Comptes Rendus
no. 11-12
The “turbulent flame speed” of wrinkled premixed flames
Moshe Matalon1  ; Francesco Creta2
1 University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
2 University of Rome La Sapienza, 00185 Roma, Italy
Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 845-858.

The determination of the turbulent flame speed is a central problem in combustion theory. Early studies by Damköhler and Shelkin resorted to geometrical and scaling arguments to deduce expressions for the turbulent flame speed and its dependence on turbulence intensity. A more rigorous approach was undertaken by Clavin and Williams who, based on a multi-scale asymptotic approach valid for weakly wrinkled flames, derived an expression that apart from a numerical factor recaptures the early result by Damköhler and Shelkin. The common denominator of the phenomenological and the more rigorous propositions is an increase in turbulent flame speed due solely to an increase in flame surface area. Various suggestions based on physical and/or experimental arguments have been also proposed, incorporating other functional parameters into the flame speed relation. The objective of this work is to extend the asymptotic results to a fully nonlinear regime that permits to systematically extract scaling laws for the turbulent flame speed that depend on turbulence intensity and scale, mixture composition and thermal expansion, flow conditions including effects of curvature and strain, and flame instabilities. To this end, we use a hybrid Navier–Stokes/front-capturing methodology, which consistently with the asymptotic model, treats the flame as a surface of density discontinuity separating burned and unburned gases. The present results are limited to positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures, and to wrinkled flames of vanishingly small thickness, smaller that the smallest fluid scales. For simplicity we have considered here two-dimensional turbulence, which although lacks some features of real three-dimensional turbulence, is not detrimental when using the hydrodynamic model under consideration, because the turbulent flame retains its laminar structure and its interaction with turbulence is primarily advective/kinematic in nature.

Publié le :
DOI : 10.1016/j.crme.2012.10.031
Mots clés : Turbulent flame speed, Darrieus–Landau instability, Premixed flames, Wrinkled flames, Flamelets, Markstein length, Flame stretch
Moshe Matalon 1 ; Francesco Creta 2

1 University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
2 University of Rome La Sapienza, 00185 Roma, Italy 
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Moshe Matalon; Francesco Creta. The “turbulent flame speed” of wrinkled premixed flames. Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 845-858. doi : 10.1016/j.crme.2012.10.031. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.031/

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☆ This article is dedicated to Paul Clavin for his distinctive contributions to flame theory, on the occasion of his 70th birthday.

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