Relationships for maximum flame surface density and brush thickness through conditional analysis in turbulent premixed combustion

Abstract

A new conditional averaging method is introduced in terms of the reaction progress variable, c, and its derivatives of successively higher orders, Sigma&apos;(f) (or -partial derivative c/partial derivative n) and partial derivative(2)c/partial derivative n(2), in high Damkohler number (Da) turbulent premixed combustion. c is continuous and differentiable in space so that conditional averages may be defined for flamelets of finite thicknesses as well as for infinitesimally thin flamelets. A coupled set of transport equations are derived with corresponding conditional coefficient terms for mean reaction progress variable, (c) over bar, and flame surface density (FSD), Sigma(f). Statistics for all component terms are consistent with previous results and show the same qualitative trends irrespective of compressibility by the new averaging practice. It is shown that the maximum FSD, Sigma(max), occurs at the location where the relationship, del(2)(c) over bar + <del . n >(f) Sigma(f) = 0, holds in a flame brush. An analytical expression is derived for Sigma(max) under the assumption of constant tangential strain rate and linear variation of mean curvature and mean displacement speed, < S-d >(f), in the (c) over bar space. Sigma(max) becomes equal to one fourth <vertical bar del . n vertical bar >(f) or half the mean absolute curvature for fully turbulent flames with the magnitude of < n >(f) close to zero. Once the turbulent burning velocity, S-T, is determined by asymptotic behavior at the leading edge, the brush thickness, l(F), may be obtained from local and integral relationships for the product, l(F)Sigma(max), in a steadily propagating one-dimensional flame. The newly proposed relationships reproduce proper trends of variation for S-T, Sigma(max), and l(F) against measurement data in literature. They are validated to show good agreement with direct numerical simulation (DNS) results of the Lewis number equal to unity for freely propagating incompressible and stagnating compressible turbulent premixed flames. (C) 2013 AIP Publishing LLC.