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

Abstract

The 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.

Vortex-induced vibration of a rotating sphere

“…case (e) and case ( f ), the recirculation bubble is evidently mostly suppressed. This near wake is very similar to the 'shear-layer instability' regime reported by Giacobello et al (2009), Kim (2009) and Poon et al (2014) for rigidly mounted rotating spheres at low Reynolds number (Re 1000). They reported single-sided shedding on the advancing side of the rotating sphere.…”

“…Previous studies (e.g. Giacobello, Ooi & Balachandar 2009;Kim 2009;Poon et al 2014, and references therein) have shown that the onset of the shear-layer instability wake state of a non-oscillating rotating sphere occurs beyond this α value. That wake state forms when fluid that passes the retreating side of the sphere is pushed towards the other side of the wake to form a distinctive one-sided separating shear layer, thus changing the characteristic formation and release of vortex loops that defines the non-rotating wake state.…”

“…From previous studies on rigidly mounted spheres, it is known that the transverse rotation imposes strong asymmetry in the wake, causing the loops to bend towards the advancing side (the side of the sphere moving in the direction opposite to the fluid) of the sphere due to the Magnus effect (Magnus 1853), which in consequence increases the 'lift force' towards the retreating side (the side of the sphere moving in the same direction as the fluid). Previous numerical studies by Giacobello et al (2009), Kim (2009 and Poon et al (2014) reported suppression of the vortex shedding for a certain range of rotation rates that depended on the Reynolds number. However, when α was increased, the vortex shedding resumed, although it was very different to the vortex shedding at lower α values that is associated with the 'buildup and release' of the recirculation bubbles behind the sphere.…”

“…Previous numerical studies on the effect of rotation on rigidly mounted rotating spheres at low Reynolds numbers (Re 300) (Kim 2009;Poon et al 2014) have revealed suppression of the vortex shedding for a certain range of rotation rates. These studies were performed computationally at relatively low Reynolds numbers.…”

Vortex-induced vibration of a transversely rotating sphere

“…Previous numerical studies on the effect of rotation on rigidly mounted rotating spheres at low Reynolds numbers (Re ≤ 300) ( [7], [4]) revealed suppression of the vortex shedding for a certain range of spin ratios. So can the structural vibrations of a sphere be suppressed by an imposed rotation once the sphere is free to oscillate?…”