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.
Stratified flow past a sphere at moderate Reynolds numbers