Flow and motion characteristics of a freely falling square particle in a channel

•The motion of square particle is classified into three types.•Off-center distance, Reynolds number and density ratio affect the particle motion.•Oscillation amplitude is mainly influenced by density ratio.•Drag coefficient converges at the high Reynolds number. This study numerically simulated the motion of a square particle free falling in a two-dimensional vertical channel to investigate the effects of the off-center distance and the Reynolds number. The motion regimes were classified into non-oscillatory motion, regular oscillatory motion, and irregular oscillatory motion. The effect of the off-center distance on the particle motion became significant as the Reynolds number increased, resulting in the bifurcation of the motion regime. There was a critical off-center distance beyond which the critical Reynolds numbers corresponding to the limits of the regimes depended on the off-center distance. The mean amplitude of the transverse oscillation decreased as the ratio of the density of the particle to that of the fluid increased, and this was more significant as the off-center distance and Reynolds number increased. Moreover, as the Reynolds number increased, the drag coefficient decreased and eventually converged.