Conditional moment closure for large eddy simulation of nonpremixed turbulent reacting flows

Abstract

A method for closing the chemical source terms in the filtered governing equations of motion is proposed. Conditional filtered means of quantities appearing in the chemical reaction rate expressions are approximated by assuming that these conditional filtered means are constant for some ensemble of points in the resolved flow field; for such an ensemble, integral equations can be solved for the conditional filtered means. These conditional filtered means are then used to approximate the conditional filtered mean of the chemical source term by invoking the Conditional Moment Closure hypothesis. The filtered means of the chemical source terms are obtained by integrating their conditional filtered means over the filtered density function of the conditioning variable(s). The method is applied to direct numerical simulation results to directly compare the prediction of the reaction rates with the actual filtered reaction rates. The results of this a priori test appear to show that the method is capable of predicting the filtered reaction rates with adequate accuracy—even in the presence of heat release, and local extinction phenomena. This is especially true for predictions obtained using two conditioning variables.