Study of the conditional covariance and variance equations for second order conditional moment closure

Abstract

Presence of transient events like extinction/ignition in turbulent reacting flows increase conditional fluctuations. Thus, one needs to include the conditional fluctuations of reactive scalars, second order quantities, for conditional moment closure calculation when there are transient events and for predictions of sensitive species like NOx. Transport equations for conditional variances Gii and covariances Gij are derived and studied using a direct numerical simulation (DNS) data base. In high Damköhler number situations, chemically reactive and turbulent diffusive processes balance the effect of scalar dissipation–scalar fluctuations correlation on Gij evolution. Additionally, the dissipation of scalar fluctuation becomes important for low Damköhler number situations. Simple models for the different physical processes are proposed and evaluated. Chemical contributions are modeled using a presumed probability density function (PDF) approach which includes second order contributions. The conditional joint PDF of progress variables for the two steps used are observed to be jointly log-normal or jointly Gaussian depending on whether there is extinction or not. The scalar dissipation rate–scalar fluctuations correlation coefficient does not depend on Reynolds or Damköhler numbers. However, the model constant in the classical model for conditional dissipation of scalar fluctuations depends on Damköhler number. Based on the gradient alignment characteristics observed in the DNS, a new model for the above dissipation is proposed using stationary laminar flamelet theory. This model prediction of the above dissipation is better than the classical model prediction.