Resonance in the flow past a highly confined circular cylinder

A three-dimensional direct numerical simulation is carried out to investigate the response of the flow past a highly confined circular cylinder to single-mode sinusoidal perturbations. The Reynolds number is fixed at 1000, and the blockage ratio (the ratio of the cylinder diameter to the distance between two lateral walls) is fixed at 0.6. Local perturbations are introduced upstream of the cylinder at normalized excitation frequencies (fe/f0) from 0.2 to 3.4, where f0 is the vortex shedding frequency in an unperturbed flow. It is observed that the vortex shedding frequency of the perturbed flows (fs) and the excitation frequency (fe) are locked-on in four distinct modes including fs = 2.0fe, fs = 1.5fe, fs = 1.0fe, and fs = 0.5fe, respectively. Among them, the fundamental lock-on with fs = 0.5fe appears over a wide range of excitation frequencies (fe/f0 = 1.4–2.8). By contrast, only the fundamental lock-on regime of fs = 0.5fe is observed when perturbing an unconfined flow at the same Reynolds number, highlighting the significant impact of confinement on the lock-on behavior. It is further revealed that the lock-on behavior is controlled by the responses of separated shear layers in the near wake, which switch from higher modes to lower modes with increasing excitation frequency in the confined flow.