Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime

Abstract

AbstractThe flow past a transversely rotating sphere at Reynolds numbers of $\mathit{Re}=500{-}1000$ is directly simulated using an unstructured finite volume collocated code. The effect of rotation rate on the flow is studied by increasing the dimensionless rotation rate, ${\it\Omega}^{\ast }$, from 0 to 1.20, where ${\it\Omega}^{\ast }$ is the maximum sphere surface velocity normalised by the free stream velocity. This study investigates the marked unsteadiness of the flow structures at $\mathit{Re}=500{-}1000$. Comparison with previous numerical data (Giacobello et al., J. Fluid Mech., vol. 621, 2009, pp. 103–130; Kim, J. Mech. Sci. Technol., vol. 23, 2009, pp. 578–589) reveals a new flow regime, namely a ‘shear layer–stable foci’ regime, besides the widely reported ‘vortex shedding’ and ‘shear layer instability’ regimes. The ‘shear layer–stable foci’ regime is observed at $\mathit{Re}=500$ and ${\it\Omega}^{\ast }=1.00$; $\mathit{Re}=640{-}1000$ and ${\it\Omega}^{\ast }\geqslant 0.80$. In this flow regime, the shear layer on the advancing side of the sphere (where the sphere surface velocity vector opposes the free stream velocity) shortens significantly while fluid from the retreating side (opposite to the advancing side) is drawn towards the mid-plane normal to the peripheral velocity. This results in the formation of a stable focus near the onset of the shear layer instability. This stable focus becomes more pronounced with increasing $\mathit{Re}$ and ${\it\Omega}^{\ast }$. It increases the oscillation magnitude and decreases the oscillation frequency of the hydrodynamic forces.