Direct numerical simulation of flow around a heated/cooled isolated sphere up to a Reynolds number of 300 under subsonic to supersonic conditions

In this study, an analysis of the flow properties around an isolated sphere under isothermal conditions for flows with high Mach numbers and low Reynolds numbers is conducted via direct numerical simulation (DNS) of the three-dimensional compressible Navier–Stokes equations. The calculations are performed with a boundary-fitted coordinate system. The Reynolds number based on the diameter of the sphere and the freestream quantities is varied from 100 to 300, the freestream Mach number is varied between 0.3 and 2.0, and the temperature ratio between the sphere surface and the freestream is varied between 0.5 and 2.0. We focus on the effects of the Mach number and the temperature ratio on the flow properties. The results show the following characteristics: (1) unsteady vortex shedding from the sphere is promoted (suppressed) when the temperature ratio is less (greater) than unity; (2) the drag coefficient increases with the temperature ratio, but previous drag relations give poor prediction on effect of the temperature ratio on the drag coefficient in the continuum regime; (3) Nusselt number relations proposed in previous studies can be applied if the temperature ratio is close to unity under subsonic conditions; (4) the changes in several flow properties can be characterized by a separation point in the range investigated.