Optimization of Smart Spoiler for Race Car


 Peter Rich
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1 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 Optimization of Smart Spoilr for Rac Car M.H. Djavarshkian, A. Esmali Abstract A prssurbasd implicit procdur to solv Navir Stoks quations on a nonorthogonal msh with collocatd finit volum formulation is usd to simulat flow around th smart and convntional flaps of spoilr undr th ground ffct. Cantilvr bam with uniformly varying load with rollr support at th fr nd is considrd for smart flaps. Th bounddnss critria for this procdur ar dtrmind from a Normalizd Variabl diagram (NVD) schm. Th procdur incorporats th k ε ddyviscosity turbulnc modl. Th mthod is first validatd against xprimntal data. Thn, th algorithm is applid for turbulnt arodynamic flows around a spoilr sction with smart and convntional flaps for diffrnt attack angl, flap angl and ground claranc whr th rsults of two flaps ar compard. Finally, th bst position of spoilr basd on PSO optimization algorithm is calculatd. Kywords Smart spoilr, Ground Effct, Flap, Arodynamic cofficints, Rac car. I. INTRODUCTION h total arodynamic packag of th rac car is Tmphasizd now mor than vr bfor. Th us of arodynamics to incras th cars' grip was pionrd in Formula on in th lat 96s by Lotus, Frrari and Brabham. Arodynamics plays a vital rol in dtrmining spd and acclration and thus prformanc. hil drag rduction is an important part of th rsarch, down forc gnration plays a gratr rol in lap tim rduction. Ground ffct arodynamics of rac cars is concrnd with gnrating down forc, principally via low prssur on th surfacs narst to th ground. Ths phnomna happn whn a wing is going nar th surfac. Airfoils or wings ar usd in th front and rar of th car in an ffort to gnrat mor down forc. Th front wing of a rac car is an important pic to mak safty at high spd and producs about /3 of th car s down forc, it has xprincd mor modifications than rar wing. Th front wing assmbly is th first part of th car to mt th air mass. Th flow fild hr is bttr than at othr parts of th car bcaus th air hr has bn disturbd th last. Th wing is dsignd to produc down forc and guid th air as it movs toward th body and rar of th car. Flaps and winglts may also b usd. In stting up th front wing assmbly, nginrs M.H. Djavarshkian is with th Frdowsi Univrsity of Mashhad (corrsponding author to provid phon: ; fax: ; mail: A. Esmali, is with th Frdowsi Univrsity of Mashhad. H is now M.S Studnt in th Dpartmnt of Michanics, Frdowsi Univrsity of Mashhad, must considr what happns to th airflow as it travls toward th back of th car. Jonathan and Xin [], studid about flap wing in ground ffct for racing car application. A gnral ovrviw of th racing vhicl R&D procss is studid by Daisuk t al. [2]. A CFD simulation and analysis for a 5% scald car modl is prsntd in sufficint dtail, with an mphasis on addrssing its arodynamic aspcts. Kngo and Hiroshi [3] found th optimal flap chord lngth with using CFD simulations in twodimnsion FX6337 airfoil. Jagadp and Mayank [4] invstigatd about front wing in th rac car by using CFD softwar and foundd th optimum angl of attack for a F car(formula on rac). Josph [5] invstigatd arodynamic of rac car and typical dsign tools such as wind tunnl tsting, computational fluid dynamics, track tsting and thir rlvanc to rac car dvlopmnt ar discussd as wll. Mokhtar [6] and [7] studid for low Rynold's numbr flow around wings with and without ground ffct. Th mntion study was xtndd to thrdimnsional flow around a wing with ground ffct [7]. Mokhtar and Jonathan [8], invstigatd about a numrical study of a rac car front wing. Th focus of thir study is to invstigat th arodynamics charactristics of a wing oprating in a small ground claranc. A computational study in ordr to modl th flow around an invrtd airfoil in ground ffct wr prformd by Zrihan and Zhang [9]. Th knowldg of th ffcts that th ground can hav on airfoils dats back to th arly 92 s. In rcnt yars, thr hav bn succssful invstigations on th arodynamics of airfoil and wing. On of th mor rcnt wind tunnl xprimnts was don by Ahmd and Sharma [] and []. Jung t al. [2], simulatd thrdimnsional NACA649 in ground proximity. Smith [3] prformd th computational analysis of airfoils in ground ffct. Influnc of ndplat on arodynamic charactristics for lowaspctratio wing in ground ffct is prformd by Park and L [4]. Effct of ground proximity on th arodynamic prformanc and stability of a light unmannd arial vhicl has bn prformd by Boschtti t al. [5]. Th shap optimization using th multiobjctiv gntic algorithm and th analysis of th thrdimnsional wings in ground ffct hav bn prformd by L t al. [6]. Du to th potntial bnfits of mploying adaptiv airfoil, thr has bn an intnsiv attmpt by rsarchrs in dvloping a working modl. ith th advancmnt of matrials, many ar now considring using smart matrials to produc airfoil with variabl cambr capability. An analytical study conductd by NASA on th bnfits of variablcambr capability [7]. Anothr advantag of adaptiv airfoil is that it
2 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 causs smallr vortx with lss powr. This was th rsult of Prn and Jacob [8] rsarch. Thy usd pizolctric stimulus with a stl layr in airfoil. Kudva t al. [9] discussd about smart structur tchnologis and thir bnfits. In 23, Forstr t al. [2] dsignd a two dimnsional airfoil with a control surfac in trailing dg that has a chord wis gomtrical changs. Convntional spoilrs hav bn usd in most of th rsarchs for rac cars. To improv arodynamic cofficint prformanc, a smart spoilr can b usd in ths cars. In this rsarch, th smart flap is mployd and simulatd for a spoilr sction in ground claranc. In this simulation, th prformanc of airfoil with smart and convntional flaps for diffrnt lngth, flap angl and ground claranc ar studid. Bsid, in ordr to achiv maximum of lift to drag ratio, th PSO algorithm is usd to find th bst of distanc approximation of surfac, angl of flap dflction and flap lngth. Fig. Smart and Convctional Flap II. NUMERICAL SOLUTION SETUP AND CONDITIONS A. Simulation smart flap dflction In this study, a smart flap dflction is dsignd with a cantilvr bam so that th bam bnding quation is sam a smart flap chord dflction. Bsid a flap shap is a triangl (s.g. Fig. ), so th cantilvr bams with uniformly varying load ar considrd (s.g. Fig. 2). Th mntion profil is givn blow: w ( 2 ) X + BX BX Y = () 2EIB Sinc th paramtric quation only nds, quation () is substitutd by quation (2). 5 3 Y Uppr =Y u +k u (X ax +X) 5 3 Y Lowr =Y L +k L (X ax +X) 4 B a= B 2 Th bnding quation can b usd for midlin. For uppr and lowr flap surfac, th configuration was manipulatd by making minor modifications. Th cofficints of quation(2) ar dtrmind by an itrativ procss. Each profil is visualizd using FORTRAN, and th valu of th cofficint is ithr incrasd or dcrasd until th dsird profil is obtaind. A paramtric smart airfoil is dsignd, and computational fluid dynamics simulation is don ovr thm. (2) Fig. 2 Cantilvr bam modl. B. Govrning Equation for Fluid Th basic quations, which dscrib consrvation of mass, momntum and scalar quantitis, can b xprssd in th following vctor form, which is indpndnt of th coordinat systm. div ( ρ V r ) = S m (3) div( ρ V V T ) = S r v (4) div( ρ V r φ q) = S r Φ (5) Th lattr two ar usually xprssd in trms of basic dpndnt variabls. Th strss tnsor for a Nwtonian fluid is: r 2 r r T= ( P+ µ div V) I+ (6) 3 and th Fourirtyp law usually givs th scalar flux vctor:
3 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 q r = Γ φ gradφ (7) Sinc th k ε modl is simpl and has good stability with asy convrgnc. Bsids th angl of attack is zro, th maximum angl of flap is 7.5 and thr is not strong sparation thrfor, flow fild is not swirl and complicat. Th k ε modl has bn chosn in this simulation. C. FinitVolum Discrtization Th discrtization of th abov diffrntial quations is carrid out using a finitvolum approach. First, th solution domain is dividd into a finit numbr of discrt volums or clls, whr all variabls ar stord at thir gomtric cntrs (s.g. Fig.3). Th quations ar thn intgratd ovr all th control volums by using th Gaussian thorm. Th discrt xprssions ar prsntd affctd concrning only on fac of th control volum, namly, for th sak of brvity. For any variabl φ (which may also stand for th vlocity componnts), th rsult of th intgration yilds: I Iw + In Is = S φ δ υ (8) c whr I s ar th combind cllfac convction I and D diffusion I fluxs. Th diffusion flux is approximatd by cntral diffrncs and can b writtn for cllfac of th control volum in Fig. 3 as: D I = D ( φ φ ) (9) P E xprssion for th φ is dtrmind by th SBIC schm [2], that is basd on th NVD tchniqu, usd for intrpolation from th nods E, P and. Th xprssion can b writtn as: φ So that: whr ~ φ + ( φ φ ). φ = () P E ~ ~ φ = φ,if ~ φ [,] (2) ~ φ p φ φ p =, φ φ ~ x p E x = x p E x x, C ~ φ φ φ = φe φ ~ x x x = x x E (3) Th limits on th slction of K could b dtrmind in th following way. Obviously, th lowr limit is K =, which would rprsnt switching btwn upwind and cntral diffrncing. This is not favorabl bcaus, it is ssntial to avoid th abrupt switching btwn th schms in ordr to achiv th convrgd solution. Th valu of K should b kpt as low as possibl in ordr to achiv th maximum rsolution of th schm. Th final form of th discrtizd quation from ach approximation is givn as: A. ϕ = A. ϕ + S (4) ϕ P P m m m = E,, N, S Fig. 3 Finit volum and storag arrangmnt. Th rsults ar prsntd and discussd in th nxt sction. At th first, grid stup and computational domain has bn dscribd. D. Grid Stratgy Th grid structur that usd in CFD simulation was cratd by a structurd msh mployd bcaus of its simplicity and applicability to th currnt flow configuration (i.., with a narby ground). Schmatic shap of ths twodimnsional structurd grids is shown in Fig. 4. Th discrtization of th convctiv flux, howvr, rquirs spcial attntion and is th subjct of th various schms dvlopd. A rprsntation of th convctiv flux for cllfac is: I c = ρ. V. Α) φ = F φ ( () Th valu of φ is not known and should b stimatd by intrpolation, from th valus at nighboring grid points. Th Fig. 4 grid topology and H grid. According to Fig. 5 th dimnsion of domain has bn
4 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 obtaind aftr doing svral various lngths for b, f, u and indpndnt lngths hav bn chosn. Th grid sizing was dtrmind aftr grid indpndnc that was found by doing svral diffrnt trials, which show for surfac prssur cofficint distribution. For xampl, th ffct of grid siz is shown in Fig. 6. For othr cass, th abov procss is usd for grid and domain indpndncs. own flying xprinc as wll as th flying xprinc of othr particls. Each particl kps track of its coordinats in th solution spac which ar associatd with th bst solution (fitnss) that has achivd so far by that particl. This valu is calld prsonal bst, pbst. Anothr bst valu that is trackd by th PSO is th bst valu obtaind so far by any particl in th nighborhood of that particl. This valu is calld gbst. Th basic concpt of PSO lis in acclrating ach particl toward its pbst and th gbst locations, with a random wightd acclration at ach tim stp as shown in Fig. 7. v k v k+ s k+ v gbst Fig. 5 Dimnsion of domain. s k v pbst 2 Fig.7 Concpt of modification of a sarching point by PSO Cp Each particl tris to modify its position using th following information: th currnt positions, th currnt vlocitis, th distanc btwn th currnt position and pbst, th distanc btwn th currnt position and th gbst. Th modification of th particl s position can b mathmatically modld according th following quation:  9*5 Grid 3*2 Grid 45*2 Grid 2.5 X/C Fig. 6 Effct of grid sizing on prssur distribution on th surfac of th airfoil for an angl of attack and h/c=.2. E. Boundary Conditions Fig. 5 shows th boundary condition. At th inlt, vlocity has bn prscribd. At th outlt, th prssur is fixd. Slip boundary conditions ar usd on uppr walls of th domain and wall boundary conditions ar usd for airfoil surfac and ground surfac. III. PARTICLE SARM OPTIMIZATION (PSO) Th PSO mthod is a robust stochastic optimization tchniqu basd on th movmnt and intllignc of swarms. This mthod applis th concpt of social intraction to problm solving. It was dvlopd in 995 by Jams Knndy (socialpsychologist) and Russll Ebrhart (lctrical nginr). It uss a numbr of agnts (particls) that constitut a swarm moving around in th sarch spac looking for th bst solution. Each particl is tratd as a point in a N dimnsional spac which adjusts its flying according to its V + = wv + c rand (...) x ( pbst  s ) + c rand x gbst s k k k i i i i k 2 2(...) (  i )... (5) Rand is uniformly distributd random numbr btwn and. Th pbst i is th prsonal bst of agnt i, and th gbst is global bst of th particl group. Th following wighting function (w) is usually utilizd in (5): ( ) /max w = w Max  éw Max w Min xitr ù ë  û itr (6) hr w Max is initial wight, w Min is final wight, maxitr is maximum itration numbr, and itr is currnt itration numbr. s = s + V (7) k + k k + i i i IV. RESULTS AND DISCUSSION Th rsults ar prsntd and discussd in this sction. Tabl I shows th stting for numrical simulation. At th first, simulation of flow around th airfoil NACA5 has bn prformd. Thn, th ffcts of flow around airfoil NACA9 with flap in smart and convntional conditions, angl of flap and ground claranc hav bn invstigatd.
5 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 Th simulation is twodimnsional. Prssur cofficint distribution, Lift and drag cofficints of th airfoil hav bn analyzd. Th Rynolds numbr for this study is This numbr indicats that th airflow has both laminar and turbulnt rgions. TABLEI SETTINGS FOR NUMERICAL SIMULATION Flow turbulnt Prcision Twodimnsion Doubl Prcision Schm Normaliz variabl diagram Solvr SIMPLE turbulnt modl k ε Th numrical and xprimntal prssur cofficint distributions on th surfac of th airfoil for angls of attack 7.5 and ground claranc h/c=.8 ar compard in Fig. 8. It can b sn that thr is good agrmnt btwn prsnt numrical and xprimntal data []. Tabl II also shows lift cofficints and rror prcnt. Th numrical rsults ar in good agrmnt with xprimnt data. 2 Numric Exprimnt for AOF= +5 and diffrnt ground claranc. hn th flap dflctd to upward, prssur sid is rlatd to th uppr surfac of airfoil and suction sid is rlatd to th lowr surfac of airfoil. As figurs show prssur is rducd with dcrasing ground claranc in th prssur sid. This bhavior happns in both smart and convntional flaps. CP .5 X/C Fig. 9 Prssur cofficint distribution on th surfac of th smart airfoil for AOF= +5º. h/c=.2 h/c=.5 h/c=.8 h/c=.2 h/c=.5 h/c=.8 CP  2 CP 3.5 x/c Fig. 8 Prssur cofficint distribution on th surfac of th airfoil NACA 5 for an AOA 7.5º and h/c=.8. Th airfoil which was slctd to b usd in this study is th NACA9. Th simulation mthod for this tst cas is th sam of prvious tst. Airflow tratmnt and ffct of th flap in smart and convntional conditions in ground proximity ar invstigatd. TABLEII COMPARISON OF LIFT COEFFICIENTS FOR AIRFOIL NACA 5 AND AOA= 7.5. h/c Exprimnt Numric Error% Fig. 9 and, rspctivly, show th prssur cofficint distribution on th surfac of smart and convntional airfoils .5 X/C Fig. Prssur cofficint distribution on th surfac of th convntional airfoil for AOF= +5º. Tabl III shows down forc(lift) and drag cofficints and L/D for smart and convntional flaps. Comparisons show that down forc cofficints of smart flaps incras and thir drag cofficints dcras as rsults L/D ratio for smart flaps ar highr than convntional flaps. TABLE III DON FORCE(LIFT) (A) AND DRAG (B) COEFFICIENTS AND LIFT  DRAG RATIO(C) FOR SMART AND CONVENTIONAL AIRFOILS FOR AOF= +5. h/c Smart Flap Convction Flap
6 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527, (a) h/c Smart Flap Convction Flap (b) h/c Smart Flap Convction Flap (c) CD CF, AOF= +2.5 dg CF, AOF= +5 dg CF, AOF= +7.5 dg SF, AOF= +2.5 dg SF, AOF= +5 dg SF, AOF= +7.5 dg Tabl VI shows down forc(lift), and Drag cofficints and L/D for smart and convntional airfoils for h/c=.8. Comparisons show that down forc cofficint of a smart flap is mor than a convntional flap. Down forc and drag cofficints incras slightly with angl of flap for two airfoils. TABLE VI DON FORCE (LIFT) (A) AND DRAG (B) COEFFICIENT AND LIFT  DRAG RATIO(C) FOR SMART AND CONVENTIONAL AIRFOILS FOR H/C=.8. AOF (dg) Smart Flap Convction Flap (a) AOF (dg) Smart Flap Convction Flap (b) AOF (dg) Smart Flap Convction Flap (c) Fig. and 2 show lift and drag cofficints for th diffrnt h/c. Fig. shows that drag cofficint incrass with rduction ground claranc and this cofficint for convntional flaps is mor than th smart mod for all th h/c and AOF h/c Fig. Variations in CD as a function of h/c for smart and convntional flap and diffrnt angl of flap. Fig. 2 indicats lift cofficint incrass with ground claranc initially, thn this cofficint dcrass with incrasing ground claranc. Th positiv dflction of flap passs flow btwn th lowr surfac of airfoil and ground surfac lik flow passing a nozzl. Nozzl Charactristics rvald that vlocity incrass and prssur rducs in th convrgnt part so vlocity rachs maximum in th gorg and prssur incras and vlocity dcras in th divrgnt part. hn th ground claranc is rducd, th cross sction ratio is gratr and flow xpansion is mor on th lowr surfac of airfoil. As a rsult, vlocity on th lowr surfac of airfoil incrass. This incras of vlocity in th lowr surfac with ground claranc from h / c =.8 to h / c =.5 incrass lift cofficint. hn th ground claranc dcrass from h/c=.5 to h/c=.2, boundary layr has an important rol, th vlocity in lowr surfac and lift cofficint dcras. Fig. 3 shows th L/D absolut valu ratio for th diffrnt h/c. CL .2 CF, AOF= +2.5 dg CF, AOF= +5 dg CF, AOF= +7.5 dg SF, AOF= +2.5 dg SF, AOF= +5 dg SF, AOF= +7.5 dg h/c Fig. 2 Variations in CL as a function of h/c for smart and convntional flap and diffrnt angl of flap.
7 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 5 CF, AOF= +2.5 dg CF, AOF= +5 dg CF, AOF= +7.5 dg SF, AOF= +2.5 dg SF, AOF= +5 dg SF, AOF= +7.5 dg CL/CD h/c Fig. 3 Variations in L/D as a function of h/c for smart and convntional flap and diffrnt angl of flap. Fig. 5 Variations in absolut valu of L/D as a function of h/c and angl of smart flap. TABLE V VOLUME FLO RATE PASSING BETEEN LOER SURFACE OF AIRFOIL AND GROUND FOR H/C=.2. AOF(dg) Smart Flap Convntional Flap So far, th ffcts of angl of flap dflction, distanc approximation from th car surfac and flap lngth hav bn invstigatd. Th rsults show that if th smart flap is usd, th arodynamic prformanc of spoilr will b incrasd. In ordr to gt th bst optimal mod, th optimization has bn don basd on PSO algorithm. Fig. 4 shows variations in absolut of lift to drag ratio as a function of flap lngth and angl of flap. This figur shows that th absolut valu of th lift to drag ratio is incrasd with incrasing th angl of flap and flap lngth. Fig. 6 Variations in absolut valu of L/D as a function of h/c and flap lngth for smart flap. Finally, th optimization is don with th prsnt rsults. Initially th absolut valu of th lift to drag ratio is obtaind as a function of flap lngth(fl/c), flap angl(aof) and distanc approximation from th surfac by using nural ntworkfuzzy and ultimatly optimization is prformd basd on L/D=f(FL/c,h/c,AOF). According to th availabl data optimization mod is obtaind in tabl VI. L/D AOF(dg) TABLE VI OPTIMIZATION CASE FOR SMART FLAP h/c FL/c Abs(L/D) Fig. 4 Variations in absolut of L/D as a function of flap lngth and angl of smart flap. Fig. 5 shows variations in absolut valu of th lift to drag ratio as a function of h/c and angl of flap. This figur shows that th absolut valu of th lift to drag ratio is incrasd with incrasing th distanc. Fig. 6 shows variations in absolut valu of th lift to drag ratio as a function of flap angl and flap lngth. This figur shows that th absolut valu of th lift to drag ratio is incrasd with incrasing flap lngth and h/c. hil flap lngth to chord ratio, angl of flap dflction and spoilr distanc from surfac ar.28, 7.47 and.78 rspctivly, th maximum of arodynamic prformanc is obtaind. In th mntion conditions, th lift to drag ratio is V. CONCLUTION A prssurbasd implicit procdur to solv NavirStoks quations on a non orthogonal msh with collocatd finit volum formulation is usd to simulat flow around th smart and convntional flaps of a spoilr sction undr th ground ffct. Th algorithm is applid for diffrnt flap lngth, flap
8 Intrnational Confrnc on Fluid Dynamics and Thrmodynamics, Dubai, January 2527,2 angl and ground claranc. Th main findings can b summarizd as follows: Th agrmnt btwn prsntd prdation and xprimntal data is considrabl 2Th prssur cofficint distribution in a smart flap is smoothr than convntional flap 3 Liftdrag ratio in a smart flap is highr than a convntional flap 4 Th highst liftdrag ratio is at flap angl 7.5º 5 Th ground claranc with h/c=.5 has th highst lift cofficint 6 Th lift and drag cofficints slightly incras for longr flap lngth and L/D ratio incrass too 7 Th optimal mod is obtaind basd on PSO algorithm. NOMENCLATURE h = Ground Clarancs AOA = Angl of Attack A = Cll Fac Ara µ = Dynamic Viscosity = Normalizd Scalar Quantity φ % K = a factor in SBIC schm to dtrmin a spcial schm ω = ight/unit Lngth(N/m) I = Ara momnt of inrtia(m 4 ) B = Lngth of th Bam X = Horizontal Cartsian Coordinat Y = Vrtical Cartsian Coordinat E = Young s Modulus ρ = Dnsity P = Prssur Γ = Diffusivity Cofficint q r = Scalar Flux Vctor F = Mass Flux T r = Strss Tnsor δυ = Cll Volum S r = Sourc Trm V r = Vlocity Vctor φ = Scalar Quantity I = Flux S k = Currnt Sarching Point S k+ = Modifid Sarching Point V k = Currnt Vlocity V k+ = Modifid Vlocity V pbst = Vlocity basd on pbst V gbst = Vlocity basd on gbst k v i = Vlocity of agnt i at Itration k c j = ighting Factor k s i = Currnt Position of agnt i at Itration k REFERENCES [] J. Zrihan and X. Zhang, "Arodynamics of Gurny Flaps on a ing in Ground Effct," AIAA journal, vol. 39, pp , 2. [2] D. Uno, G. Hu, I. Komada, K. Otaki, and Q. Fan, "CFD Analysis in Rsarch and Dvlopmnt of Racing Car," prsntd at th Motorsports Enginring Confrnc & Exposition, Darborn, MI, USA, 26. [3] K. Goto and H. Sakurai, "Numrical Study for th Optimal Flap Chord Lngth of a TwoElmnt Airfoil," SAE Intrnational Journal of Passngr CarsMchanical Systms, pp , 26. [4] J. Rddy and M. Gupta, "Finding th Optimum Angl of Attack for th Front ing of an F Car Using CFD," in 4th SEAS Intrnational Confrnc on Fluid Mchanics and Arodynamics, Elounda, Grc, 26, pp [5] J. Katz, "Arodynamics of Rac Cars," Annual Rviw of Fluid Mchanics, vol. 38, p. 27, 25. [6]. Mokhtar, "A Numrical Study of HighLift Singl Elmnt Airfoils with Ground Effct for Racing Cars," SAE transactions, vol. 4, pp , 25. [7]. Mokhtar, "Arodynamics of HighLift ings with Ground Effct for Raccars," prsntd at th SAE orld Congrss, 28. [8]. Mokhtar and J. Lan, "Raccar Front ing Arodynamics," SAE Intrnational Journal of Passngr CarsMchanical Systms, vol., p. 392, 29. [9] J. Zrihan and Z. Xin, "Arodynamics of a Singl Elmnt ing in Ground Effct," Journal of aircraft, vol. 37, pp , 2. [] M. Ahmd, S. H. Ali, G. M. Imran, and S. D. Sharma, "Exprimntal Invstigation of th Flow Fild of a Symmtrical Airfoil in Ground Effct," in 2st Applid Arodynamics Confrnc, Orlando, Florida, 23. [] M. Ahmd and S. Sharma, "An Invstigation on th Arodynamics of a Symmtrical Airfoil in Ground Effct," Exprimntal Thrmal and Fluid Scinc, vol. 29, pp , 25. [2] K. Jung, H. Chun, and H. Kim, "Exprimntal Invstigation of inginground Effct with a NACA649 Sction," Journal of marin scinc and tchnology, vol. 3, pp , 28. [3] J. Smith, "Computational Analysis of Airfoils in Ground Effct for Us as a Dsign Tool," M.Sc Mchanical and Arospac Enginring Dpartmnt, st Virginia Univrsity, st Virginia, 27. [4] K. Park and J. L, "Influnc of Endplat on Arodynamic Charactristics of LowAspctRatio ing in Ground Effct," Journal of mchanical scinc and tchnology, vol. 22, pp , 28. [5] J. P. Boschtti, M. E. Cárdnas, and A. AmrioCLq, "Stability and Prformanc of a Light Unmannd Airplan in Ground Effct," in 48th AIAA Arospac Scincs Mting Including th Nw Horizons Forum and Arospac Exposition, Florida, 2. [6] J. L, C. Hong, B. Kim, K. Park, and J. Ahn, "Optimization of ings in Ground Effct Using MultiObjctiv Gntic Algorithm," in 48th AIAA Arospac Scincs Mting Including th Nw Horizons Forum and Arospac Exposition, Florida, 2. [7] A. Bolonkin, G. Gilyard, H. L. D. F. R. Cntr, U. S. N. Aronautics, and S. Administration, Estimatd bnfits of variablgomtry wing cambr control for transport aircraft: Citsr, 999. [8] N. J. Prn and J. D. Jacob, "ak Vortx Mitigation using Adaptiv Airfoils," prsntd at th 37th AIAA. Arospac Scincs Mting and Exhibit, 999. [9] J. Kudva, C. Martin, A. Jardin, G. Sndckyj, T. Harris, A. McGowan, and R. Lak, "Dsign, Fabrication, and Tsting of th DARPA/right Lab" Smart ing" ind Tunnl Modl," Journal of Amrican Institut of Aronautics and Astronautics (AIAA), 997. [2] E. Forstr, B. Sandrs, and F. Eastp, "Synthsis of a Variabl Gomtry Trailing Edg Control Surfac," AIAA papr, vol. 77, 23. [2] M. Djavarshkian, "A nw NVD Schm in PrssurBasd Finit Volum Mthods," in 4th Australasian Fluid Mchanics confrnc,, Adlaid Univrsity, Adlaid, Australia, 2, pp. 4.
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