Laminar flow past a sphere rotating in the streamwise direction

Abstract

Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.