Skip to main content
SpringerLink
Log in

Efficient Numerical Schemes for Simulation and Optimization of Turbulent Reactive Flows

  • Chapter
  • First Online:
Flow and Combustion in Advanced Gas Turbine Combustors

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 1581))

  • 4523 Accesses

Abstract

An approach for the efficient simulation and optimization of turbulent reactive flow problems is presented. A gradient-based optimization strategy is employed involving a parallel multigrid solver for the flow and sensitivity equations. The geometry variation is realized using NURBS surfaces providing a large scale of possible deformations with a small number of design variables. The sensitivity-based computation of the gradient of the objective function is systematically verified by comparisons with finite-difference approximations. The efficiency of the multigrid method and the parallelization is investigated. The functionality of the optimization approach is illustrated by results for representative test cases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Durst, F., Schäfer, M.: A parallel block-structured multigrid method for the prediction of incompressible flows. Int. J. Numer. Methods Fluids 22, 549–565 (1996)

    Article  MATH  Google Scholar 

  2. Harth, Z., Sun, H., Schäfer, M.: Comparison of derivative free Newton-based and evolutionary methods for shape optimization of flow problems. Int. J. Numer. Methods Fluids 53, 753–777 (2007)

    Article  MATH  Google Scholar 

  3. Hirschen, K., Schäfer, M.: Artifical neural networks for shape optimization in CFD. In: Proceedings of Design Optimization International Conference, Athens (2004)

    Google Scholar 

  4. Gunzburger, M.D.: Perspectives in Flow Control and Optimization. Society for Industrial and Applied Mathematics, Philadelphia (2003)

    Book  MATH  Google Scholar 

  5. Gunzburger, M.: Adjoint equation-based methods for control problems in viscous, incompressible flows. Flow Tubul. Combust. 65, 249–272 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Borggaard, J., Burns, J.: A PDE sensitivity equation method for optimal aerodynamic design. Int. J. Comput. Phys. 136, 366–384 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Burkhardt, J., Peterson, J.: Control of steady incompressible 2d channel flows. Flow Control IMA Vol. Math. Appl. 68, 111–216 (1995)

    Google Scholar 

  8. Ferziger, J.H., Perić, M.: Computational Methods for Fluid Dynamics. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  9. Launder, B.E., Spalding, D.B.: The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3, 269–289 (1974)

    Article  MATH  Google Scholar 

  10. Chien, K.H.: Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model. AIAA J. 22, 33–38 (1982)

    Article  Google Scholar 

  11. Griewank, A., Corliss, G.F.: Automatic Differentiation of Algorithms: Theory, Implementation, and Application. Defense Technical Information Center OAI-PMH Repository (1998)

    Google Scholar 

  12. É, T., Pelletier, D., Borggaard, J.: A continuous sensitivity equation approach to optimal design in mixed convection. Numer. Heat Trans. A Appl. 38(8), 869–885 (2000)

    Article  Google Scholar 

  13. Duvigneau, R., Pelletier, D.: On accurate boundary conditions for a shape sensitivity equation method. Int. J. Numer. Methods Fluids 50, 147–164 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Siegmann, J., Becker, G., Michaelis, J., Schäfer, M.: A general sensitivity based shape optimization approach for arbitrary surfaces. In: Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, WCSMO, Lisbon (2009)

    Google Scholar 

  15. Jacoby, S.L.S., Kowalik, J.S., Pizzo, J.T.: Iterative Methods for Nonlinear Optimization Problems. Prentice-Hall, Englewood Cliffs (1972)

    MATH  Google Scholar 

  16. Mohammadi, B., Pironneau, O.: Applied Shape Optimization for Fluids. Oxford Science, Oxford (2001)

    MATH  Google Scholar 

  17. Becker, G., Siegmann, J., Michaelis, J., Schäfer, M.: Comparison of a derivative-free and a gradient-based shape optimization method in the context of fluid–structure interaction. In: 8th World Congress on Structural and Multidisciplinary Optimization, WCSMO, Lisbon (2009)

    Google Scholar 

  18. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)

    Book  MATH  Google Scholar 

  19. Becker, G., Falk, U., Schäfer, M.: Shape optimization with higher-order surfaces in consideration of fluid–structure interaction. In: Fluid–Structure Interaction: Theory, Numerics and Applications. Kassel University Press, Kassel (2009)

    Google Scholar 

  20. Schäfer, M., Heck, M., Yigit, S.: An implicit partitoned method for the numerical simulation of fluid–structure interaction. In: Bungartz, H.-J., Schäfer, M. (eds.) Fluid–Structure Interaction: Modelling, Simulation, Optimization, 53, pp. 171–194. Springer, Berlin/Heidelberg (2006)

    Google Scholar 

  21. Lehnhäuser, T., Ertem-Müller, S., Schäfer, M., Janicka, J.: Advances in numerical methods for simulating turbulent flows. Prog. Comput. Fluid Dyn. 4(3–5), 208–228 (2004)

    Article  Google Scholar 

  22. Lehnhäuser, T.: Eine effiziente numerische Methode zur Gestaltoptimierung von Strömungsgebieten. TU Darmstadt (2005)

    Google Scholar 

  23. Lehnhäuser, T., Schäfer, M.: Improved linear practice for finite-volume schemes on complex grids. Int. J. Numer. Methods Fluids 38, 625–645 (2002)

    Article  MATH  Google Scholar 

  24. Gauß, F., Schäfer, M.: A local adaptive grid refinement strategy for block-structured finite-volume solvers. In: Proceedings of the 6th International Conference on Engineering Computational Technology, Athens (2008)

    Google Scholar 

  25. Gauß, F., Schäfer, M., Siegmann, J., Sternel, D.: On the influence of boundary discretization schemes on the accuracy of flow simulation with local refinement. In: IV International Conference on Adaptive Modelling and Simulation 2009, Brussels (2009)

    Google Scholar 

  26. Gauß, F.: Strategien zur lokalen adaptiven Gitterverfeinerung für Strömungslöser. TU Darmstadt (2005)

    Google Scholar 

  27. Schäfer, M.: Computational Engineering – Introduction to Numerical Methods. Springer, Berlin (2006)

    Google Scholar 

  28. Briggs, W.L., Henson, V.E., Kaspar, B.: A Multigrid Tutorial. SIAM, Philadelphia (2000)

    Book  MATH  Google Scholar 

  29. Hackbusch, W.: Multi-Grid Methods and Applications. Springer, Berlin (1985)

    MATH  Google Scholar 

  30. Trottenberg, U., Oosterlee, C.W., Schüller, A.: Multigrid. Elsevier Academic Press, San Diego (2001)

    MATH  Google Scholar 

  31. Michaelis, J., Siegmann, J., Becker, G., Schäfer, M.: Efficiency of geometric multigrid methods for solving the sensitivity equatins within gradient based flow optimzazion problems. In Proceedings of the V European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, Lisbon (2010)

    Google Scholar 

  32. Michaelis, J., Siegmann, J., Schäfer, M.: Parallel efficiency of multigrid methods for solving flow sensitivity equations. In: Proceedings of the CFD and OPTIMIZATION 2011–002, Antalya (2011)

    Google Scholar 

  33. Hempel, R.: The MPI standard for message passing. Lect. Notes Comput. Sci. 797, 247–252 (1994)

    Article  Google Scholar 

  34. Stanley, L.G., Stewart, D.L.: Design Sensitivity Analysis. SIAM, Philadelphia (2002)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Numerical Methods in Mechanical Engineering, Mechanical Engineering, Technische Universität Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany

    J. Siegmann, G. Becker, J. Michaelis & M. Schäfer

Authors
  1. J. Siegmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Becker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Michaelis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Schäfer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Siegmann .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Technische Universität Darmstadt, Petersenstrasse 30, Darmstadt, 64287, Germany

    Johannes Janicka

  2. Department of Mechanical Engineering, Darmstadt University of Technology, Petersenstrasse 30, Darmstadt, 64287, Germany

    Amsini Sadiki

  3. Department of Mechanical Engineering, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Michael Schäfer

  4. Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 32, Darmstadt, 64287, Germany

    Christof Heeger

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Siegmann, J., Becker, G., Michaelis, J., Schäfer, M. (2013). Efficient Numerical Schemes for Simulation and Optimization of Turbulent Reactive Flows. In: Janicka, J., Sadiki, A., Schäfer, M., Heeger, C. (eds) Flow and Combustion in Advanced Gas Turbine Combustors. Fluid Mechanics and Its Applications, vol 1581. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5320-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-5320-4_10

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5319-8

  • Online ISBN: 978-94-007-5320-4

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation