Path instability of falling sphere induced by the near-wall effect

This study employs laboratory experiments and a fluid/solid coupled numerical model to investigate the path instability of a falling sphere near a vertical sidewall. The falling trajectory of an acrylic sphere resembles a zigzag curve when the initial gap between the sphere and the sidewall is smaller than the sphere diameter D. The maximum lateral displacement of an acrylic sphere was about 0.85D, while the steel sphere falls nearly in a rectilinear path under the same gap distance. The Reynolds number, based on the diameter and terminal velocity of the sphere, is in the range of Re = 1.88 × 10⁴-4.16 × 10⁴. The flow fields and forces on the falling spheres were simulated by a turbulence model and the immersed boundary (IB) method. The simulated trajectories agree with the experimental results, and the simulation results demonstrate that the periodic vortex shedding only occurs in the wall-normal direction, not in the wall-parallel direction. The terminal velocity, drag, and lateral force are all affected by the vortex shedding. The vortex-induced lateral force coefficients vary in the range of C_L = −0.30-0.30, regardless of the sphere density and the initial gap. Moreover, a dimensionless force ratio between the gravitational force and vortex-induced lateral force is proposed herein to measure the effect of vortex shedding on the sphere trajectory in high Reynolds number flows.