Flow-Induced Vibrations of a Square Cylinder in the Combined Steady and Oscillatory Flow

The paper presents a two-dimensional RANS–SST k–ω investigation of vortex-induced vibration of a square cylinder with two degrees of freedom under combined steady and oscillatory flow at the Reynolds number of 5000, Keulegan–Carpenter number of 10, mass ratio of 2.5, and zero structural damping. Flow ratio a (steady-to-total velocity) is varied from 0 to 1.0, and the reduced velocity $U_r$ from 2 to 25 to map lock-in regimes, response amplitudes, frequency content, hydrodynamic loads, trajectories, and wake patterns. At low a ≤ 0.4, in-line vibrations dominate at $U_r$ > 5, with double-frequency transverse lock-in peaking near $U_r$ = 5. As a → 1.0, in-line motion diminishes, and single-frequency transverse oscillation prevails, with the maximum transverse displacement up to 0.54D. The mean drag coefficient increases with increasing flow ratio; the fluctuating drag coefficient decreases with increasing a; while the lift coefficient peaks at a = 1, $U_r$ = 2. Wake topology transitions from a mixed vortex shedding towards a 2S pattern, as a → 1.