About the prediction of turbulent prandtl and schmidt numbers from modeled transport equations

Abstract

Relationships for the turbulent Prandtl and Schmidt number are presented. They are based on modeled transport equations for the turbulent kinetic energy, for the turbulent heat flux, and the turbulent mass flux. The final results are simple formulae Pr t = C + B Pr and Sc t = F + E Sc where the constants have to be adjusted from experimental data. This has been done for the constants in the relationship for the turbulent Prandtl number which is in very good agreement with experiments. The agreement can be improved by assuming B to be a function of the Reynolds number. The result is specially interesting for liquid metals, because for low Prandtl numbers the turbulent Prandtl number obviously depends strongly on the molecular Prandtl number. The influence of the Reynolds number, which is increasing for decreasing Prandtl numbers, seems to be weaker.