Eddy Diffusivity Based Comparisons of Turbulent Prandtl Number for Boundary Layer and Free Jet Flows With Reference to Fluids of Very Low Prandtl Number

Abstract

It is shown that turbulent Prandtl numbers for turbulent boundary layer and jet flows correlate well if compared on the basis of eddy diffusivity. Experimental data for liquid sodium (Pr= 0.0058) lead to a universal expression relating turbulent Prandtl number to eddy diffusivity of heat with the same expression applying to boundary layer and jet flows. This suggests that the length and velocity scale dependence of the turbulent Prandtl number is associated predominantly with the eddy diffusivity of momentum. Since turbulent flow codes generally include eddy diffusivity of momentum calculations, simple and accurate estimates of eddy diffusivity of heat are possible without reliance on a variety of turbulent Prandtl number functional relationships for prediction of the temperature field. Available results also indicate that turbulent Prandtl number can be set at 0.9–1.0 irrespective of molecular Prandtl number, provided that εM/ν > 3Pr−1 and the structures of the mean temperature gradient and mean shear are similar.