New oscillatory instability of a confined cylinder in a flow below the vortex shedding threshold

Abstract

AbstractA new type of flow-induced oscillation is reported for a tethered cylinder confined inside a Hele-Shaw cell (ratio of cylinder diameter to cell aperture, $D/ h= 0. 66$) with its main axis perpendicular to the flow. This instability is studied numerically and experimentally as a function of the Reynolds number $\mathit{Re}$ and of the density ${\rho }_{s} $ of the cylinder. This confinement-induced vibration (CIV) occurs above a critical Reynolds number ${\mathit{Re}}_{c} \ensuremath{\sim} 20$ much lower than for Bénard–Von Kármán vortex shedding behind a fixed cylinder in the same configuration (${\mathit{Re}}_{\mathit{BV K}} = 111$). For low ${\rho }_{s} $ values, CIV persists up to the highest $\mathit{Re}$ value investigated ($\mathit{Re}= 130$). For denser cylinders, these oscillations end abruptly above a second value of $\mathit{Re}$ larger than ${\mathit{Re}}_{c} $ and vortex-induced vibrations (VIV) of lower amplitude appear for $\mathit{Re}\ensuremath{\sim} {\mathit{Re}}_{\mathit{BV K}} $. Close to the first threshold ${\mathit{Re}}_{c} $, the oscillation amplitude variation as $ \mathop{ (\mathit{Re}\ensuremath{-} {\mathit{Re}}_{c} )}\nolimits ^{1/ 2} $ and the lack of hysteresis demonstrate that the process is a supercritical Hopf bifurcation. Using forced oscillations, the transverse position of the cylinder is shown to satisfy a Van der Pol equation. The physical meaning of the stiffness, amplification and total mass coefficients of this equation are discussed from the variations of the pressure field.