Aerodynamic Influence Coefficient Comptuations Using Euler Navier

AIAA JOURNAL Vol. 37, No. 11, November 1999

Aerodynamic Influence Coefficient Computations Using Euler/Navier-Stokes Equations on Parallel Computers

Chansup Byun,* Mehrdad Farhangnia, Gurd an Guruswamy. fu P * NASA Ames Research Center, Moffett Field, California 94035-1000

efficienn A t procedur computo et e aerodynamic influence coefficients (AICs), using high-fidelity flow equations suc Euler/Navier-Stokes ha s equations presenteds ,i AICe computee .Th sar perturbiny db g structures using mode shapes. The procedure is developed on a multiple-instruction, multiple-data parallel computer. In addition to discipline parallelizatio coarse-graid nan n parallelizatio floe th w f ndomaino , embarrassingly parallel implementation of ENSAERO code demonstrates linear speedup for a large number of processors. Demonstration of the AIC computatio statir nfo c aeroelasticity analysi arromads sn i a n weo wing-body configuration. Validatioe th f no current procedure is made on a straight wing with arc-airfoil at a subsonic region. The present flutter speed and frequency of the wing show excellent agreement with those results obtained by experiment and NASTRAN. The demonstrated linear scalability for multiple concurrent analyses shows that the three-level parallelism in the code is well suited for the computation of the AICs.

Introduction transonic flows over fighter wings undergoing unsteady motions at ODERN design requirement aircrafr sfo t push current tech- small to moderately large angles of attack.3'5 The code has been M nologie sdesige useth n di n proces theio t s r limit somer so - extended to simulate unsteady flows over rigid wing and wing-body times require more advanced technologie meeo st requirementse tth . configurations wit oscillatinn ha g trailing edge fla usiny b p - gei mane th f yo essentiae On l factors neede improvo dt perfore th e - ther singl patcher eo d multizonal grids. cod e bees 5'Th 6eha n par- mance is accurate prediction of aerodynamic loads. In the current allelized and used for aeroelastic computations for wing and wing- design process lineae th , r aerodynamic widele ar s y use predico dt t body configurations8 on the Intel iPSC/860 parallel computer, using aerodynamic loads. However lineae th , r aerodynamice b t no y ma s a single-zone computational grid for the fluids. adequat desige advancen th a r f o nfo e d subsonic civil transport. Furthermore numericae th , l simulatio f flowo n s over complex Becaus fluie eth d flow shows strong nonlinearitie transonie th t sa c geometries typically requires the use of a multizonal method. This regime, high-fidelity equations ,Eulee sucth Navier-Stoker s hro a s method is based on domain decomposition techniques, with the equations predicn ca , t flow characteristics more accurately thae nth flow domain being partitioned into a number of subdomains (zones). linear aerodynamics. Within each subdomain, the flow equations are solved in an indepen- However, high-fidelity flow equation e computationallar s - ex y dent manner, with the global nature of the flow being accounted for pensiv requird an e orden ea f magnitudo r e longer tim obtaio et n periodie byth c exchang boundarf eo y information between neigh- aerodynamic loads require designe th cost e n di Th . s become par- boring zones. Thus multizonae ,th l metho fluidr dbeefo s sha n inte- ticularly acut flutten ei r analyses because ther larga s ei e number grated into the aeroelasticity analysis process to simulate problems of analysis conditions. Because traditional aeroelastic analysis sha involving flexible complex geometries.9 The code has been paral- been performed with quite a modest amount of computer time, it has lelized based on the multizonal method on the IBM SP2 parallel been difficul justifo t t y using high-fidelity flow equation prea n si - computer, which is a multiple-instruction, multiple-date (MIMD) liminary design environment.1 Parallel computin possibilite on s gi y type of parallel computer.9 This type of parallelization is called to cut down the computational turnaround time in using high-fidelity coarse-grain parallelization, in contrast to fine-grain parallelization equations so that high-fidelity equations could be incorporated into that parallelize solvesa r itself without introducing explicit zonal the preliminary design process. boundaries demonstratioA . n computatio r statinfo c aeroelasticity presene Th t investigation use ENSAERe sth O code, whic- ca s hi simulatio bees nha n arromadn a r wefo wing-body configuration9'10 pable of computing aeroelastic responses by simultaneously inte- usin parallee gth l versio ENSAEROf no . gratin Euler/Navier-Stokee gth s equation e modae th th r d o l an s Because this parallel implementatio multizonae bases ni th n do l finite element structural equations of motion using aeroelastically method, there may be significant load imbalance between proces- adaptive dynamic grids. patchee 2"6Th d zonal grid technology based sors. This load imbalance can be avoided by designing the size of wore o nth bee s Refn ki ha n7 . implemente floe th w r compudfo - each grid block to be as close to each other as possible. Load bal- tations of rigid complex geometries. The code has been applied to ancing can also be achieved by decomposing each grid block into smaller subgrid conjunction si n wit fine-graie hth n parallelization floe oth fw solver. However t considere, thino s si d here becaust ei is beyon scope dth thif eo s paper. Presente Papes da r 97-108 AIAA/ASME/ASCE/AHS/ASe th t 6a C 38th This paper presents an efficient procedure on MIMD parallel Structures, Structural Dynamics, and Materials Conference, Kissimmee, FL, 7-10 April 1997; receive dFebruar4 y 1998; revision receive Octobe0 d3 r computer obtaio st aerodynamie nth c influence coefficients (AICs) 1998; accepted for publication 13 April 1999. Copyright © 1999 by the based on mode shapes by solving the Euler/Navier-Stokes equa- American Institute of Aeronautics and Astronautics, Inc. No copyright is tions. Demonstration computation e performear s n arroa r wdfo asserte Unitee th n di d States under Titl , U.Se17 . Code U.Se .Th . Govern- wing-body configuration, which has been studied as a design con- royalty-frea men s ha t e licens exerciso et l righteal s unde copyrighe th r t cep supersonir fo t c civil transport.11 This mode selectes i l valr dfo - claimed herein for Governmental purposes. All other rights are reserved by idation of steady flow computations because experimental data for the copyright owner. surface pressure distribution wele sar l documented additionn I . s a , * Senior Research Scientist, Computational Physic d Simulatioan s n a validation of the current procedure, the present flutter speed and Branch, MCAT, Inc.; currently Staff Engineer, Market Developmen- En t frequenc straigha yof t wing with 6%-thick arc-airfoi comparelis d gineering Microsystemsn Su , Antonin , Sa Inc. 1 o,90 Road, Palo AltoA C , 12 94303. Member AIAA. with those results obtained by the experiment and NASTRAN. The t Research Scientist, Computational Physic d Simulatioan s n Branch, results show excellent agreement with each other. Because the pro- MCAT, Inc. Member AIAA. cedure uses a high-fidelity flow solver with multizonal capability, it * Senior Research Scientist, Computational Physics and Simulation usee b computo dn t ca AICe eth morr sfo e complex configurations Branch. Associate Fellow AIAA. in the transonic regime. 1393 1394 BYUN, FARHANGNIA, AND GURUSWAMY

AIC Aeroelasticitn si y Analysis the pressure at /th surface point because of the unit modal deforma- 16 The governing aeroelastic equations of motion can be formulated modh yt matrie C tioshapeth AI f definens xe o i Th . d as by using the Rayleigh-Ritz method. In this method, the resulting aeroelastic displacement timy expressee an e ar t sa functioa s da a f no (7) assumef finito t ese d modes contributione .Th eacf o h assumed mode wher emodae [$th s ]i l matrix compose vibratioe th f do n modes totae toth l motio derives ni Lagrange'y db s equation. Furthermore, [AC/>d matrie an th s ]i x compose vectoe th f do r solviny ACB . g

assumeis ti d tha deformatioe tth structure th represente e f b n o n eca d the Euler or Navier-StokePj s flow equations with forced structural by deflection discretf o t se a e t pointssa . From this assumptione th , motion based on a selected mode shape, ENSAERO can compute displacement vecto expressee b rn [d]ca s da the AIC matrix in concurrent fashion. Then the AICs can be used to obtai aerodynamie nth c force whe) usin(6 y structure sb . nth gEq e [d] = (D has changed. Substituting Eqs. (3) and (4) into Eq. (2) and introducing the where [<£] is the modal matrix and [h] is the generalized displace- 17 ment vector. concep artificiaf o t representee b l damping,n t ca se ) a (2 s da . Eq finae Th l matrix aeroelastie forth f mo c equation motiof so s ni of complex eigenvalue equations givey nb

= {Z} (2) wher pc= 3eC /2k 2, A . -=f1 ( ig)/c*) comples i 2 x eigenvalue= k , where [M] modae , th [G] [Kd e l]ar , an mass , damping stiffnesd ,an s reduces coc/i U dartificiae frequencyth s i g l d dampinan , g coeffi- matrices, respectively e vectoTh . modae r th {Z s }i l aerodynamic cient. Because the coefficient (2/7 is computed from the unsteady force vector. motion dependens i t ,i reducee th n to d frequency tha implicitls ti - yin Wit precedine hth g modal equation motionf so fluttee ,th r bound- 13 clude ACdn i eac r yFo h reduced frequency chosen generalizee ,th d computee b arn yca usiny db g couple uncoupled dan d approaches. aerodynamic force matrix [Q obtaines ]i solviny db unsteade gth y couplee Th d approach requires direct time integratio f flod no wan flow equations and then, in turn, the complex eigenvalue problem structural equations. Although this approac accurats hi r flowefo s [Eq. (8)] can be solved to obtain the damping coefficient g. There with strong nonlinearities, it is computationally expensive. On the are several approaches13'15' 18~20 to compute the generalized aerody- other hand, the uncoupled approach that is computationally less namic force matrix. Byun and Guruswamy21 compared the time inte- expensive requires an additional assumption that the aerodynamic gration and pulse transfer-function approaches to compute the gen- data can be linearly superimposed among the vibration modes. As eralized aerodynamic force matri wina r xgfo configuration thin I . s demonstrate mord an e, recentl14 d Refsn dan i Ref n y3 i 1 . . 15e th , work pulse transfer-function approac uses hi computin r dfo g AIC. uncoupled method can be an effective approach to predict the prelim- r divergencFo e prediction droppiny b ,l time-dependenal t gou t inary flutter characteristics required in early stages of design. Based terms in Eq. (2) the resulting equations can be given by e flutteth n ro computation f airfoil o suncouplee th Refn , i s 13 . d approach requires one-tent computationae th f ho l effort required (9) couplee foth r d analysis thin I . s work traditionae th , methodg U- l ,

which is the uncoupled approach, is selected to demonstrate the ap- wher e divergence th q& s i v e dynamic pressur givea r efo n flight plication of the AICs in the aeroelasticity analysis procedure. The condition. For static aeroelasticity analysis, the aerodynamic influ- U-g method assumes that the structure will be undergoing simple ence coefficient matri obtaines xi d fro msteada y flow solutiof no harmonic motio thao generalizee ns th t d coordinates {h} take eth a perturbed configuration associated with a particular mode shape form selected as an input. The perturbation amplitude of the structure de- pends on the flow characteristics and the moving grid capability. The {h} {h}e"»= (3) perturbation from a steady solution should be small enough so that a linear superposition of the solution is applicable to the response. wher frequence eth o)s i oscillatiof yo t flutterna . Becaus modae eth l perturbatioe Th incrementalls ni y applie deforo dt structure mth e aerodynamic force vector is obtained by perturbing the structure, it unti t reachei l givesa n perturbation amplitude r obtaininFo . g con- is assumes da verged flow solution perturbea t sa d state additionan a , l numbef ro

T 2 iteration floe th w r solutiosfo performes ni d whil deformee eth d fluid } = [$>] (\/2pU c[S]{d}) (4a) gri finae fixes di th t l da state. = \/2pU2c[$>]T[S][$>]{h} (4b) Parallel Implementation {Z} = \/2pU2c[Q]{h] (4c) The domain decomposition approach used in ENSAERO is suitabl r parallelizationefo e disciplinTh . e parallelizatio s achieveni d where p is the freestream flow density, U is the freestream flight distributiny b fluide gth , structure controd an , l domains onto differ- speed, and c is the reference chord length. The diagonal force ma- ent group processorsf so . Onl singlya e processo assignes ri e th o dt trix is [S] and is obtained by integrating pressure over the structure structure and control groups because the respective computational surface. The modal matrix is [<£], and [Q] is the generalized aero- loads are relatively small. The fluid domain is further parallelized dynamic force matrix on the modal coordinates system. Thus the based on the multizonal method. This method partitions the fluid generalized aerodynamic force Q can be written as domain into several subdomains (zones solved )an floe sth w equa- fj tion f eacso h zone independently. Therefore, parallelizatioe th f no fluid domai achieves ni assigniny db processoe gon e eaco rth t f ho Qu = (5) zones in the fluid domain. Each processor solves the flow equations of each zone concurrently. The zonae nth l boundarie updatee sar d coefficiene Th t Q/; represent force sth e actin/te hth modn gi e because of pressure generated by the modal motion associated with by exchanging boundary information between neighboring zones. modeh yt force e computee Th .b th e n matrica ] usiny db x[S e gth e datTh a communication between different discipline modules AICs defined next. and between fluid zones is accomplished by using the Message 22 AICe Th s base modan do l mode definee followine ar sth s a d g Passing Interface (MPI) standard, which is a set of library inter- equation: face standard messagr sfo e passing partitionine Th . processorsf go , loading, and execution of different programs onto processors are en- (6) able usiny d b MPIRUN e gth 23 library, whic utilita s hi y developed ParalleS NA e bl yth System s Grou NASt pa A Ames Research Cen- where ACpchange pressure th s th 7i f eo e coefficients inducee th y db ter. MPIRUN flexibly allocates a group of processors and enables modal deformation on the yth mode shape and {,} is the yth mode point-to-point communication withi grouna r betweepo n groups. shape. The aerodynamic influence coefficient denotes the change of MPIRU standardI MP Nbasee thus d i paralle e th ,an sth n d o l version BYUN, FARHANGNIA, AND GURUSWAMY 1395

of ENS AERO shoul withoun dru t modificatio MIMD-typy an n no e computer supportin MPe gth I standard demonstratior .Fo n purposes, compute2 SP M th selecteds eIB ri . seriae Th l versio ENf no S AERO treats each domaie zonth f eo n sequentially, wherea othee sth r zones resid secondara n ei y storage Craa n yo devic C90 D maie SS e .Th n e suc differencth s ha e between the serial and parallel version is that the parallel implementation exploit functionae sth l parallelism among multiple zone patchef so d grids. As a result, all zones are computed concurrently. The interpolation and communication of the zonal boundary data are also done concurrently, through a loosely synchronous approach. f eaco d h timen e Aeth t step, processors holding zonal boundary surfaces send the interpolated flowfield data to the appropriate processor othee th f rso zones. Each processor proceed compue th o st - tation nexe th tf so tim efloe steth w f po solve zonas soos it ra s na l communication phas completeds ei . To coupl fluide eth , structure controd an , l domains, communication between domain alss si o accomplished throug interfacn ha e Inter-discipline communication eacf o d h timen e aeth t stepaerodynamie Th . c load convertee sar d Inter-zone communication into the structural loads through the fluid-structural interface.8'24 Furthermore structurae th , l deformatio passes ni fluie - th ddo o dt global processor local main throug interfacee hth . The surface nth e gri deformes di - dac rank node rank cordin structurae th o gt l deformation additionn I . , control surface deflection is superimposed on the deformed surface grid. Fig .2 Data communication design suitabl multiplr efo e coupled anal- overale Th l communication desig shows ni Fign ni . usinn 1I . g yses in a multizonal ENSAERO code on MIMD parallel computers. libraryI theMP communicatoa , uses ri identifo dt grouya procf po - essor thao s processoa t communicatn rca e with others withie nth same group. Each group is represented by a box defined by dashed structures controlsd an , . However neededf i , , additional moduln eca line Fign si . thi1n I . s case, however, onl processoe yon assignes ri d be easily added to the existing modules. to each grou singla r pfo e coupled analysis allocatee th l Al . d pro- The communication design for a single coupled analysis can be cessors hav commoea n communicator called mpi_comm_worlds a , further extende perfordo t m multiple analyses concurrently. Figure2 shown in Fig. 1. The MPIRUN utility creates a distinct communi- shows the extension of the communication design for concurrent cator, denote mpirun.cos da mFign i .eacr 1fo , h grou f compupo - multiple analyses. As contrast to a single coupled analysis, several tational nodes when it loads the executable program onto the pro- processor assignee sar eaco dt h group thin I . s figure, each group cessors. Using the mpirun_com communicator, any processor can processorsN s ha , whicnumbee th s hi f differeno r t cases running communicate with others withi groupna communicato .T e between concurrently. They are locally ranked from zero to N — I within different discipline modules or different groups, communicators for groupa firse th t n run I .initializatioe th , n data withi grouna e par interdiscipline and interzone communications are also defined using distributed fro leadine mth g nod f eaceo h group throug broadha - the MPIRUN library. The denotee yar soliy ddasheb d dan d lines cast call using mpirun_com communicator. This make t eassi o yt with arrows, respectively. distribute initial input data withi groupna . Onc initiae eth l data Furthermore functionalitlibrare I th s MP ye ha ,th creato yt w ne ea distributio completeds ni , each processo groua f o r p will partici- communicator for a subset of the allocated processors. Communica- patdifferena n ei t analysis r exampleFo . caseN f i , s with different tor eacr sfo h disciplin definee ear thao ds t collective operationn sca initial angles of attack are concurrently executed, each processor accomplishee b d withi disciplinna e module. Onc communicatoea r withi same grouna th es gripha d datzona computet f ao e bu s solu- for each disciplin defineds ei quits i t i , e convenien collectiva o d o tt e tions for the different flow condition, which in this case is a different operation withi disciplinena , suc computins ha g dra d lifan tg coef- angle of attack. Within the flow domain, after solving the flow equa- ficients. The communication design shown in Fig. 1 only explains tion evert sa y time step, each zone need exchango st e zonal bound- coupline th thref go e different computational modules, e.g., fluids, ary data with adjacent zones to advance to the next step. For this purpose, data communication is limited only among computational nodes wit samhthe e local rank thiIn . s communication strategy, each node can distinguish itself from other nodes assigned to different cases. Therefore, each node having different local rann kca participat differenn ei t simulations r multiplFo . e multidisciplinary simulations, the same communication strategy is applied for data exchange among the discipline domains.

Scalability and Performance Figure 3 shows the scalability and performance of the parallel versio f ENSAEROno obtaio T . performancna e measuremenn o t codee th scalabilita , performancd yan e stud dons yi e usin wingga - body-empennage configuration. This configuration consist sina f s-o gle block H-O grid with 180 x 173 x 40 points in the streamwise, spanwise, and body-normal directions, respectively grie splids .Th i t into multiple, equally sized zones cut perpendicular to the streamwise direction, with each zone assigned to a separate processor. Inter-discipline communication Timing functions are utilized to exclude initialization and I/O CPU usage; thus only the solver portion of the code is represented. -^ Inter-zone communication Figure 3a shows the scalability of the code for steady fluids computations solie Th .d line represent ideae sth l linear speedupo Tw . global processor local rank node rank levels of parallelism are shown. The single parameter set shows con- tinued splittin volume th f go e gri zonesd6 3 fro multiple o t m.Th 9 e Fig. 1 Data communication design in a multizonal ENSAERO code on paramete t representse r s executing multipl zone9 e cases concur- MIMD parallel computers. rently with various angle f attackso . 1396 BYUN, FARHANGNIA GURUSWAMD AN , Y

For both single and multiple parameter cases, using this coarse- study configuratioe Th . thina s ,n ha low-aspect-ratio , highly swept grain parallelism e codth , e scale nicelp u s y wit increase th h n ei wing mounted belo centerline wth slendea f eo r body e winTh . g numbee th f processorso r e rat f seaTh eo . l abilit f thiyo s typf eo is flat with a rounded leading edge. Note that the exact wing tip coarse grain parallelis mencouragings i . With effort progresn i s o st definition was not available, and so the tip thickness was decreased includ functionalite eth fine-graif yo n parallelism, whic alreads hha y to zero across three grid points. been implemented and demonstrated,8 the computational potential An H-H topology grid is used for the wing-body configuration of parallel machines wil more lb e fully utilize thiy db s code. with a trailing-edge flap control surface. This grid topology is chosen The CPU speed of the flow solver is shown in Fig. 3b in to align grid lines easily with the control surface. The ICEM-CFD MFLOPS/processor. This shows that the performance is decreased software system s use2i 5 generato dt surface eth e grid. Froe mth numbee asth grif ro d block increases si singla r dfo e analysis case. surface grid volume th , e gri generates di usiny d b HYPGEe gth N Thi s mainli s y becaus increasn a ratie f th eo f communi o n ei - code.26 Although the experimental model11 has two flaps at both cation and computation time per node. The code ran consistently the leadin trailine g th edg d gean edge, onl outboare yth de flath t pa near 26 MFLOPS/processor, which corresponds to approximately trailing edge is considered in this study. 100 /^s/grid point/step for a single node case on SP2 that was precedine th r Fo g wing-body configuration detailed validation composed of RS6000/590 workstations (POWER-2 multichip with with the wind-tunnel experimental data including grid refinement 66.7-MHz clock rate). Another way to measure it is to say that, if studies were done, the d reportee an yar detain di Refn i l. Base6 . d ENSAERO utilized the full 140 processors on the IBM SP2, one on the work done in Ref. 6, the final grid is selected for this paper. can expect ove GFLOP6 r3. S performance. Figure 5 shows an overview of the surface grid for the full-span configuration. (Every other grid lin s wing.showe ei th e n no Th ) Model Geometry and Grid reference lengtmeae th s nhi aerodynami corigie chorth f d no dan Figur showe4 e geometrth s e wind-tunneth f yo l model. This bodycoordinate e e nos e bode th th th f et .o Th y a t extendse e s si th o st model is used for demonstration of the AIC computations in this downstream boundary. The half-span grid used for symmetric cases consist f 11so 0 pointstreamwise th n si e direction, 116 pointe th n si spanwise direction point0 4 d san , norma bode th yo t l surfacea r fo , 10.0 total of 510,400 points. Bilateral symmetry is imposed in the jc-z Q. (th0 plane= centey t ea body)f ro grie furthes dTh i . r divided into => 2 GFLOPS upper and lower grids at the wing with the H-topology cut condition "8 8.0 at a zonal interface. For the multizonal aeroelastic computations, the original grid was split into eight patched zonal grids, as shown 6.0 in Fig . Eac5 . e samhth gris e dha numbe f grio r d s pointi d an s assigned to one processor on the SP2 computer. Flow variables at zonae th l interfaces were update adjoinine s sooth da s na g zones 4.0 1 GFLOPS were computed. Results 2.0 •—•—-« Single Parameter Set Rigid Wing Computations ...... Multiple Parameter Set 1.0 Figure 6 shows the steady pressures compared with the experiment at 0 (body center), 20, 50, and 80% semispanwise sec- 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 12 8 tions for the half-span configuration. The 80% section is located a) Processors e midspa ath e controt th f no l surface e floTh w. conditions consist of a Mach number of M^ = 0.85, an angle of attack of a = 7.93 deg, a flap deflection of 8 = 0 deg, and a Reynolds number of /?

0.75 chord

All dimension centimetern si s

Fig. 4 Wind-tunnel model geometry of an arrow wing-body configuration. BYUN, FARHANGNIA, AND GURUSWAMY 1397

ZoneS Zone?

Zonel •ZoneS

ZoneS

Zone 2 Zone 4

Fig. 5 Overview of the upper surface grid with a deformed control surface and the grid partition for eight zones.

ENSAERO o.oo- o Experiment, Manro alt ,.e 80% half span 80% span

-0.04 [ -0.5- o o oo

s h2=0.08 0.0 -O.Oi tf 2.4 2.5 0.00 0.5 50% half span 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 ^ef

50% span h =a08 •••Cxs 2 -0.03-

-0.0^ 1.6 1.8 2.0 2.2 2.4

Fig. 7 Cross-sectional view of deformed wing for three different per- 0.0 0.2 0.4 0.6 0.8 1.0 turbation amplitudes of the second vibration mode. -1.0-1

20% span ^^> data. Overall, the computed results show good agreement with the experiment. The pressure distributions on the body center also show I -0.5- good agreement shows a , Fign i . 6 .

^ ——— o —— '— —— ot^-o~~°^, Aerodynamic Influence Coefficients o.o- —— 0 0 o ^ Demonstration of the AIC computation is performed by using the arrow wing-body configuration with the flow conditions used in the rigid computations. The first two vibration modes are used to pertur structuree bth thin I . s work, demonstration computatione sar 0 1. 8 0. 6 0. 4 0. 2 0. 0 0. limited to the AICs for static aeroelasticity (divergence) analysis. -0.30 In the coupled fluid-structure analysis for static aeroelasticity, all Body center selectee oth f d vibration mode usee sar represen o dt structurae th t l deformation under coupled aerodynamic loads. However, for the 9-0.15H AIC computations, only a single mode is selected to perturb the structure. Then flow solutions are obtained to determine the AICs 1 0.00 because of a particular structural perturbation. Figur showe7 cross-sectionae sth l vie deformef wo d wingo tw t sa different span stations. Three different perturbation amplitudes of 0.15 the second vibration mod enforcee ear deforo dt winge mth . Because secone th d mod twisa s ei t dominant mode locae ,th l angl attacf eo k changes significantly by changing the perturbation amplitude. As 0.30 0.0 0.2 0.4 0.6 0.8 1.0 amplitude increases beyond /z2 = 0.1, the volume grid used for the X/C flow analysis fails because of the magnitude of the surface grid Fig. 6 Comparison of computed steady pressures with experiment: no deformation in this particular simulation. This is mainly because of flap deflection. limitation of the grid shearing scheme to deform the volume grid 1398 BYUN, FARHANGNIA, AND GURUSWAMY

0.40 h1 =0.01 n 80% half span ^---'*Mode2 0.35-

0.30 Model

0. 2§. JO 0.05 0.10 Perturbation amplitude Lift

O.OO-i

Model -0.05-

**---..,

-0.10 '---.^^ Mode2 0.2 0.4 0.6 0.8 1.0 x/c -0.1 Mode 1 perturbation 0.05 0.10 Perturbation amplitude -0.9i h2=0.01 Pitching moment h =0.05 2 80% half span Fig. 9 Changes of lift and pitching moment coefficients for various h2=0.08 perturbation amplitudes.

800T ST

400

0.00 0.05 0.10 Amplitude, h1 Fig. 10 Variation of modal aerodynamic forces with respect to various perturbation amplitudes of the first mode.

lOOOn

Mod perturbatioe2 n 500 Fig. 8 Changes of sectional pressure distribution for three different perturbation amplitudes.

following the surface deformation. This failure can be avoided by more sophisticated scheme movinr /i e sfo 0.2= th grid1 e r gth Fo . 6V 0.05 0.10 case verticae th , l difference betwee leadinge nth trailing-edgd -an e Amplitude, h2 pointwing-tie th t sa p deflectio meae th f no increases ni % 9 o t p du aerodynamic chord length. Fig. 11 Variatio modaf no l aerodynamic forces with respec variouo tt s pressure Th e distribution spao tw n t sstationsa , give Fign ni , 8 . perturbation amplitude secone th f so d mode. are obtained when the wing is perturbed by two modes with three different amplitudes. The second mode causes significant changes totae ofth lpitchin d lifan t g moment coefficients varies linearly with in pressure distribution, whereas the first mode barely changes the increasing perturbation amplitude except at the lower perturbation pressure distributio givee th t na span station perturbatioe th s sa n range. A similar trend is obtained on the response of the modal amplitude increasede sar shows A . Fign ni , becaus 7 . secone eth d aerodynamic forces for the first- and second-mode perturbations, as mode changes local angle f attaco s k significantly change th , n ei shown in Figs. 10 and 11, respectively. Only the first three terms of pressure distribution is expected. However, the first mode does not the modal aerodynamic force vector are presented in the figures. caus noticeably ean e chang pressure th n ei e distribution becaust ei Usin modae gth l perturbation integratee th , d AIC obtainee sar d ibendinsa g dominant mode. for the first and second vibration modes. Just like steady-state com- Figur showe9 totae th s lpitchin d lifan t g moment coefficients putations, the convergence criteria is based on the residual. About variation with respect to the perturbation amplitudes. The response 9000 time steps were required for residual to drop by about three BYUN, FARHANGNIA, AND GURUSWAMY 1399

500i

Mode 2

0.05 0.10 0 50 250 750 Amplitude, h1 Speed (ft/sec) Fig. 12 Variation of aerodynamic influence coefficients because of per- NASTRAN turbation firse baseth t n modedo . ENSAERO

1500

1000-

500-

-o A12 0 50 250 750 Speed (ft/sec) Fig. 14 Flutter speed comparison among NASTRAN, ENSAERO, and 0.05 0.10 the experimental results noted by superscripts a, b, and E, respectively. Amplitude, h2 Fig. 13 Variation of aerodynamic influence coefficients because of per- Conclusion turbation based on the second mode. A three-level parallel procedure is developed and implemented into a parallel multizonal version of aeroelastic code ENSAERO orders of magnitude. The results are given in Figs. 12 and 13, respec- for the AIC computations. At the first level, parallelization of indi- tively shows A . botn ni h figures Ae Hth , term, force e actinth n go vidual discipline dons si e using various number f processorsso n I . first mode because of the first-mode perturbation, converges rather the second level, parallelization is done at the discipline level by slowly compared to the other terms. Overall, at the lower pertur- running each discipline on a different group of processors. At the bation range, some of the AICs show that the perturbation ampli- third level, multiple aeroelastic cases are run in parallel by dividing tude is not large enough to prevail over the existing aerodynamic node2 theSP s into different set f groupsso . Loading executables onto the SP2 nodes and communicating data between disciplines initiae forcth y leb flow condition. However perturbatios a , n ampli- 23 tude increases, the AICs are all converged. Furthermore, it should and between zones is enabled by MPIRUN. notee b d tha perturbatioe tth structure th f no e shoul limitee db e b do t The integrated AICs are obtained by using the perturbation of the in the range of linear superposition of the solution. Otherwise, the structure base naturan do l mode shapes varioue Th . s results show response start shoo st w nonlinear effects, even thoug presene hth t tha response tth aerodynamice th f eo force lineas si e mosr th r fo f to results wer t abl eno capturo et e these effects becaus grie th d f eo perturbation amplitudes used in this study. However, in this particu- failure in the flow computation. caser la ,t converg AICsome no th lowee o f sed o th t ea r perturbation range because the perturbation is too small to prevail over the initial aerodynamic forces. As amplitude is increased, the effect of the ini- Validation tial condition disappears. Although the demonstration is only made Validation for flutter analysis using the present procedure has for static aeroelasticity analysis, this procedure can also be applied been done for a straight rectangular wing with 6%-thick parabolic- 12 to a dynamic aeroelastic problem such as flutter analysis. arc-airfoil section. The wing has chord and half-span lengths of The demonstrated linear scalability for the multiple concurrent 4.5 11.d 6an 5 in., respectively structurae Th . l mode- dons us i l y eb analyses shows that the three levels of parallelism in the code are well ing QUAD4 elements available NASTRANn i mode .Th e shapee sar suited for the computation of the AICs. The code ran consistently generated by using NASTRAN. The freestream flow conditions are near 26 MFLOPS/processor for steady Navier-Stokes fluid compu- a Mach number of 0.715 and an angle of attack of zero degree. The tations, which corresponds to approximately 100 /xs/grid points/step Euler equations are used in the flow analysis by using ENSAERO for a single node case. By using the full 140 processors on the with 120,000 grid points, whereas a linear aerodynamics (Doublet- IBM SP2, 3.6 GFLOPS performance is expected for steady Navier- Lattice) method is used in NASTRAN. Two modes, first bending Stokes fluid computations. firsd an t torsional, were use computo dt e AIC values t requireI . d This study is ongoing work toward aeroelasticity analysis of about 1000 time steps for residual to drop by three orders of mag- complete aircraft by using the AICs based on mode shapes, which initude during which the response reached a steady-state value. Both computee ar solviny db g high-fidelity equation sEulee sucth s rha NASTRAN and ENSAERO results are compared with the experi- or Navier-Stokes equations on parallel computers. Further study ment shows a , Fig n . Solii 14 . d lines, open filled ,an d symbols rep- should be made to find the benefit of using high-fidelity equations resent the results obtained by ENSAERO, NASTRAN, and experi- compared to the low-fidelity methods using the linear aerodynamics. ment, respectively fluttee Th . r spee frequencd dan notee yar Vs da F currene Th t validation cod e worth ef k o show s excellent agreement and co. Superscript represenE d san a,, b t NASTRAN, ENSAERO, betwee resulnthe t obtaine ENSAERdby thosOand e resultob- s and experiment, respectively. The flutter speeds computed by experimentainee th y db NASTRANd an t . However, more wors ki ENSAERO and NASTRAN are 363 and 339 ft/s, whereas the exper- in progress to demonstrate the accuracy of the current method for imental ft/sresul3 36 . s Excelleni t t agreemen obtaines i t d between complex configurations. the flutter speeds obtaine experimeny db ENSAEROd tan . Alsoe ,th flutter frequencies obtaine ENSAEROy db , NASTRAN experd an , - Acknowledgments , respectivelyHz 5 3 d an ., ENSAER42 , imen38 e ar tO predicte sth The work done by the first two authors was funded through flutter frequency very close to the experimental result as well. NASA Ames Research Center Fluid Dynamics Analysis Contract 1400 BYUN, FARHANGNIA GURUSWAMD AN , Y

NAS2-14109. This wor completes kwa d usin resourcee gth e th f so Flutter Characteristics," NAS X-79M AT , Nov. 1959. High Performance Computin Communicatiod gan n Prograd man 13Guruswamy Yang"Aeroelasti, d Y. an . , T , P. , c Time-Response Analysis Numerical Aerodynamic Simulation Program at NASA Ames Re- of Thin Airfoil Transoniy sb c Code LTRAN2," Computers Fluids,d an Vol. , 19804 409-425. . pp ,No , 9 . search Center e authorTh . s would lik thano et k Kumar Bhatif ao 14 Boeing Commercial Airplan valuabls hi r efo e suggestions during Guruswamy, P., and Goorjian, P. M., "Computations and Aeroelastic Applications of Unsteady Transonic Aerodynamics About Wings," Journal this study. of Aircraft, Vol. 21, No. 1, 1984, pp. 37-43. References 15Lee-Rausch, E. M., and Batina, J. T, "Calculation of AGARD Wing 1 445.6 Flutter Using Navier-Stokes Aerodynamics," AIAA Paper 93-3476, Wertheimerd an Bhatia, G. . K , ,"Aeroelasti J. , c Challenge Higa r hsfo Aug. 1993. Speed Civil Transport," Proceedings of the AIAA/ASME/ASCE/AHS/ASC 16Chen, P. C., Sarhaddi, D., and Liu, D. D., "Transonic AIC Approach 34th Structures, Structural Dynamics, Materialsd an Conference, AIAA, for Aeroelastic and MDO Applications," Euromech Colloquium 349, DLR, Washington, DC, 1993, pp. 3661-3682. 2 Gottingen, Germany, Sept. 1996. Guruswamy, G. P., "Navier-Stokes Computations on Swept-Tapered I7Desmarais, R. N., and Bennett, R. M., "User's Guide for a Modular Wings, Including Flexibility," AIAA Paper 90-1152, April 1990. 3 Flutter Analysis Software System (FAST Version 1.0)," NASA TM-78720, Obayashi, S., Guruswamy, G. P., and Goorjian, P. M., "Streamwise Up- May 1978. wind Algorith Computinr mfo g Unsteady Transonic Flows Past Oscillating 18Ballhaus, W. F., and Goorjian, P. M., "Computation of Unsteady Tran- Wings,"A/AA/0wrmz/,Vol.29,No. 10,1991,pp. 1668-1667; "Errata," AIAA sonic Flow by Indicial Method," AIAA Journal, Vol. 16, No. 2, 1978, pp. Journal, Vol. 30, No. 2, 1992, p. 569 4 117-124. Obayashi ,Guruswamy d S.an , "Unstead, P. . G , y Shock-Vortex Interac- 19Guruswamy , E.,Tu , "Navier-Stoke d G.an , s Computation Flexin so - tion on a Flexible Delta Wing," Journal of Aircraft, Vol. 29, No. 5, 1992, ble Advanced Transport-Type Wing Configurations in Transonic Regime," pp. 790-798. 5 AIAA Paper 94-1725, April 1994. Obayashi, S., and Guruswamy, G. P., "Navier-Stokes Computations for 20Bland, S. R., and Edwards, J. W., "Airfoil Shape and Thickness Effects Oscillating Control Surfaces," AIAA Paper 92-4431, Aug. 1992. 6 on Transonic Airloads and Flutter," AIAA Paper 83-0959, May 1983. Obayashi, S., Chiu, I., and Guruswamy, G. P., "Navier-Stokes Com- 21Byun, C., and Guruswamy, G. P., "An Efficient Procedure for Flutter putations on Full-Span Wing-Body Configuration with Oscillating Control Boundary Predictio Parallen no l Computers," AIAA Paper 95-1484, April Surfaces," AIAA Paper 93-3687, Aug. 1993. 7 1995. Flores, J., "Simulation of Transonic Viscous Wing and Wing-Fuselage 22MP7: A Message-Passing Interface Standard, Message Passing Inter- Flows Using Zonal Methods," NASA TM-89421, 1987. 8 face Forum, Univ Tennesseef o . , Knoxville 1994y Ma ., TN , Byun, C., and Guruswamy, G. P., "Wing-Body Aeroelasticity on Parallel 23Fineberg, S., "MPIRUN Loade:A Multidisciplinarr rfo Multizonad yan l Computers," AIAA Journal, Vol. 33, No. 2, 1996, pp. 421-428. 9 MPI Applications," NAS News, Vol. 2, No. 6, 1994, pp. 1, 2. Byun, C., and Guruswamy, G. P., "Aeroelastic Computations on Wing- 24Byun, C., and Guruswamy, G. P., "A Comparative Study of Serial and Body-Control Configuration Parallen so l Computers," AIAA Paper 96-1389, Parallel Aeroelastic Computations of Wings," NAS ATM-108805, Jan. 1994. April 1996. 25 10 ICEM-CFD User's Guide Version 3.0, Control Data Technical Publi- Byun, C., and Guruswamy, G. P., "Static Aeroelasticity Computations cations, North Arden Hills, MN, Aug. 1992. for Flexible Wing-Body-Control Configurations," AIAA Paper 96-4059, 26Chan StegerM.. d , "Enhancemen,W an , L. . ,J Threa f to e Dimensional Sept. 1996. H Hyperbolic Grid Generation Scheme," Applied Mathematics Computa-d an Manro , Manning, HallstaffE. R. . . RogersJ d M , . an K ,, . TJ H. , , tion, Elsevier Science, Vol. 51, Oct. 1992, pp. 181-205. "Transonic Pressure Measurement Comparisod san Theorf no Experio yt - ment for an Arrow-Wing Configuration," NASA CR-2610, Aug. 1976. 12Dogget , RaineyV . R Morgan,d . G. A ,an , Experimenta n . G.H ,"A , l P. Givi Investigatio f Aerodynamicno s Effect f Airfoio s l Thicknes Transonin so c Associate Editor