Direct numerical simulations analysis of flame surface density models for nonpremixed turbulent combustion

From phenomenological considerations, Marble and Broadwell(1) have introduced the flame surface density concept to describe nonpremixed turbulent combustion. In this approach, the averaged reaction rate is modeled as the product of the local reaction rate per unit of flame area, rn,, by the flame area per unit volume, <(Sigma)over bar>. This approach is attractive because it decouples the chemical problem ((m) over dot (F)) from the description of the turbulence combustion interaction (<(Sigma)over bar>). In this paper, a theoretical analysis providing two alternatives exact, but unclosed, balance equations for the flame surface density <(Sigma)over bar> is first developed. Then, direct numerical simulations of a spatially developing turbulent reacting mixing layer are used to analyze the structure of the reaction zone and to propose and validate closures for the <(Sigma)over bar>-balance equations. The flame surface density concept is found to provide a relevant description for nonpremixed turbulent flames. (C) 1998 American Institute of Physics.