In the present paper, the three dimensional (3D) settlement process of two side-by-side free-falling spheres in a water tank was numerically investigated using coupled Smoothed Particle Hydrodynamics (SPH)–Discrete Element Method (DEM) method. The maximum particle Reynolds number, calculated based on the terminal velocity and sphere diameter, is $R{e}_m=2.4$ $\times$ $10^4$. The accuracy of the model was firstly validated by simulating the single sphere water-entry, settlement of two circular cylinders arranged in series and two identical spheres settlement side by side problems, respectively. The simulation results exhibited a satisfactory agreement with the available numerical and experimental data in the literatures. Then, the settlement process of two spheres with different sizes and transverse distances were simulated. In particular, the motion patterns of two interacting spheres with different initial gaps and diameter ratios, including motion trajectory, vertical falling distance and flow field, were systematically investigated. The results demonstrate that when initial gap $S_0^{\ast }$ < 0.75, sedimentation process in a water tank can be divided into four stages: slight gathering stage, accelerated separation stage, decelerated separation stage and re-approach stage. With the increase of diameter ratios, the trajectory of smaller sphere is more significantly affected by the larger sphere, while the effect for the larger one is just the opposite. The influence of different initial gaps is mainly reflected in the motion stage after the accelerated separation stage. When $S_0^{\ast }$ > 0.75, the interaction between the two spheres are negligible. In addition, the interaction between particles would slow down the settling velocity and affect the terminal settling distance.

在本文中，使用耦合光滑粒子流体动力学 (SPH)-离散元法 (DEM) 方法对水箱中两个并排的自由落体球体的三维 (3D) 沉降过程进行了数值研究。根据终端速度和球体直径计算的最大粒子雷诺数为$\mathrm{电阻}{\mathrm{电子}}_{米}=2.4$ $\times$ $10^4$. 首先分别通过模拟单球体入水、两个串联圆柱体的沉降和两个相同球体并排的沉降问题来验证模型的准确性。模拟结果与文献中可用的数值和实验数据表现出令人满意的一致性。然后，模拟了两个不同尺寸和横向距离的球体的沉降过程。特别是，系统地研究了具有不同初始间隙和直径比的两个相互作用球体的运动模式，包括运动轨迹、垂直下落距离和流场。结果表明，当初始间隙${秒}_0^{＊}$< 0.75，水箱中的沉淀过程可分为四个阶段：轻微聚集阶段、加速分离阶段、减速分离阶段和再接近阶段。随着直径比的增加，较小球体的轨迹受较大球体的影响更为显着，而较大球体的影响则相反。不同初始间隙的影响主要体现在加速分离阶段之后的运动阶段。什么时候${秒}_0^{＊}$> 0.75，两个球体之间的相互作用可以忽略不计。此外，颗粒之间的相互作用会减慢沉降速度并影响终端沉降距离。