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184 René A. Van den Braembussche aero aero penalty penalty stress penalty Fig. 6.29 Zoom on the low penalty region of Fig. 6.28 Table 6.5 Comparison between baseline and optimized impellers database optimization Baseline Iter. 2 Iter. 17 Iter. 25 Iter. 49 ηTS(%) 62.34 60.42 60.31 60.06 59.68 Paero 13.24 14.86 9.14 9.05 9.14 Ploadunbalance 0.06 3.84 0.26 0.04 0.00 σvonMises (MPa) 749. 440 389 367 396 Blade lean ( ◦ ) -7.8 -11.8 -8.6 -7.3 -15.0 ˙m (g/s) 25.9 19.6 20.2 20.2 20.1 Power (kW) 3.19 2.52 2.61 2.62 2.62 Spec.Pow. (W.s/kg) 1123.2 128.6 129.2 129.7 130.3 From all the geometries created during the optimization, iteration 25 performs best. It has an efficiency a little lower than iteration 17 but less loading unbalance and the stresses are 33 MPa below the limit. In spite of its high efficiency, the baseline impeller shows a high aero penalty because of a very high mass flow. The influence of the stress penalty on the optimization is clear by comparing the values of the baseline impeller with the ones of iteration 25. The reduction of the maximum stress level with 370 MPa is at the cost of a 2.3% decrease of efficiency. Figures 6.30 and 6.31 show the von Mises stresses in the baseline geometry and the one of iteration 25, respectively. The drastic reduction in stress of the optimized impeller is due to:
6 Numerical Optimization for Advanced Turbomachinery Design 185 Fig. 6.30 von Mises stresses due to centrifugal loading in the baseline Fig. 6.31 von Mises stresses due to centrifugal loading in iteration 25 • the reduced blade height at the leading edge, resulting in lower centrifugal forces at the leading edge hub; • the increase of blade thickness at the hub; • the modified blade curvature. The latter two result in a decrease of the bending stresses.
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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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Page 148 and 149: 134 Nicolas R. Gauger Fig. 5.10 Plo
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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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