Numerical Analysis of Compressible Turbulent Channel Flow between Adiabatic and Isothermal Walls. 3rd Report. Energy Transfer.

Abstract

Our main objective of this study is to clarify the energy transfer near the isothermal and adiabatic walls in the compressible turbulent flows. To this end we investigate the turbulent kinetic, mean kinetic and internal energy budgets using two cases of direct numerical simulation (DNS), Case 1 and Case 2. Case 1 is the compressible turbulent flow between isothermal walls and Case 2 is one between adiabatic and isothermal walls. In Case 1 and Case 2, 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 3 000. Moreover, two cases of DNS of the incompressible turbulent channel flow with the passive scalar transport, Case A and Case B, are carried out for comparing with the compressible one. The wall boundary conditions of Case A and Case B correspond to those of Case 1 and Case 2, respectively. In Case A and Case B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150. The main results are as follows: (1) The turbulent and mean kinetic energy budgets of compressible turbulent channel flow agree well with the data of the incompressible one, when these profiles are scaled by the local mean variables. (2) The compressibility term of turbulent energy equation is very small and that of mean kinetic energy equation is small near the wall. The direction of energy transfer of these terms near the isothermal wall is opposite to that near the adiabatic wall. (3) The compressible part of the turbulent energy dissipation is not negligible near the isothermal wall, while it is negligible near the adiabatic wall. (4) The compressible part of the mean kinetic energy dissipation is negligible near the isothermal and adiabatic walls.