Turbulent transport modeling in low Mach number flows

Model representations for the Reynolds stress and the turbulent heat flux o f flows at low Mach numbers have been theoretically derived by applying the two-scale direct-interaction approximation to their transport equations ba sed on the assumption that the density variation is relatively small. The d erived representations can be applied to general turbulent flows at low Mac h numbers, whether the Boussinesq approximation holds in the flow or not. T he model representation for the turbulent heat flux newly involves the diff erential effect of mean pressure gradients on hot, light fluids and on cold , heavy ones, in addition to the familiar effect of mean temperature diffus ion. Certain a priori tests have shown that the model can reproduce the ver tical turbulent heat flux in the natural convection along a heated vertical plate and the countergradient diffusion for the turbulent heat flux observ ed in a nonpremixed swirling flame, both of which can not be explained by t he standard turbulence model of the gradient diffusion type. (C) 1999 Ameri can Institute of Physics. [S1070-6631(99)00410-9].