PDF approach and stochastic models of the turbulent mixing of inert and reactive statistically homogeneous scalar fields

Abstract

Abstract The turbulent mixing of both inert and reactive scalar fields is investigated. Single-point moment formulations outline the closure problems related to the molecular diffusion and the chemical source terms. The external supply of a characteristic decay time is avoided by including the scalar-gradient in the formulation, but then the straining/rotation, scalar dissipation and scalar-gradient dissipation must be approximated. The scalar probability density function (PDF) approach treats exactly the reaction rate term but modelling of the diffusive transport is required. The joint PDF equation of one scalar and its gradient must also model the straining/rotation term. Inert and reactive scalars are simulated using existing approximations in the form of deterministic or stochastic models. A new closure is tested with the characteristic scalar-decay time expressed as a function of the scalar-gradient. The equations are numerically solved with a Monte Carlo technique and predictions are compared with available direct numerical simulation (DNS) results.