On velocity-conditioned scalar mixing in homogeneous turbulence

Abstract

Scalar mixing models are required to model turbulent molecular mixing in full probability density function (pdf) simulations of turbulent reacting flows. Despite the existence of direct numerical simulation (DNS) data suggesting the contrary, most scalar mixing models assume that molecular mixing is independent of the instantaneous velocity, i.e., 〈D∇2φ|V,ψ〉=〈D∇2φ|ψ〉. Since in a joint velocity, composition pdf calculation the velocity is known, this assumption is unnecessary and leads to a lack of local isotropy in the scalar field. Moreover, since velocity conditioning offers a numerically tractable approach for including the effects of local anisotropy and mean velocity gradients on scalar mixing, it should be of considerable interest for the numerical simulation of scalar mixing in inhomogeneous turbulent flows. An efficient numerical implementation of velocity-conditioned scalar mixing for full pdf simulations is proposed and verified against DNS data for homogeneous turbulence (isotropic and shear flow) with a uniform mean scalar gradient. A second-moment closure relating the velocity-conditioned scalar dissipation to the scalar fluxes and Reynolds stresses that is exact in the limit of a joint Gaussian pdf is also derived for use with moment closure models.