Travelling waves in model reacting flows with reversible kinetics

The authors study the existence of wavefront-type travelling wave solutions in the Fickett-Majda model of viscous reactive flow when the chemistry is modelled by a reversible chemical reaction. The problem is reduced to proving the existence of a heteroclinic orbit, in a two-dimensional phase space,...

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Bibliographic Details
Published in:IMA journal of applied mathematics 1992, Vol.49 (2), p.103-121
Main Authors: LOGAN, J. DAVID, DUNBAR, STEVEN R.
Format: Article
Language:English
Subjects:
Applied sciences
Combustion. Flame
Energy
Energy. Thermal use of fuels
Exact sciences and technology
Theoretical studies
Theoretical studies. Data and constants. Metering
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Summary:The authors study the existence of wavefront-type travelling wave solutions in the Fickett-Majda model of viscous reactive flow when the chemistry is modelled by a reversible chemical reaction. The problem is reduced to proving the existence of a heteroclinic orbit, in a two-dimensional phase space, connecting two critical points that represent the equilibrium states at plus and minus infinity. Reactions in which the forward reaction can be either endothermic or exothermic are examined, and it is shown that compression waves must be accompanied by a shift in the equilibrium composition in the endothermic direction, while rarefac-tions are accompanied by a shift in the exothermic direction. Although compression waves occur on a larger parameter domain, there are regimes where the rarefactions appear. Finally, the stability of an equilibrium state under small perturbations is discussed.
ISSN:1471-678X
0272-4960
1471-6798
1464-3634
DOI:10.1093/imamat/49.2.103