Abstract
The effects of the different thermal wall boundary conditions on the mean velocity and temperature profiles in the compressible turbulent channel flows are investigated. Dimensional analysis says that the mean velocity and temperature profiles depend on the non-dimensional heat flux Bq and the friction Mach number Mτ, when the Prandtl number and the ratio of specific heats are constants. The effects of Bq and Mτ on the mean velocity and temperature profiles are examined using direct numerical simulation (DNS). Two cases of DNS are carried out. The first case is the compressible turbulent flow between isothermal walls, which is the same as that performed by Coleman et al. The second case is one between adiabatic and isothermal walls. In the DNS, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5 and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000. The main results are as follows : (1) The mean velocity profile with Van Driest transformation is independent of Bq and Mτ, while the untransformed one increases with an increase of -Bq and decreases with an increase of Mτ. (2) The mean temperature increases with an increase of -Bq and decreases with an increase of Mτ. (3) The similarity law between the mean velocity and temperature is not satisfied when the effect of friction work is large. As a result, logarithmic law of the mean temperature is not obtained.
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