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

Presence of transient events like extinction/ignition in turbulent reacting flows increase conditional fluctuations. Thus, one needs to include the co nditional fluctuations of reactive scalars, second order quantities, for co nditional moment closure calculation when there are transient events and fo r predictions of sensitive species like NOx. Transport equations for condit ional variances G(ii) and covariances G(ij) are derived and studied using a direct numerical simulation (DNS) data base. In high Damkohler number situ ations, chemically reactive and turbulent diffusive processes balance the e ffect of scalar dissipation-scalar fluctuations correlation on G(ij) evolut ion. Additionally, the dissipation of scalar fluctuation becomes important for low Damkohler number situations. Simple models for the different physic al processes are proposed and evaluated. Chemical contributions are modeled using a presumed probability density function (PDF) approach which include s second order contributions. The conditional joint PDF of progress variabl es 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 dissip ation rate-scalar fluctuations correlation coefficient does not depend on R eynolds or Damkohler numbers. However, the model constant in the classical model for conditional dissipation of scalar fluctuations depends on Damkohl er number. Based on the gradient alignment characteristics observed in the DNS, a new model for the above dissipation is proposed using stationary lam inar flamelet theory. This model prediction of the above dissipation is bet ter than the classical model prediction. (C) 1999 American Institute of Phy sics. [S1070-6631(99)01309-4].