Heat and Mass Transfer Equations for Turbulent Flow with Wide Ranges of Prandtl and Schmidt Numbers

Abstract

Turbulent statistics near the wall region were obtained by DNS (direct numerical simulation) method in recent years. Numerical models for the turbulent diffusivity and turbulent Prandtl number were improved based on these data. New logarithmic laws for the scalar distribution in the fully turbulent region were proposed by regression analysis of DNS results. Different values for the coefficients of these logarithmic law were proposed. The functions for Prandtl number effects on temperature distribution were also different in the literature. In the current investigation, an exponential function for the ratio of turbulent to molecular diffusivity is presented. Molecular and turbulent contributions to the diffusion process are compared. The critical points separating the linear and logarithmic regions are determined with a fixed criterion. New logarithmic law is derived for the scalar distribution, which shows good prediction of experimental data and DNS results. Using the derived equation for scalar distribution, new Nusselt and Sherwood number equations are obtained. The derived equations agree well with experimental data over wide ranges of Prandtl and Schmidt numbers. Compared with conventional correlations, the derived equations show better prediction of experimental data at high Schmidt numbers (larger than 930).