A new correlation of average temperature and maximum heat flux for turbulent supersonic flow in a large size channel up to Mach 5

Abstract

Supersonic compressible turbulent flow through a large size channel is studied numerically. The flow is modeled by the Favre averaged Navier-Stokes (FANS) equation with k−ω as turbulence model, the resulting governing equations are solved by employing an in-house unsteady state density based solver developed using sixth order accuracy compact finite difference schemes. The effect of Mach number and different wall thermal boundary conditions influencing, the variation of velocity, temperature and density across the channel height are reported in the present study. In the present study, the height of the channel is considered as 10 mm and the bulk Reynolds number is in the range of 3.42×105 to 1.14×106 which is higher compared to previous studies. Furthermore, the present Reynolds number represents a fully turbulent flow scenario, common in many aerospace applications. The results indicate that for an adiabatic wall with higher Mach number, there is a substantial increase in the wall temperature. The flow characteristics for a heated wall carried at low and medium Mach numbers indicate that for higher wall temperature, the behaviour of flow characteristics shifts towards that of the adiabatic wall behaviour. However, for higher Mach numbers the flow characteristics behaves like that of isothermal wall condition. In the present work, mathematical correlations for average temperature and maximum heat flux based on the Mach number are developed for adiabatic and isothermal wall conditions, respectively. The present results are validated with direct numerical simulation (DNS) results reported in the literature.