Wake of transversely rotating and translating sphere in quiescent water at low Reynolds number

Abstract

The unsteady wake of a rotating and translating sphere is experimentally investigated at Reynolds numbers (Re) ranging from 115 to 550 for two rotational speeds. Non-dimensional rotational speed, $$\Omega^{ * }$$ , is defined as the ratio of the maximum azimuthal speed of the sphere and the speed of translation. Motion of the sphere is generated using a specially designed mechanism in a channel, and its wake has been visualized using fluorescent dye. Unlike the steady flow past a stationary sphere where the limiting Reynolds number is 270, the flow becomes unsteady when sufficient rotation rate is introduced at much lower Reynolds number ( $${\text{Re}} = 115,\Omega^{ * } = 0.375$$ ). The transition from one-sided to double-sided hairpin vortex occurs at one critical Re for a given rotational speed, and it switches back to one-sided hairpin vortex shedding at another critical Re. Particle image velocimetry results demonstrate the vorticity distribution in the wake and the variation of the wake width with axial distance. At very low Re, velocity profiles in the wake are nearly self-similar. The strength of the vortex rings weakens in the far wake. The decay of centerline velocity in axial direction confirms the dissipation of the vorticity in the far wake. In this unsteady flow, the time-averaged value of the separation angle is higher than that of the steady flow on the advancing side due to enhanced adverse pressure gradient. The Strouhal number calculated from the dye visualization in this range of $$\Omega^{ * }$$ and Re varies from 0.175 to 0.25, a clear increasing trend both with increasing Re and $$\Omega^{ * }$$ . The coefficient of drag evaluated at the center plane remains constant at 0.94 for the present investigation up to $${\text{Re}} = 550$$ . The wavelength of the unstable hairpin vortices is found to scale inversely with the translational velocity of the sphere.