Why does preferential diffusion strongly affect premixed turbulent combustion?

Abstract

Combustion of premixed reactants in a turbulent flow is a classical but unresolved problem. The key problem is to explain the following data: the maximal turbulent and laminar burning velocities u(sub t) and u(sub L) occur at different equivalence ratios Phi. It is known that the equivalence ratio varies along a curved flame if molecular diffusivity D(sub fuel) does not equal D(sub oxygen). However, the mean flame radius of curvature is much larger than the laminar flame thickness delta-L. Therefore, significant influence of preferential diffusion should occur only if the flame propagation speed varies with flame curvature. This conclusion agrees with Zel'dovich's long-standing idea about the important role of leading points of a flame. The main objective of this paper is to prove Zel'dovich's hypothesis. An equation for the mean flame surface area density (MFSAD) is employed for this purpose. The second objective of this paper is to suggest a different approach to the derivation of the equation for MFSAD. It is based on the pdf equation for the reaction progress variable C and the relation between the pdf and MFSAD. This treatment suggests an entirely different closure assumption.