DNS of Turbulent Heat Transfer in Impinging Jets at Different Reynolds and Prandtl Numbers

The heat transfer between an impinging circular jet and a flat plate is studied by means of direct numerical simulations for different Prandtl numbers of the fluid. The thermal field is resolved for $Pr=1$, $0.72$, $0.025$, and $0.01$. The flow is incompressible and the temperature is treated as a passive scalar field. The jet originates from a fully developed turbulent pipe flow and impinges perpendicularly on a smooth solid heated plate placed at two pipe diameters distance from the jet exit section. The values of Reynolds numbers based on the pipe diameter and bulk mean velocity in the pipe are set to $Re=5300$ and $Re=10000$. Inflow boundary conditions are enforced using a precursor simulation. Heat transfer at the wall is addressed through the Nusselt number distribution and main flow field statistics. At fixed Reynolds number it is shown that the Prandtl number influences the intensity of the Nusselt number at a given radial location, and that the Nusselt number distribution along the plate exhibit similar features at different Prandtl numbers. The characteristic secondary peak in the Nusselt number distribution is found for both Reynolds numbers for $Pr=0.025$ and $Pr=0.01$. All the simulations presented in this study were performed with the high order spectral element code Nek5000.