FINDING THE OPTIMUM ANGLE OF ATTACK FOR THE FRONT WING OF AN F1 CAR USING CFD

Transcription

1 Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34) FINDING THE OPTIMUM ANGLE OF ATTACK FOR THE FRONT WING OF AN F1 CAR USING CFD J. Jagadeep Reddy B. Tech (Mech) IIIrd year VIT, Vellore-14(TN),India Mayank Gpa B. Tech (Mech) IIIrd year VIT, Vellore-14(TN),India Absrac:-The F1 car is vehicle designed o obain mamm speed across a race rack. Earlier, he main mode for achieving speed was he developmen of engine b now aerodynamic forces downforce and drag are an objec of concern by he eam o achieve higher speeds. The drag and downforce are he wo imporan forces governing he efficiency of a road vehicle. They inflence he op sraigh line speed and cornering speed significanly for an F1 car. This in rn inflences he performance of he car. The general design of he vehicle is sch ha lo of downforce is reqired o keep he car gled o he rack.. The fron wing, rear wing and he diffser are he imporan componens o achieve his. The fron wing is spposed o generae abo 5% of his downforce. These forces are dependen on C L & C D which depend on he angle of aack. The paper ses a nmerical approach o finding he variaion of hese parameers on angle of aack sing he CFD sofware FLUENT. In he meshing sofware GAMBIT he bondary condiions for he problem were specified as per he real problem analysis. The Reynold s nmber for his kind of flow is beween 10 6 o 3*10 6. Hence, k-ε model of rblence was sed. The resls were correlaed wih previos resls. Sbseqenly, he angle of aack was alered for obaining he parameers a varios angles o obain he opimm angle of aack. Keywords: CFD compaional flid dynamics, CAE, Reynold s nmber, downforce 1. Inrodcion:- The main objecive of he F1 eams is o achieve op speed. Earlier he designers were dependen on he horsepower for achieving heir aim b recenly hey are rying o achieve heir aim hrogh aerodynamic forces. The aerodynamic sep for a car can vary considerably beween race racks, depending on he lengh of he sraighs and he ypes of corners; and he opimm sep is always a compromise beween he wo. The wings fied o hese cars are very significan facors of aerodynamic forces. Negaive lif is indced by creaing a lower pressre below he wing which is creaed by higher-velociy airflow below he wing srface. This negaive lif comes a a cos. For any amon of lif gained, drag also increases. The drag forces are an imporan facor in deermining he aainable op speed. These forces are deermined by he angle of aack se p by he fron wing as i is he firs par of he car o come in conac wih he air..1 Lierare:- Angle of aack is a erm sed in aerodynamics o describe he angle beween he airfoil's chord line and he direcion of airflow wind, The amon of lif generaed by a wing is direcly relaed o he angle of aack, wih greaer angles generaing more lif and more drag. This remains re p o he sall poin, where lif sars o decrease again becase of airflow separaion. A minor change in angle of aack or heigh of he vehicle has cased he car o

2 Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34) experience lif, no downforce, someimes wih disasros conseqences.[1] The goal of any designer in he wind nnel is o mamize negaive lif while also minimizing drag. The greaer he Lif-o-Drag raio, he faser he lap imes raio, he faser he lap imes are. []The wind nnel provides an effecive means of simlaing real flows. Recen works have shown he variaion of C l & C d wih he angle of aack of high performance vehicle [3] for wind nnel esing. In he design of eqipmen ha depends criically on he flow behavior, like he aerodynamic design of an aircraf, fll-scale measremen, as par of he design process is economically impracical. This siaion has led o an increasing ineres in he developmen of a nmerical wind nnel. Coss incrred by he F1 companies in rnning he wind-nnels have been ablaed for he op for F1 eams in he year 005 Table 1. Wind Tnnel Coss[4] Company Cos incrred in wind nnel name esing in 005(in millions dollars) 1. Ferrari Mclaren Mercedes 3. BMW Wiliiams 4. Toyoa 8.95 This siaion has led o an increasing ineres in he developmen of a nmerical wind nnel. In [5], he ahor has calclaed he C l and C d for an airfoil by simlaing he bondary layer scion heory wih a aerodynamic design program in he FORTRAN sorce code.. CFD Review:- The Physical aspecs of any flid flow are governed by hree fndamenal principles: Mass is conserved; Newon's second law and Energy is conserved. These fndamenal principles can be expressed in erms of mahemaical eqaions, which in heir mos general form are sally parial differenial eqaions. This branch of flid dynamics complemens experimenal and heoreical flid dynamics by providing an alernaive cos effecive means of simlaing real flows. Compaional Flid Dynamics is he science of deermining a nmerical solion o he governing eqaions of flid flow whils advancing he solion hrogh space or ime o obain a nmerical descripion of he complee flow field of ineres. This branch of flid dynamics complemens experimenal and heoreical flid dynamics by providing an alernaive cos effecive means of simlaing real flows. As sch i offers he means of esing heoreical advances for condiions navailable on an experimenal basis. CFD echnology is now mare enogh o provide sfficienly accrae resls for he exernal aerodynamic analysis. Choice of cell shapes, mesh srcres and grid resolion, inflences he qaliy of he CFD resls more han any oher single facor. Mos aomaic mesh generaion sraegies se erahedral cells ha are highly diffsive, reqiring very large nmber of cells o prodce accrae resls. I is no nsal for an all-erahedral mesh cells o accraely predic flow arond an F1 racing car. Oher isses affecing he qaliy of resls inclde he choice of rblence models, choice of wall reamen, bondary posiions and condiions, and assming wheher flow arond he car is seady or ransien. [8] F.Morel in his hesis [6] in he year 003 has shown he emphasis of differen designs of airfoils for achieving aerodynamic efficiency. The C l variaion wih he angle of aack for a finie wing has also been shown. [7].(a) Airflow Modeling [9] Airflow modeling based on Compaional Flid Dynamics (CFD), for he fndamenal conservaion eqaions for mass, momenm and energy in he form of he Navier-Sokes eqaion, are:- ρ ( ρϕ ) + div( ρvϕ gradϕ = Γ ) ϕ Transien + Convecion- Diffsion=Sorce Where, = Densiy v ρ = Velociy Vecor ϕ = Dependen variable = Γϕ Exchange Co-efficien( Laminar+ Trblen) Sϕ =Sorce and Sink Airflow modeling solves he se of Navier-Sokes eqaions by sperimposing a grid of many ens or even hndreds of hosands of cells ha describe he physical geomery and hea sorces and air iself. S ϕ

3 Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34).(b) k-ε model The k-ε model is derived by sbsiing he sm of an average erm pls a flcaing erm for he insananeos qaniies in he eqaions below:- p + ρ = 0 1 ρ( + w) + p ρg = σ α The average erms are expeced o vary less han he insananeos qaniies and, herefore, can be resolved over a coarser grid. This averaging procedre yields an addiional nknown erm called he Reynold s Sress ( ρ ' ). The addiional i ' nknowns are resolved by inrodcing he eddy viscosiy concep, which resls in wo addiional ranspor eqaions, one each for k and ε, and five empirical consans.[10] For he wo-eqaion model based on boh a ranspor eqaion for rblen kineic energy k and a ranspor eqaion for he dissipaion of rblen kineic energy ε. A general formlaion is given by [11] Dρε k K = (( µ + ) ) + P+ G ρε D C µ Eqaion 1 Dρε = D C f (( µ + ε ρ + k C µ σ k µ σ ε 4 µ ε ) ) + C1 f 1 µ ( i ) x i x j i ( i + ρ x i ε ( P+ k j Where P=µ ) j And he boyancy erm, G= β j g C G) 3 µ iσ ( ) 5 T Eqaion The rblen viscosiy µ is obained from µ = k ρ µ f c µ ε Eqaion 3 The convenional k-e model is achieved when ƒ 1, ƒ, ƒ µ and C 3 are eqal o one and C 4 and C 5 are zero. A low Reynolds nmber k-ε describing flow close o a solid srface can be obained from eqaions 1, and 3 sing he following expressions ƒ 1 = C 3 = C 4 = C 5 = 1.0 ƒ = exp ( - R * R ) ƒ = exp ( -3.4/(1+ R / 50) ) where he rblen Reynolds nmber is R = ρk / µε The ieraion procedre in a nmerical predicion ofen will be sabilized by a high level of rblence. Iniial ieraions can be performed wih a high and consan eddy viscosiy and he predicion, a a laer sage, be conneced o a k-e model. 3. CAD Model:- 3.1 Fron Wing- Model of he fron wing was designed in he SOLIDWORKS 005 as per he reglaions for he year 005 and considering all he above menioned facors inflencing he aerodynamic properies. The relevan reglaions are ablaed below in able Table [1] Aricle FIA Formla 1 Technical reglaion 1. Overall heigh No par of he bodywork may be more han 950mm above he reference plane.. Fron bodywork heigh All bodywork siaed forward of a poin lying 330mm behind he fron wheel cenre line, and more han 50mm from he cenre line of he car, ms be no less han 100mm and no more han 300mm above he reference plane. 3. Bodywork arond he fron wheels Wih he excepion of brake cooling dcs, in plan view, here ms be no bodywork in he area formed by wo longidinal lines parallel o and 400mm and 900mm from he car cenre line and wo ransversal lines, one 350mm forward of and one 800mm behind he fron wheel cenre line. The wheel was designed wih a radis of 330mm, here wheel were c on boh faces wih a circle of 100mm. radis for a deph of 100mm. o make space for he sspension rods on he inside and for he wheel monings on he oside. The sspension rod is sed o connec he wheel o he nose of he car.

4 Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34) Also he edges of he wheel were ronded off wih a fille of radis 50mm. o lessen he drag. The frhermos poin of he fron wing is 900mm. from he wheel cener as per he reglaions and he end plaes are 00mm. hick. The sweep back angle sed for he wing is 5 degree. The chord lengh of he wing is 00mm. and i is exended for 1360mm. beween he end plaes. The widh of he whole fron wing is 1400mm. where as he wheel base of he car is 1800mm. The wing main plane is ofen raised in he cener. This again allows a slighly beer airflow o he nder floor aerodynamics, b i also redces he wings ride heigh sensiiviy.[13] Each fron aerofoil is made a main plane rnning almos he whole widh of he car sspended from he nose. The flaps are sally made of one piece of carbon fiber. On each end of he main plane here are endplaes.the end plaes are 00mm. hick The primary fncion of he end plae is o sop he highpressre air on he op of he wing from being encoraged o roll over he end of he wing o he low-pressre air beneah, casing indced drag. Also, he design aim of he endplaes is o discorage he diry air creaed by he fron ire from geing nder he floor of he car. cenre line. To apply he Finie Volme Approach a volme [100x1000x000] was creaed arond he spli model where he bondary condiions were defined. The wheel base was made o coincide wih he floor of he volme. The volme creaed was meshed separaely han he wheel and wings. The meshing sed was Qadrilaeral\Pave for wih a spacing of 40mm. for wing faces and wheel and Terahedral-T-grid wih 60mm. of spacing for he volme. The mesh spacing was kep large o avoid excessive ime consmpion in comping. The bondary condiions have been se as follow: [6] -he inle of he domain: The flow psream of he fron wing is no disrped by he oher devices of he car even if he flow may be disrped if he car follows anoher one. So he inle was se as velociy inle wih an inensiy and lengh scale rblence ype: -he airspeed a he enrance is eqal o 60 m/s. he rblence inensiy is se o 3% which is a sandard vale recommended (o ge siable resls for he wheel & oher rblence inensiy (down o 0.1%) coefficiens were ried b he resls did no change as expeced. -he lengh scale is se o 0.3 m which is he average lengh of he chord of he wo airfoils from -I is obvios for he side ha deals wih he cenre of he car as he laer was spli ino wo secions. 4 1 Figre 1 If angled, he vane can generae more downforce as air flows over he op srface more qickly han i does over he lower srface. This gives he car greaer sabiliy dring cornering while redcing sraigh line speed.[14]. The main aim is o deflec he sir over he car as nder he car he air faces a lo of obsrcion o i s flow and can no be smoohened o a greaer accracy compared o over i. 3. Meshing- The creaed model in SOLIDWORKS was expored o he GAMBIT for meshing. In GAMBIT, as he model is symmeric abo i s cenre line, hence, i was spli in halves abo he 3 Figre. 1-symmery -Velociy Inle 3-Wall 4- Oflow Table 3 Bondary Condiions S. no The par Bondar y Type moion of Speed

5 Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34). condiion 1. Fron Saionar None NA wing y wall. Road Moving Translaion 60m\s wall al 3. Wheel Moving Roaional ( 181.8ra wall abo i s d\s as) 4. Domai Oflow NA NA n sides 5. Car cenre side Symmer y NA NA As is clear from he bondary condiions, he real problem was analyzed wih he applicaion of relaive moion. The moving objecs in he acal problem were se saionary and he saionary objecs were made moving wall (road and flid). The basic idea for seing he problem like ha lies in he fac ha he relaive moion beween he wo remains he same as in he acal problem. In wind nnel esing, hey se he same approach as defined for he problem o here wih he air being se a a high velociy. The Reynold s nmber for his flow was calclaed o be beween 10 6 and 3x10 6 [4]. So, he rblen kε model is seleced as per he real condiions as i is a hree dimensional model and he flow can be considered o a low Reynold s nmber flow. The CFD eqaions for he model have been shown in he review. The flid seleced was air narally, and was se a a velociy of 60m/s in he direcion opposie o he direcion of he road. The convergence crierion and oher force moniors were all defined wih a convergence crierion of 1e-03. The solion for all he angles converged a 170 ieraions. 4. Resl:- Table 4 Angle of aack Coefficien of lif(cl) Coefficien of drag(cd) Raio= (Cl/Cd) - 1 degree degree degree degree degree degree CFD SOLVER:- The CFD solions were carried o wih Flen 6.1. The laer is a solver of he Navier-Sokes eqaions. The remaining condiions for solving he problem were defined in he solver. The grid size was checked and he 811 faces impored ino FLUENT were smoohened and swapped for covering he enire face and volme. The ransien componen of he eqaion above was solved sing he explici approach. A segregaed solver is sed in sch a mehod as he eqaions are only solved as dependens of ime. The convergence crierion defined was of he order of 1e-03. For he convecion componen, he SIMPLE algorihm was sed for resricing he compaion ime. The file impored in he solver had nodes, 1530 mixed wall faces in zone 3, 034 mixed wall faces in zone 4, 147 mixed wall faces in zone 5, 770 mixed oflow faces in zone 6, 768 mixed velociy-inle faces in zone 7, 401 mixed symmery faces in zone 8, mixed inerior faces in zone 10, erahedral cells in zone. Figre 3. (Residals plo) Cl/Cd Angle Of Aack Fig. 4 (-C L / C D v/s Angle of Aack)

6 Proceedings of he 4h WSEAS Inernaional Conference on Flid Mechanics and Aerodynamics, Elonda, Greece, Ags 1-3, 006 (pp9-34) Angle Of Aack Fig. 5 (C L & C D v/s Angle of Aack) 5. Conclsion:- From fig. 4, i can be inferred ha he opimm angle occrs a 4degree. The downforce iniially increases wih he increase in angle of inclinaion b declines beyond for degree. The air is defleced by he air over he body of he car. The iniial increase arises de o he defleced air having he effec on he flow of air over he body as i is defleced in close viciniy of he car body, b as he angle of inclinaion increases he air is defleced farher away from he body hs redcing i s inflence on he airflow, and hence decreasing downforce. The drag co-efficien rises as he angle of inclinaion is increased. This is mainly de o increase in he fronal area being exposed o he incoming air, hs providing more resisance o he airflow. As he angle of inclinaion increases, he exposed fronal area keeps increasing frher. The Monza circi has long sraigh sreches forming significan porions of he circi. To achieve op sraigh line speed in his porion, he designers shold consider for he angle wih he leas vale of C D. So an angle less han he opimm angle of aack is o be considered. Monaco circi, de o a nmber of high speed corners more downforce is significan han drag as here is no a sraigh srech sfficien enogh for he cars o reach op sraigh line speed. Beer resl can be achieved only wih high speeds a corners in his circi. The opimm angle of aack provides he highes vale of C l. So he fron wing shold be se a ha angle. The Isanbl circi has a good combinaion of sraigh Cl Cd sreches and rns. An angle beween he opimm and wih he leas vale of C D can be decided pon depending pon he weaher condiions, wind speed and oher facors for ha day. [15] References: 1. hp://en.wikipedia.org\wiki\formla_one_carsaerodynamics. Cirlnick Daniel, Design consideraions for Formla one, Engineer s Form, pp 6-7, Sepember 005 isse, Baker corporaions (005) 3. Hcho, Wolf-Heinrich Aerodynamics of Road Vehicles, 4 h ediion, Pg. no. 396, SAE Inernaional,(1998) 4. F1 Racing, April 005 isse, Pg. no. 61Haymarke Magazines Ld., (005) 5. Terry,L.N., Exension of he Aerodynamic Design Program MSES for Simlaing he Bondary Layer Scion, pp 9,(004) 6. F Morel, Cranfield Team F1: The Fron Wing,pp 1, 7, 31, 003/F.Morel.003.pdf (003) 7. Anderson John D.,JR., Inrodcion o Fligh, pp. 39,McGraw-Hill Pblicaions (000) 8. mlaion.hml 9. Peer V. Nielsen, The Selecion of Trblence Model for Predicion of Airflow, Inernaional Jornal of Bilding & Environmen, pp.119, ASHRAE Transacions: Symposia, Elsewhere Pblicaions, 10. Emmerich Seven J., McGraan Kevin B., Applicaion of a Large Eddy Simlaion Model o Sdy Room Airflow, pp. 119,1131, ASHRAE Transacions: Symposia, Elsewhere Pblicaions, 11. Memarzadeh Farhad, Manning Andrew P., Comparison of he Operaing Room Venilaion Sysems in he Proecion of he Srgical Sie, pp. 5, Inernaional Jornal of Bilding & Environmen, ASHRAE Transacions: Research, Elsewhere Pblicaions, Aerodynamics Feares of he F1 Vehicle, Fron wing and Nose Assembly, engineer/aerodynamics/f1-aerodynamics.hml F1 Racing, Ocober 005 isse, Pg. no. 144,15,160,Haymarke Magazines Ld., (005)