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Journal of Chemical Physics / Volume 124 / Issue 11 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 124, 114111 (2006); http://dx.doi.org/10.1063/1.2177243 (15 pages)

The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics

Zhuyin Ren1, Stephen B. Pope1, Alexander Vladimirsky2, and John M. Guckenheimer2

1Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
2Department of Mathematics, Cornell University, Ithaca, New York 14853

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(Received 14 October 2005; accepted 24 January 2006; published online 20 March 2006)

This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr−1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr “major” species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The “inputs” to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2/O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region.

© 2006 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE INVARIANT CONSTRAINED EQUILIBRIUM EDGE (ICE) MANIFOLD
    1. Homogeneous reacting system
    2. Idealized H2/O system
    3. Gibbs function, entropy, and chemical equilibrium
    4. Reaction trajectories
    5. Reduced composition
    6. Attracting manifolds and species reconstruction
    7. Constrained equilibrium manifold
    8. Invariant constrained equilibrium edge (ICE) manifold
  3. ICE-PIC: A METHOD TO DETERMINE POINTS ON THE ICE MANIFOLD USING THE CONSTRAINED EQUILIBRIUM PRE IMAGE CURVE
    1. The preimage manifold
    2. The constrained equilibrium preimage curve (CE-PIC)
    3. The ICE-PIC method
  4. ICE-PIC METHOD FOR ADIABATIC SYSTEMS
  5. COMPARATIVE TESTING OF SPECIES RECONSTRUCTION METHODOLOGIES
    1. Computations of a premixed laminar flame
    2. Species reconstruction using ICE-PIC
    3. Species reconstruction using RCCE
    4. Species reconstruction using ILDM
    5. Species reconstruction using QSSA
    6. Comparison of species reconstruction errors
  6. DISCUSSION AND CONCLUSION

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KEYWORDS and PACS

Keywords

hydrogen neutral molecules, atom-molecule reactions, oxygen, reaction kinetics theory, reduction (chemical), flames

PACS

  • 82.20.Fd

    Collision theories; trajectory models

  • 82.40.-g

    Chemical kinetics and reactions: special regimes and techniques

  • 82.30.Cf

    Atom and radical reactions; chain reactions; molecule-molecule reactions

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2177243

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    M. J. Davis and R. T. Skodje, J. Chem. Phys. 111, 859 (1999)JCPSA6000111000003000859000001.

    S. Singh, J. M. Powers, and S. Paolucci, J. Chem. Phys. 117, 1482 (2002)JCPSA6000117000004001482000001.


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