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A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

Hmaidi, A, McIntosh, AC and Brindley, J (2010) A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction. Combustion theory and modelling, 14 (6). 893 - 920 . ISSN 1364-7830

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Abstract

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.

Item Type: Article
Keywords: gasless combustion, large activation energy asymptotics, flame propagation, heat loss, competitive reaction, propagation
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Process, Environmental and Materials Engineering (Leeds) > Centre for Computational Fluid Dynamics (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds)
The University of Leeds > Faculty of Engineering (Leeds) > School of Process, Environmental and Materials Engineering (Leeds) > Energy and Resources Research Institute (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 28 Apr 2011 10:14
Last Modified: 22 Jun 2014 04:17
Published Version: http://dx.doi.org/10.1080/13647830.2010.519050
Status: Published
Publisher: Taylor & Francis Limited
Identification Number: 10.1080/13647830.2010.519050
URI: http://eprints.whiterose.ac.uk/id/eprint/42955

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