Direct numerical simulation of turbulent forced convection in a wavy channel at low and order one Prandtl number

Turbulent forced convection in a channel with one planar wall and one wall of sinusoidal shape is investigated by Direct Numerical Simulation. The flow is fully developed and the Reynolds number based on the mean bulk velocity and the average hydraulic diameter is Re ≈ 18,900; in this weakly turbulent flow regime three different Prandtl number values are investigated, Pr = 0.025, 0.20, 0.71. The fluid is in contact with the colder channel walls at an equal, uniform temperature. The main statistical quantities, like the root-mean-square of temperature fluctuations and the turbulent heat fluxes, the local heat transfer coefficient and turbulent Prandtl number values are reported. Effects of flow separation and reattachment on the local heat transfer rate and turbulent Prandtl number distribution are also presented and discussed. An a priori analysis of the behavior of the simple gradient diffusion model of turbulent heat fluxes is performed in the low Prandtl number, separated flow conditions of the present work. While the low Prandtl number effect can be accounted for by an appropriate selection of the turbulent Prandtl number value to be provided to the model, deviations form the expected behavior of turbulent heat fluxes are seen to occur in the flow separation region and downstream reattachment.