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Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

Sharpe, G.J. (2008) Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit. Combustion Theory and Modelling, 12 (4). pp. 717-738. ISSN 1364-7830

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Abstract

The linear stability of freely propagating, adiabatic, planar premixed ames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-di�usive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable ames predicted by the constant density model disappears, and instead the ame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak e�ect on the critical fuel Lewis number required for instability. These e�ects of thermal expansion on the two-step chain-branching ame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic ame temperature, the two-step model can be described to leading order by the one-step model with a suitably de�ned e�ective activation energy.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Taylor & Francis. This is an author produced version of a paper published in 'Combustion Theory and Modelling'. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Thermal expansion, planar premixed flames
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds)
Depositing User: Mrs Fiona Slade
Date Deposited: 15 Jan 2010 16:30
Last Modified: 19 Sep 2013 16:20
Published Version: http://dx.doi.org/10.1080/13647830802032849
Status: Published
Publisher: Taylor & Francis
Refereed: Yes
Identification Number: 10.1080/13647830802032849
URI: http://eprints.whiterose.ac.uk/id/eprint/10273

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