Wake dynamics and flow-induced vibration of a freely rolling cylinder

This article examines numerically the two-dimensional fluid-structure interaction problem of a circular cylinder rolling under gravity along an inclined surface under the assumption of a fixed but small gap. The motion of the cylinder is governed by the ratio of cylinder and fluid densities and the Reynolds number based on a velocity scale derived from the momentum balance in the asymptotic regime. For increasing Reynolds number, the cylinder wake undergoes a transition from steady to periodic flow, causing oscillations of the cylinder motion. The critical Reynolds number increases for light cylinders. Whereas the time-averaged characteristics of the asymptotic rolling states depend only on the Reynolds number, the density ratio has an additional influence on the vibration amplitude and on the cylinder motion during a start-up transient from rest. Light cylinders reach their final state quickly after the initial acceleration; heavier cylinders traverse a series of quasi-steady states, including a temporary velocity overshoot, before settling in the asymptotic regime. The amplitudes of the flow-induced vibrations remain small over the entire parameter range, which can be attributed to the value of the added-mass force associated with a rolling cylinder. Special attention is paid to the influence of the small but finite gap between cylinder and wall, since lubrication theory predicts a diverging pressure drag for a vanishing gap. The variations with gap size of the forces, torque and added mass are explored. The gap also influences the characteristics of the cylinder vibrations in the unsteady wake regime, in particular their amplitude.