Moderate-aspect-ratio elliptical cylinders in simple shear with inertia

Abstract

The effects of fluid inertia, geometry and flow confinement upon the dynamics of neutrally buoyant elliptical and non-elliptical cylinders over a wide range of aspect ratios in simple shear are studied experimentally for moderate shear-based Reynolds numbers Re. Unlike circular cylinders, elliptical cylinders of moderate aspect ratio cease to rotate, coming to rest at a nearly horizontal equilibrium orientation above a critical Reynolds number Recr (‘stationary behaviour’). Simple dynamics arguments are proposed to explain the effects of aspect ratio and flow confinement upon critical Reynolds number and particle dynamics. Experiments confirm results from previous numerical simulations that the normalized rotation period for Re < Recr (‘periodic behaviour’) is proportional to (Recr − Re)−0.5 for small Recr − Re. For periodic behaviour, maximum and minimum angular cylinder speeds both decrease, and period increases, as Recr − Re decreases. For stationary behaviour, the cylinder rotates until it achieves a nearly horizontal equilibrium orientation, which increases as the Reynolds number approaches the critical value. The experimental results are in good agreement with previous lattice-Boltzmann simulations for a 0.5 aspect ratio cylinder.Variation in angular speed over a rotation period decreases as aspect ratio increases, while Recr increases as flow confinement and aspect ratio increase. A non-elliptical cylinder of 0.33 aspect ratio also ceases to rotate above a certain Reynolds number. Although Recr is different from the corresponding elliptical case, the scaling of the normalized rotation period for this body as Recr → Re is identical to that for the elliptical cylinder, suggesting that this scaling is independent of particle shape (i.e. ‘universal’, as conjectured in previous numerical studies). The results also demonstrate that a variety of centrosymmetric bodies with aspect ratios below unity transition from periodic to stationary behaviour.