Numerical study on flow-induced vibration of an oscillating cylinder with an unattached downstream square plate at a low Reynolds number

Based on the Lattice Boltzmann Method, we numerically studied the flow around a transversely oscillating cylinder with a downstream stationary square plate at a Reynolds number Re = 150 and a mass ratio m* = 2.0. This paper initially considered a zero-damping ratio and a wide range of reduced velocities (Ur = 3–30) to investigate the effects of the gap ratio (L/D = 0.3–3.0) and the dimensionless width of the square plate (W/D = 0.5–2.0) on the response characteristics, force coefficients, wake patterns, and pressure distribution. The energy conversion performance is further tested by applying different non-zero damping ratios (ζ = 0.01–0.3). The main conclusions are as follows: (1) Three vibration behaviors are identified: vortex-induced vibration (VIV), wake interference galloping, and a newly reported “bifurcation” phenomenon of oscillation. For L/D = 0.3, at high reduced velocities (Ur ≥ 15), the cylinder experiences the “bifurcation” phenomenon, where it oscillates on one side of the square plate with a small vibration amplitude. Similar behavior is achieved for the system with L/D = 0.5 and 0.7 but requires a wider square plate than one diameter and higher reduced velocities of Ur ≥ 17.5. (2) Considering both the response amplitude and drag coefficient exerted on the square plate, the cylinder-square plate system with L/D = 0.7 and W/D = 1.0 exhibits a wide wake interference galloping response and an expected vibration amplitude with a lower drag coefficient. (3) For L/D = 0.7 and W/D = 1.0, as Ur increases from 10 to 15, the inclusion of the square plate leads to an increased difference in pressure coefficient between the front of the square plate and the rear of the cylinder. The amplified pressure difference enhances the response of the cylinder, potentially explaining the transition from VIV to wake interference-induced galloping. (4) With a non-damping ratio (ζ = 0.01–0.3), the cylinder-square plate system with L/D = 1.0 and W/D = 1.0 achieves the highest maximum energy harvesting efficiency η_M = 12.01% at the optimum damping ratio ζ_O = 0.2.