Confinement Induced Oscillation of a cylinder at Reynolds number below the Vortex Induced Vibration Flow-induced oscillation of a confined tethered cylinder below the vortex shedding threshold
Résumé
A new type of flow induced oscillation has been observed by placing a tethered cylinder in a Hele Shaw cell. This novel instability is studied numerically and experimentally as function of the Reynolds number and as function of the mass of the cylinder in Hele Shaw cell such that the cylinder diameter to cell aperture ratio: $D=0.66$). The cylinder is found to oscillates above a Reynolds number $\Rey_c \simeq 20$. This critical $Re$ is much lower than the threshold for Bénard--Von Kármán vortex shedding behind a fixed cylinder in the same configuration. Close to the threshold, the growth rate of the amplitude varies like $(\Rey - \Rey_c)^{1/2}$ and the lack of hysteresis demonstrate that the process is a supercritical Hopf bifurcation. The adjustement of the position of the cylinder by a Van der Pol equation allows for the identification of the stiffness, the amplification coefficient and to study the effect of the total mass: Forced oscillation is used to study their behavior and their physical meaning is discussed using the pressure field. For dense cylinder, the CIV is observed to end abruptly and new oscillations are observed when the $Re$ is increased above $110$; this oscillation corresponds to Vortex Induced Vibration (VIV). If the mass falls below a critical value, the CIV is not observed to vanish.
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