Compressible flow over a heated sphere at Reynolds numbers 100 and 300

We study flow over a heated sphere to investigate the effects of the temperature ratio (TR) between the free-stream flow and the surface of the heated sphere rigid body. We solve fully compressible Navier-Stokes equations, where the solid sphere geometry in the flow domain is represented by a second-order ghost cell immersed boundary method. In addition, we use a variable temperature-dependent (power-law with a power of 0.75) fluid transport coefficient model for the shear viscosity and a constant Prandtl number model for the thermal conductivity with the temperature-varying viscosity. Numerical simulations are carried out at Mach number 0.4 and Reynolds numbers 100 and 300, with TR values of 1.2 (low TR) and 3.0 (high TR). For validation purposes, fully adiabatic cases at these Reynolds numbers are also simulated and are shown to have good agreement with available experimental and numerical data. At Re 100, the flow is steady and axisymmetric for all investigated cases. However, at Re 300, the adiabatic case shows an unsteady flow, whereas for the high TR case, the flow stays steady and axisymmetric. This stabilization effect with an increase in TR is attributed to the larger viscosity coefficients in the vicinity of the sphere due to the increased temperature. Moreover, low and high TR cases lead to higher values for both the mean pressure and viscous drag coefficients compared to their adiabatic counterparts, with the changes becoming more prominent for the high TR cases. It is also observed that the TR effect on the mean wake recirculation length depends on the Re number. For example, at Re 100, compared to the adiabatic case, the recirculation length decreases with an increased TR, whereas at Re 300, it increases with TR.