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Thermal-diffusion instability of premixed flames for a simple chain-branching chemistry model with finite activation energy

Sharpe, G.J. (2009) Thermal-diffusion instability of premixed flames for a simple chain-branching chemistry model with finite activation energy. SIAM Journal on Applied Mathematics (SIAP), 70 (3). pp. 866-884. ISSN 0036-1399

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Abstract

A linear stability of freely propagating, adiabatic premixed flames is investigated in the context of a thermal-diffusive or constant density model, together with a simple two-step chain-branching model of the chemistry. This study considers the case of realistic, finite activation energy of the chain-branching step, and emphasis is on comparing with previous high activation energy asymptotic results. It is found that for realistic activation energies, a pulsating instability is absent in regimes predicted to be unstable by the asymptotic analysis. For the cellular instability, however, the finite activation energy results are in qualitative agreement with the asymptotic results, in that the flame is unstable only below a critical Lewis number of the fuel and becomes more unstable as the Lewis number is decreased. However, it is shown that very high activation energies would be required for the asymptotic analysis to be quantitatively predictive. The flame is less unstable for finite activation energies than predicted by the asymptotic analysis, in that a lower fuel Lewis number is required for instability. It is also shown that the flame structure and stability can have nonmonotonic dependencies on the activation energy.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 Society for Industrial and Applied Mathematics. Reproduced in accordance with the publisher's self-archiving policy.
Keywords: flames, linear stability, chain-branching chemistry
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 16:16
Last Modified: 08 Feb 2013 17:06
Published Version: http://dx.doi.org/10.1137/090750366
Status: Published
Publisher: Society for Industrial and Applied Mathematics
Refereed: Yes
Identification Number: 10.1137/090750366
URI: http://eprints.whiterose.ac.uk/id/eprint/10272

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