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136 Nicolas R. Gauger drag, lift, s tres s [ % variation ] range, stress, C D ,C L [% variation] 0 -10 -20 -30 70 60 50 40 30 20 10 0 -10 -20 stress C D C L eval. grad stress eval. grad C D eval. grad C L 10 20 30 40 50 60 70 80 90 100 It (a) range stress C D C L eval. grad range eval. grad stress eval. grad C D eval. grad C L 10 20 30 40 50 60 70 80 90 100 It (b) Fig. 5.14 Optimization history (a) for the drag reduction by constant lift while taking into account the static deformation and (b) for the range maximization (bottom picture) of the AMP wing (M∞ =0.78, α =2.83 ◦ ). For both optimizations free-form deformation is considered, 240 design variables are used for parameterization and the optimization strategy relies on feasible directions � � ∂I ∂R ∂S δI = + ψT + φT δX ∂X ∂X ∂X � � � � ∂I ∂R ∂S ∂I ∂R ∂S + + ψT + φT δw + + ψT + φT δZ (5.40) . ∂w ∂w ∂w ∂Z ∂Z ∂Z
5 Efficient Deterministic Approaches for Aerodynamic Shape Optimization 137 z 1.1 cp 0.893142 0.720791 1 0.548439 0.376087 0.203736 0.9 0.0313842 -0.140967 0.8 -0.313319 -0.485671 -0.658022 0.7 -0.830374 -1.00273 -1.17508 0.6 -1.34743 -1.51978 0.5 0.4 0.3 0.2 0.1 0 0.25 0.5 0.75 baseline (a) z 1.1 cp 0.893142 0.720791 1 0.548439 0.376087 0.203736 0.9 0.0313842 -0.140967 -0.313319 0.8 -0.485671 -0.658022 -0.830374 0.7 -1.00273 -1.17508 0.6 -1.34743 -1.51978 0.5 0.4 0.3 0.2 0.1 z 1.1 cp 0.893142 0.720791 1 0.548439 0.376087 0.203736 0.9 0.0313842 -0.140967 0.8 -0.313319 -0.485671 -0.658022 0.7 -0.830374 -1.00273 -1.17508 0.6 -1.34743 -1.51978 0.5 0.4 0.3 0.2 0.1 0 0.25 0.5 0.75 range optimal (c) 0.25 0.5 0.75 minimal drag Fig. 5.15 Pressure distribution for the baseline AMP wing shape and for the optimal wing shapes for drag minimization and range maximization (M∞ =0.78, α =2.83 ◦ ) Since we want to avoid recalculation of the (w,Z) fields, we cancel the terms in δw and δZ from δI by imposing the fields φ and ψ, tobethe (b)
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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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4 Adjoint Methods for Shape Optimiz
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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 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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