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 implemen- tation 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.