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A Reduced Model for Flame-Flow Interaction

Published online by Cambridge University Press:  15 June 2008

P. Gordon ,
M. Frankel  and
G. Sivashinsky
P. Gordon
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
M. Frankel
Affiliation:
Department of Mathematical Sciences, Indiana University Purdue University, Indianapolis, IN 46202, USA
G. Sivashinsky*
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
*
grishas@post.tau.ac.il
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Abstract

The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system of second-order dynamic equations for the flame interface and its temperature. As an illustration the new model is applied for description of diffusively unstable stagnation-point flow flames.

Keywords

premixed flamesinstabilities in flamesflame stretch
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 2 , Issue 2: Reaction-diffusion waves , 2007 , pp. 1 - 12
Copyright
© EDP Sciences, 2007

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