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128 Nicolas R. Gauger (a) (b) Fig. 5.5 Quotients of (a) Hicks-Henne and (b) cosine functions parameterization for parameters 6, 10 and 15 and varying stepsizes as mentioned in Sect. 5.4. Therefore, the quotients of both parameterizations have been calculated for varying stepsizes with respect to all n =20 parameters. As can be seen in Fig. 5.5, a good choice for the stepsize h is 10 −3 for both parameterizations. Another possibility which has not been used is to
5 Efficient Deterministic Approaches for Aerodynamic Shape Optimization 129 drag drag (a) step (b) Fig. 5.6 Optimization history of FD and AD for (a) Hicks-Henne and (b) cosine functions parameterization tune the stepsize for each parameter separately, which means selecting n stepsizes hi for every approximation in (5.33). With this possibility, a more accurate result might be achieved for the original airfoil, but based on the fact that this tuning cannot be done for every optimization step due to the high computational effort, it might cause worse optimization results at the end. Therefore, a stepsize of 10 −3 has been used for all gradient computations within the optimizations for both parameterizations. In Fig. 5.6, the optimization history for both parameterizations can be seen. In case of the Hicks-Henne functions parameterization, the optimization step
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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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Page 156 and 157: 142 Nicolas R. Gauger Fig. 5.16 Con
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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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