Numerical Analysis of Compressible Turbulent Channel Flow between Adiabatic and Isothermal Wall. 2nd Report. Profiles of Turbulence Statistics.

Abstract

The effects of the variable-property on the profiles of the turbulence statistics and the near-wall asymptotic behavior for the compressible turbulent channel flows are investigated using direct numerical simulation (DNS). Two cases of DNS are carried out. The first case is the compressible turbulent flow between isothermal walls, and 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) When the velocity fluctuations, kinetic energy, and turbulent dissipation profiles are scaled by the wall variables, these profiles are larger near the isothermal wall and smaller near the adiabatic wall, comparing with those of the incompressible turbulent channel flow. On the other hand, these profiles agree well with the data of the incompressible turbulent channel flow, when these profiles are scaled by the local mean variables. It means Morkovin's hypothesis is applicable to these profiles. (2) The rms temperature fluctuation profile scaled by the mean temperature is almost the same as the rms density fluctuation profile scaled by the mean density, except that the rms temperature fluctuation on the isothermal wall is zero. (3) Differences between Favre and Reynolds averages on the Reynolds stresses are negligible in the wall bounded flow. (4) Morkovin's hypothesis is not applicable to the wall asymptotic behavior. (5) The rms temperature fluctuation profile scaled by the wall temperature varies linearly with the wall unit y+ near the isothermal wall and approaches a constant non-zero value with the decrease of y+ near the adiabatic wall.