Wake-induced vibration interference between a fixed square cylinder and a 2-DOF downstream square cylinder at low Reynolds numbers

Wake-induced vibration (WIV) of a two-degree-of-freedom (2-DOF) downstream square cylinder behind a stationary equal-size upstream square cylinder is numerically investigated at low Reynolds numbers by using Characteristics-Based Split (CBS) finite element algorithm. Due to the interference between the cylinders, the flow pattern and dynamic characteristics of become more complex than an isolated cylinder case. The spacing ratio of the two equal-sized square cylinders in the tandem arrangement is fixed as L/D = 5.0. The Reynolds numbers of this two-cylinder system have five types, varying between 40 and 200 with a unit step of △Re = 40. The reduced mass of the square cylinder is Mr = 2.0, while its reduced velocity changes between Ur = 3.0–18.0. The numerical results show that the reduced velocity and Reynolds number can affect the characteristics of the flow patterns, oscillatory frequency, maximum amplitudes, and X-Y trajectories of the downstream square cylinder. The predominant vortex shedding patterns are 2S, 2S* 2P, P + S, 2T and steady mode. Additionally, the figure “8” and figure “dual-8” are observed in the X-Y vibrating trajectories of the downstream square cylinder. Finally, the interactions between cylinders underlying the vibration characteristics of the square cylinder behind a stationary square cylinder with different Reynolds numbers are revealed.