Flow around an oscillating circular disk at low to moderate Reynolds numbers

Abstract

Direct numerical simulations of the flow induced by a circular disk oscillating sinusoidally along its axis are performed. The aspect ratio ($\unicode[STIX]{x1D712}=\text{diameter}/\text{thickness}$) of the disk is 10. The Reynolds number ($\mathit{Re}$), based on the maximum speed and the diameter of the disk, is in the range of $50\leqslant \mathit{Re}\leqslant 800$. The Keulegan–Carpenter number ($KC$) is in the range of $1\leqslant KC\leqslant 24$. Five flow regimes are observed in the considered $\mathit{Re}$–$KC$ space: (I) axisymmetric flow (AS), (II) planar symmetric flow in the low-$KC$ region (PSL), (III) azimuthally rotating flow in the low-$KC$ region (ARL), (IV) planar symmetric flow in the high-$KC$ region (PSH) and (V) azimuthally rotating flow in the high-$KC$ region (ARH). The critical boundaries between different flow regimes are identified based on the evolutions of the magnitude and direction of transverse force acting on the disk. For the non-axisymmetric flow regimes, the flow is one-sided with respect to the axis of the disk and is associated with a non-zero mean value of the transverse force acting on the disk.