Modelling of differential diffusion effects in nonpremixed nonreacting turbulent flow

The modelling of differential diffusion with a conditional moment closure (CMC) method is considered. Direct numerical simulations for scalar fields in homogeneous isotropic decaying turbulence are used to quantify the non-unity Schmidt number effects. Unlike the equal molecular diffusion case, where terms involving deviations from the conditional average usually make a negligible contribution, these terms contribute significantly to the equations governing the evolution of the conditional average scalar in the presence of different molecular diffusion coefficients. Together with the conditional scalar dissipation they come to balance conditional scalar diffusion, the driving force of the differential diffusion effects. The shape of the conditional averages of these terms in mixture fraction space coincides with the approximate shape of the conditional average differential diffusion, $Qz.$ Therefore, dividing by $Qz$ they are only functions of time. Conditional moment closure leads to good predictions of $Qz$ provided the time function is properly modelled. A model for the time scale is suggested.