A unified model of flames as gasdynamic discontinuities

Class, A. G., Matkowsky, B. J. and Klimenko, A. Y. (2003) A unified model of flames as gasdynamic discontinuities. Journal of Fluid Mechanics, 491 11-49. doi:10.1017/S002211200300507X

Author Class, A. G.
Matkowsky, B. J.
Klimenko, A. Y.
Title A unified model of flames as gasdynamic discontinuities
Journal name Journal of Fluid Mechanics   Check publisher's open access policy
ISSN 0022-1120
Publication date 2003
Sub-type Article (original research)
DOI 10.1017/S002211200300507X
Volume 491
Start page 11
End page 49
Total pages 39
Place of publication New York, USA
Publisher Cambridge University Press
Collection year 2003
Language eng
Subject C1
291803 Turbulent Flows
780102 Physical sciences
Abstract Viewed on a hydrodynamic scale, flames in experiments are often thin so that they may be described as gasdynamic discontinuities separating the dense cold fresh mixture from the light hot burned products. The original model of a flame as a gasdynamic discontinuity was due to Darrieus and to Landau. In addition to the fluid dynamical equations, the model consists of a flame speed relation describing the evolution of the discontinuity surface, and jump conditions across the surface which relate the fluid variables on the two sides of the surface. The Darrieus-Landau model predicts, in contrast to observations, that a uniformly propagating planar flame is absolutely unstable and that the strength of the instability grows with increasing perturbation wavenumber so that there is no high-wavenumber cutoff of the instability. The model was modified by Markstein to exhibit a high-wavenumber cutoff if a phenomenological constant in the model has an appropriate sign. Both models are postulated, rather than derived from first principles, and both ignore the flame structure, which depends on chemical kinetics and transport processes within the flame. At present, there are two models which have been derived, rather than postulated, and which are valid in two non-overlapping regions of parameter space. Sivashinsky derived a generalization of the Darrieus-Landau model which is valid for Lewis numbers (ratio of thermal diffusivity to mass diffusivity of the deficient reaction component) bounded away from unity. Matalon & Matkowsky derived a model valid for Lewis numbers close to unity. Each model has its own advantages and disadvantages. Under appropriate conditions the Matalon-Matkowsky model exhibits a high-wavenumber cutoff of the Darrieus-Landau instability. However, since the Lewis numbers considered lie too close to unity, the Matalon-Matkowsky model does not capture the pulsating instability. The Sivashinsky model does capture the pulsating instability, but does not exhibit its high-wavenumber cutoff. In this paper, we derive a model consisting of a new flame speed relation and new jump conditions, which is valid for arbitrary Lewis numbers. It captures the pulsating instability and exhibits the high-wavenumber cutoff of all instabilities. The flame speed relation includes the effect of short wavelengths, not previously considered, which leads to stabilizing transverse surface diffusion terms.
Keyword Mechanics
Physics, Fluids & Plasmas
Premixed Flames
Q-Index Code C1
Additional Notes The JFM paper is the most recent publication on asymptotic analysis of premixed flames using so called intrinsic disturbed flame equations (IDFE). IDFE not only dramatically simplified the derivation of known relationships in the area but also allowed for unified consideration of premixed flames disturbed by fluid flows and and resulted in finding the asymptotic solutions for several previously unsolved problems. I would like to stress my originating and leading role in establishing the IDFE methodology.

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Created: Tue, 14 Aug 2007, 19:26:31 EST