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178 René A. Van den Braembussche Fig. 6.23 Definition of θ distribution Fig. 6.24 Parameterized thickness distribution perpendicular to the blade camber line (not to scale) can vary between 20% and 35% at hub and shroud (2 extra design parameters). The number of blades could also be a design parameter to be optimized, but has been fixed to 7 for manufacturing reasons. This brings the total number of design parameters that need to be defined by the optimizer to 23. 6.6.2 Multidisciplinary Objective Function The OF driving the multidisciplinary optimization increases with decreasing aero performance and when the aero and mechanical requirements are not met OF = wm · Pmech + wη · Pperf + wm · Pmass + wM · PMach The first penalty concerns the mechanical stresses. Limiting the maximum stress results in an inequality and geometries that do not satisfy this condition should be eliminated. However, this information about undesired geometries can also be used to guide the optimization algorithm towards acceptable ones. This is achieved by adding to the OF an extra term that increases
6 Numerical Optimization for Advanced Turbomachinery Design 179 Pmech σallowable Fig. 6.25 Penalty function for not respecting stress limits σmax when the stress exceeds the prescribed maximum allowable value. Adding those geometries to the database makes this information available to the ANN which in turn informs the GA about what part of the design space is unacceptable in terms of stress level. Those geometries will therefore not be proposed for further investigation by the NS and FEA. The penalty increases linearly when a prescribed value σallowable is ex- ceeded and is zero when the inequality σmax
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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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Page 150 and 151: 136 Nicolas R. Gauger drag, lift, s
Page 152 and 153: 138 Nicolas R. Gauger solution of t
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Page 206 and 207: 192 Laurent Dumas 7.1 Introducing A
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Page 226 and 227: 212 Laurent Dumas Fig. 7.13 Blades
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8 Multi-objective Optimization in C
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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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