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52 Gábor Janiga Error for Re∗ = 2000 14000 12000 10000 8000 6000 4000 2000 0 1000 2000 Error for Re∗ = 950 3000 4000 Fig. 2.21 Two objectives in Case C showing a dominantly linear correlation Error for Re∗ = 590 1000 Pareto front 900 800 700 600 500 400 300 200 100 100 200 300 Error for Re∗ = 395 400 5000 Fig. 2.22 Two objectives in Case C showing the best results and the resulting Pareto front All EA parameters of the optimization procedure are listed in Table 2.6. 2.6 Conclusions In this study, EAs have first been applied to a multi-objective shape design optimization problem concerning a heat exchanger configuration close 500
2 A Few Illustrative Examples of CFD-based Optimization 53 u + u + 25 20 15 10 25 20 5 15 10 0 1 10 5 0 0 y + y + DNS Modified model Wilcox (1998) 100 1000 DNS Modified model Wilcox (1998) 200 400 600 800 1000 Fig. 2.23 Velocity profiles in a semi-logarithmic plot (top) and in a standard plot (bottom) to practical applications. The characteristic Pareto front associated with this problem has been obtained within a very reasonable computational time. The heat exchanger model problem is based on a description of the tube positions
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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
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 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 64 and 65: 50 Gábor Janiga The modified k-ω
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 93 and 94: 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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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 Optimizatio Fig.
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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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