Aerodynamic analysis involving moving parts with XFlow

Transcription

1 Aerodynamc analyss nvolvng movng parts wth XFlow Ths report presents some of the possbltes of XFlow 2011, specfcally those related to the aerodynamc analyss of movng parts. Usng tradtonal Computatonal Flud Dynamcs (CFD) software, ths knd of problems requre tme consumng remeshng processes, whch often lead to errors or dvergence of the smulaton. Due to the partcle-based fully Lagrangan approach of XFlow, movng parts such as a vehcle wth suspenson system or the forced rotaton of the wheels can be easly handled, namely the only parameters requred as nput are the physcal and mechancal propertes of the objects. Furthermore, full vehcle models can be drectly used n the smulaton, and thus the complexty of the surfaces s not a lmtng factor. 1: Introducton The development of vehcle aerodynamcs based on a combnaton of vrtual and physcal methods has become an ntegral part of the desgn process. When aerodynamc forces are calculated, the change of rde heght due to lft forces actng on the vehcle s often neglected. Ths approach mght be applcable for standard cars, but may lead to msleadng results for sports and race cars, where large downforce values change rde heghts substantally (Drage and Redler, 2009). Usng the software presented here, t s possble to smulate the vehcle full (6 DOFs) movement accordng to the aerodynamc forces. 2: Numercal Methodology In the lterature there are several partcle-based numercal approaches to solve the computatonal flud dynamcs. They can be classfed n three man categores: Algorthms modellng the behavour of the flud at mcroscopc scale (e.g. Drect Smulaton Montecarlo); algorthms whch solve the equatons at a macroscopc level, such as Smoothed Partcle Hydrodynamcs (SPH) or Vortex Partcle Method (VPM); and fnally, methods based on a mesoscopc framework, such as the Lattce Gas Automata (LGA) and Lattce Boltzmann Method (LBM). The algorthms that work at molecular level have a lmted applcaton, and they are used manly n theoretcal analyss. The methods that solve macroscopc contnuum equatons are employed most frequently, but they also present several problems. SPHlke schemes are computatonally expensve and n ther less sophstcated mplementatons show lack of consstency and have problems mposng accurate boundary condtons. VPM schemes have also a hgh computatonal cost and besdes, they requre addtonal solvers (e.g. schemes based on boundary element method) to solve the pressure feld, snce they only model the rotatonal part of the flow. Fnally, LGA and LBM schemes have been ntensvely studed n the last years beng ther affnty to the computatonal calculaton ther man advantage. Ther man dsadvantage s the complexty to analyze theoretcally the emergent behavour of the system from the laws mposed at mesoscopc scale. XFlow's approach to the flud

2 physcs takes the man deas behnd these algorthms and extends them to overcome most of the lmtatons present on these schemes. 2.1: Lattce Gas Automata LGA schemes are smple models that allow solvng the behavour of gases. The man dea s that the partcles move dscretely n a d-dmensonal lattce n one of the predetermned drecton at dscrete tmes t = 0, 1, 2,... and wth velocty c, = 0,...,b, also predetermned. The smplest model s the HPP, ntroduced by Hardy, Pomeau and de Pazzs, n whch the partcles move n a two-dmensonal square grd and n four drectons. The state of an element of the lattce at nstant t s gven by the occupaton number n (r; t), wth = 0,..., b, beng n = 1 presence and n = 0 absence of partcles movng n drecton. The equaton that governs the evoluton of the system s as follows: n r ct, t t) n ( r, t) ( n1,..., nb ) where Ω s the collson operator, whch for each prevous state (n 1,...,n b ) computes a post-collson state (n 1 C,..., n b C ) conservng the mass, lnear momentum and energy, r s a poston n the lattce and c a velocty. From a statstcal pont of vew, a system s consttuted by a large number of elements whch are macroscopcally equvalent to the system nvestgated. The macroscopc densty and lnear momentum are: 1 b n 1 v b 1 b 1 b n c 2.2: Boltzmann s transport equaton Boltzmann s transport equaton s defned as follows: B f ( r ct, t t) f ( r, t) ( f1,..., fb ) where f s the dstrbuton functon n the drecton and Ω B the collson operator. From ths equaton and by means of the Chapman-Enskog expanson, the compressble Naver-Stokes equatons can be recovered. The man advantage of these methods s ther great affnty wth computers. They are easly programmed and very effcent. Some schemes have sotropy problems (do not satsfy Gallean nvarance) and produce very nosy results. The man contrbuton of LGA schemes s that they were precursor of the Lattce Boltzmann method. 2.3: Lattce Boltzmann method The orgns of the Lattce Boltzmann Method (LBM) (Chen, Chen and Matthaeus, 1992; Hguera and Jmenez, 1989; McNamara and Zanett, 1988) le n the LGA schemes. Whle the LGA schemes use dscrete numbers to represent the state of the

3 molecules, the LBM method makes use of statstcal dstrbuton functons wth real varables, preservng by constructon the conservaton of mass, lnear momentum and energy. It can be shown that f the collson operator s smplfed under the Bhatnagar- Gross-Krook (BGK) approxmaton, the resultng scheme reproduces the hydrodynamc regme also for low Mach numbers. Ths operator s defned as follows: BGK 1 f eq f where f eq s the local equlbrum functon and τ s the relaxaton characterstc tme, whch s related to the macroscopc vscosty n the followng way: c 2 s 1 2 wth c s the speed of sound. For a postve vscosty, the relaxaton tme must be greater than 0.5. The most nterestng aspect s that these schemes are able to model a wde range of vscostes n an effcent way even usng explct formulatons. 2.4: Turbulence modellng The approach used for turbulence modellng s the Large Eddy Smulaton (LES). These schemes solve the turbulence n a local way, modellng only the smallest scales, and are closer to the physcs. The turbulence at smallest scales has been extensvely studed and ts behavour can be reproduced wthout usng arbtrary parameters. The LES scheme adopted by default by XFlow s the Wall-Adaptng Local Eddy vscosty (WALE) (Ncoud and Ducros, 1999), whch has good propertes both near and far of the wall and n lamnar and turbulent flows. 2.5: Treatment of movng geometres The treatment of movng boundary condtons s straghtforward and smlar to the handlng of fxed boundares. In basc LBM mplementatons the wall boundary condtons for straght boundares are typcally mplemented followng a smple bounceback rule for the no-slp boundary condton and a bounce-forward rule for the free-slp. In XFlow the statstcal dstrbuton functons f comng from the boundares are reconstructed takng nto account the wall dstance, the velocty and the surface propertes. The set of statstcal dstrbuton functons to be reconstructed s recomputed each tme-step based on the updated poston of the movng boundares. A reference dstance to the wall, velocty, surface orentaton and curvatures are taken nto account n order to solve the wall boundary condton. As the physcs are not mplemented usng surface elements XFlow relaxes the requrements mposed to the geometres and s tolerant to crossng or complex surfaces. Fnally, a unfed non-equlbrum law of the wall model takes nto account for the under-resolved scales at the boundary layer.

4 3: Numercal results In ths secton we wll show the capabltes of XFlow for smulatng the dynamc vehcle response to changng flow condtons n two cases: a smplfed reference model and a real race car. In the frst case we wll compare the behavour of the suspenson system n condtons of regular aerodynamc forces (vertcal dsplacement and ptchng) and gusty sde wnd (wth rollng as addtonal DOF). For the real race car we wll nclude the effect of the rotatng wheels and compare the suspenson behavour at dfferent rde veloctes. Fnally, we also smulate the maneuver of a car overtakng a truck and measure the forces experenced by both vehcles. 3.1: Smplfed reference car The model chosen s the well known Aerodynamsches Studenmodel (ASMO). It comprses a square-back rear, smooth surfaces, boat talng, underbody dffuser and no pressure nduced boundary layer separaton (Perzon and Davdson, 2000). The geometry has a well defned separaton lne and s characterzed by a low drag shape. For ths model, expermental data from Damler Benz and the Volvo model scale wnd tunnel are avalable. CFD valdatons usng the ASMO have already been publshed by several authors. Perzon and Davdson (2000) showed that usng transent CFD smulatons, surface pressure values can be computed farly accurate. The overall drag coeffcent however, s not predcted satsfactorly. The present smulatons are performed usng a wnd tunnel of dmensons 9 x 1.5 x 3m (whch corresponds to a blockage rato of 1.38%) and Reynolds number Re=2.7x10 6 (takng the length of the vehcle as reference). Partcle resoluton n the far feld s 0.1m, whle n the wake and on the model surface, scales up to 2.5mm are resolved. Dynamc wake refnement s appled, so the partcle resoluton s automatcally adopted n regons wth hgh turbulence, whle less turbulent regons are treated wth fewer partcles. The ntal number of partcles s 1 mllon, whle at fnal tme t=0.25 the number of partcles acheves 20 mllon. Fgure 1: Snapshot of sosurfaces of vortcty Typcally, drag stablzes n a characterstc tme n the order of the tme requred for the flow to travel along the vehcle length. In 0.1 seconds, the flow has travelled more than sx tmes the whole body. The tme averaged drag coeffcent between 0.05 and 0.1 seconds of physcal smulaton s c d = 0.151, whch s n good agreement wth the values measured n the experments, shown n Table 1. RANS turbulence models tend to overestmate the drag.

5 Smulaton XFlow Experments Volvo Experments Damler Benz Table 1: drag coeffcent of the ASMO Fgure 2 shows valdaton results of surface pressure measurements, whch have been performed both n the Volvo and the Damler Benz wnd tunnel. Data s avalable n the symmetry plane and s shown for roof, underbody, front and base regon of the vehcle. It can be seen, that the comparson wth the measurements s good, although some devatons can be observed. Especally the base pressure s slghtly underpredcted, and shows some unphyscal peak at the transton from roof to base. The proper level of the base pressure s not known exactly, as there s a large dfference between the two experments. a) symmetry plane roof b) symmetry plane underbody c) symmetry plane front regon d) symmetry plane base Fgure 2: Comparson of surface pressure measurements wth the smulaton (Drage et al, 2010). Next we show the results of the ASMO calculaton when the vehcle poston wth respect to the ground s modfed due to aerodynamc forces. Studes to analyze vehcle response to turbulence and sde wnd, or the effect of ptchng and rollng moton have already been performed and publshed by several authors; see for example Schröck, Wddecke and Wedemann (2009) and Tsubokura et al (2009).

6 For the analyss of the ASMO wth ptchng and vertcal moton, the wheels have been separated from the man body and a wheel space has been created to allow the dsplacement of the man body. It s assumed that the vehcle s a rgd body of mass m and moment of nerta I z wth a suspenson that wll be modelled as a two-degree-offreedom (DOF) system. The DOFs are: the bounce dsplacement about the body's centre of gravty (y, n meters) and the ptchng angle (rotaton wth respect to the z-axs, α, n radans), see Fgure 3. k and c are the equvalent sprng stffness and dampng of the suspenson respectvely. The centre of gravty (CoG) has been defned slghtly lower than the locaton of the geometrcal centre to make t more realstc. Fgure 3: Schematc of the ASMO case wth sprng and dampng element The equatons for the external force F y and external moment M z read: F y m y c 1 y k 1 y M z I c 2 k z 2 and the values taken n the smulaton are the followng: m 1 kg I z Kg m 2 k N m -1 c N s m -1 k 2 25 N m -1 c 2 5 N s m -1 Table 2: Physcal propertes for the ASMO suspenson system smulaton Fgure 4 shows snapshots of velocty n the symmetry plane for dfferent smulaton tmes. It can be seen how the vehcle changes ts vertcal poston due to aerodynamc forces. Specally n the underbody and dffusor regon, the modfed vehcle poston changes the flow consderably.

7 a) t = 0.2 s b) t= 0.25 s Fgure 4: Instantaneous velocty feld at symmetry plane and ground plane. In the case ncludng rollng, the stffness and dampng coeffcents for the rotatonal sprng n x-drecton (k 3 and c 3 ) are scaled by a factor of transversal dstance/longtudnal dstance between wheels = 0.4, so that k 3 = 10 N m -1 and c 3 =2 N s m -1. A sde wnd n z-drecton of 50 km/h (13.88 m/s) was appled for the smulaton. Because n the vrtual wnd tunnel doman type the boundary condtons n the z- drecton are perodc, the lateral wnd has been modelled as a varable external acceleraton law; see Fgure 5a. Fgures 5b and 5c compare the vertcal dsplacement and ptchng angle for the cases wthout and wth sde wnd. We can observe that the vehcle poston s automatcally adapted to reach equlbrum. The presence of lateral forces cause a smaller dsplacement and slghtly smaller ptchng angles. The rollng (Fgure 5d) s manly caused by the gust. The changng flow condtons and the moton of the car body lead to an ncrease of the drag and sde force coeffcents (Fgure 6).

8 a) Sde wnd velocty (n m/s) b) Vertcal dsplacement at CoG (n meters) b) Ptchng angle (n degrees) d) Rollng angle (n degrees) Fgure 5: Sde wnd velocty and comparson of vertcal dsplacement, ptchng and rollng angle a) Drag coeffcent

9 b) Sde force coeffcent Fgure 6: Comparson of drag and sde force coeffcents 3.2: Race car The aerodynamcs of race cars s hghly dependent on rde heght. Rde heght agan depends on aerodynamc forces, whch n turn depend on vehcle setup and drvng velocty. In ths secton we analyze the aerodynamcs of the KTM XBow (see Fgure 7) and compare the suspenson behavour at veloctes 140 km/h and 200 km/h. In the smulatons 2 DOFs are enabled (vertcal dsplacement and ptchng), the weght of the vehcle and the sprng forces n front and rear axles are set usng the values provded by the manufacturer, and the wheels are modelled as real rotatng parts. A resoluton of 2 cm has been used close to the vehcle and n the wake. The ntal rde heght s approxmately the equlbrum heght at 140km/h. Fgure 7: KTM XBow race car

10 The results are shown n Fgure 8. As expected, the larger downforces at 200km/h cause larger vertcal dsplacements and ptchng angles. a) Vertcal dsplacement at CoG (n meters) b) Ptchng angle (n degrees) Fgure 8: Vertcal dsplacement and ptchng angle for the KTM XBow at 140 and 200 km/h 3.3: Overtakng maneuver The last example s a proof of concept of an overtakng maneuver under sde wnd condtons; see Fgure 9. The car follows a forced moton that descrbes the overtakng of a truck. The nlet flow velocty s of 30 m/s n x-drecton and the lateral wnd velocty of 20 m/s n z-drecton.

11 Fgure 9: Car overtakng a slower truck The smulaton allows to montor the evoluton of the aerodynamc coeffcents durng the maneuver, as shown n Fgure 10. For t<3 s the car s nsde the wake of the truck and ths causes ts lateral wnd force coeffcent c z to progressvely decrease. From there on, c z ncreases (due to the flow that passes under the truck) untl reachng a maxmum when the car overtakes the truck and s fully exposed to the wnd. The car experences a low drag whle the car s wthn the wake of the truck and stablzes at a reasonable value once the maneuver has fnshed. Forces on the truck reman qute unform durng the whole maneuver. a) Trajectory of the car b) Aerodynamc coeffcents of car and truck Fgure 10: Evoluton of aerodynamc coeffcents durng overtakng

12 REFERENCES Chen, H., Chen, S., and Matthaeus, W. (1992) "Recovery of the Naver-Stokes equatons usng a lattce-gas Boltzmann method", Physcal Revew A, vol. 45, pp Drage, P., and Redler, S. (2009) "On the Aerodynamc Development of a Lght Weght Sports Car by Means of CFD", 7 th FKFS Conference, Stuttgart. Drage, P., Kussmann, C., Holman, D.M. and Mer-Torreclla, M. (2010) "Smulaton of Unsteady Aerodynamcs usng a Mesh-less Partcle Approach", 8th MIRA Internatonal Vehcle Aerodynamcs Conference, pp Hguera, F.J., and Jmenez, J.(1989) "Boltzmann approach to lattce gas smulatons", Europhyscs Letters, vol. 9, pp McNamara, G., and Zanett, G., (1988) "Use of the Boltzmann equaton to smulate lattce-gas automata", Physcal Revew Letters, vol. 61, pp Ncoud F. and Ducros F. (1999) "Subgrd-scale stress modelng based on the square of the velocty gradent tensor", Flow, Turb. & Comb., vol 62, pp Perzon, S., and Davdson, L.(2000) "On Transent Modellng of the Flow Around Vehcles Usng the Reynolds Equatons", ACFD 2000, Bejng. Schröck, D., Wddecke, N., Wedemann, J.(2009) "Aerodynamc Response of a Vehcle Model to Turbulent Wnd", 7 th FKFS Conference, Stuttgart. Tsubokura, M., Nakashma, T., Ktoh, K., Sasak, Y. (2009) "Development of Unsteady Aerodynamc Smulator Usng Large-Eddy Smulaton", 7 th FKFS Conference, Stuttgart.