Optimization and Computational Fluid Dynamics - Department of ...

More documents

Recommendations

Info

206 Laurent Dumas Table 7.3 Comparison of ES and AHM for the Rastrigin function Rast6 Method Mean best (success rate) same after same after 500 evaluations 1000 evaluations 2000 evaluations ES 6.47(0%) 3.46(0.5%) 0.46(80.5%) AHM, 4 clust. 4.97(2.5%) 1.86(6%) 0.47(63.5%) AHM, 8 clust. 3.54(7%) 1.77(11%) 0.34(67%) AHM 3.52(10.5%) 1.51(17%) 0.34(68%) As can be seen from this table, any AHM overperforms the ES at the early stage of the process in both performance criteria. Moreover, during this phase, the strategy of reduced clustering (last line in Table 7.3) significantly improves the results of a hybrid algorithm with a fixed number of clusters. When a large number of evaluations are done, the pure ES takes a slight advantage on the number of successes (but not on the mean best value) in this special case compared to any AHM. These results can be summarized by saying that a hybrid algorithm will hasten convergence by enhancing the best elements in the population but on the other hand, such strategy can sometimes lead to a premature convergence. However, such drawback may not be too critical in a real applicative situation as it has only been observed with very special functions with a huge number of local minima like the Rastrigin function. Moreover, the main performance criterion of an algorithm for industrial purposes is its ability to achieve the best decrease of the cost function for a given amount of computational time. 7.3.4.2 AGA vs. GAs Another statistical study has also been realized on the Rastrigin function with 3 parameters in order to compare the GA in Sect. 7.3.1 and the socalled AGA in Sect. 7.3.3. In order to achieve a quasi-certain convergence, the population number is fixed equal to Np = 30 whereas the crossover and mutation probability are set to pc =0.3andpm =0.9. In this case, the average gain of an AGA compared to a classical GA is nearly equal to 4. It means that on average, the number of exact evaluations to achieve a given convergence level has been divided by a factor of 4. In view of their promising results, both global optimization methods AHM and AGA are now used in the next two sections for solving realistic optimization problems.
7 CFD-based Optimization for Automotive Aerodynamics 207 Fig. 7.8 3D car shape parametrized by its three rear angles α, β and γ 7.4 Car Drag Reduction with Numerical Optimization In this section, the main results obtained on a car drag reduction problem are presented. All of them have been done in collaboration with two research engineers from Peugeot Citroën PSA, V. Herbert and F. Muyl, and have already been published in various journals [4, 5, 6]. 7.4.1 Description of the Test Case In order to test the fast and global optimization methods presented in Sect. 7.3 on a realistic car drag reduction problem, a simplified car geometry has been extensively studied. It comprises minimizing the drag coefficient, also called Cd anddefinedinEq.(7.7),ofasimplified car shape with respect to the three geometrical angles defining its rear shape (see Fig. 7.8): the slant angle (α), the boat-tail angle (β) and the ramp angle (γ). The forebody of the vehicle is fixed and closely resembles the shape of an existing vehicle, namely the Xsara Picasso from Citroën. The objective is thus to find the best rear shape that will reduce the total drag coefficient of the car, ignoring any aesthetic considerations. As it has been previously seen in Sect. 7.1 on the Ahmed bluff body, it is expected that modifying the rear shape will lead to a very important drag reduction. 7.4.2 Details of the Numerical Simulation An automatic optimization loop has been implemented and is summarized in Fig. 7.9. This loop includes the following steps:
Page 1 and 2:
Optimization and Computational Flui
Page 3 and 4:
Editors: Prof. Dr.-Ing. Dominique T
Page 5 and 6:
vi Preface Our first research proje
Page 7 and 8:
viii Contents 2.4.1 GoverningEquati
Page 9 and 10:
x Contents 6.2.3 Parameterization..
Page 11 and 12:
xii Contents 9.4.1 Multi-objectiveO
Page 13 and 14:
xiv List of Contributors Gábor JAN
Page 15:
Part I Generalities and methods
Page 18 and 19:
4 Dominique Thévenin 12 10 8 6 4 2
Page 20 and 21:
6 Dominique Thévenin Objective 10
Page 22 and 23:
8 Dominique Thévenin Objective 10
Page 24 and 25:
10 Dominique Thévenin Parameter 2
Page 26 and 27:
12 Dominique Thévenin three-dimens
Page 28 and 29:
14 Dominique Thévenin Let us come
Page 30 and 31:
16 Dominique Thévenin References 1
Page 32 and 33:
18 Gábor Janiga 2.1 Introduction D
Page 34 and 35:
20 Gábor Janiga y Tinlet = 293 K 0
Page 36 and 37:
22 Gábor Janiga y [mm] 25 20 15 10
Page 38 and 39:
24 Gábor Janiga Table 2.1 Number o
Page 40 and 41:
26 Gábor Janiga A dominates the in
Page 42 and 43:
28 Gábor Janiga be shown later, th
Page 44 and 45:
30 Gábor Janiga INPUT FILE Gambit
Page 46 and 47:
Page 48 and 49:
34 Gábor Janiga ∆T ∆P Position
Page 50 and 51:
36 Gábor Janiga ∆P [mPa] 2.2 2.0
Page 52 and 53:
38 Gábor Janiga Table 2.3 Speed-up
Page 54 and 55:
40 Gábor Janiga For all computatio
Page 56 and 57:
42 Gábor Janiga y [mm] 4 2 0 -1 0
Page 58 and 59:
44 Gábor Janiga Air mass flow-rate
Page 60 and 61:
46 Gábor Janiga Temperature variat
Page 62 and 63:
Page 64 and 65:
50 Gábor Janiga The modified k-ω
Page 66 and 67:
52 Gábor Janiga Error for Re∗ =
Page 68 and 69:
54 Gábor Janiga Error for Re∗ 20
Page 70 and 71:
56 Gábor Janiga References 1. Ali,
Page 72 and 73:
58 Gábor Janiga 43. Janiga, G., Th
Page 75 and 76:
Chapter 3 Mathematical Aspects of C
Page 77 and 78:
3 Mathematical Aspects of CFD-based
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Chapter 4 Adjoint Methods for Shape
Page 95 and 96:
4 Adjoint Methods for Shape Optimiz
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123:
Part II Specific Applications of CF
Page 126 and 127:
112 Nicolas R. Gauger Nomenclature
Page 128 and 129:
114 Nicolas R. Gauger Fig. 5.1 Cost
Page 130 and 131:
116 Nicolas R. Gauger and the four
Page 132 and 133:
118 Nicolas R. Gauger CL := 1 � C
Page 134 and 135:
120 Nicolas R. Gauger the cost func
Page 136 and 137:
122 Nicolas R. Gauger Table 5.1 An
Page 138 and 139:
124 Nicolas R. Gauger The main adva
Page 140 and 141:
126 Nicolas R. Gauger Spalart-Allma
Page 142 and 143:
128 Nicolas R. Gauger (a) (b) Fig.
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
134 Nicolas R. Gauger Fig. 5.10 Plo
Page 150 and 151:
136 Nicolas R. Gauger drag, lift, s
Page 152 and 153:
138 Nicolas R. Gauger solution of t
Page 154 and 155:
140 Nicolas R. Gauger the presence
Page 156 and 157:
142 Nicolas R. Gauger Fig. 5.16 Con
Page 158 and 159:
144 Nicolas R. Gauger optimization
Page 161 and 162:
Chapter 6 Numerical Optimization fo
Page 163 and 164:
6 Numerical Optimization for Advanc
Page 165 and 166:
Page 167 and 168:
Page 169 and 170: 6 Numerical Optimization for Advanc
Page 203: 6 Numerical Optimization for Advanc
Page 206 and 207: 192 Laurent Dumas 7.1 Introducing A
Page 208 and 209: 194 Laurent Dumas C Fig. 7.2 Wake f
Page 210 and 211: 196 Laurent Dumas Table 7.1 Example
Page 212 and 213: 198 Laurent Dumas Fig. 7.5 Numerica
Page 214 and 215: 200 Laurent Dumas 7.3.1.1 Genetic A
Page 216 and 217: 202 Laurent Dumas START Random init
Page 218 and 219: 204 Laurent Dumas • if ˜ J(x ng
Page 222 and 223: 208 Laurent Dumas Fig. 7.9 General
Page 224 and 225: 210 Laurent Dumas Table 7.4 Four ex
Page 226 and 227: 212 Laurent Dumas Fig. 7.13 Blades
Page 228 and 229: 214 Laurent Dumas Table 7.5 Converg
Page 231 and 232: Chapter 8 Multi-objective Optimizat
Page 233 and 234: 8 Multi-objective Optimization in C
Page 237 and 238: 8 Multi-objective Optimizatio Fig.
Page 271 and 272:
8 Multi-objective Optimization in C
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Chapter 9 CFD-based Optimization fo
Page 283 and 284:
9 CFD-based optimization for paperm
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Page 293 and 294:
Page 295 and 296:
Page 297 and 298:
Page 299 and 300:
Page 301 and 302:
Page 303:
Page 306 and 307:
292 Index heat exchanger, 222, 224,
show all

Optimization and Computational Fluid Dynamics - Department of ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?