Influence of confinement on the oscillations of a free cylinder in a viscous flow

Abstract

We demonstrate and study experimentally two instabilities of a horizontal free cylinder in a vertical viscous Hele-Shaw flow; we show that they depend critically on the confinement of the flow with a different influence of transverse and lateral confinement characterized respectively by the ratios of the diameter (resp. the length) of the cylinder to the gap (resp. the width) of the cell. The onset of the instabilities depends largely on the transverse confinement: for a parameter between 0.4 and 0.6, one observes transverse horizontal oscillations of the cylinder perpendicular to the walls: their frequency is constant with the lateral and transverse confinements at a given cylinder velocity. This instability is shown to be locally two-dimensional and controlled by the local relative velocity between the cylinder and the fluids: it occurs down to Reynolds numbers based on the cell gap ≃ 15, far below the corresponding 2D vortex shedding thresholds (150-250) for fixed cylinders between parallel planes. Above transverse confinements of the order of 0.55, we observe a fluttering motion with periodic oscillations of the tilt angle of the cylinder from the horizontal and of its horizontal position: their frequency decreases strongly as the lateral confinement increases but is independent of the transverse confinement and the cylinder velocity.