Numerical Analysis of Compressible Turbulent Channel Flow with Wall-Temperature Difference

Abstract

The objective of this study is to clarify the effect of different thermal wall boundary conditions on turbulence statistics and structures in the compressible turbulent flow. We performed direct numerical simulation (DNS) of the compressible turbulent channel flow between isothermal walls with temperature difference (Case C1). The DNS data was compared with that of the compressible turbulent channel flow between adiabatic and isothermal walls (Case C2), and that of the incompressible turbulent channel flow between isothermal walls with temperature difference (Case I). The main results are as follows : (1) The mean velocity in the logarithmic region and the maximum of the RMS streamwise velocity fluctuation in wall units are smaller than those of Case I near the high temperature isothermal wall, while they are larger than those of Case I near the adiabatic wall. (2) Near the high temperature isothermal wall, the mean temperature profile has an additional maximum due to the friction work, and the RMS temperature fluctuation has the corresponding maximum. This is consistent with the fact the production term of temperature variance has the additional maximum in the region very close to the high temperature isothermal wall. (3) The correlation coefficient between streamwise velocity and temperature fluctuations of Case C1 is significantly different from those of Cases C2 and I in the region very close to the high temperature wall. (4) The direction of energy transfer due to pressure work near the high temperature isothermal wall is the same as that of near the adiabatic wall. (5) The compressible terms of the temperature variance transport equation are not negligible near the low temperature isothermal wall.