Direct numerical simulation of subsonic, transonic and supersonic flow over an isolated sphere up to a Reynolds number of 1000

In the present study, compressible low-Reynolds-number flow past a stationary isolated sphere was investigated by direct numerical simulations of the Navier-Stokes equations using a body-fitted grid with high-order schemes. The Reynolds number based on free-stream quantities and the diameter of the sphere was set to be between 250 and 1000, and the free-stream Mach number was set to be between 0.3 and 2.0. As a result, it was clarified that the wake of the sphere is significantly stabilized as the Mach number increases, particularly at the Mach number greater than or equal to 0.95, but turbulent kinetic energy at the higher Mach numbers conditions is higher than that at the lower Mach numbers conditions of similar flow regimes. A rapid extension of the length of the recirculation region was observed under the transitional condition between the steady and unsteady flows. The drag coefficient increases as the Mach number increases mainly in the transonic regime and its increment is almost due to the increment in the pressure component. In addition, the increment in the drag coefficient is approximately a function of the Mach number and independent of the Reynolds number in the continuum regime. Moreover, the effect of the Mach and Reynolds numbers on the flow properties such as the drag coefficient and flow regime can approximately be characterized by the position of the separation point.