Ordinary and inverse Magnus effects on rotating spheres: laminar separation bubble, secondary vortex and wing-tip-like vortices

This paper provides direct experimental evidence for the coexistence of both a laminar separation bubble and a secondary vortex on the advancing side of a rotating sphere when subjected to the inverse Magnus effect. Detailed experiments were conducted in a wind tunnel on two spheres of varying surface roughness to investigate both ordinary and inverse Magnus effects. Experiments took place for $0.5\times 10^{5}\leqslant {\textit{Re}}\leqslant 3\times 10^{5}$ and rotation rates $0\leqslant \alpha \leqslant 0.45$ , where the spheres were rotated via a shaft that was oriented perpendicularly to the free stream flow. Static pressure measurements were made on the non-shaft hemisphere using a spline of taps spanning from the equator to the pole. The ordinary Magnus effect was generally observed at the lowest ${\textit{Re}}$ tested, with a transition to the inverse Magnus effect occurring as ${\textit{Re}}$ increased. Time-averaged pressure coefficient distributions across the equatorial plane were obtained for the smooth and rough spheres. Cross-flow particle image velocimetry was used to visualise the downstream wake velocity field. A pair of counter-rotating wing-tip-like vortices were detected when the sphere experienced the ordinary Magnus effect, generated by flow leakage from the advancing to the retreating side. When the sphere experienced the inverse Magnus effect, the polarity of the counter-rotating vortex pair reversed. This is the first experimental observation of the vortex polarity reversal associated with the inverse Magnus effect in the wake of a rotating sphere. The results provide qualitative visualisation of the complex fluid dynamics and inform future applications of the Magnus effect.