Derivative Free Optimization of Stirrer Configurations

  • M. Schäfer
  • B. Karasözen
  • Ö. Uğur
  • K. Yapıcı
Conference paper

Abstract

In the present work a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a parametrized grid generator, a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The grid generator allows the parametrized generation of block-structured grids for the stirrer geometries. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method for block-structured, boundary-fitted grids. As optimization tool the two approaches DFO and CONDOR are considered, which are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. Both are designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate. An exemplary application for a standard stirrer configuration illustrates the functionality and the properties of the proposed methods also involving a comparison of the two optimization algorithms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berghen, F.V.: CONDOR: a constrained, non-linear, derivative-free parallel optimizer for continuous, high computing load, noisy objective functions. PhD thesis, Université Libre de Bruxelles, Belgium (2004)Google Scholar
  2. 2.
    Conn, A.R., Scheinberg, K., Toint P.: On the convergence of derivative-free methods for unconstrained optimization. In: Iserles, A., Buhmann, M. (ed) Approximation Theory and Optimization: Tribute to M.J.D. Powell. Cambridge University Press, Cambridge, UK (1997)Google Scholar
  3. 3.
    Conn, A.R., Scheinberg, K., Toint P.: Recent progress in unconstrained nonlinear optimization without derivatives. Mathematical Programming, 79, 397–414 (1997)MathSciNetGoogle Scholar
  4. 4.
    Conn, A.R., Toint, P.: An algorithm using quadratic interpolation for unconstrained derivative free optimization. In: Pillo G.D., Giannessi F. (ed) Nonlinear Optimization and Applications. Plenum Publishing, New York (1996)Google Scholar
  5. 5.
    Durst, F., Schäfer, M.: A Parallel Blockstructured Multigrid Method for the Prediction of Incompressible Flows. Int. J. for Num. Meth. in Fluids, 22, 549–565 (1996).MATHCrossRefGoogle Scholar
  6. 6.
    FASTEST — User Manual, Department of Numerical Methods in Mechanical Engineering, Technische Universität Darmstadt (2004).Google Scholar
  7. 7.
    Ferziger J., Perić M.: Computational Methods for Fluid Dynamics. Springer, Berlin (1996)MATHGoogle Scholar
  8. 8.
    Lehnhäuser, T.: Eine efiziente numerische Methode zur Gestaltsoptimierung von Strömungsgebieten. PhD thesis, Technische Universität Darmstadt, Germany (2003)Google Scholar
  9. 9.
    Mohammadi, B., Pironneau, O.: Applied Shape Optimization for Fluids. Oxford University Press, (2001)Google Scholar
  10. 10.
    Powell, M.J.D.: A direct search optimization method that models the objective and constraint functions by linear interpolation. In: Gomez S., Hennart J. (ed) Advances in Optimization and Numerical Analysis. Kluwer Academic, (1994)Google Scholar
  11. 11.
    Schäfer, M., Karasözen, B., Uluda¢g Y., Yapýcý K., U¢gur Ö.: Numerical method for optimizing stirrer configurations. to be published in Computers & Chemical EngineeringGoogle Scholar
  12. 12.
    Sieber, R., Schäfer, M., Lauschke G., Schierholz F.: Strömungssimulation in Wendel- und Dispersionsrührwerken. Chemie Ingenieur Technik, 71, 1159–1163 (1999)CrossRefGoogle Scholar
  13. 13.
    Sieber, R., Schäfer, M., Wechsler K., Durst F.: Numerical prediction of timedependent flow in a hyperbolic stirrer. In: Friedrich R., Bontoux P. (ed) Computation and Visualization of Three-Dimensional Vortical and Turbulent Flows. volume 64 of Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig (1998)Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • M. Schäfer
    • 1
  • B. Karasözen
    • 2
  • Ö. Uğur
    • 3
  • K. Yapıcı
    • 4
  1. 1.Department of Numerical Methods in Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  2. 2.Department of Mathematics and Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  4. 4.Department of Chemical EngineeringMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations