Turbulent transport modeling in low Mach number flows

Model representations for the Reynolds stress and the turbulent heat flux of flows at low Mach numbers have been theoretically derived by applying the two-scale direct-interaction approximation to their transport equations based on the assumption that the density variation is relatively small. The derived representations can be applied to general turbulent flows at low Mach numbers, whether the Boussinesq approximation holds in the flow or not. The model representation for the turbulent heat flux newly involves the differential effect of mean pressure gradients on hot, light fluids and on cold, heavy ones, in addition to the familiar effect of mean temperature diffusion. Certain a priori tests have shown that the model can reproduce the vertical turbulent heat flux in the natural convection along a heated vertical plate and the countergradient diffusion for the turbulent heat flux observed in a nonpremixed swirling flame, both of which can not be explained by the standard turbulence model of the gradient diffusion type.