292 Index heat exchanger, 222, 224, 227, 228 module, 222, 231, 234, 235, 258, 263 crossover, 18, 27, 35, 152, 155, 200, 206, 209, 243, 245, 246 Darwin, 24, 152, 200 degree <strong>of</strong> freedom, 5, 9, 11, 74, 232–234, 247, 250 Design <strong>of</strong> Experiment, 35, 164, 165, 182, 187, 238, 239, 249, 258 Direct Numerical Simulation, 22, 47, 48, 50, 51, 55, 268, 287 drag, 3, 121, 124, 125, 130, 139, 141, 143, 150, 192–196, 210 aerodynamic, 192 coefficient, 113, 119, 127, 193–196, 198, 199, 207, 208, 210, 211, 214 force, 192, 194 pressure, 194 viscous, 194 minimization, 81, 82, 137, 191, 195 minimum, 209 reduction, 119, 136, 141–143, 191, 195, 199–201, 204, 207, 209, 214 value, 209, 210 eddy viscosity, 49, 198 elite, 9, 26, 35, 37, 246 elitism, 200, 245, 246 entropy, 19, 79, 82, 91, 93, 103, 104 Euler equation, 3, 14, 86, 87, 97, 113, 117, 120, 121, 125, 126, 138, 140, 268 Euler flow model, 67 evolution strategy, 199–202, 205, 206, 221 fabricability check, 251–253 fiber orientation probability distribution, 273, 274 finite element, 147, 148, 157, 218, 277 finite volume, 31, 42, 93, 219, 235 fitness, 25, 154, 243, 253 -based selection, 24 assignment, 245 rank, 200 sharing, 245 space, 159 value, 24–26, 37, 242, 243 floating-point, 24, 27, 122, 123 friction coefficient, 103, 104 factor, 217 losses, 180 Headbox <strong>Optimization</strong> Control Simulator, 273, 274, 276, 277 Hessian, 64, 66, 68, 76, 80, 83, 95, 96, 98 -based optimization, 98 matrix, 79, 82, 83, 94–99, 101, 104, 105 exact, 82, 94 symmetrical, 94 method, 82 individual, 24–27, 33–38, 54, 55, 152, 154, 155, 181, 200, 242, 243, 245, 248–250, 258 inviscid adjoint solver, 125 case, 144 flow, 79, 81, 82, 86, 87, 104, 142 flux, 87 Jacobian, 63, 74–76, 120, 125 matrix, 40, 75, 87, 93, 97 k − ω model, 19, 46, 48, 50, 126 k − ε model, 197, 198, 208, 271, 275 laminar, 17–19, 21, 22, 38, 40, 42, 44, 47, 169, 218, 220, 222, 223, 228, 262, 271, 273 Large-Eddy Simulation, 22, 197 low solidity diffuser, 149, 172 Mach number, 21, 38–40, 98, 127, 169–171, 179, 180 distribution, 98, 100, 102, 103, 105, 158, 168–170, 180–182, 187 penalty, 158 machine direction, 273, 276 multi-objective Evolutionary Algorithm, 19, 21, 238, 243, 245 multi-objective Genetic Algorithm, 218, 245, 246, 248–251, 253, 258 multidisciplinary, 149 optimization, 81, 111, 113, 133, 147, 150, 156, 175, 176, 178, 219 problem, 133, 188, 278 multidisciplinary design optimization, 111, 113, 219 multigrid, 12, 40, 70, 72, 81, 126, 134 optimization, 61, 70, 71 multiphysical, 267, 278 mutation, 18, 27, 28, 152, 155, 200–202, 206, 209, 221, 238, 243, 245 Navier-Stokes, 67 equations, 3, 7, 12, 21, 40, 41, 79, 81, 82, 90, 99, 113, 125, 197, 223, 268, 275 depth-averaged, 269, 273–276 solver, 40, 125, 147, 170 non-dominated
Index 293 case, 32 configuration, 26–28, 36 design, 243, 246 individual, 26, 35, 37, 245 parameter, 27 solution, 221, 245 sorting, 246 Non-Uniform Rational Basic Splines, 219, 231–234, 247, 253, 255–258, 262, 263 Nondominated Sorting Genetic Algorithm, 245, 246 Nusselt number, 220, 225, 229–231, 234, 247–249, 253, 256–258, 261, 262 objective function, 5–9, 23, 25, 30, 41, 43, 62, 63, 74, 79, 80, 82, 83, 85, 87, 88, 90, 92–94, 96, 99–101, 103, 104, 150–154, 156, 159, 160, 164, 169, 170, 173, 175, 176, 178, 181, 188, 219–221, 236, 237, 239, 241, 243–245, 253, 256, 268, 279, 280, 282 <strong>of</strong>fspring, 24, 26, 27, 35, 152, 154, 155, 201, 242, 245, 246 one-shot approach, 143, 144 method, 81, 82, 111, 113, 142 optimization, 61, 67, 144 Pareto, 9, 10, 19, 25–27, 34–36, 51–53, 55, 159, 160, 218, 221, 222, 241–246, 249–254, 256, 258–261, 280, 284–286 partial differential equation, 40, 73, 80, 81, 84, 85, 135, 268 population, 18, 24–28, 33, 35, 152, 154, 155, 163, 200, 201, 203, 206, 242–245, 249, 250 number, 209 size, 154, 155 Pr<strong>and</strong>tl number, 218, 222, 262 probability, 24–28, 34, 151, 152, 155, 169, 200, 206, 242, 243, 273 recombination, 200, 201, 221, 238, 243 recuperator compact, 219 design, 219 gas turbine, 217, 222 gas-gas, 225 microturbine, 222, 230 module, 217, 227 Reynolds number, 22, 28, 29, 32, 47, 48, 50, 51, 100, 169, 192, 193, 197, 208, 222, 224, 228, 256 stress-tensor, 49 Reynolds Stress Model, 198, 208 Reynolds-Averaged Navier-Stokes, 12, 19, 22, 23, 46, 197 roulette, 154 wheel, 26 method, 26, 35 process, 200 slot, 26 Runge-Kutta, 126, 142 selection, 18, 24, 26, 27, 151, 154, 200, 201, 238, 239, 242–245, 249 separation, 103, 169, 193 area, 193–195 bubble, 250 bulb, 193, 195 flow, 169, 192 region, 104, 105 zone, 163, 196, 214 Simplex, 6, 18, 24, 33, 41, 63, 253 simulated annealing, 63, 150–152, 214 Sobol, 35, 239, 250, 258 Spalart-Allmaras model, 81, 82, 99, 126 spline, 67, 115, 117 stiffness matrix, 139, 140 survival, 27, 200, 238 tournament selection, 24, 154 size, 154 trade-<strong>of</strong>f, 23, 26, 159, 221, 230, 247 trial <strong>and</strong> error, 47, 149, 236 turbine, 21, 149, 167, 181 blade, 147, 157, 158, 166, 168–170, 179, 188 gas, 217, 222 low pressure, 213 micro-, 222, 226, 230 micro-gas, 176 stage, 148 viscous behavior, 224 dissipation, 223 drag, 194, 210, 211 flow, 79, 81, 82, 91, 104 flux, 90 inverse design, 92 loss, 79, 82, 91, 93, 99 Navier-Stokes equations, 268 stress, 90, 91 stress tensor, 199 vortex, 193, 195, 258, 260, 263
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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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32 Gábor Janiga y [mm] 100 50 0 0
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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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48 Gábor Janiga y [mm] 18 16 14 12
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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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3 Mathematical Aspects of CFD-based
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3 Mathematical Aspects of CFD-based
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3 Mathematical Aspects of CFD-based
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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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4 Adjoint Methods for Shape Optimiz
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4 Adjoint Methods for Shape Optimiz
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4 Adjoint Methods for Shape Optimiz
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4 Adjoint Methods for Shape Optimiz
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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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130 Nicolas R. Gauger (a) (b) Fig.
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132 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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6 Numerical Optimization for Advanc
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192 Laurent Dumas 7.1 Introducing A
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194 Laurent Dumas C Fig. 7.2 Wake f
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196 Laurent Dumas Table 7.1 Example
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198 Laurent Dumas Fig. 7.5 Numerica
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200 Laurent Dumas 7.3.1.1 Genetic A
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202 Laurent Dumas START Random init
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204 Laurent Dumas • if ˜ J(x ng
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206 Laurent Dumas Table 7.3 Compari
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208 Laurent Dumas Fig. 7.9 General
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210 Laurent Dumas Table 7.4 Four ex
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212 Laurent Dumas Fig. 7.13 Blades
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214 Laurent Dumas Table 7.5 Converg
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Chapter 8 Multi-objective Optimizat
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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8 Multi-objective Optimizatio Fig.
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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8 Multi-objective Optimization in C
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