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On-shell description of unsteady flames

Published online by Cambridge University Press:  11 July 2008

GUY JOULIN ,
HAZEM EL-RABII  and
KIRILI A. KAZAKOV
GUY JOULIN
Affiliation:
Laboratoire de Combustion et de Détonique, CNRS/ENSMA, 1 av. Clément Ader, 86961 Futuroscope, Poitiers, France
HAZEM EL-RABII
Affiliation:
Laboratoire de Combustion et de Détonique, CNRS/ENSMA, 1 av. Clément Ader, 86961 Futuroscope, Poitiers, France
KIRILI A. KAZAKOV
Affiliation:
Department of Theoretical Physics, Physics Faculty, Moscow State University, 119899, Moscow, Russian Federation
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Abstract

The problem of a non-perturbative description of unsteady premixed flames with arbitrary gas expansion is addressed in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas velocity jumps, we show that the flame-front dynamics can be determined without having to solve the flow equations in the bulk. On the basis of the Thomson circulation theorem, an implicit integral representation of the downstream gas velocity is constructed. It is then simplified by a successive stripping of the potential contributions to obtain an explicit expression for the rotational component near the flame front. We prove that the unknown potential component is left bounded and divergence-free by this procedure, and hence can be eliminated using the dispersion relation for its on-shell value (i.e. the value along the flame front). The resulting system of integro-differential equations relates the on-shell fresh-gas velocity and the front position. As limiting cases, these equations contain all the theoretical results on flame dynamics established so far, including the linear equation describing the Darrieus–Landau instability of planar flames, and the nonlinear Sivashinsky–Clavin equation for flames with weak gas expansion.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 217 - 242
Copyright
Copyright © Cambridge University Press 2008

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