TY - JOUR
T1 - The "turbulent flame speed" of wrinkled premixed flames
AU - Matalon, Moshe
AU - Creta, Francesco
N1 - Funding Information:
This work has been partially supported by the National Science Foundation under Grant CBET-1067259. The authors are indebted to Navin Fogla who have helped in preparing some of the figures presented in this article.
PY - 2012/11
Y1 - 2012/11
N2 - 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.
AB - 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.
KW - Darrieus-Landau instability
KW - Flame stretch
KW - Flamelets
KW - Markstein length
KW - Premixed flames
KW - Turbulent flame speed
KW - Wrinkled flames
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U2 - 10.1016/j.crme.2012.10.031
DO - 10.1016/j.crme.2012.10.031
M3 - Short survey
AN - SCOPUS:84872391038
SN - 1631-0721
VL - 340
SP - 845
EP - 858
JO - Comptes Rendus - Mecanique
JF - Comptes Rendus - Mecanique
IS - 11-12
ER -