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Time-Scale Splitting-Based Mechanism Reduction

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Cleaner Combustion

Part of the book series: Green Energy and Technology ((GREEN))

Abstract

Chemical reaction systems, including those in combustion, often exhibit a large range of time-scales which can lead to stiffness in the resulting rate equations. This feature can however be exploited in the context of model reduction by recognising that certain fast species can relax to a quasi-equilibrium state or, in geometrical terms, that the evolution of the system of equations in composition space relaxes to lower and lower dimensional attractors. Time-scale separation therefore forms a basis for model reduction. This chapter introduces model reduction techniques based on time-scale splitting which may differ in their approach, but which all utilise the fact that chemical kinetic systems evolve with time-scales that often differ by orders of magnitude. The chapter will first discuss the mathematical basis on which time-scale separation is defined. It will then discuss approaches for model reduction based on algebraic approximations such as the quasi-steady state approximation or QSSA, trajectory-based approaches such as computational singular perturbation methods, geometrical approaches based on the presence of intrinsic low dimensional manifolds in composition space and methods based on thermodynamic principles such as the rate-controlled constrained-equilibrium method. Methods will be introduced for homogeneous reaction systems. The extension to reaction diffusion systems will then be discussed.

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Acknowledgments

UM thanks DFG for financial support.

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Authors and Affiliations

  1. Institute of Engineering Thermodynamics, Karlsruhe Institute of Technology, Engelbert-Arnold-Straße 4, 76131, Karlsruhe, Germany

    Ulrich Maas

  2. Energy Research Institute, University of Leeds, Leeds, LS29JT, UK

    Alison S. Tomlin

Authors
  1. Ulrich Maas
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  2. Alison S. Tomlin
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Correspondence to Ulrich Maas .

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Editors and Affiliations

  1. Laboratoire Reactions et Genie des Proce, ENSIC, Nancy Cedex, France

    Frédérique Battin-Leclerc

  2. Combustion Chemistry Centre, National University of Ireland, Galway, Ireland

    John M. Simmie

  3. Department of Energy Sciences, Division, University of Lund, Lund, Sweden

    Edward Blurock

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Maas, U., Tomlin, A.S. (2013). Time-Scale Splitting-Based Mechanism Reduction. In: Battin-Leclerc, F., Simmie, J., Blurock, E. (eds) Cleaner Combustion. Green Energy and Technology. Springer, London. https://doi.org/10.1007/978-1-4471-5307-8_18

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  • DOI: https://doi.org/10.1007/978-1-4471-5307-8_18

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