Numerical Analysis of Compressible Turbulent Channel Flow between Adiabatic and Isothermal Walls. 4th Report. Near-Wall Turbulence Structure and Reynolds Analogy.

Abstract

Our main objective is to clarify the near-wall streak struture and Reynolds Analogy near isothermal and adiabatic walls in the compressible turbulent flow, using direct numerical simulation (DNS). 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 3000. Moreover, we compare the DNS data of the compressible turbulent flow with that of the incompressible turbulent channel flow with the passive scalar transport, Case A and Case B. 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 near-wall streak structures of compressible and incompressible turbulent flows are comparable and are independent of the thermal wall boundary condition, when the variable property effect is taken into account. (2)The low-speed streaks coincide with the low-temperature streaks and exist in the high-temperature regions in the compressible turbulent flow near isothermal and adiabatic walls, respectively. On the other hand, such a relationship between streamwise velocity and temperature fluctuations are not observed near the adiabatic wall for the incompressible turbulent flow. It indicates that Morkovin's hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall. (3)The existing modified Reynolds analogies do not agree well with the DNS data of the compressible turbulent flow between adiabatic and isothermal walls.