Derivation from the Field Equation of the Mean Consumption Velocity for Front Propagation in Homogeneous Turbulent Flow

Abstract

Based on purely geometrical considerations of the level sets of the scalar G(x, t) satisfying the field equation ( G - equation), A. Kerstein, T. Ashurst and F. Williams [Phys. Rev. A, 37, 2728, (1988)] derived the expression for the mean flame consumption velocity in a 1D premixed turbulent flame in a homogeneous flow of uniform density in terms of the volume average of |▽ G(x, t)| for a particular choice of the initial condition G(x, t = 0). In the present study we develop further the KAW work in two directions. First, in section 2, in contrast with the KAW approach, we consider the G - equation immediately and, using ensemble averaging, obtain the expression for the mean flame consumption velocity in terms of ensemble averages equivalent to the KAW result. Then, in section 3 the developed approach is applied to the case of homogeneous turbulent flow with a uniform mean strain rate field depending only on time.