Advertisement

Towards the Numerical Solution of a Large Scale PDAE Constrained Optimization Problem Arising in Molten Carbonate Fuel Cell Modeling

  • Hans Josef Pesch
  • Kati Sternberg
  • Kurt Chudej
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 83)

Summary

Molten carbonate fuel cells (MCFCs) allow an efficient and environmentally friendly energy production by converting the chemical energy contained in the fuel gas in virtue of electro-chemical reactions. Their dynamical behavior can be described by large scale embedded systems of 1D or 2D nonlinear partial differential algebraic equations (PDAEs) up to dimension 28. They are of mixed parabolic-hyperbolic type with integral terms in the right hand side and initial and nonlinear boundary conditions, the latter governed by a system of ordinary differential equations.

In this paper a new 2D model together with results of its numerical simulation is presented. The numerical results show a good correspondence with the expected dynamical behavior of MCFCs. The ultimate goal is to optimize this large scale nonlinear PDAE system to increase efficiency and service life of MCFCs.

Key words

partial differential algebraic equations numerical simulation PDE constrained optimization fuel cells 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Büskens, C.: Optimierungsmethoden und Sensitivitätsanalyse für optimale Steuerprozesse mit Steuer-und Zustands-Beschränkungen. Dissertation, Univ. Münster, Germany, 1998.Google Scholar
  2. 2.
    Chudej, K.: Index Analysis for Singular PDE Models of Fuel Cells. to appear in Proc. of ECMI 2004.Google Scholar
  3. 3.
    Chudej, K.; Heidebrecht, P.; Petzet, V.; Scherdel, S.; Schittkowski, K.; Pesch, H.J.; Sundmacher, K.: Index Analysis and Numerical Solution of a Large Scale Nonlinear PDAE System Describing the Dynamical Behaviour of Molten Carbonate Fuel Cells. Zeitschrift für Angewandte Mathematik und Mechanik 85,2, 132–140 (2005).MathSciNetCrossRefGoogle Scholar
  4. 4.
    Heidebrecht, P.: Modelling, Analysis and Optimisation of a Molten Carbonate Fuel Cell with Direct Internal Reforming (DIR-MCFC). Dissertation, Fortschritt-Berichte, Reihe 3, Nr. 826, VDI-Verlag, Düsseldorf, 2005.Google Scholar
  5. 5.
    Heidebrecht, P., Sundmacher, K.: Molten carbonate fuel cell (MCFC) with internal reforming: model-based analysis of cell dynamics, Chemical Engineering Science 58 (2003) 1029–1036.CrossRefGoogle Scholar
  6. 6.
    Heidebrecht, P., Sundmacher, K.: Dynamic Modeling and Simulation of a Countercurrent Molten Carbonate Fuel Cell (MCFC) with Internal Reforming, Fuel Cells 3–4 (2002), 166–180.CrossRefGoogle Scholar
  7. 7.
    Pesch, H.J.; Chudej, K.; Petzet, V.; Scherdel, S.; Schittkowski, K.; Heidebrecht, P.; Sundmacher, K.: Numerical Simulation of a 1D Model of a Molten Carbonate Fuel Cell. Proc. Appl. Math. Mech. 3 (2003) 521–522.CrossRefGoogle Scholar
  8. 8.
    Rang, J.; Chudej, K.: A perturbation index for a singular PDE model of a fuel cell. Mathematik-Bericht Nr. 2004/6, Institut für Mathematik, Technische Universität Clausthal (2004).Google Scholar
  9. 9.
    Sternberg, K., Chudej, K., Pesch, H.J.: A partial differential algebraic dynamic model of a molten carbonate fuel cell. Proc. Appl. Math. Mech. 4 (2004) 584–585.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Hans Josef Pesch
    • 1
  • Kati Sternberg
    • 1
  • Kurt Chudej
    • 1
  1. 1.Lehrstuhl für IngenieurmathematikUniv. BayreuthBayreuthGermany

Personalised recommendations