Direct numerical simulations of compressible turbulent channel flows with asymmetric thermal walls

This paper extends the work of Tamano the pseudo-adiabatic case T32, where the top wall is isothermal with temperature Tₖ, ₓ=TA ; the sub-adiabatic case T25, with Tₖ, ₓ=0. 77TA ; and the super-adiabatic case T40, with Tₖ, ₓ=1. 24TA. Here, TA=3. 234 is the mean temperature at the adiabatic wall in the TAd case. The objective of this study is to compare and contrast the TAd case with its corresponding T32 case, and to investigate the effect of the wall temperature difference between the two isothermal walls. Comparisons of the basic turbulent statistics, the heat transfer between the Favre-averaged mean-flow kinetic energy, the Favre-averaged turbulent kinetic energy and the Favre-averaged mean internal energy, as well as the wall heat transfer properties, indicate that the TAd case and its corresponding T32 case are generally equivalent. The only discernible difference is in the region very close to the top wall for the temperature-fluctuation-related quantities. The analysis reveals that the asymmetry of the thermal walls causes asymmetry in the flow and thermal fields. In addition, the transfer of the heat generated by the pressure dilatation and the viscous stress is facilitated by the turbulent heat flux term and the mean molecular heat flux term.