DNS of thermal channel flow up to [formula omitted] for medium to low Prandtl numbers

Abstract

Direct Numerical Simulations of turbulent heat transfer in a channel flow are presented for three different Reynolds numbers, namely Reτ=500,1000 and 2000. Medium and low values of the molecular Prandtl number are studied, ranging from 0.71 (air), down to 0.007 (molten metals), in order to study its effect on the thermal flow. Mixed boundary conditions at both walls are used for the thermal flow. Mean value and intensities of the thermal field were obtained. Two different behaviors were observed, depending on the Prandtl and Péclet numbers. The expected logarithmic behavior of the thermal flow completely disappears for Prandtl below 0.3. This is a direct effect of the thicker viscous thermal layer generated as the Prandtl number is reduced. Von Kármán constant was computed for cases above this Prandtl, and turbulent Prandtl and Nusselt numbers were obtained for all the cases. Finally, the turbulent budgets for heat fluxes, temperature variance and its dissipation rate are presented. As a general result, there is a scaling failure near the wall in very cases studied, which is accentuated for lower Prandtl numbers. The statistics of all simulations can be downloaded from the web page of our group.