasis, or a one-of-a-kind application of CAE, will be examined asprogress in CAE. Finally, problems which continueto contest CAE

methodology and roadblocks to the future development and appli-cation of CAE will be discussed as the challenges to CAE.

This categorizationprovides a reasonableroadmap for the futuredevelopment of CAE. The successes provide us with a template forfuture development. They represent the tools that the user commu-nity is willing to employ on a day-to-day basis, and the problemsthat are important to the developmentof currentaerospace vehicles.The progresscategorizationillustratesthe typesof problemsthat arebeginning to limit the development and/or performance of vehiclesand analysis techniquesthat can be developedby stretchingthe cur-rent technology. The challenge categorization provides a target orfocus for future development.Even with todays advancedmethod-ologiesand computationalcapability,there are problemsthat cannotbe accurately or efciently modeled using current techniques, par-

ticularly in the area of nonlinear unsteady aerodynamics.Each of these areas will be discussedin detailwith specic exam-

ples illustratingthe various assertions.Finally, our viewof the grandchallenge to the future development of CAE methodology will beoutlined and discussed.

Successes in CAE

Despite the complexity of coupling three distinct engineeringdisciplines, aerodynamics, structures, and dynamics into a uniedaeroelasticanalysis capability, computationalaeroelasticityhas en-

joyed a signicant number of su ccesses over its course of develop-ment.Today, every crewed vehicle that ies through our atmosphereundergoes some level of aeroelasticanalysisbefore ight. Virtuallyevery major uncrewed ight vehicle is similarly analyzed.

Flutter is a catastrophic aeroelastic phenomenon that must beavoided at all costs, and all ight vehicles must be clear of ut-ter and many other aeroelastic phenomena in their ight envelope.Flight and wind-tunnel testing are two ways to clear a vehicle forutter, but both are expensive and occur late in the design process.Therefore, engineers rely heavily on computational methods to as-sess the aeroelastic characteristics of ight vehicles. The successesof CAE are rooted in this aeroelastic characterizationproc ess.

Problem Formulation

When examining the subject of CAE, one cannot overlook thesimple eleganceof theformulationof theproblem.The developmentof the generalized aeroelastic equations of motion is enabling for

most modern CAE tools and should be viewed as one of the truesuccesses in CAE. The generalizedaeroelasticequationsof motionare given by

[M]f Rq.t/g C[D]f Pq.t/g C[ K]fq.t/g D f F.t/g (1)

fw.x;y;z; t/g D

NmodesX

i D1

qi .t/fi.x;y;z/g (2)

wherefw.x;y;z; t/gis the structural displacement at any positionand time on the vehicle and fq.t/gis the so-called generalized dis-placement vector, both of which are simply geometric propertiesdescribingthe time history of the aeroelasticdeformation.[M], [D],and [K] are the generalized mass, damping, and stiffness matrices,respectively, and i represents the normal modes of the structure.These terms result purely from the structural and mass propertiesof the vehicle. Thef F.t/gterm is the generalized force vector andrepresents the coupling of the unsteady aerodynamics and inertialloads with the structural dynamics. Thus, the coupled aeroelasticequations of motion comprise distinct terms that can be related to

the structures, aerodynamics,and dynamics disciplines that are re-quired to formulate the problem. This allows great exibility in thechoice of methods that can be used to model a given system. Forinstance, for linear structural models, the generalized mass, damp-ing, and stiffness matrices are constants that do not vary with timeor the structural deformation. This remains true independent of theaerodynamics chosen for representation of the generalized force.Thus, the structural and aerodynamic models under this formula-tion remain completelyindependentof each other. Varyinglevelsof

delity, sometimes termed variable delity modeling, of structuraland aerodynamic modeling can be readily matched to the prob-lem under analysis without changingthe overall formulationof theequations of motion.

This mix and match characteristic is exploited quite regularlythroughthe choice of the unsteady aerodynamicsimulation used toconstruct the generalized force term. This term has been modeledusing aerodynamics methods that range from linear doublet latticeandkernelfunctionsolutionsin the frequencydomainto solutionofthe three -dimensional unsteady Reynolds averaged NavierStokes(RANS) equations in the time domain. When both the structuresand aerodynamics are linear, solution of the generalized aeroelas-tic equations of motion reduces to computation of the complexeigenvalues of the stability matrix, whose values determine the

stability of the system. Computations involving nonlinear aerody-namics and/or structures are typically performed in the time do-main, which tend to complicate the process of determining systemstability, but nevertheless stem from the same formulation of theproblem.

This unique formulation of the equations of motion also facili-tatesthe systematicevaluationof an aeroelasticsystem. Virtually allaeroelastic analyses begin with an analysis of the system stabilitythat involves the use of linear structural and aerodynamic mod-els. As critical points in the aircraft design and/or ight envelopeare identied, the analysis can be, and regularly is, rened throughincorporation of higher delity structural or aerodynamic models,as appropriate. This approach to the analysis provides the design-ers with an improved condence that the design will be free from

aeroelastic anomalies throughout the ight envelope. In addition,the approach provides designers with important data regarding thesensitivity of the design to nonlinear effects.

Subsonic/Supersonic Aeroelastic Analysisof General Aircraft Congurations

Linear subsonic and supersonic aeroelastic analysis of generalaircraft congurationshas matured over the last 20 years,and thesetypes of computationsare performedroutinelytoday. Tools are nowcommercially available that allow aeroelastic modeling and analy-sis to be performeddirectly from existingstructuralFEM. Trimmedstatic aeroelasticity, utter, divergence, gust response, and aeroser-voelastic response are among the simulations that can be readilycomputed using these tools.

Linear analysestypicallyinvolvemodelingcomplexsystemswitheithersimplied geometricor physical properties.In the case of lin-ear aeroelastic analysis, the physics of the problem are modeled ata lower delity so that the problem can be linearized. Geometricapproximations are usually introduced into the aeroelastic modelsas well, but, in general, these methods are capable of modeling rel-atively complete, geometrically complex congurations. The ma-

jority of modern linear aeroela stic methods are highly developedtools that provide the user with a broad range of functionality andanalysisoptions.The methods arecomputationallyefcient,makingthem expedient as rapid analysis and multidisciplinary design andoptimization (MDO) tools. They also have the desirable propertythat classical problems with exact solutions can usually be easilymodeled, signicantly simplifying the verication tasks for newlydeveloped methods.

Two types of linear aeroelastic analysis will be highlighted here.The rst describes examples of linear utter analysis using thesetechniques. The second discusses linear aeroservoelastic and gustresponse simulations.


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Fig. 1 X-43A utter analysis.

Linear Flut ter Analysis

An example utter analysis of the X-43A research and launch

vehicle is shown in Fig. 1. In this case the complete X-43A hy-personic research and launch vehicles were modeled structurallyusing FEM techniques. The model for this portion of the analy-sis is shown in the upper-left portion of Fig. 1. A normal modesstructural dynamics analysis was performed to obtain rigid-bodyand structurally exible mode shapes and frequencies as shown inthe lower-left portion of Fig. 1. The model for the unsteady aero-dynamics portion of the analysis is shown in the upper-right cor-ner. For this analysis, doublet lattice2 aerodynamics was used inthe subsonic ight regime, whereas the ZONA51 (Ref. 3) linearunsteady aerodynamics methodology was used in the supersonicregime.

Mode shapes from the structural dynamics analysis are interpo-latedontothe aerodynamicsgrid usinga surfacespliningtechnique.4

This allows the generalized aerodynamic force term of Eq. (1) tobe computed directly from the unsteady aerodynamic analysis. Fi-nally, the resulting utter analysis obtained at a xed Mach numberis shown in the lower-rightcorner. Figure 1 outlinesthe generalpro-cedure used for most of todays linear utter and aeroelastic anal-yses. There are a number of proprietary and off-the-shelf packagesavailableto perform this type of analysis, and the choice of methodis primarily one of user preference. Thus, linear utter analysis issubstantially viewed as a mature science.

Linear Aeroservoelastic and Gust Response Analysis

Aeroservoelastic(ASE) and gust response analyses are also per-formed on a relativelyregularbasis using linearaeroelasticanalysismethods. For these applications, external forcing terms are addedto the generalizedforce term of Eq. (1), a term describing the gen-eralized force due to control deection and a term describing thegeneralized force due to a gust. The equations are typically solvedin state-spaceform andare constructedfrom separatemodels of theaeroelastic system, the vehicle dynamics sensors, the control actu-ators, the control system, and the gust spectrum. The generalizedforce terms are expressedas rational functions of Laplace variablesinthe sdomain.This is done,for example,usingthe classicalRogersapproximation5 or the minimum-state method of Karpel,6 which isapplied presently.

Two ASE examples are presented. The rst demonstrates uttersuppression on an F-16-like wing, and the second investigates gustresponse reduction for a modied F/A-18 aircraft.7 A modied ver-sion of the Automated StructuralOptimizationSystem8 (ASTROS)is used as an ASE analysis tool for both examples. The method,ASTROS*,9 seamlessly interfaces with the ZAERO l inear aerody-namic and ASE modules.

Figure 2 shows the structural, aerodynamic,and controls modelsfor the utter suppressionanalysis of this wing. The control systemfor this utter suppression system consists of seven piezoelectric

a) FEM

b) Aerodynamic model

c) Control actuators

Fig. 2 Finite element, aerodynamic,and control actuatormodels of anF-16-like wing (Ref. 7).

Fig. 3 Open- and closed-loop eigenvalues of the system at design air-speed, Mach = 0.9 (Ref. 7): M, mode 1 (open); , mode 2 (open); s,

mode 3 (open); O, mode 4 (open); s, others (open); N, mode 1 (closed);, mode2 (closed);, mode3 (closed);H, mode 4 (closed); and , others(closed).

(PZT) actuators,as shown in Fig. 2. An active control systemusingthe PZT actuators was designed to increase the open-loop utterspeed by approximately 12%.

Bothopen- and closed-looputter analyseswere performedusingthe ASTROS* methodology and results are summarized in Fig. 3.At the design condition, the rst and second modes of the open-loop system are unstable,as shown by the open square and triangleresiding in the right-half plane in Fig. 3. Under the closed-loopcontrol, these two modes move to the left-half plane as designatedby the solid symbols, thus, stabilizing the system.

Figure 4 shows the modal displacement time histories for theopen- and closed-loop systems after a perturbation of the system.


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a) Open-loop system

b) Closed-loop system

Fig. 4 Modal time histories for the open- and closed-loop utter sup-

pression system (Ref. 7).

The open-loopsystem is clearly divergent, whereas the closed-loopsystem rapidly converges to a stable state.

Figure 5 shows the FEM and aerodynamic models of a mod-ied F/A-18 aircraft10 that is used to design and analyze a gustresponse reduction system. This model has four control surfaces:inboard/outboard leading-edgeaps, trailing-edgeap, and aileron.Thesecontrol surfacesare actuatedto reduce the structuralresponseof the aircraft to an atmospheric gust.

The ASTROS* open-looputteranalysisresultsin a utterdrivenby the wings torsion mode at an airspeed of 636 ft/s. The gustresponse reduction active control system is tailored at the designairspeed of 500 ft/s, which is 78% of the open-loop utter speed.Figure 6 shows the rms values of the second structural mode, thetorsion mode, due to a gust over a range of airspeeds. For compari-son, the rms values of both open-loop and closed-loop systems areshown. The rms values of the closed-loop system are substantiallyreduced throughout the airspeeds of interest.

Both of theseexamplesdemonstratethat relatively complex ASEsystems can be analyzed using state-of-the-art linear aeroelasticmethodologies. Advanced control systems can be analyzed withand without aeroelastic effects to determine the sensitivity of thedesign to aeroelasticity. Gust response of aeroelstic systems can beassessed using these methods, and control systems to reduce thisresponse can be readily evaluated. Flutter suppression control sys-tems can be investigated, and any number of ASE phenomena canbe analyzed using these techniques.

The methodology behind these analyses is among the most re-markable of the CAE success stories.

a) FEM

b) Aerodynamic model

Fig. 5 F/A-18 FEM and aerodynamic models for gust load alleviationanalyses (Ref. 7).

Fig. 6 Modal response rms values due to a gust vs airspeed (Ref. 7).

Transonic Wing Flutter

In the transonic speedrange, aeroelasticanalysis becomes signif-icantly more complicated. Under theseconditions,shockwaves canform and disappear as the aircraft undergoes unsteady, structurallyexible motion. In addition, regions of separated ow can appearand disappear as these shock waves strengthen and weaken. Theseare highly nonlinear events that can have a profound impact on theaeroelasticbehavior of ight vehicles.With utterused as an exam-ple phenomenon,the impact of transonicunsteadyaerodynamicsonaeroelasticstability will be discussed.

The appearanceof shock waveson the vehicle cancausea furtherdrop in the utter boundary in the transonic speed regime over that


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Fig. 7 Idealized utter boundary and CAE predictions.

produced by linear compressible ow effects. This drop is termedthe transonic dip. The important feature of the transonic dip is thebottom of the dip, which denes the minimum velocity at whichuttercan occuracrossthe ight envelopeof the vehicle.Therefore,predicting the bottom of this dip is often crucialto the designof thevehicle.

Figure 7 presents an idealized utter boundary through the tran-sonic speed regime along with illustrations of typical computedresults using various CAE methods.The solid line depictsthe mea-sured utter boundary, and an expected result from a utter analysisusing linear unsteady aerodynamics is shown as the long-dashedline. As can be seen, the linear analysis typically predicts the ut-ter boundary adequately at subsonic and supersonic speeds, but isunconservativein the transonicspeed regime, where it typicallypre-dicts a higher utter dynamic pressure, and consequently velocity,than experiment. The utter boundary predicted by a nonlinear, in-viscidunsteadyaerodynamicsanalysisis depictedby the dottedline.This analysis could be obtained by solving the unsteady transonicsmall disturbance potential ow, full potential ow, or Euler aero-dynamic equations of motion. All of these methodologies have thecapabilityof predictingshockwavesin theow, frequentlyresultingin a drop in the utterboundaryin thetransonicspeed regime.How-ever, if viscouseffectsare notincludedin the analysis,the predictedboundary can often be overconservative,predicting a signicantlylower utter speed at the bottom of the transonic dip. Viscous ef-fects in the form of signicant boundary-layer thickening and/orshock-inducedow separationtend to dene the bottom of the tran-sonic dip, and it is only when these effects are added, as shown bythe short-dashedline, that an accurate predictionof transonic uttercharacteristicscan be anticipated.

The severity of the dip and its Mach number range are highlydependent on the aerodynamic characteristics of the vehicle to beanalyzed. Moderntransportsemploying supercritical wing technol-ogy can experience signicant transonic effects due to large un-steady motion of the shock wave across the wing chord. Wingswith weaker shocks or shocks whose position is not highly sen-sitive to changes in local angle of attack will not experience asdrastic transonic effects. These characteristics are directly relatedto the wing sweep, thickness, and camber distribution. Thus, theprediction of utter characteristics in the transonic speed regimecan be precarious because it is difcult, if not impossible, to pre-dict when transonic effects will have a major impact on the utterboundary.

The addition of nonlinearity and viscous effects to the unsteadyaerodynamicsanalysisis not trivial.The nonlinearityof the problemtypically forces the analyses to be performed in the time domain asopposedto the frequencydomainfor linearows. Methodsfordeter-mining the stability boundaryusing time-domain aerodynamicsarenot as simple and require a signicant amount of computation anduser interfacingto determine the boundary. The additionof viscouseffects further complicates the process by adding longer compu-tation times and more uncertainty in the form of turbulence mod-eling. Therefore, the successes in transonic utter prediction havebeenlimited primarilyto transonicwing utter. Modelingand com-

Fig. 8 AGARD 445.6 utter computations using Euler and NavierStokes unsteady aerodynamics (Ref. 11).

putational requirements for more complete conguration unsteadyviscousanalyses have limited the widespread development and ap-plication of these types of methods to anything but the simplest ofgeometries. However, the advances in the use of these methods fortransonic aeroelastic analysis of wings are remarkable.

Two examples of this type of application that illustrate the prob-lemswith predictingtransonicaeroelasticityarepresentedhere.Therst is a series of transonicwing utter computationsby Lee-Rauschand Batina11 using Euler and NavierStokes unsteady aerodynam-ics for the AGARD 445.6 wing. The CFL3DAE code12 was usedfor these computations. The planform for this wing and a sum-mary of the utteranalysisusing Euler andNavierStokes unsteadyaerodynamics is shown in Fig. 8. The AGARD 445.6 wing has aquarter-chord sweep of 45 deg, and a symmetrical airfoil with amaximum thickness of 4%. Although there is an appreciable tran-sonic dip for this wing, as tested in air, utter computations usingthe Euler equations were able to predictthe bottom of the utter dipin the transonic speed regime, and addition of viscous effects to theanalysis did not show an appreciablechange in the results. The thinairfoil prole and high wing sweep combine to minimize transoniceffects on this wing, resulting in this benign utter behavior in thetransonic range. At the low supersonic Mach numbers, however,the Euler equation analysis predicted a signicantly higher utterboundary, and addition of viscous effects through solution of theRANS equations improved the simulation considerably.

Gibbons13 demonstrateda somewhat differentresultin his analy-sisof thetransonicutter characteristicsof a businessjet wing usingthe CAP-TSD14 and CFL3DAE aeroelastic methods.


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Fig. 9 Inviscid and viscous utter calculations on a business jet wing(Ref. 13).

The wing planform and utterresults from this analysisare sum-marized in Fig. 9. In contrast to the AGARD 445.6 wing, this winghas a quarter-chords weep of approximately 27 deg, and the airfoilthickness varies from 13% at the wing root to 8.5% at the wingtip. The utter boundary shown in Fig. 9 is plotted as utter speedindex vs Mach number. Results from two inviscid analyses and aviscous analysis are compared with wind-tunnel data. For both in-viscid cases, the calculated utter boundary drops off rapidly asMach number increases into the transonic regime. The faired linein Fig. 9 represents the CFL3D Euler computations. At Mach 0.90,the Euler computationscontainedenough aerodynamicdamping toidentify the utter boundaryshown by the squaresymbol.However,at this Mach number, the inviscid CAP-TSD result indicated a freeresponse with no appreciable aerodynamic damping even for verylow dynamicpressures.Euler calculationswere performedat Mach0.92 and 0.94 and showed a similar free-response characteristic.Thus, the inviscid transonic methodologies employed on this wingpredicta utter boundarythat dips to very low, unrealisticvelocitiesat transonicspeeds.The additionof the viscous terms in the CFL3Dcomputations,with appropriate changesto the wing grid, raises thepredicted Mach 0.92 and 0.94 utter boundaries to the level indi-cated by the triangle symbols in Fig. 9. These viscous results are inmuch improved agreement with the behavior observed in the windtunnel. Similar improved agreement has been obtained with a vis-cous version of the CAP-TSD transonicsmall disturbancepotentialow code.15

Although there are data that indicate that nonlinear inviscidanal-ysis methods may be capable of predicting the transonic dip inisolated utter cases, it would certainly seem prudent to include

viscous effects in all transonic utter analyses. It appears thatnonlinear inviscid methods produce results that are conservativein the transonic speed regime, but this has not been denitivelyproven. Flutter margin is often a critical parameter in aircraftdesign, and overly conservative utter margins can often resultin unnecessary added structural weight and/or reduced vehicleperformance.

The results discussed here are enlightening from a research andphenomenological understanding standpoint and certainly demon-

stratethe high-qualityresults that can be obtained when using high-order viscous unsteady aerodynamics. However, these applicationsare for wing-alone geometriesand have limited value in vehicle de-sign application, where the interactiono f complex geometric com-ponentscan have a rst-order effect on the aeroelasticperformanceof the vehicle. Thus, although these applications are viewed as asuccess, they also highlight one of the chief roadblocks to applica-tion of higher-order unsteady aerodynamics methods to aeroelasticproblems. The human and computational resources required to ap-ply these methods to problems of highercomplexitythan individualvehicle components precludes them from being used more exten-sively in general aeroelasticanalysis.

Progress in CAE

The discussedsuccesses of CAE have led to a number of isolatedinvestigations and applications that tend to use the available CAEtechnology in innovative or novel ways, but have not yet receivedthe attention to elevate the capability to mainstream application orresearch. This section highlightsa few of these areas and discussestheir role in current and future CAE development.

In general, the applications discussed here tend to stretch theavailable technology beyond the current accepted limits of appli-cation. In doing so, they highlight the shortcomings of the currenttechnology and provide direction for future, more generalized de-velopment. In short, they represent the breeding ground for futureCAE research and development.

Nonlinear ASE Analysis

CAE methods have been applied to a number of problems in-volving aeroservo and ASE analyses. CAE methods involving lin-ear aerodynamics can be applied to some problems in this area aslong as the control surface deections are small and the geomet-rical discontinuities generated by activation of the control systemdo not generate aerodynamic nonlinearities in and of themselves.Unfortunately for most realistic control surface deections, this isnot the case, and separated ows in the vicinity of hinge lines andnear control surface edges quickly degrade the accuracy of linearaerodynamicanalyses.To combat these problems,researchershaveapplied various levels of nonlinear unsteady aerodynamic analysismethods to the prediction of unsteady airloads due to control sur-face deection. Two notable examples of this type of analysis arepresented here.

B-2 Residual Pitch Oscillation

During ight testing of the B-2 bomber, a nonlinear aeroelasticresidual pitch oscillation(RPO) was encountered after control sur-face pitch doublets were input at conditions outside the aircraftsight envelope.16 The initial vehicle response to the control sur-face doublet decayed in amplitude to a small limit-cycle RPO afterseveral pitch cycles. Video from a chase plane showed a movingshock in the condensation cloud on the upper surface of the air-craft. Further analysis of the data suggested that the RPO was aresult of the interaction of the aircraft short period and rst exiblebending mode of the aircraft with the oscillating shock. To betterunderstand this RPO, an analysis effort was undertaken in whicha viscous/inviscid interaction version of the CAP-TSD CAE code,CAP-TSDV,15 was modied to include the short period dynamicsand the active ight control system of the aircraft.Time simulationsof two conditionsresultingin RPO wereanalyzedusingCAP-TSDVwith mixed results.

Figure 10 shows the B-2 planform, with the CAP-TSDV modelsuperimposed on it. The dashed line in Fig. 10 shows the actual


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Fig. 10 CAP-TSDV model and actual B-2 planform and control

surfaces (Ref. 16).

planform and control surfaces, whereas the solid line shows theCAP-TSDV representation of these components. There are a num-ber of restrictions to the modeling capability in CAP-TSDV thatprecluded modeling the actual vehicle planform and control sur-faces. Thus, the control surface hinge lines and edges, as well asthe aircraft wing tip geometry, can only be approximated by theCAP-TSDV methodology.In this analysis,only the control surfacesactively moving during the observed RPO response were modeled,allowing the middle elevon and the outboard split drag rudders tobe omitted from the model.

The rst ve elastic modes, as well as the rigid-body pitch andplunge modes, were modeled in the CAP-TSDV analysis. A sim-plied pitch control augmentationight control system (FCS) wasalso included in the CAP-TSDV model to actively deect the con-trol surfaces during the simulation. This allowed both open- andclosed-loopsimulations to be performed and the impact of the con-trolsystem on theRPO behaviorto be assessed.Verticalaccelerationand pitch rate responsescomputed by CAP-TSDV at the ightvehi-clesensor locationswere used as feedbacksensorinputsfor theFCSmodel. In addition, some of the nonlinear actuator characteristicsofthe ight vehicle were also modeled in the CAP-TSDV analysis.

CAP-TSDV time simulations were initiated using a converged,steady-state, trimmed analysis of the aircraft at a specied ightcondition. The inboardelevon was deected using a control surfacedoublet command to perturb the vehicle, and the resulting pitchresponse was computed by CAP-TSDV.

Both open- and closed-loopsimulations were performed, and re-sults for the closed-loop, heavy weight, forward c.g. congurationare shown in Fig. 11. The closed-loop results closely match theight-testresults at these conditions.The sharp break in the closed-loop damping characteristics has been assessed to be due to theformation of shock waves on the vehicle. The predicted frequencycharacteristicsof the RPO, which are not shown here, also correlatewith the ight-test data at these conditions.

A second, lighter weight conguration that exhibited the RPOphenomenon was also analyzed. CAP-TSDV did not predict thephenomenon as accurately as for the heavy-weight case. It over-predicted the severity of the RPO as compared to ight test andalso did not capture the fact that the RPO tended to stabilize asthe Mach number was further increased. Several reasons for thispoorer performance have been postulated, including CAP-TSDVsability to predict accuratelythe streamwise and spanwise separatedow regions at these conditions,but further research is required toformulate hard conclusions.

Fig. 11 Computed and ight test B-2 RPO damping characteristics(Ref. 16).

RANS Anal ysis of Oscillating Flap and Sp oiler Congurat ions

The CAP-TSDV a nalyses of the B-2 have demonstrated the util-ity of viscous/inviscid interaction methods in computing fully cou-pled ASE problems of relativelyseverecomplexity. However, thesemethods have known limitations, particularly when attempting tosimulate moderately to severely separated and three-dimensionalseparated ows. The next step up in ow physics delity is to solvethe RANS equations, and ow around deected control surfaces isa prime candidate for applicationo f this technology.

A number of studies have been performed modeling deectedcontrolsurfaceswith higher-orderaerodynamicmethods.1723 Ref-erences 1720 represent a signicant body of work investigatingmodeling and solution techniquesfor trailing-edgecontrolsurfaces.In these studies, particular attention has been paid to the accuratemodeling of the discontinuities at the spanwise edges of controlsurfaces. The ENSAERO Euler/NavierStokes CAE method24 wasused for these studies, which were conned primarily to low aspectratio, high sweep, thin wings, and wingbody congurations. Thecorrelation with experimental data for these cases is, in general,very good, but transonic effects for these types of geometries aretypically small compared to lower sweep wings with thicker wingsections.

Schuster et al.,21 Bartels and Schuster,22 and Schuster andBartels23 performed computations on the NASA Langley ResearchCenter benchmark active controls technology (BACT) wing com-paring two different RANS methods, CFL3D version 5.0 (Ref. 25)and ENS3DAE.26 The BACT wing has a rectangular planform anda 12% thick symmetrical airfoil section. The planform and con-trol surfaces for the wing are shown in Fig. 12. The two methodswere compared with each other and against experimentally mea-sured unsteady pressures along the midchord of the aileron. Theanalyses were performed at Mach 0.77 with the aileron oscillat-ing sinusoidally at 5 Hz. Figure 12b shows the real and imaginarypressure coefcient plotted vs percent chord along the wing sec-tion. The computations were performed on identical grids with theonly differences in the calculations being in the formulation of theequations and the turbulence modeling. The ENS3DAE calcula-tions were performed using a central nite difference method andthe BaldwinLomax turbulence model, whereas the CFL3D calcu-lations were performed using an upwind nite volume method andthe SpalartAllmaras turbulence model. For the most part, the twomethods give similar results with differences in the peaks at theaileron hinge line and in the imaginary component of the pressurecoefcient. The imaginary component of the pressure is very smallcompared to the real component for this case, and differences in theimaginarycomponentplot are overexaggeratedbecause the verticalaxis scale factor is ve times that used for the real component plot.

CFL3D calculations of the wing with an oscillatingspoiler havealso been performed by Schuster et al.27 The results of these cal-culations at Mach 0.77 with a mean spoiler deection of 5 deg anda spoiler oscillation of 4.5 deg at 9.56 Hz are shown in Fig. 13.


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a) BACT planform

b) Unsteady pressure distributions

Fig. 12 BACT wingplanformand unsteadypressure distributions due

to aileron oscillation,M= 0.77, = 0.0 deg, ail= 0.0 deg, ail= 2.0 deg,andfail= 5 Hz (Ref. 22).

The computation of an oscillating spoiler geometry and quantita-tive comparison with experimental data is believed to be unique

and representsthe type of analysis that can be accuratelyperformedusing innovative modeling techniques.

Limit-Cycle Oscillation Using Viscous/InviscidInteraction Aerodynamics

Considerable progresshas beendemonstratedin the use of lower-order viscous/inviscidinteractionmethods to model separationonsetand mildly separated ows, particularlythose cases leadingto limitcycle oscillation (LCO).

The LCO phenomenon can be triggeredby several mechanisms.Nonlinearitiesin the aerodynamics,structures,or thevehiclecontrolsystem can result in the quenching of an instability, or in the caseof the B-2, in prevention of a convergent system from reaching astaticsteadystate. Aerodynamicnonlinearitiesare difcultto modeland predictdue to the complex ow interactionsinvolved.Also, thenonlinearities producing the LCO often involve a transitionin owstate, such as the appearance and disappearance of shock waves,vortices, and separated ow regions.

Coupling of transonic small disturbance (TSD) potential owmethods, such as CAP-TSD, with interactive boundary-layer

Fig. 13 Real componentof unsteadyp ressure for the BACT wing with

an oscillating upper surface spoiler,M= 0.77, = 0.0 deg, s = 5.0 deg,s = 4.5 deg, and f= 9.56 Hz (Ref. 27): , CFL3D; , experiment(upper surface); and , experiment (lower surface).

a) Amplitude decaying to LCO

b) Amplitude growing to LCOFig. 14 Computed business jet wing tip deection timehistories show-ing LCO,M= 0.89 (Ref. 28).

schemes has proven to be effective in the prediction of LCO phe-nomena triggered by separation onset and shock-inducedseparatedow. The B-2 RPO example discussed earlier is a prime exampleof the use of this type of methodology to predict complex LCOproblems.

Edwards28 has presented a second example for a business jetwing operating at transonic conditions. This case is interesting be-cause it is purely an aerodynamics/structural LCO triggered onlyby nonlinear aerodynamics. The mechanism involved in this LCOis one of shock-induced separation at conditions below the tran-sonic utter boundary. The LCO involves the excitation of the rstbending mode of the wing. Figure 14 summarizes the result of aCAP-TSDV an alysis of the business jet wing at Mach 0.89 and dy-namic pressure of 79 psf. In Fig. 14, the vertical deection of thewing tip is plotted as a function of time for two different initialdisplacements of the wing tip. Figure 14a shows that, if the wingtip is displaced to a large deection, the motion will decay to theexperimental limit-cycle amplitude. Likewise, if the tip is initiallydisplaced to a small deection, the amplitude will grow until itreaches the LCO amplitude. This behavior is an important charac-teristic of the LCO phenomenon.The CAP-TSDV analysiscapturesa transient shock-inducedseparationon the outboard portion of thewing that is responsiblef or the LCO behavior. Further experimentson this wing29 have veried this mechanism and identied a secondtransonic LCO phenomenon that involves the wings rst torsionmode.

The two LCO examples presented have demonstrated the utilityof viscous/inviscid interaction methods for these types of predic-tions. However, the current methodology requires renement andimprovement in a number of areas.


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At present, the boundary-layerformulationsincludedin the anal-yses are a simple stripimplementationof the two-dimensionalcom-pressibleintegralboundary-layerequations.The implementationofthe viscous equations is also only quasi steady. Three-dimensionaleffects can be very important if not dominant on many modern con-gurations,and the two-dimensionalimplementationof the viscousmodeling is certainly restrictive. The impact of the quasi-steadyimplementation of the equations has yet to be fully quantied.

On the inviscid side of the methodology, the TSD potential ow

formulationof the equations limits the applicationof the method toows with weak shocks and those without vortices. Higher-orderinviscid formulations, such as the Euler equations, would relievesome of these restrictions.

The coupling of the methodologies, although well posed forsteady ows, remains somewhat in question for unsteady ows.Addition of the viscous simulation using present techniques canhave a destabilizing effect, and many times viscous computationscannotbe performed,due to stabilityissues, in regionswhere similarinviscid computationscan be performed.

Each of the preceding topic areas is ripe for further investigationby the research community.

Reduced-Order Modeling for Aeroelastic Applications

Finally, one cannot ignore the recent advances and contributionsof reduced-order modeling (ROM) for aeroelastic and ASE appli-cations. ROM proposesto dene methodologyby which physicallycomplex dynamic phenomena can be characterized and modeledat a reduced computational cost. In addition, important physicalcharacteristics of the system can be extracted that often cannot beidentied using traditional simulation techniques. The methodol-ogy formulates strategies for identication of linear and nonlinearkernels for a given aeroelastic system. These kernels are generatedusing a xed number of numerical time simulations of the systemresponse due to a generic input, such as a pulse. These kernels canthen be superimposed, through convolution, to model the systemresponse to an arbitrary input. This type of methodologyespeciallybenets applicationssuchas nonlinearcontrolsystemdesign,wherethe burden of many nonlineartime simulationsof the complete sys-tem for each control input can be reduced to just a few simulationsof the complete systemfor a generic input followed by many simu-lations using the ROM.

Beran and Silva30 and Dowell and Hall31 provide excellentoverviews of the ROM techniques under development today. A re-cent application by Silva and Bartels32 has demonstrated the use ofRANS simulationmethodologyto model the transonic utter of theAGARD 445.6 wing. Hong et al.33 have also used this ROM tech-nique to simulate the unsteady aeroelastic characteristics of morecomplex and realistic congurations. In Refs. 32 and 33, the effortrequired to perform a transonic utter analysis of the wing usingtime simulation techniques is compared with the use of ROM.

The techniqueutilizedin Ref. 32 requiresthat an aeroelastictran-sientduetopulseinputsineachstructuralmodebecomputedtobuildthe ROM. In general, each of these pulse responsecomputationsareless expensive than an aeroelastic transient because the pulse re-sponses tend to return to a steady state in fewer cycles of motionthan what is required to extract frequency and damping informationfroma typical aeroelastictransient.Once thepulse responsefor eachmode has been computed,the fullycoupledaeroelasticresponsecanbe computed for any dynamic pressure by superimposing the im-pulse response characteristics through convolution. The transientscomputed using the ROM are relatively inexpensive to compute.

For highly complex problems where a large number of structuralmodes are required, the computational cost of generating modalROM responses will increase and may surpass the cost of standardsimulations. However, a primary reason for generating aeroelasticROM models is to develop insight into the nature of the compu-tational responses as contrasted with traditional linear aeroelasticanalyses. As shown in Ref. 32, the comparisonbetween CFD-basedaeroelasticanalyses and linear frequency-domainaeroelasticanaly-ses can be easily performedusing the CFD-based aeroelasticROMs.In addition, methods are being developed that will enable the gen-

eration of modal-based ROMs using a single input, as opposed toan input per mode.

Thomas et al.34;35 present a method whereby the order reductionmore directly attacks the uid solution, thus, relieving the depen-dence of the ROM on the specic modal motions of the body. Theirmethod, known as the harmonic balance technique,allows reduced-ordermodelsof theuidproblemto be developedby a superpositionof a seriesof harmonics.These reduced-orderuid modelscan thenbe coupled to structural dynamics and control simulations to per-

form aeroelastic and aeroservoelastic analyses efciently. In thiscase, the issue becomes how many harmonics to retain to obtain asufciently accurate aerodynamic analysis of the problem.

Further research and application of ROM techniques will relievemany of the issues discussed in this section, and this methodologycertainly holds signicant promise for future aeroelastic analysis.

Challenges to CAE

The preceding sections have discussed the areas where CAE hasbeen used to model problems of interest to both the aircraft devel-opment and design community as well as for aeroelastic researchapplications.However, thereare a number of areaswhere CAE tech-niquesfallwell shortof known analysisrequirements.Some of theseareas will be discussed here as the challenge to CAE.

Robust, Automated Linear Flutter Analysis for Design

As an analysis tool, linear utter methods havecertainlymaturedto the state where they are widely applied in the aerospace indus-try on a day-to-day basis. Whereas great strides have been madein coupling these methodologies with mainline structural analysistools used in the design environment, linear utter analysis still re-quires a signicant amount of user interaction to perform a givensimulation. This lack of automation of the analysis itself has pre-cludedits integrationinto the designoptimization environment andit continues to be exercised as a post-design analysis tool.

Part of this problem is due to the complexity of the utter anal-ysis itself, but a stagnation of algorithm development focused onautomating the process is probably also to blame. Output from atypicalp kutter analysis for a transport wing is shown in Fig. 15.In contrast to the wing utter analyses shown earlier, which con-sistedof 10 structuralmodes or less, this analysis contains 34 struc-tural modes, plus 6 rigid-body degrees of freedom. Figure 15 plotsmodal damping vs airspeed with negative values of damping indi-cating aeroelasticallystable motions and positive values indicatingunstable motion. The critical point is when a given mode crossesthe zero-dampingaxis,which denes the utter boundary.Figure 15is very complicated with several modes crossing the zero-dampingaxis.

To incorporate utter effectively in the design optimization pro-cess, the data of an analysis similar to that shown in Fig. 15 mustbe interrogated at each design condition to determine if a utterconstrainthas been compromised. Simply tracking the modes in thepreceding data is a formidable task, and although we have tools forthis purpose,they are not infallible.Forcomplicatedsystemsas this,

Fig. 15 Typical utter analysis results for a transport aircraft.


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it is easy to lose track of modes and inaccuratelypredict the criticalutter crossing.

It also is common for the utter mechanism to change as thestructuralproperties and evenight conditionschange. Vehiclesof-ten have multiple utter modes simultaneously active for any givenight condition. The most critical mode is the one that occurs atthe lowest airspeed becausethe vehicle will encounterit rst. How-ever relatively small changes in the vehicle structural propertiesand/or ight conditions can cause utter modes to shift dramati-

cally, making formerly benign utter modes critical. This can bevery confusing to an automated design process because vastly dif-ferentstructuralpropertiesmay be importantto the individualuttermodes.

Further complicating the issue is that some utter crossings arevery shallow, as shown by the mode labeled E in Fig. 15. Theseshallow crossings can be physical utter modes as is the case in so-called hump uttermodes, or they can be an artice of thestructuralmodeling. One common cause for these types of crossings is thepresence of in-plane modes. For a lifting surface such as a wing,this would be a mode with deection that is primarily in the planeof the wing, as opposed to one with deection normal to the wingplane. Linear utter analyses cannot accurately account for thesetypes of motions,and the simulationcan predict nonphysicalutter

mechanisms. When this occurs, these in-plane modes are usuallyexcluded from the utter analysis to avoid the confusioncaused bytheir presence. Aeroelasticiansa lso often perform modal reductionto exclude modes that are not important to the utter analysis and,thus, provide a clearer picture of the utter characteristics of thevehicle. These types of operations are difcult to automate for usein a design environment.

Finally, the simple mathematics of the linear utter problem cangenerate spurious roots to the equations that can ag false-positiveresults. These spurious roots are due to poor conditioning of thematrices as the problems become more complex and more modesare retained in the utter analysis. Edwards and Wieseman36 dis-cuss many of these issues when describing the development of theGeneralized Aeroelastic Analysis Method (GAAM). Automatically

detecting and eliminating these roots from consideration is a mustfor incorporationof linear utter methods in the automated designprocess.

In short, linear utter an alyses require a higher level of automa-tion and further improvements in robust operation before they canbe realistically incorporatedin an MDO environment. The compu-tational requirements of these methods are well suited to todayscomputer resources, and efciency is not a major issue prevent-ing this assimilation. At present, the entire utter analysis processrequires too much user intervention and control to be effectivelyincorporatedin the design environment.

Efcient Nonlinear Unsteady Aerodynamic Analysis

A signicant deterrent to the widespread use of high-level CFDmethods in aeroelastic and ASE analysis is the computational ef-ciency of the methods. Signicant effort has been devoted to thedevelopment and application of steady CFD, and this attention tothe efciency issues haspaid off with the routine useof steady CFD,throughoutthe industry,as a mainstreamaerodynamicanalysistech-nique. Unfortunately, unsteady aerodynamicanalysis has tended tobe neglected during this development period, and we are only nowbeginning to seriouslyassess the ability of many of the steady CFDcodes to handle unsteady problems effectively.

In retrospect, some of the techniques used to improve the ef-ciencyof steadyCFD methods may not be amenable to the analysisof unsteady ows. For instance, it has long been known that thelow-frequency transients in a CFD simulation are a primary con-tributor to slow convergence rates. Signicant efforts have beenfocused on rapidly eliminating these low-frequency transients toimprove convergence to a steady state. However, many aeroelasticand ASE problems involve relatively low-frequency phenomenon,and the techniques used to develop some of todays fastest steadyCFD codesmay make them inappropriatefor unsteady analyses dueto their low-frequency damping characteristics.

A second example illustratingthis point is the widespread use ofdomain decompositionto perform parallel computationsfor steadyCFD analyses. When the computational grid is broken into manysubdomains, or blocks, CFD computations about complex cong-urations involving millions of grid points can be effectively spreadacross many computer processors. However, extending this tech-nique to unsteady ows results in the introduction of time lags inthe unsteady analysis alongeach of the arbitrary subdomain bound-aries.These lags forcethe userto usesubiterationsas the problem is

brokeninto smaller blocksand spreadacross more processors.Thishas a profound impact on efciency because the addition of just asingle subiteration at best doubles the computer time required tosolve the problem. Solution of the unsteady ow problem becomesdependent on the number of subdomains and the manner in whichthe global domain is subdivided.

New parallel processing algorithms for unsteady ows must beinvestigatedto remove the dependence of the problem on the num-ber of processors used to solve the equations. In other words, thesolutions obtained for any given unsteady ow analysis should beidentical for any number of processors used to solve the equations.This requires that implicit boundaryconditionsbe employedat sub-domainboundarieswhen using domain decomposition,or new par-allelstrategies that operate at the numericalalgorithm level must be

developed.Another limiting factor is the size of time step that can be taken

by a given CFD code to perform an unsteady computation. Manytechniques, including implicit formulations, are limited to smalltime steps to maintain stability. One method that has become pop-ular among CFD developers is the incorporation of subiteration tohelp converge the nonlinear aerodynamic solution between timesteps. Pulliam37 recommends this approach to improve the accu-racy of diagonal implicit methods, and Jameson,38 Melson et al.,39

and Rumsey et al.40 describe methods incorporating a dual time-stepping technique and multigrid for both accuracy and efciencyimprovement of traditionalfactored schemes.

One must be careful, however, when assessing these methods forefciency because each subiteration within a time step is as costly

or more costly thana single time step by conventionaltime-steppingalgorithms. This issue is highlighted by Bartels and Schuster22 us-ing the earlier discussed oscillatingaileron case as an example. Theresults of their experience are shown in Table 1, which shows thatthe CFL3D aeroelastic method using subiterationcould take a timestep over 25 times larger than the ENS3DAE method without subit-eration. However, the CFL3D calculation required 6 subiterationsper time step, and the net gain in computational work was reducedto a factor of 4.3 over the ENS3DAE solution. Comparing this netgain in efciency to the potentialloss in accuracyfor takinga signif-icantly larger time step, one can quickly see that there is a complextradeoffbetweenaccuracyandefciencythatmustbeweighedwhenemploying subiteration.

Currently, unsteadycomputationscanbe an orderof magnitudeor

more costly than a steady ow analysis. This cost has constrainedmost unsteady ow applications, beyond simple research demon-strations,to be performedusing structuredgrid formulations,whichare inherentlymore computationallyefcientthan unstructuredgridmethods. This restriction has a direct impact on the amount of hu-man resources required to simulate a given problem, particularlyfor complex congurations,and ultimatelylimits the acceptanceofthe methodology by potential users outside the CFD community.Both of these issues are discussed in subsequent sections. In short,

Table 1 Impact of subiteration on efciency of BACToscillating aileron calculation.22

BACT oscillatingaileron analysis ENS3DAE CFL3D

Time steps per cycle 3300 128Subiterations 1 6Computational work per cycle 3300 768CPU time per cycle, (Min) 175 35


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there is signicant margin for further development of efcient andaccurate methods for the computation of unsteady nonlinear ows.As steady method developmentcontinuesto mature, it is hoped thatthe resourcesand effort devoted to steady methods will be directedtoward the developmentof new unsteadyalgorithms and strategies.

Robust Moving Grid Methodology

A key issue that separates the application of Euler and RANSaeroelasticmethodsfrom linearand even TSD potentialow aeroe-lastic schemes is the requirement of the former methods to physi-cally move and deform the model and its surrounding grid. Linearmethods eliminate the physical deformationof the vehicle from theproblemby assuming small perturbation boundary conditions.TSDunsteady aerodynamics methods make a similar assumption. How-ever, most Euler and RANS formulations employ the full surfaceboundarycondition in their formulation, and the physical motion ofthe boundaries, as well as the grid surroundingthe vehicle, is cap-tured directly in the equations of motion. This is the most accurateapproach to simulating the unsteady aerodynamics of the vehicle,but it introduces a major complication to the analysis. Efcientlymoving what can amount to millions of grid points thousands oftimes during an aeroelastic calculation is a daunting task in and ofitself. The fact that the grids must also be moved in such a fashionas to not degrade grid quality or introducecrossed grids or negativecell volumes adds further complication.

A signicant body of research has been performed in the areaof grid motion schemes for aeroelastic analysis. These range fromsimple algebraic shearing methods to those that model the vehicleand the surrounding grid as a physical eld equation that can becoupled with the analysis. Schuster et al.26 introduce a simple one-dimensional algebraic shearing technique that is very efcient andis suitable for structured grid topologies. This method is effectivefor many geometries of interest, particularly planar lifting surfaceand some controlsurface deection21 applications.However, as ge-ometric and/or grid topology complexity increases, these simplemethods begin to break down. Several researchers have extendedthe algebraic grid deformation approach to the use of transniteinterpolation (TFI) of the structural deformations,4143 which en-able applicationto more complex block, structuredgrid topologies.Batina44;45 introduceda deformingmesh algorithmbasedon a springanalogy that was originally developed for triangular and tetrahedralunstructuredgrid applicationsand was later extended to hexahedralcells for structured grid applications by Robinson et al.46 Both theTFI approach and the basic spring analogy suffer from the similarcharacterthat grid skew can be exaggeratedas the gridis deformed,and in extreme cases, grid crossing can occur. To combat this prob-lem, Farhat et al.47 recommend the use of vertex-placed torsionalsprings to control the angle between grid element edges. Bartels48

further addresses these issues by imposing more strict orthogo-nality rules on the grid deformation in the vicinity of the vehiclesurface.

Each of the described methods requires some knowledge of thegrid topologyand/or connectivitybetween grid points. Recent griddeformation research appears to be moving toward the removal ofthis restriction.Chen and Hill49 describea techniquethat modelsthevolume surrounding the vehicle with an elastic homogenous solid.In this case, each grid point surrounding the vehicle is associatedwith a specic locationin the solid,while the vehicle surface lies onthe boundary of the solid. As the vehicle deforms, the elastic equa-tions of motion are solved using a boundary element method. Eachpoint in the grid moves accordingto the elastic deformation of thesolid; therefore, no informationconcerningthe structure,topology,or connectivity of the grid is required to dene the grid deforma-tion. Melville50 describes a similar procedure that uses a distancerelationshipbetween the individualgrid points and the vehicle sur-face to determine the grid deformation, again without knowledgeof the grid topology or grid point connectivity. He has used thistechnique to perform an aeroelastic simulation of a complete F-16conguration. The grid system and one of the structural modes as-sociated with the analysisare shown in Fig. 16. As can be seen, thegeometry, the associatedstructured,multiblock grid, and the struc-

a) Complex multiblock grid system

b) Complex structural deformation

Fig. 16 Grid and structural deformation associated with the aeroelas-tic analysis of an F-16 aircraft (Ref. 50).

tural deformation for this analysis are all very complex. The factthat an aeroelastic simulation can be performed on a model of thiscomplexity is a testament to the grid motion scheme employed inthe analysis.

Although signicant progress has been realized in the develop-ment of grid deformation schemes, no single technique has beenidentied as having signicant benets over the others. It appears

the preprocessing approaches to the problem are gaining favor be-causetheyallow theuserto assessthesuitabilityofthe grid,aheadoftime,for worst-casedeformations.However, thereis still signicantopportunity to make advances in this area of research.

Complex Conguration Aeroelasticity

Many linear and nonlinear aeroelastic phenomena are the re-sult of subtle structural and aerodynamic interactions between air-craft components. Engine/nacelle/pylon, wing s tore/pylon, strakes,chines, vortex generators, and fences are among the long listof components that can have a dramatic impact on both thesteady and unsteady character of the vehicle aerodynamics andstructural dynamics. It is often imperative to model these de-tails accurately and efciently when performing some aeroelasticanalyses.

The importance of geometric details to the aerodynamic andaeroelastic performance of air vehicles is shown in Fig. 17. Shetaand Huttsell51 have numerically investigated the buffeting of theF/A-18 vertical tails due to the leading-edge extension (LEX)vortices. The effects of adding LEX fences to the aircraft are


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a) LEX fences off

b) LEX fences on

Fig. 17 Effect of LEX fences on the vortex ow patterns on an F/A-18aircraft.

clearly observed in Fig. 17. In this 35-deg angle-of-attack calcu-lation, the LEX vortex pattern is signicantly altered through ad-dition of the fences. This pattern has a direct impact on the dy-namic loads experienced on the vertical tails of this aircraft. Thus,this relatively small geometric detail has a major impact on theaeroelastic performance of the F/A-18 and other twin-vertical-tailghters.

A second example is the LCO experienced on the F-16.52 Thisnonlinear aeroelastic phenomenon manifests itself only for certainunderwing store congurations and ight conditions. It was notdiscovered before ight testing of the aircraft. To date, this phe-nomenon continues to be the subject of signicant debate through-out the aeroelastic community, and potential causes ranging fromcomplex, unsteady transonic ow interactions to structural nonlin-earities have been offered as the root cause for the LCO. Unfor-tunately we do not possess high-order aeroelastic tools capable ofaccurately simulating the unsteady transonic ow about the highlycomplex store geometries of the F-16 to help answer some of thesequestions.

As these types of detailsare added to thesimulation,the issuesofthe preceding two sections become enabling to the aeroelasticanal-ysis, particularly for high-order methods. However, just the model-ing requirementsassociated with these conguration details can besignicant even for steady ow problems. For this reason, the useof unstructured grids has become popular for many steady compu-tational aerodynamicssimulations on complex congurations. Thecomputationalresourcesrequiredto performunstructuredgrid com-putations are generally higher than those required for structuredgrid, but the time and human resources required to model complexcongurations using unstructured grids is much smaller than forstructured grids.

Unfortunately, the extension of unstructured grid technology tounsteady ows has not been thoroughly investigated, and furtherresearch in this area is required. Batina53 and Rausch and Batina54

haveappliedan unstructuredgrid Euler analysismethod to aeroelas-ticproblemson complex congurations,and this work is most notedfor the developmentof the spring analogyfor grid deformationandtheirinvestigationsintoadaptivegrid techniquesfor unsteadyows.Farhat et al.55 use a similar method to perform aeroelastic analysison an F-16 conguration.Viscous computations using unstructuredgrids are becoming more commonplacefor steady ows, but unfor-tunately their extension to unsteady ows and aeroelastic problemshas not yet been realized.

Nonexpert User Environment

Perhaps the most daunting challenge faced by developers of fu-ture aeroelastic analysis and design methods is the formulation oftools that can be employed by engineerswho are not experts in theindividual disciplines that form the methods. Aeroelasticity has asignicant impact on the performance of modern air vehicles, andincorporatingaeroelasticconsiderationsearly in the design processcan help developers avoid design surprises in the latter stages ofthe aircraft development, where xes to the problem can be verycostly both nancially and to vehicle performance. If these meth-ods are integrated into the preliminary design process, engineersthat are experts in elds other than CFD, nite element struc-tural modeling, ight controls,or even aeroelasticitywill use them.

This will require that the methods be signicantly more robust andautomated than current methods, particularly for the higher-orderformulations.

The developers of higher-order methods must aggressively ad-dress this situation if these tools are to be used in a fashion evensimilar to present linear methods. Aeroelastic analysis of ight ve-hicles is not optional, and organizations will take the path of leastresistanceto meet their aeroelasticanalysisneeds. At present, high-order aeroelastic methods require a signicant investment in time,human, and computer resources. Until these investments are re-duced, high-order aeroelastic methods will continue to be viewedas optional, and their application will be intermittent at best. Eventhough the cost of aeroelasticwind-tunnel and ight testing is veryhigh, maintaining a specialized staff simply to employ high-order

aeroelastic methods is h igher. Aircraft manufactures will continueto maintainthe statusquo in regardto aeroelasticanalysisuntilthesemethods become more cost effective.

Conclusions

CAE continuesto play a critical role in the developmentof mod-ern air vehicles. The current suite of linear aeroelastic, ASE, andgust response methodologies serves as the mainstay for aeroelas-tic analysis and they form a solid base on which to build futuredevelopments. Unfortunately, modern aircraft systems continuallyuncover aeroelastic issues that cannot be effectively predicted bythese methods, and as a result, costly aeroelastic wind-tunnel andight tests must be conducted to investigateand rectify these prob-lems. This situation is envisioned to worsen as new concepts, suchas morphing, continuous moldline controls, etc., call for vehicleswith higher degrees of structural exibility.

Many of todays analysesinvestigateonly the aeroelasticstabilityof the vehicle,where small aeroelasticperturbationscan be assumedand the impact of wing thickness and camber and even static aeroe-lastic deformationcanbe neglected.These characteristicswill notbenegligibleon many future vehicles,and heretofore accepted and/orcalibrated errors from linear aeroelastic analysis will no longer beacceptable.

Therefore, it is imperative that higher-orderaeroelastic methodscontinue to be developed and rened. Many of todays problemsalready require the inclusion of transonic and separated ow ef-fects, detailed structural modeling, and provisions for includingstructural nonlinearities.Future applicationswill likely require thattemperature effects and chemical reactionsbe included in the sim-ulations. It is our opinion that methods should continue to be de-veloped on three levels of complexity: 1) linear methods 2) mod-erate delity methods (including viscous/inviscid interaction tech-niques, ROM, etc.) and 3) high-delity methods (RANS aerody-namics, structuredand unstructuredgrid methods, nonlinear FEM,


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etc.). During this development,considerationmust be given to howthe methods can be effectively employed in a design environment,not just as a postdesign analysis tool. They should also be de-veloped with the specic objective that they be readily integratedinto existing aeroelasticanalysis frameworks.Finally, and most im-portant, the new methods must be sufciently general in applica-tion, robust and efcient in operation, and simple in implementa-tion to make them a viable tool for general use in the aerospaceindustry.

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