Numerical Study of Compressible Wall-Bounded Turbulence – the Effect of Thermal Wall Conditions on the Turbulent Prandtl Number in the Low-Supersonic Regime

Direct numerical simulation is used to determine the turbulent Prandtl number Prt above cold (isothermal) and hot (adiabatic) walls in a family of low-supersonic channel flows. A range of mean temperature/density variations, corresponding to effective/edge Mach numbers between 1.1 to 2.2, and wall-variable-based Reynolds number Reτw from 73 to 3800, is considered. The adiabatic condition is a new feature of special interest. The value of Prt away from the wall approaches 0.85 above both the isothermal and adiabatic walls. The variations of the near-wall Prt profiles in both the present and previous, passive-scalar simulations collapse as a function of the semilocal yw∗ wall scaling proposed in 1995 by [Huang, P. G., G. N. Coleman, and P. Bradshaw. 1995. "Compressible Turbulent Channel Flows: DNS Results and Modelling." Journal of Fluid Mechanics 305: 185–218. doi:10.1017/S0022112095004599.], with only a weak dependence on Reτw. This leads to a rather simple proposal for a model of heat transfer, attached to an eddy-viscosity model.