Study of two free-falling spheres interaction by coupled SPH–DEM method

Abstract

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 Rem=2.4×104. 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 S0∗ < 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 S0∗ > 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.