OPTIMIZATION OF TWO-DIMENSIONAL WING IN GROUND EFFECT CONSIDERING AERODYNAMIC CENTER OF HEIGHT AND LIFT

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1 28 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES OPTIMIZATION OF TWO-DIMENSIONAL WING IN GROUND EFFECT CONSIDERING AERODYNAMIC CENTER OF HEIGHT AND LIFT Juee Lee*, Sungjun Joo** *Hoseo Unversty, **EeGen Keywords: Aerodynamc caracterstcs; CFD (Computatona Fud Dyamcs); WIG (Wngn-ground) effect vece; Pareto set; Aerodynamc center of egt st Abstract Te Numerca optmzatons of a 2-dmensona wng n ground effect consderng aerodynamc caracterstcs and aerodynamc center of egt ave been performed and Pareto optma (potenta soutons) ave been cosey nvestgated. Due to te ground effect (reducng nduced drag and ncreasng ft), t s expected tat a WIG effect vece sows g operatona effcency. However, n terms of te trade-off between te aerodynamc forces and te stabty, te WIG effect vece scarfes ts effcency to meet te stabty somewat. In ts study, te ft coeffcent, te ft drag rato and te aerodynamc center of egt are cosen as te objectve functons to obtan te optma wng profes for te WIG effect vece. Te optma soutons of te mut-objectve optmzaton are not unque but a set of te nondomnated optma: te Pareto fronters or a Pareto set. As te resuts of te mut-objectve optmzaton, te one undred fourteen of Pareto optma tat ncude g-ft, g effcency, and more stabe arfos on te edge of te 3-dmensona objectve space, are obtaned at trty evoutons. Introducton Te wng-n-ground (WIG) effect vece s an advanced vece tat cruses cose to water or ground surface (.e., at a egt of 30% of ts cord engt or ower) by utzng an ar cuson among te wng, te fuseage and te ground. Due to te ar cuson at ow egts, tere s a consderabe ncrease n ft and a decrease n drag and terefore enancement of te ft drag rato. Neter te speed of a fast sp nor te effcency of an economca arcraft can be better tan tat of te WIG effect vece. However, tere are a few tecnca dffcutes n crampng te progress of te potenta WIG effect vece; ump drag [], statc egt stabty [2] and so on. Kornev and Matveev [3] performed an anayss of te statc egt stabty usng vortex attce metods (VLM). In ter study, tere were tree mportant factors for statc egt stabty: ta unt, profes of wng sectons, and man wng pro-fe. Te statc egt stabty for te WIG effect vece coud not be satsfed by movng te center of gravty. Te favorabe range of te egt stabty for te stabe fgt n ground effect was between and For te stabe fgt, tey nssted tat te center of gravty soud be ocated between te aerodynamc centers of attude and ptc and, furtermore, te cose ocaton to te center of attude was favorabe. Im and Cang [4] nvestgated te aerodynamc caracterstcs of a cambered arfo, NACA445, under te free-fgt condtons of M = 0.5, 2, 4 and = 0.5, 0.3, 0.5. Tey sowed tat te ft-to-drag rato of NACA445 s sgty ncreased as te vece s approacng to te ground. Tey aso found tat te pressure s ncreased at te eadng edge ony for te case of sma ange of attack (α ). Recenty, Park and Lee [5] carred out a numerca nvestgaton nto te effect of an endpate at varous ange attacks and ground

2 JUHEE LEE, SENGJUN JOO cearances. Tey found tat te endpate preventng te g-pressure ar escapng from te ower wng surface reduced te nfuence of wng-tp vortex and augmented ft and ft-drag rato furter. Te endpate aso reduced te devaton of te statc egt stabty wt respect to ptc anges and egts. However, te comparson of Irodov's stabty crtera [6] sowed tat te endpate was not favorabe for statc egt stabty. Optma desgn of te WIG arfo was studed by ony a few researcers. Most of tem treated te snge objectve optmzaton wt te oca optmzaton tecnque. Km and Cun [7] performed te computatona optmzaton for arfo sape. Tey cose te pressure dstrbutons (nverse desgn) and ft coeffcent as te objectve functons and obtaned te optma soutons by usng a sequenta quadratc programmng (SQP) metod wc s one of te gradent-based oca optmzaton tecnooges. However, t s ard to fnd researces on te arfo sape optmzaton of WIG craft consderng mutatera desgn objectves. For desgnng a WIG effect vece wt g cruse performance, t s dffcut to satsfy te desgn requrements suc as effcency and stabty, smutaneousy, because of te tradeoff penomena between tem. Park and Lee [] per-formed a mut-objectve optmzaton for te 2-dmensona WIG effect vece by ntegratng CFD and MOGA (mut-objectve genetc agortm). In ts study, n order to obtan stabe and g-performance arfos under te nfuence of ground effect, te sape optmzaton wt genetc agortm (GA) s performed numercay. Te ft coeffcent, ft-to-drag rato and aerodynamc center of egt ( X ), wc sgnfcanty nfuence te performance of te WIG craft, are adopted as te objectve functons. Te arfo sape s parameterzed by Bezer curves and ter contro ponts are used as te desgn varabes. Te non-domnated optma soutons, known as te Pareto fronter (or sets), can be obtaned by usng a mutobjectve genetc agortm (MOGA). Due to te trade-offs between te confctng objectve functons, te optma soutons become a number of te ndvduas (.e., desgns), wc are not domnated by te oter ndvduas wtn te desgn space. 2 Computatona Mode and Optmzaton 2. Governng Equaton Te fow around an arfo s assumed to be twodmensona, turbuent and steady state wt ncompressbe fud. Te turbuent fow of ar s descrbed by te Reynods-Averaged Naver- Stokes (RANS) equatons and t can be expressed n tensor notaton for mass and momentum as foows: ( ρu j ) = 0 () j j ( ρuu j τj) p = 2 uk τj = μtsj μt δj ρuu j 3 k (2) (3) were x, j =, 2 are te Cartesan coordnate vector, u are te mean veocty components. ρ uu j s te Reynods stress tensor. μ t and sj are te turbuent vscosty and te moduus of te mean stran rate tensor, respectvey, wc are defned as 2 t ft C ρk u u j (4) μ = t, Sj = + ε j In te present study, te RNG k ε mode proposed by Yakot et a. [8] s apped to mode te turbuent fow around te arfo. It s known tat te RNG k ε mode ncuded an addtona term n te ε -equaton can sgnfcanty mprove te accuracy for arfo fows. 2.2 Vadaton of CFD Modes Ar s taken as te workng fud and s assumed to be steady, ncompressbe, and turbuent fow. 2

3 OPTIMIZATION OF TWO-DIMENSIONAL WING IN GROUND EFFECT Te fud proper-tes are taken to be constant and te effect of vscous dsspaton s assumed to be neggby sma. Te numerca smuatons presented n ts work were done by means of STAR-CD [9] wc s a genera purpose commerca software. For representng te exact fgt condtons, te movng wa boundary condton wt a fgt veocty s apped at te ground. Te soutons are treated as converged ones wen te sum of normazed resdua s ess tan 0 7. In order to ceck te grd dependency and to verfy te CFD modes and te evauaton processes, te aerodynamc forces of te NACA005 arfo are compared wt te expermenta resuts [5] as sown n Fg.. Te C as a functon of a and drag poar for te two 6 Reynods numbers ( Re =.27 0 and ) are cacuated and tey are compared wt tose of te experment, wc were conducted by Jacobs and Serman [0]. Te tree consecutve numbers of meses, around,000 (coarse), 7,000 (base) and 24,000 (refned), are used to test te grd dependency and te resuts are presented. Te computatona doman used n ts study s ex-tended 0 tmes of te cord for eac drecton to avod te nfuence of te far boundares but s extended 20 tmes for te downstream drecton. Te upstream boundary s modeed usng a veocty net boundary condton wt a unform veocty dstrbuton. Te downstream boundary s modeed usng a pressure-outet boundary condton. A sp-wa boundary condton s mposed on te undsturbed far boundary, tereby mposng a zero cross-fow condton. Te arfo surface modeed as sod was wt a no-sp boundary condton enforced. To predct te boundary fow on te arfo surface propery, te non-unformy dstrbuted -type grd, wc s dense n te vcnty of te arfo surface, s used. Te grd system and te computatona doman are same except for te ground. It s found n Fg. tat and te drag poar are overestmated for te coarse grd compared wt te experment, we tose for te base and refned grd are estmated propery. In order to save computatona tme, te base grd s empoyed n ts study. Fg. Comparson of aerodynamc forces: drag poar for two Reynods numbers (oow: experments (Jacobs and Serman, 937); fed: present study). (0, x ) (0,0) (x 3, x 2 ) (0,x 0 ) (x 2,x ) (x 4,x 5 ) (x 6,x 5 ) (x 3, x 4 ) (x 5, x 4 ) (x 7, x 5 ) (x 6, x 4 ) (x 8, x 7 ) Fg. 2 Arfo geometry parameterzaton. (x 9, x 8 ) (0,) A scematc confguraton and a coordnate system of ar-fos n WIG craft consdered n ts study are sown n Fg Optmzaton Twenty-fve ndvduas for one popuaton are used and te seecton pressure s adopted so as to enance te convergence rate. In eac tournament, two canddates are randomy seected from te current generaton, and troug two compettons, te wnner as a cance to become a parent for reproducton. Te number of cuttng nes used for excangng genes for te crossover operaton s mportant. In ts study, two cuttng nes are used to maxmze te fe of te scema, wc s a usefu pattern n te gene. Mutaton s te occasona random ateraton of te vaue of a strng wt a sma probabty. Wen te vaue of mutaton s about a few percent, te GA cannot converge to proper soutons wt te evoutons and becomes a competey random searc. To prevent te operaton from becomng a random searc and keep te baance between expotaton and exporaton, a 0.5% mutaton rate s cosen. On te oter and, wen a new 3

4 JUHEE LEE, SENGJUN JOO offsprng ndvdua s found to be a genetc twn n te next generaton, tat ndvdua s gnored, and one more ndvdua w be generated. Te formuaton of te optmzaton s as foows; Fnd contro ponts T X = x, x,, x { } 2 8 (5) To maxmze F ( ) x = C (6) To mnmze F2 = X = Cm, / C, at x = ac (7) To maxmze F3 = C / C (8) Te aerodynamc center of egt s empoyed as one of objectves nstead of stabty wc conssts of two aerodynamc centers of ptc and egt. Te aerodynamc center of ptc s many controed by a orzonta ta. If te X s paced next to te quarter-cord, te strct stabty condton, X Xcg < Xa and X X ac, can be easy satsfed by orzonta ta and reduce te area of te orzonta ta. 3 Resuts and Dsccusson 3. Pareto Set SMOGA (smpe mut-objectve genetc agortm) deveoped by autors and based on te GA s dfferent from te random searc but cannot obtan exacty same Pareto set every performance because of ts random work n mutaton operatons and seecton operaton. To confrm computatona feasbty of SMOGA, te optmzaton s performed tree tmes n a raw. Te tree Pareto set obtaned are potted n Fg. 3. Approxmatey 00 potenta soutons (Pareto ndvduas) can be obtaned eac performance. To observe te tendency of te Pareto set, ony one-fourt ndvduas are potted n Fg. 3. Te nes n Fg. 3 are near regresson. Every try as a tte devaton but tey sow smar tendency and a Pareto d X Try0 Try02 Try03 try02 try0 try Fg. 3 Comparson of Pareto set from tree optmzatons. ndvduas are paced n a sma band. As a resut, SMOGA used n ts study can fnd Pareto optma propery wtout any wegng functons tat a vaue of te functon s cumbersome probem for a snge-objectve optmzaton. Genetc agortm s a eurstc process and te average ftness of a te ndvduas n a generaton s graduay mproved as te evouton. Fg. 4 sows te on- and offne performance accordng to te generaton, n order to examne te convergence stores for ft, aerodynamc center of egt and ft-drag rato. DeJong [] devsed two performance measures (.e., onne and offne) to quanttatvey evauate te performance of te GAs and tey are defned as foows, Abbrevatons soud be spet out n fu te frst tme tey appear and ter abbrevated form ncuded n brackets mmedatey after. Words used n a speca context soud appear between snge quotaton marks te frst tme tey appear. j= C on ne fe () = fe( j) f j off ne * () = e e( ) j= (9) (0) 4

5 OPTIMIZATION OF TWO-DIMENSIONAL WING IN GROUND EFFECT Onne performance Offne performance Domnated Pareto 3 c Generaton X C Onne performance Offne performance x 0.04 X Generaton C c /c d Generaton Onne performance Offne performance Fg. 4 On- and offne-performance for convergence story. Were fe( j ) s te vaue of objectve functons at generaton for envronment e, fe* ( j ) te best vaue of objectve functons unt a gven generaton for j =,2,...,. Te onne on ne performance, fe ( ), s an average ftness of a tras up to te current generaton and te Fg. 5 Pareto set and domnated ndvduas wt respect to C and X. off ne offne, fe (), s a runnng average of te best ndvduas up to a partcuar generaton. In addton, te onne performance s used to measure te deveopng performance we te offne one s orgnay devsed to gauge te convergence of optmzaton process for te snge objectve optmzaton probem. As sown n Fg. 4, te objectve functons are graduay converged as te generaton s advanced. It can be seen tat a moderate convergence s aceved for a of objectve functons after 20~25 generatons are proceeded. Pareto ndvduas are numbered accordng to ter ft coeffcent from (te owest ft coeffcent) to 4 (te gest ft coeffcent) n Fg. 5. In order to observe effects between profe and objectves, seven ndvduas are randomy seected among Pareto set as sown n Fg. 5. A mut-objectve optmzaton does not 5

6 JUHEE LEE, SENGJUN JOO Cp y/c x/c p00 p052 p4 Fg. 6 Comparson of C p and arfo profe; p00, p052 and p4. ook for a unque souton but a set of tem. From te Pareto fronter pont of vew, none of te optma are domnated. Ts mpes tat none of te objectves can be mproved wtout te worsenng of at east one of te oter objectves. Te tradeoff between objectves (ft coeffcent and X ) can be observed n Fg. 5. Wen te ft s mproved, te X s degraded and vce versa. Te actua vaues of X are negatve (-), and tus ocatons of te aerodynamc center of egt are downstream of a quarter-cord. It ead dffcuty of desgnng WIG vece because of t aerodynamc center of ptc ange soud be downstream of X. It mpes tat te WIG vece soud equp a arge orzonta ta and sopstc contro to sustan ts stabe condton wen t cruses n ground effect. 3.2 Caracterstcs of Pareto Set In order to compare aerodynamc caracterstcs and stab-ty, te profe and ts pressure dstrbuton aong te surface are potted n Fg. 6. Accordng to profe s caracterstcs, dfference n upper and ower surface around trang edge can be observed. Te stragt ower surface n Fg. 6 can utze te ground effect and mnmze te Ventur effect wc en-forces negatve ft force ocay. In ts study, te tckness of p4 (g ft) s tck we tckness of p00 (g X ) sows stragt ower surface wc mproves ft furter. In case of te p00, dstance between ower surface and ground s decreased unt mnmum pont around x/ c= After te mnmum pont, te dstance ncrease sgty and tus, t mpes dverge-converge passage next to te trang edge. Ts dverge-converge passage mgt reduce te ft but X mgt be mproved. Te passage reduces te C m at a quarter-cord as we as devaton of te C m wt respect to egts. Te pressure dstrbuton on te ower surface w be ncreased wt decreasng dstance between ground and arfo. At te same tme te Ventur effect w ncrease. Consequenty, te moment coeffcent wt respect to aerodynamc center w sgt ncrease or sustan. Tese penomena can mprove X. Te negatve C, mpes tat te vece cannot sustan ts fgt egt wen t meets a sma dsturbance and be-comes unstabe. Terefore, te operaton n te ange of attack s not acceptabe and s excuded from anayss. Consderng arfo ony used n ts study, te vaues of X can be weter t s negatve or postve. More mportant factor for epng successfu desgn of WIG vece s te ocaton of te X. Tat s, te ocaton of te s as cose to AC (aero-dynamc center) as possbe and suffcent stabty margn ( X X α ) can be obtaned consequenty and center of gravty (CG) s convenenty ocated between X and X α ; wc s a strct condton for statc egt stabty [2]. As sown n Fg. 7, te ocatons of X accordng to anges of attack (α ) move backward aong te down stream of te AC. X s for tree Pareto ndvduas are ocated at 25% downstream from AC (a quarter cord) and te ocaton of te X from te eadng edge terefore s about 50%. CG soud be ocated bend 50% of a cord and te stabty margn s reduced aso. To compensate te reduced stabty margn and satsfy te statc egt stabty ( X X α ), t s requre te arge orzonta ta at g ange of attack suc as α = 0. It soud be avod suc a g ange of 6

7 OPTIMIZATION OF TWO-DIMENSIONAL WING IN GROUND EFFECT x /C α=0 α=2 α=4 α=6 α=0 p00 and p052 move upstream as te decreasng egt wereas X for p4 s statonary. X for p00 and p052 sgty move forward and 6 tat X for p4 s constant for α = 4 and 6 as te egt canges for tree cases. From Fg. 7, p00 and p052 wc ave a s-sape ower surface sow upstream ocaton of X (stabe) tan tat of p4 wc as stragt ower surface and sow te gest ft coeffcent. 4 Concusons x x /C α=0 α=2 α=4 α=6 α= /C α=0 α=2 α=4 α=6 α=0 Fg. 7 Stabty of Pareto ndvduas: p00, p052 and p4. attack wen te vece s n ground effect. Except ts ange of attack of 0, te X s bounded wtn 0.5 as sown n Fg. 7. X s of bot p00 and p052 become smar. Te optmzaton s performed at α = 2 and / c = 0.25 and terefore, te smaest absoute vaue of can be observed for tree cases. s of Te sape optmzaton of a 2-dmensona arfo under ground effect as been carred out by te ntegraton of CFD (computatona fud dynamcs) and MOGA (mut-objectve genetc agortm). From te anayss of tese Pareto optma, wc ncude te varous arfo sapes, t was found tat te reaton between C and C / C d s neary dependent but te oter two reatonsps, between X and C and between X and C / C d, are not. Te arfo profes of te ower sde become fat for te g ft ndvduas and dverge-converge sape next to te trang edge for te favorabe X. Ts fat arfo can prevent te Ventur effect and mproves te ram effect furter. Ts fat sape eps to reduce te drag and ncrease te ft smutaneousy. On te oter and, te Ventur effect mproves te X by decreasng moment coeffcent wt respect to egt and devaton of te moment. In near future, we are gong to bud a WIG effect vece wose wng secton s one of te Pareto ndvdua. Te statc egt stabty ( X X α ) of a WIG effect vece wc as a compartments suc as man wng, orzonta wng and fuseage w be cosey nvestgated. References [] K.W. Park and J.H. Lee, Optma desgn of twodmensona wngs n ground effect usng mutobjectve genetc agortm, Ocean Engneerng, Vo. 37, pp ,

8 JUHEE LEE, SENGJUN JOO [2] K.V. Rozdestvensky, Wng-n-Gground Effect Veces, Progress n Aerospace Scences, Vo. 42, pp , [3] N. Kornev and K. Matveev, Compex numerca modeng of dynamcs and crases of wng-n-ground veces, AIAA , [4] Im, Y.H., Cang, K.S., Fow Anayss of a Tree- Dmensona Arfo n Ground Effect, Journa of te Korean Socety for Aeronautca and Space Scences, Vo. 29, No. 5, pp. -8, (n Korean) [5] Park, K.W., Lee, J.H., Infuence of endpate on aerodynamc caracterstcs of ow-aspect-rato wng n ground effect, Journa of Mecanca Scence and Tecnoogy, Vo. 22, pp , [6] Irodov, R.D., Crtera of ongtudna stabty of Ekranopan, Ucenye Zapsk TSAGI, Vo., No. 4 Moscow 970. [7] Km H.J., Cun H.H., Desgn of 2-Dmensona WIG Secton by a Nonnear Optmzaton Metod, Journa of te Socety of Nava Arctects of Korea, Vo. 35, No. 3, pp , 998. [8] Yakot, V., Orszag, S.A., Tangam, S., Gatsk TB, Spezoae CG, Deveopment of Turbuent Modes for Sear Fows by a Doube Expanson Tecnque, Pyscs Fuds, Vo. 4, No. 7, pp , 992. [9] STAR-CD+ v4.02, Metodoogy, Computatona Dynamcs, Co., London. U. K, [0] E.N. Jacobs and A. Serman, Arfo Secton Caracterstcs as Affected by Varatons of te Reynods Number, NACA TM586, 939. [] DeJong KA, An Anayss of te Beavor of a Cass of Ge-netc Adaptve Systems, Doctora Tess, Department of Computer and Communcaton Scences Unversty of Mcgan, Ann Arbor, 975. [2] Kornev, N., and Matveev, K., Compex Numerca Modeng of Dynamcs and Crases of Wng-nground veces, AIAA , Copyrgt Statement Te autors confrm tat tey, and/or ter company or organzaton, od copyrgt on a of te orgna matera ncuded n ts paper. Te autors aso confrm tat tey ave obtaned permsson, from te copyrgt oder of any trd party matera ncuded n ts paper, to pubs t as part of ter paper. Te autors confrm tat tey gve permsson, or ave obtaned permsson from te copyrgt oder of ts paper, for te pubcaton and dstrbuton of ts paper as part of te ICAS202 proceedngs or as ndvdua off-prnts from te proceedngs. 8