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188 René A. Van den Braembussche The Mach number-based criteria included in the Objective Function help enforce the convergence to the optimum and improve the off-design performance. The reduction in computer effort makes the design of customized profiles and the multipoint optimizations affordable, as illustrated by the design of a transonic turbine blade and a Low Solidity Diffuser. The use of a pseudo Objective Function to account for the mechanical and other constraints is presented, and the advantages and disadvantages are discussed. It is shown that the method is able to find the optimum combination of design parameters allowing a drastic reduction of the stresses with minimum penalty on efficiency. The optimization algorithm provides the designer more insight into the multidisciplinary design problem. The main parameters that allow a reduction of the stresses are identified during the optimization process. This optimum combination may result in unexpected geometries that would not be accepted when using simplified stress criteria. It has been shown how the use of computerized design techniques is a powerful tool to cope with the increasing complexity of advanced turbomachinery component design. However, the outcome of this valuable support still depends on the input of the designer in terms of a careful selection of design parameters, a clear definition of objectives and constraints as well as validation of results. Acknowledgements The contributions by Dr. Stephane Pierret, Dr. Zuheyr Alsalihi and Dr. Tom Verstraete to the development of this method are gratefully acknowledged. References 1. Aarts, E.H.L., Korst, J.H.M.: Simulated annealing in Boltzmann machines. Wiley Chichester (1987) 2. Alsalihi, Z., Van den Braembussche, R.A.: Evaluation of a design method for radial impellers based on artificial neural network and genetic algorithm. In: Proc. of ESDA 2002, 6th Biennial Conference on Engineering Systems Design and Analysis. Istanbul (2002) 3. Arnone, A.: Viscous analysis of three-dimensional rotor flow using a multigrid method. ASME Journal of Turbomachinery 116, 435–445 (1994) 4. Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996) 5. Carroll, D.L.: FORTRAN genetic algorithm (GA) driver version 1.7.1a (2001). URL URL:http:/cuaerospace.com/carroll/ga.html 6. Cosentini, R., Alsalihi, Z., Van den Braembussche, R.A.: Expert system for radial compressor optimization. In: Proc. 4th European Conference on Turbomachinery. Firenze (2001) 7. Demeulenaere, A., Van den Braembussche, R.A.: Three-dimensional inverse design method for turbine and compressor blades. In: Design Principles and Methods for Aircraft Gas Turbine Engines, RTO MP-8 (1998)
6 Numerical Optimization for Advanced Turbomachinery Design 189 8. Harinck, J., Alsalihi, Z., Van Buytenen, J.P., Van den Braembussche, R.A.: Optimization of a 3D radial turbine by means of an improved genetic algorithm. In: Proceedings of European Turbomachinery Conference. Lille (2005) 9. Kostrewa, K., Van den Braembussche, R.A., Alsalihi, Z.: Optimization of radial turbines by means of design of experiment. Tech. Rep. VKI-PR-2003-17, von Kármán Institute for Fluid Dynamics (2003) 10. Lichtfuss, H.J.: Customized profiles – the beginning of an area. In: ASME Turbo Expo 2004, Paper GT2004-53742 (2004) 11. Montgomery, D.C.: Design of Experiments. John Wiley & Sons, Inc. (1997) 12. Nursen, C., Van den Braembussche, R.A., Alsalihi, Z.: Analysis and multipoint optimization of low solidity vaned diffusers. Tech. Rep. VKI-SR-2002-31, von Kármán Institute for Fluid Dynamics (2002) 13. Pierret, S., Van den Braembussche, R.A.: Turbomachinery blading design using Navier Stokes solver and artificial neural network. ASME Journal of Turbomachinery 121, 326–332 (1999) 14. SAMTECH group: SAMCEF FEA code. URL www.samcef.com 15. Siamion, J., Coton, T., Van den Braembussche, R.A.: Design and evaluation of a highly loaded LP turbine blade. In: Proc. 5th ISAIF Conference (International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows). Gdansk (2001) 16. Thilmany, J.: Walkabout in another world. Mechanical Engineering 122(11), 1–9 (2000) 17. Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design. McGraw-Hill (1984) 18. Verstraete, T., Alsalihi, Z., Van den Braembussche, R.A.: Multidisciplinary optimization of a radial compressor for micro gas turbine applications. In: ASME Turbo Expo 2007, Paper GT2007-27484 (2007) 19. Verstraete, T., Alsalihi, Z., Van den Braembussche, R.A.: Numerical study of the heat transfer in micro gas turbines. Journal of Turbomachinery 129(4), 835–841 (2007) 20. Volpe, G.: Geometric and surface pressure restrictions in airfoil design. In: Special Course on Inverses Methods for Airfoil Design for Aeronautical and Turbomachinery Applications, AGARD-R-780 (1990)
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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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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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