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258 Marco Manzan, Enrico Nobile, Stefano Pieri and Francesco Pinto 10 8 f/f 0 6 4 2 Linear−piecewise wall profile NURBS wall profile 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Nu/Nu 0 Fig. 8.20 Pareto front comparison between linear piecewise and NURBS-based channels and longitudinal steady vortices on the heat transfer rate is again clear. For illustrative purposes, the secondary flow pattern for two channels obtained with a 20 ◦ and 40 ◦ extrusion respectively, are depicted in Fig. 8.22. Finally, a MOGA optimization has been started on extruded linear piecewise channels for a short number of generations. The Pareto front of this optimization is compared in Fig. 8.23 with the 2D linear piecewise and 2D NURBS fronts. Though the 3D linear piecewise front is rather sparse because of a small number of individuals processed, the heat transfer augmentation due to secondary motions is clearly visible. 8.8.5 CC Module Again with MOGA-II, an original design was used for the DOE when optimization was first attempted. The design had sinusoidal wall profile (design 0), characterized by a corrugation angle θ =60 ◦ , and 35 designs have been chosen with Sobol method. The value of the angle θ has been chosen, following Stasiek et al. [52], as a good compromise in terms of heat transfer rate and friction factor. The six design variables were, with reference to Fig. 8.6, P1, P2, P3, P4, W and θ. The three objectives to be minimized were the pressure gradient β, the temperature difference between the two fluids ∆T and the heat transfer surface area. The first objective has been selected to reduce the pressure drop across the regenerator. The second one drives the heat transfer performance of the regenerator. For instance, based on inspection of Eq. (8.35), a lower ∆T leads to a higher mean Nusselt number. The last objective has been selected to reduce the overall cost of the
8 Multi-objective Optimization in Convective Heat Transfer 259 24 22 20 18 16 f/f14 0 12 10 8 7 6 f/f 5 0 4 3 2 8 6 4 2D channel 3D channel 3D channel 3D channel 3D channel 1.2 1.4 1.6 1.8 2 Nu/Nu 0 2D channel 3D channel 3D channel 3D channel 3D channel 3D channel (a) 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Nu/Nu 0 Fig. 8.21 Pareto front comparison: (a) linear piecewise profile; (b) NURBS profile (b) material. All three objectives were constrained to be smaller or at least equal to those for the reference design 0. This preliminary attempt, however, was quite unsuccessful, with most of the computed designs considered unfeasible (outside the constraints domain).
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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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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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