Flow induced oscillation of a cylinder in a Hele-Shaw cell

Spontaneous regular oscillations of a confined cylinder in a steady Poiseuille flow are observed down to small Reynolds numbers ($Re=15$). In this study, the cylinder is perpendicular to the mean flow, parallel to the walls of a Hele-Shaw cell and free to move only in the direction perpendicular to them; the ratio of the diameter of the cylinder by the cell aperture is $0.7$. Experimentally, the cylinder is held by long thin threads. This flow-structure coupling, resulting from the confinement, has also been modelled successfully using $2D$ finite elements simulations. The oscillations are quasi-sinusoidal in a wide range of $Re$ value ($Re$ is defined using the mean velocity and the diameter of the cylinder). The threshold value ($Re=15$) is much smaller than for classical vortex shedding past a nonconfined cylinder ($Re=45$). The amplitude increases with the Reynolds number until saturation. The frequency increases almost linearly with $Re$ (Strouhal number close to $1$) even when contact with the walls occurs; it increases with the diameter of the cylinder and decreases with its density.