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288 J. Hämäläinen, T. Hämäläinen, E. Madetoja, H. Ruotsalainen examples presented here are from the paper industry but, nevertheless, independent of the industrial sector (motor, or aircraft industries, for example), CFD-related optimization problems set the same challenges everywhere. As a matter of fact, the industrial application in question is described by a state equation, that is, the CFD model. All the other aspects are common including optimization methods, needs for model reductions, and handling multiple criteria. Acknowledgements Many colleagues of the authors have contributed results discussed in this paper, especially Pasi Tarvainen, Ph.D., and Eeva-Kaisa Rouhiainen, M.Sc., from Numerola Oy (Ltd). We are also thankful to Finnish Agency for Technology and Innovation (Tekes) and Metso Paper, Inc. for financial support of this work. References 1. Baines, W., Nicholl, C., Cook, R., Mardon, J.: The taper-flow headboxes (a new design concept). Pulp and Paper Magazine of Canada pp. 139–148 (1956) 2. Birke, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer (1997) 3. Brooks, A., Hughes, T.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods Applied in Mechanics and Engineering 32, 199–259 (1982) 4. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Inc. (2001) 5. Franca, L., Frey, S.: Stabilized finite element methods: II. the incompressible Navier- Stokes equations. Computer Methods Applied in Mechanics and Engineering 99, 209–233 (1992) 6. Giunta, A., Eldred, M.S., Swiler, L.P., Trucano, T.G., Wotjkiewicz, S.F.J.: Perspective on optimization under uncertainty: algorithms and applications. Tech. Rep. 4451, AIAA, American Institute of Aeronautics and Astronautics (2004) 7. Gowda, M.S.: Inverse and implicit function theorems for H-differentiable and semismooth functions. Optimization Methods and Software 19(5), 443–461 (2004) 8. Gunawan, S., Azarm, S.: Multi-objective robust optimization using a sensitivity region concept. Structural and Multidisciplinary Optimization 29, 50–60 (2005) 9. Hadamard, J.: Leçons sur le calcul des variations. Gauthier-Villars (1910) 10. Hämäläinen, J.: The optimal shape design of the header. In: Proc. Finite Element Method in Simulation, no. R07/90 in CSC Research Reports, pp. 18–23. Jyväskylä, Finland (1990) 11. Hämäläinen, J.: Numerical modelling and simulation of fluid flow in headboxes of paper machines. Licentiate Thesis, University of Jyväskylä (1991). Reports on Applied Mathematics and Computing 12. Hämäläinen, J.: Mathematical modelling and simulation of fluid flows in the headbox of a paper machine. Ph.D. thesis, University of Jyväskylä, Department of Mathematics (1993) 13. Hämäläinen, J., Mäkinen, R., Tarvainen, P.: Optimal design of paper machine headboxes. International Journal for Numerical Methods in Fluids 34, 685–700 (2000) 14. Hämäläinen, J., Malkamäki, T., Toivanen, J.: Genetic algorithms in shape optimization of a paper machine headbox. In: Proc. Evolutionary Algorithms in Engineering and Computer Science, EUROGEN 99, pp. 435–443. Jyväskylä, Finland (1999)
9 CFD-based optimization for papermaking 289 15. Hämäläinen, J., Tarvainen, P.: CFD-optimized headbox flows. Pulp & Paper Canada 103(1), 39–41 (2002) 16. Hämäläinen, J., Tarvainen, P., Aspholm, P.: HOCS FIBRE – new tool for optimized fibre orientation angles. In: Proc. 91st annual meeting of Pulp and Paper Technical Association of Canada, PAPTAC 2005. Montreal, Canada (2005) 17. Hämäläinen, T., Hämäläinen, J.: Modelling of fibre orientation in the headbox jet. Journal of Pulp and Paper Science 33(1), 49–53 (2007) 18. Haslinger, J., Neittaanmäki, P.: Finite Element Approximation for Optimal Shape, Material and Topology Design. John Wiley & Sons, Inc. (1996) 19. Jin, R., Du, X., Chen, W.: The use of metamodeling techniques for optimization under uncertainty. Structural and Multidisciplinary Optimization 25, 99–116 (2003) 20. Karlsson, M., Hämäläinen, J.: A model-based decision-aid system to add value to papermaking. In: P. Neittaanmäki, T. Rossi, K. Majava, O. Pironneau (eds.) Proc. of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2006). Jyväskylä, Finland (2006) 21. Madetoja, E., Mäkelä, M.M.: On sensitivity analysis of nonsmooth multidisciplinary optimization problems in engineering process line applications. Structural and Multidisciplinary Optimization 31(5), 355–362 (2006) 22. Madetoja, E., Rouhiainen, E.K., Tarvainen, P.: A decision support system for paper making based on simulation and optimization. Engineering with Computers (accepted for publication) (2007) 23. Madetoja, E., Tarvainen, P.: Multiobjective process line optimization under uncertainty applied to papermaking. Structural and Multidisciplinary Optimization (accepted for publication) 24. Mardon, J., Manson, D., Wilder, J., Monahan, R., Trufitt, A., Brown, E.: The design of manifold systems for paper machine headboxes, part II – taper flow manifolds. TAPPI 46 (1963) 25. Mattson, C.A., Messac, A.: Pareto frontier based concept selection under uncertainty, with visualization. Optimization and Engineering 6(1), 85–115 (2005) 26. Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publisher (1999) 27. Miettinen, K., Mäkelä, M.M.: On scalarizing functions in multiobjective optimization. OR Spectrum 24, 193–213 (2002) 28. Miettinen, K., Mäkelä, M.M.: Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research 170, 909–922 (2006) 29. Mohammadi, B., Pironneau, O.: Applied Optimal Shape Optimization for Fluids. Oxford University Press (2001) 30. Odaka, Y., Furuya, H.: Robust structural optimization of plate wing corresponding to bifurcation in higher mode flutter. Structural and Multidisciplinary Optimization 30, 437–446 (2005) 31. Parsheh, M.: Flow in contractions with applications to headboxes. Ph.D. thesis, Royal Institute of Technology (KTH), Department of Mechanics (2001) 32. Pironneau, O.: Optimal Shape Design for Elliptic Systems. Springer-Verlag (1984) 33. Rodi, W.: Turbulence Models and Their Application in Hydraulics. International Association for Hydraulic Research (1993) 34. Steuer, R.: Multiple Criteria Optimization: Theory, Computations, and Applications. John Wiley & Sons, Inc. (1986) 35. Trufitt, A.: Design aspect of manifold type flowspreaders. Pulp and Paper Technology Series, Joint Textbook Committee of the Paper Industry, C.P.P.A. and TAPPI (1975)
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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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138 Nicolas R. Gauger solution of t
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140 Nicolas R. Gauger the presence
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142 Nicolas R. Gauger Fig. 5.16 Con
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144 Nicolas R. Gauger optimization
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Chapter 6 Numerical Optimization fo
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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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