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Linear stability of planar premixed flames: reactive Navier-Stokes equations with finite activation energy and arbitrary Lewis number

Sharpe, G.J. (2003) Linear stability of planar premixed flames: reactive Navier-Stokes equations with finite activation energy and arbitrary Lewis number. Combustion Theory and Modelling, 7 (1). pp. 45-65. ISSN 1741-3559

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Abstract

A numerical shooting method for performing linear stability analyses of travelling waves is described and applied to the problem of freely propagating planar premixed flames. Previous linear stability analyses of premixed flames either employ high activation temperature asymptotics or have been performed numerically with finite activation temperature, but either for unit Lewis numbers (which ignores thermal-diffusive effects) or in the limit of small heat release (which ignores hydrodynamic effects). In this paper the full reactive Navier-Stokes equations are used with arbitrary values of the parameters (activation temperature, Lewis number, heat of reaction, Prandtl number), for which both thermal-diffusive and hydrodynamic effects on the instability, and their interactions, are taken into account. Comparisons are made with previous asymptotic and numerical results. For Lewis numbers very close to or above unity, for which hydrodynamic effects caused by thermal expansion are the dominant destablizing mechanism, it is shown that slowly varying flame analyses give qualitatively good but quantitatively poor predictions, and also that the stability is insensitive to the activation temperature. However, for Lewis numbers sufficiently below unity for which thermal-diffusive effects play a major role, the stability of the flame becomes very sensitive to the activation temperature. Indeed, unphysically high activation temperatures are required for the high activation temperature analysis to give quantitatively good predictions at such low Lewis numbers. It is also shown that state-insensitive viscosity has a small destabilizing effect on the cellular instability at low Lewis numbers.

Item Type: Article
Copyright, Publisher and Additional Information: © 2003 Institute of Physics and IOP Publishing Limited. 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.
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: Sherpa Assistant
Date Deposited: 07 Mar 2008 18:14
Last Modified: 08 Feb 2013 17:05
Published Version: http://dx.doi.org/10.1088/1364-7830/7/1/303
Status: Published
Publisher: Taylor and Francis Group
Refereed: Yes
Identification Number: 10.1088/1364-7830/7/1/303
URI: http://eprints.whiterose.ac.uk/id/eprint/3683

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