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

摘要

A 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 Re and of the density ρs of the cylinder. This confinement-induced vibration (CIV) occurs above a critical Reynolds number Re_c～20 much lower than for BénardVon Kármán vortex shedding behind a fixed cylinder in the same configuration (Re_(BVK)= 111). For low ρs values, CIV persists up to the highest Re value investigated (Re= 130). For denser cylinders, these oscillations end abruptly above a second value of Re larger than Re_c and vortex-induced vibrations (VIV) of lower amplitude appear for Re～ReBVK. Close to the first threshold Re_c, the oscillation amplitude variation as Re-Re_c1/2 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.