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.

中文翻译：

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水中两个自由落体的相互作用

这项研究使用双向动态耦合数值模型和实验室实验来研究水中两个自由下落的球形颗粒之间的相互作用。直径D和密度相同的两个球体在水箱中同时并排释放。根据球的最终速度和直径，雷诺数为Re = 1.36×10 ⁴。实验和数值结果表明，当两个球之间的初始间隙小于0.75 D时，球的下落轨迹看起来像S曲线。数值模拟表明，间隙区域中的流体压力小于外部压力。间隙的变化，并导致球体在下落时朝彼此移动。然后，涡流交替掉落在球体后面，并产生横向力使球体偏离垂直轨迹。当两个球体之间的横向距离大于0.75 D时，球体之间的相互作用可忽略不计。当一个单个的下降球非常靠近垂直侧壁时，也会观察到类似现象。