Linear mean profiles in compressible turbulent channel flows with asymmetric thermal walls

As one of the canonical flows in compressible wall-bounded turbulence, compressible turbulent channel flow with asymmetric thermal walls has been studied a lot in recent years. Numerous numerical results show that the mean temperature exhibits a linear distribution with asymmetric temperature walls. In this paper, a semi-empirical formula for the mean temperature within the range of the channel center is proposed. In order to evaluate the proposed formula, the available numerical simulation data are used, with Reynolds numbers ranging from around 2200 to 20 000 and Mach numbers ranging from 0.3 to 3.44. It is found that the empirical formula is quite accurate in the range y/h∈(−0.5,0.5), and most of the relative errors are less than 3.0%. Furthermore, the ideal gas equation and Sutherland's formula can be utilized for quantitative determination of the mean density and viscosity profiles in the channel.