Active control of flow over a sphere for drag reduction at a subcritical Reynolds number

Active control of flow over a sphere at $\hbox{\it Re}\,{=}\,10^5$, based on the free-stream velocity $U_{\infty}$ and sphere diameter $d$, is carried out for drag reduction using a time-periodic blowing and suction from a slit on the sphere surface. The forcing frequency range considered is one to thirty times the natural vortex-shedding frequency. With the forcing, the drag on the sphere significantly decreases by nearly 50% for the forcing frequencies larger than a critical frequency (about $2.85 U_\infty$/{\it d}$). For the forcing frequencies smaller than this critical frequency, the drag is either nearly the same as, or slightly smaller than, that without forcing. The critical forcing frequency is found to be closely associated with the onset of the boundary-layer instability. It is shown from the surface-pressure measurement, surface oil-flow visualization and near-wall streamwise velocity measurement that the disturbances from the high-frequency forcing grow inside the boundary layer and delay the first separation while maintaining laminar separation, and they grow further along the separated shear layer and high momentum in the free stream is entrained toward the sphere surface, resulting in the reattachment of the flow (thus forming a separation bubble above the sphere surface) and the delay of the main separation. The reverse flow region in the wake is significantly reduced and the motion in that region also becomes weak owing to the forcing. Finally, the variation of drag by the present forcing with respect to the Reynolds number is very similar to that by dimples on the surface, but is different from that by surface roughness.