Interaction of two free-falling spheres in water

This study uses a two-way dynamic coupled numerical model and laboratory experiments to investigate the interaction of two free-falling spherical particles in water. Two spheres, with identical diameters D and densities, are released side-by-side simultaneously in a water tank. The Reynolds number, based on the terminal velocity and diameter of the sphere, is Re = 1.36 × 10⁴. The experimental and numerical results reveal that the falling trajectories of the spheres look like S-curves when the initial gap between the two spheres is less than 0.75 D. The numerical simulation demonstrates that the fluid pressure in the gap region is less than the pressure outside of the gap and causes the spheres to move toward each other as they fall. Then, the vortices alternately shed behind the spheres and generate a lateral force to deviate the spheres from the vertical trajectory. When the lateral distance between the two spheres is greater than 0.75 D, the interaction between the spheres becomes negligible. A similar phenomenon is also observed when one single falling sphere is very close to a vertical sidewall. The sidewall effect on the sphere's trajectory is noticeable when the gap between the falling sphere and the sidewall is less than 0.5 D. Nonetheless, the influence of a sidewall is more significant than that of an adjacent sphere.