Vol.2, Issue.3, May-June 2012 pp-1253-1259 ISSN: 2249-6645 Dag Optimization on Rea Box of a Simplified Ca Model by Robust Paamete Design Sajjad Beigmoadi 1, Asgha Ramezani 2 *(Automotive Engineeing Depatment, Ian Univesity of Science and Technology, Ian) ** (Automotive Engineeing Depatment, Ian Univesity of Science and Technology, Ian) ABSTRACT Reducing fuel consumption of cas is one of the main tagets of the automotive manufactues. Optimum design of ca fom the aeodynamic viewpoint to educe dag coefficient is one of the efficient methods towad this aim. In this pape, optimum geometical paametes of ea box in a simplified ca model ae obtained to minimize aeodynamic dag. Fo this pupose, the poweful method of obust paamete design (RPD) along with computational fluid dynamics is used. Optimum values of the paametes obtained by the RPD method is compaed with the esults of numeical simulations. The compaisons show good ageement between the esults. Keywods: Vehicle Aeodynamic, Dag Coefficient, Robust Paamete Design, CFD 1. INTRODUCTION Diffeent models ae used in the liteatue to study aeodynamics of vehicles [1]. One of the standad models to study ai flow ove the vehicle ea end is the Ahmed model [2], which is used in many expeimental [3-7] and numeical [8-13] investigations. In sedan cas, besides the slant angle consideed in the standad Ahmed model, thee ae othe geometic paametes like ea box length, ea box angle, and boat tail angle, which have consideable effect on the aeodynamic dag coefficient of the vehicle [14]. Conventional methods fail in finding optimal values of aeodynamic paametes of the vehicle ea end due to lage numbe of paametes and time-consumption and expense of conducting expeimental and numeical pocedues fo diffeent levels of paametes. Theefoe, Taguchi and esponse suface methods of design of expeiments appoach ae used in these studies. These methods ae applied not only in expeimental and industial woks [15-18] but also in expensive and timeconsuming numeical studies such as CFD and cash simulations [19-24]. In this pape, a simplified vehicle model with fou paametes, namely slant angle, ea box length, ea box angle, and tail boat angle is studied. Each of the paametes ae consideed in five levels. Fo educing computational cost, Taguchi method based on the obust paamete design is used in the study and the optimal levels of paametes fo dag eduction ae detemined. The pocess of optimization using Taguchi method is shown in Fig. (1). Fig. (1) Aeodynamic optimization using Taguchi method 2. VEHICLE MODEL The vehicle model used in this eseach is an extended vesion of Ahmed model [2] which is poposed fo studying dag coefficient vaiation due to slant angle. In sedan cas, geometic paametes of ea box has consideable effect on the aeodynamics of the vehicle. These paametes ae ea box length, ea box angle, and boat tail angle. In this study, as well as slant angle which was consideed by Ahmed, ea box angle, boat tail angle, and ea box length, which ae effective paametes on dag coefficient [14] ae consideed. The paametes and dimensions of the model ae shown in Fig. (2). Fig. (2) Extended Ahmed model (dimensions ae in mm) 1253 Page
Vol.2, Issue.3, May-June 2012 pp-1253-1259 ISSN: 2249-6645 The ange of paamete values ae assumed to be fo slant angle, fo ea box angle, box length fo boat tail angle, and fo ea 3. TAGUCHI METHOD Robust paamete design (RPD) is an appoach to obtain the levels of contollable paametes in a pocess to set the output mean at a desied taget and to minimize the vaiability aound this taget value. Taguchi fomulated the geneal RPD poblem and poposed an appoach to solving it based on designed expeiments. He also pesented some novel methods fo analysis of the esults [25]. Taguchi s methodology povides some ules, which simplify and standadize design of expeiments. The key tool in Taguchi s method of paamete design is designed expeiments by statistical methods. The expeiments ae designed using a set of othogonal aays and conducted in-paallel. Utilizing othogonal aays in design of expeiments, consideably deceases the numbe of equied expeiments. I n Taguchi s method, esults of expeiments ae analyzed fo: Detemining Optimal opeation conditions Investigating the influence of each of the factos on the esponse Estimating the esponse in optimal conditions The tool used in Taguchi s method fo analyzing esults of expeiments is signal to noise atio (SN). SN is the atio of signal vaiables to noise vaiables, which ae uncontollable. The aim of SN analysis is detemining the best combination of vaiables to obtain optimal esponse. SN paamete is obtained by minimization of loss function, which is defined as SN= -10 log MSD (1) MSD stands fo Mean Squaed Deviations. Definition of MSD depends on the desied conditions, i.e., When smalle is moe desiable 2 Yi i1 MSD = (2) When bigge is moe desiable 1 i Y 2 1 i MSD = (3) When close is moe desiable 2 ( Yi M ) i1 MSD = (4) Whee Yi is esponse value, M is mean value, and is numbe of epetition of each expeiment. Using this method ensues that the effects of noise vaiables ae less than the signal vaiables, i.e., the final esponse has the minimum sensitivity with espect to noise vaiables. The attactiveness of Taguchi method is that instead of contolling noise vaiables, by educing thei effects minimizes deviation in the quality chaacteistic. This is cost effective since contolling noise vaiables in the poduction pocess is vey expensive. In this study, since the taget is to obtain minimum dag coefficient, the SN definition in (1) is used with MSD in the case of smalle is moe desiable, i.e. (2). Consideing the numbe of paametes and levels assumed fo each paamete, L25 design is used in this study, which educes numbe of simulations fom 625 cases to 25 cases. Table (1) Paamete values at each level Paamete levels The studied paametes and thei levels ae given in Table (1). The configuation of Taguchi L25 design fo the poblem with 4 vaiables, each of which ae in 5 levels, ae shown in Table (2). Afte pefoming 25 simulations of the designs given in Table (2), equations (1) and (2) ae used to calculate signal to noise atio. It should be noted that since the numbe of epetition of each expeiment is 1, the value of is set to 1 in (2). Theefoe, Table (2) Taguchi L25 design fo aeodynamic optimization poblem with 4 vaiables and 5 levels Simulation No. (mm) (mm) 1 5 80 0 0 2 10 160 5 5 3 15 240 10 10 4 20 320 15 15 5 25 400 20 20 1 1 1 1 1 (5) 1254 Page
Vol.2, Issue.3, May-June 2012 pp-1253-1259 ISSN: 2249-6645 2 1 2 2 2 3 1 3 3 3 4 1 4 4 4 5 1 5 5 5 6 2 1 2 3 7 2 2 3 4 8 2 3 4 5 9 2 4 5 1 10 2 5 1 2 Taguchi analysis esults ae given in Figs. (3) and (4) as signal to noise atios and mean value of dag coefficient fo diffeent levels of paametes, espectively. The mean value of dag coefficient epoted fo each level of paametes is summation of dag coefficients at that level divided by 5, e.g., The mean value of dag coefficient at the fist level of the paamete is the aveage of dag coefficients in the simulation numbe 1, 9, 12, 20, and 23. Consideing the signal to noise atio gaphs fo diffeent levels of paametes, the optimum value of paametes ae obtained. Reminding the definition of signal to noise atio in (5), it is obvious that maxima of these gaphs ae the optimal levels of paametes fo minimum dag coefficient. Table (3) Simulation esults and signal to noise atios 11 3 1 3 5 12 3 2 4 1 Simulation No. (mm) Dag Coef. SN atio 13 3 3 5 2 14 3 4 1 3 15 3 5 2 4 16 4 1 4 2 17 4 2 5 3 18 4 3 1 4 19 4 4 2 5 20 4 5 3 1 21 5 1 5 4 22 5 2 1 5 23 5 3 2 1 24 5 4 3 2 25 5 5 4 3 1 5 80 0 0 0.253 11.948 2 5 160 5 5 0.207 13.666 3 5 240 10 10 0.169 15.422 4 5 320 15 15 0.138 17.188 5 5 400 20 20 0.130 17.688 6 10 80 5 10 0.203 13.830 7 10 160 10 15 0.176 15.077 8 10 240 15 20 0.146 16.701 9 10 320 20 0 0.231 12.728 10 10 400 0 5 0.207 13.696 11 15 80 10 20 0.196 14.158 12 15 160 15 0 0.232 12.687 13 15 240 20 5 0.188 14.530 14 15 320 0 10 0.206 13.710 4. RESULTS AND DISCUSSION 4.1. Taguchi Results Analysis Afte pefoming 25 simulations based on the Taguchi L25 design and using othogonal aays algoithm, the esponse can be pedicted in the othe levels of vaiables. The simulation esults fo each design ae shown in Table (3). Using equation (5), the signal to noise atio is computed fo each dag coefficient obtained by simulations. 15 15 400 5 15 0.149 16.527 16 20 80 15 5 0.222 13.058 17 20 160 20 10 0.187 14.569 18 20 240 0 15 0.195 14.195 19 20 320 5 20 0.166 15.592 1255 Page
Vol.2, Issue.3, May-June 2012 pp-1253-1259 ISSN: 2249-6645 20 20 400 10 0 0.207 13.686 21 25 80 5 15 0.213 13.435 22 25 160 0 20 0.208 13.656 23 25 240 5 0 0.234 12.616 24 25 320 10 5 0.189 14.479 25 25 400 15 10 0.167 15.566 As can be seen in Fig. (3), slant angle, length, ea box angle, and boat tail angle ae the optimum values of paametes, which ae veified by mean value of dag coefficient gaphs in Fig. (4). Fig. (4) shows that inceasing slant angle has diect effect while inceasing the ea box length and boat tail angle has invese effect on inceasing dag. Inceasing ea box angle up to deceases the dag coefficient and beyond this value inceases the dag coefficient. The paamete ange is defined as Whee can be eplaced by,,, and. The contibution atio of paametes to dag coefficient is estimated by (7) (6) Whee is The pie chat obtained by equation (13) is shown in Fig. (5). It is obseved that contibution of paametes to dag coefficient eduction is in the ode of boat tail angle, ea box length, and slant angle. (8) Fig. (3) Signal to noise atios fo diffeent levels of paametes 1256 Page
Vol.2, Issue.3, May-June 2012 pp-1253-1259 ISSN: 2249-6645 Fig. (5) Contibution atios of paametes to dag coefficient 4.2. Validation of Taguchi Results In the pevious section, the optimum values of paametes fo obtaining minimum dag coefficient is computed by Taguchi method. The optimal dag coefficient pedicted by Taguchi method is. Now Taguchi pediction is validated by simulation. Table (4) Optimum values of paametes and dag coefficient Paamete Optimum Value Slant angle (degee) Rea box length(mm) Rea box angle (degee) Boat tail angle (degee) Dag coefficient by Taguchi Dag coefficient by simulation Diffeence between Taguchi & simulation 5 400 15 20 0.124 0.132 6% Fig. (4) Mean value of dag coefficient fo diffeent levels of paametes As can be seen in Table (4), Taguchi esults ae in good ageement with the simulation esults. Theefoe, the paamete values obtained by Taguchi method can be accepted as optimum values. 4.3. Investigation of Flow Aound Optimal Model Figues (6) and (7) show that simila to the Ahmed model, 2 D and 3 D votices ae fomed at the ea end of the optimal model. In contast to the Ahmed model, due to the configuation of optimal model, the size of votices is deceased consideably and the existence of ea box makes delay in sepaation of flow. Despite this fact, fomation of fou 3 D votices on side edges of the ea box slipping downwad is clealy obseved. The othe impotant issue to be noted is fomation of votices due to 1257 Page
Vol.2, Issue.3, May-June 2012 pp-1253-1259 ISSN: 2249-6645 boat tail angle compaable to votices on ea box due to slant angle and ea box angle. As can be seen in Fig. (8), the vaiation of pessue coefficient distibution on the optimal model is educed. The fiction dag is inceased due to geneation of bounday laye on the ea box. Theefoe, the contibution of the pessue dag is educed and the contibution of the fiction dag is inceased to oveall dag. In optimal model 51% and 49% of oveall dag is due to fiction dag and pessue dag, espectively. In contay to Ahmed model with 80% and 20% of oveall dag is due to pessue dag and fiction dag, espectively. This discepancy between the optimal and Ahmed models can be justified by steamlining of the optimal model. Fig. (8) Pessue coefficient distibution on the optimal model 5. CONCLUSION In this pape, Taguchi method is used fo optimal aeodynamic design of a simple vehicle model. The optimum values of paametes ae obtained and the contibution of paametes to aeodynamic dag ae detemined. Using Taguchi method has consideable effect on educing computational cost of the CFD simulations in design pocess. Compaing simulation esults of optimal model with the Ahmed model eveals that the contibution of fiction dag inceases and the contibution of pessue dag deceases to oveall dag. Fig. (6) (a) Steamlines based on velocity field on symmety plane, (b) 2 D votices fomed at the ea end of the optimal model Fig. (7) Fomation of 3 D votices at ea end of the optimal model REFERENCES [1] G. M. Le Good, K. P. Gay, On the Use of Refeence Models in Automotive Aeodynamics,SAE TECHNICAL PAPER SERIES, 2004-01-1308. [2] S.R.Ahmed, G.Ramm, Salient Featues of the Time- Aveaged Gound Vehicle Wake,SAE-Pape 840300, 1984. [3] P.Gilliéon, A.Leoy, S.Aubun,P.Audie, Influence of the Slant Angle of 3D Bluff Bodies on Longitudinal Votex Fomation Jounal of Fluids Engineeing, Vol. 132 / 051104-1, MAY 2010. [4] J. Aide,J.Fanc o.beaudoin,j.e.wesfeid, Dag and lift eduction of a 3D bluff-body using active votex geneatos, Exp Fluids (2010) 48:771 789. [5] G. goie Fouie, L. Keisbulck,L. Labaga, P. Gillie on, Bluff-body dag eduction using a deflecto, Exp Fluids (2010), DOI 10.1007/s00348-010-0937-6. [6] R. K. Stachan, K. Knowles, N. J. Lawson, The votex stuctue behind an Ahmed efeence model in the pesence of a moving gound plane, Exp Fluids (2007) 42:659 669. [7] P. Gillie on, A.Kouta, Aeodynamic dag eduction by vetical splitte plates, Exp Fluids (2010) 48:1 16. [8] E. Faes, Unsteady flow simulation of the Ahmed efeence body usinga lattice Boltzmann appoach, Computes & Fluids 35 (2006) 940 950. 1258 Page
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