Numerical investigations of flow over a sphere in the subcritical and supercritical regimes

Abstract

The flow field around a sphere in an uniform flow has been analyzed numerically for conditions corresponding to the subcritical (laminar separation) and supercritical (turbulent separation) regimes spanning a wide range of Reynolds numbers (104–106). Particular attention has been devoted to assessing predictions of the pressure distribution, skin friction, and drag as well as to understanding the changes in the wake organization and vortex dynamics with the Reynolds number. The unsteady turbulent flow is computed using detached-eddy simulation, a hybrid approach that has Reynolds-averaged Navier–Stokes behavior near the wall and becomes a large eddy simulation in the regions away from solid surfaces. For both the subcritical and supercritical solutions, the agreement with experimental measurements for the mean drag and pressure distribution over the sphere is adequate; differences in skin friction exist due to the simplistic treatment of the attached boundary layers in the computations. Improved agreement in the skin-friction distribution is obtained for the supercritical flows in which boundary layer transition is fixed at the position observed in experiments conducted at the same Reynolds numbers. For the subcritical flows the Strouhal number, St, associated with the large-scale shedding is predicted at St∼0.195 along with a higher frequency component associated with the development of the Kelvin–Helmholtz instabilities in the detached shear layers. If in the subcritical regime the wake assumes a helical-like form due to the shedding of hairpin-like vortices at different azimuthal angles, in the supercritical regime the wake structure is characterized by “regular” shedding of hairpin-like vortices at approximately the same azimuthal angle and at a much higher frequency (St∼1.3) that is practically independent of the Reynolds number and not sensitive to the position of laminar-to-turbulent transition.