Math. Model. Nat. Phenom.
Volume 2, Number 2, 2007Reaction-diffusion waves
|Page(s)||1 - 12|
|Published online||15 June 2008|
A Reduced Model for Flame-Flow Interaction
Department of Mathematical Sciences, New Jersey Institute of Technology,
University Heights, Newark, NJ 07102, USA
2 Department of Mathematical Sciences, Indiana University Purdue University, Indianapolis, IN 46202, USA
3 Department of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Corresponding author: firstname.lastname@example.org
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.
Mathematics Subject Classification: 92D30 / 35K57 / 35B20 / 35B40
Key words: premixed flames / instabilities in flames / flame stretch
© EDP Sciences, 2007
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