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

• Main Authors: Vladimir A. Sabelnikov, Alan R. Kerstein
• Format: Article
• Language: English
• Published: SAGE Publishing 2012-03-01
• Series: International Journal of Spray and Combustion Dynamics
• Online Access: https://doi.org/10.1260/1756-8277.4.1.61

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.