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214 Laurent Dumas Table 7.5 Convergence results on the blade optimization problem Algorithm number of evaluations best obtained value Evolutionary algorithm 460 163.5 AHM 480 158.6 The results are compared in Table 7.5 with those obtained with a classical evolutionary algorithm, here a simulated annealing. It can be seen that for the same simulation time (approximately 80 hours CPU), the AHM overperforms the simulated annealing. Indeed, even if the relative decrease obtained on the cost function appears to be small (3% approximately), it actually represents a significant improvement for the blade design. 7.6 Conclusion In order to reduce fuel consumption, the minimization of the drag coefficient of cars has become a major research topic for car manufacturers. The development of fast and global optimization methods based either on hybridization of evolutionary algorithms with a local search process or on the use of surrogate models, has allowed only recently a first numerical and automatic approach for the drag reduction problem. The results obtained from a simplified geometry called Ahmed bluff body are presented here. They confirm the experimental analysis saying that the drag coefficient is very sensitive to the rear geometry of the car due to the presence of separation and recirculation zones in this region, and thus can be largely reduced by shape optimization. After this experimental validation, the numerical tool is now ready to be used by car designers for improving the drag coefficient of future car models. References 1. Ahmed, S.R., Ramm, R., Faltin, G.: Some salient features of the time averaged ground vehicle wake. SAE Paper 840300 (1984) 2. Beyer, H.G., Schwefel, H.P.: Evolution Strategies. Kluwer Academic Publisher (2002) 3. Druez, N., Dumas, L., Lecerf, N.: Adaptive hybrid optimization of aircraft engine blades. Journal of Computational and Applied Mathematics, special issue in the honnor of Hideo Kawarada 70th birthday (in press) (2007) 4. Dumas, L., Muyl, F., Herbert, V.: Hybrid method for aerodynamic shape optimization in automotive industry. Computers and Fluids 33, 849–858 (2004)
7 CFD-based Optimization for Automotive Aerodynamics 215 5. Dumas, L., Muyl, F., Herbert, V.: Comparison of global optimization methods for drag reduction in the automotive industry. In: Lecture Notes in Computer Science, vol. 3483, pp. 948–957. Springer (2005) 6. Dumas,L.,Muyl,F.,Herbert,V.:Optimisationdeformeenaérodynamique automobile. Mécanique et Industrie 6(3), 285–288 (2005) 7. Espinoza, F., Minsker, B., Goldberg, D.E.: A self adaptive hybrid genetic algorithm. In: Proceedings of the Genetic and Evolutionary Computation Conference GECCO 2001, pp. 75–80. Morgan Kaufmann Publishers (2001) 8. Franck, G., Nigro, N., Storti, M., d’Elía, J.: Numerical simulation of the Ahmed vehicle model near-wake. Int. J. Num. Meth. Fluids (in press) (2007) 9. Giannakoglou, K.C.: Acceleration of ga using neural networks, theoretical background. GA for optimization in aeronautics and turbomachinery. In: VKI Lecture Series (2000) 10. Gillieron, P., Chometon, F.: Modelling of stationary three dimensional separated flows around an Ahmed reference model. In: ESAIM Proceedings. Third International Workshop on Vortex Flows and Related Numerical Methods, vol. 7, pp. 173–182 (1999) 11. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley (1989) 12. Han, T.: Computational analysis of three-dimensional turbulent flow around a bluff body in ground proximity. AIAA Journal 27(9), 1213–1219 (1988) 13. Han, T., Hammond, D.C., Sagi, C.J.: Optimization of bluff body for minimum drag in ground proximity. AIAA Journal 30(4), 882–889 (1992) 14. Jin, Y.: A comprehensive survey on fitness approximation in evolutionary computation. Soft Computing 9, 3–12 (2005) 15. Jin, Y., Olhofer, M., Sendhoff, B.: A framework for evolutionary optimization with approximate fitness functions. IEEE Transactions on Evolutionary Computation 6, 481–494 (2002) 16. Makowski, F.T., S.-E., K.: Advances in external-aero simulation of ground vehicles using the steady RANS equations. SAE Paper 2000-01-0484 (2000) 17. Mohammadi, B., Pironneau, O.: Analysis of the k–ε turbulence model. John Wiley & Sons (1994) 18. Morel, T.: Aerodynamic drag of bluff body shapes characteristic of hatch-back cars. SAE Paper 7802670 (1978) 19. Ong, Y.S., Nair, P.B., Keane, A.J., Wong, K.W.: Surrogate-assisted evolutionary optimization frameworks for high-fidelity engineering design problems. In: Knowledge Incorporation in Evolutionary Computation, Studies in Fuzziness and Soft Computing Series, pp. 307–332. Springer Verlag (2004) 20. Poloni, C.: Hybrid GA for multi objective aerodynamic shape optimisation, Genetic algorithms in engineering and computer science. In: G. Winter, J. Périaux, M. Galan, P. Cuesta (eds.) Genetic Algorithms in Engineering and Computer Science. John Wiley & Sons, Inc., New York, NY, USA (1995)
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Optimization and Computational Flui
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Editors: Prof. Dr.-Ing. Dominique T
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vi Preface Our first research proje
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viii Contents 2.4.1 GoverningEquati
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x Contents 6.2.3 Parameterization..
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xii Contents 9.4.1 Multi-objectiveO
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xiv List of Contributors Gábor JAN
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Part I Generalities and methods
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4 Dominique Thévenin 12 10 8 6 4 2
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6 Dominique Thévenin Objective 10
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8 Dominique Thévenin Objective 10
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10 Dominique Thévenin Parameter 2
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12 Dominique Thévenin three-dimens
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14 Dominique Thévenin Let us come
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16 Dominique Thévenin References 1
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18 Gábor Janiga 2.1 Introduction D
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20 Gábor Janiga y Tinlet = 293 K 0
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22 Gábor Janiga y [mm] 25 20 15 10
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24 Gábor Janiga Table 2.1 Number o
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26 Gábor Janiga A dominates the in
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28 Gábor Janiga be shown later, th
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30 Gábor Janiga INPUT FILE Gambit
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34 Gábor Janiga ∆T ∆P Position
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36 Gábor Janiga ∆P [mPa] 2.2 2.0
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38 Gábor Janiga Table 2.3 Speed-up
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40 Gábor Janiga For all computatio
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42 Gábor Janiga y [mm] 4 2 0 -1 0
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44 Gábor Janiga Air mass flow-rate
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46 Gábor Janiga Temperature variat
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50 Gábor Janiga The modified k-ω
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52 Gábor Janiga Error for Re∗ =
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54 Gábor Janiga Error for Re∗ 20
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56 Gábor Janiga References 1. Ali,
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58 Gábor Janiga 43. Janiga, G., Th
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Chapter 3 Mathematical Aspects of C
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3 Mathematical Aspects of CFD-based
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Chapter 4 Adjoint Methods for Shape
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4 Adjoint Methods for Shape Optimiz
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Part II Specific Applications of CF
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112 Nicolas R. Gauger Nomenclature
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114 Nicolas R. Gauger Fig. 5.1 Cost
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116 Nicolas R. Gauger and the four
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118 Nicolas R. Gauger CL := 1 � C
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120 Nicolas R. Gauger the cost func
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122 Nicolas R. Gauger Table 5.1 An
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124 Nicolas R. Gauger The main adva
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126 Nicolas R. Gauger Spalart-Allma
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128 Nicolas R. Gauger (a) (b) Fig.
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134 Nicolas R. Gauger Fig. 5.10 Plo
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136 Nicolas R. Gauger drag, lift, s
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138 Nicolas R. Gauger solution of t
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140 Nicolas R. Gauger the presence
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142 Nicolas R. Gauger Fig. 5.16 Con
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144 Nicolas R. Gauger optimization
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Chapter 6 Numerical Optimization fo
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6 Numerical Optimization for Advanc
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8 Multi-objective Optimization in C
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Chapter 9 CFD-based Optimization fo
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9 CFD-based optimization for paperm
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292 Index heat exchanger, 222, 224,
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