DLM/FD Simulation On The Motion Of Sphere Particles In A Vertical Tube

The DLM/FD method is applied to the sedimentation of spheres in three-dimensional vertical tube. The binary hard model and soft-sphere model are introduced in the collision strategy to deal with the interactions in contact. Two new models are compared with the simple repulsive force model, and the dominant role of long-range hydrodynamic force and short-range interactions are established in different cases. Effect of some parameters like Reynolds number, initial positions are studied using soft-sphere model under different conditions.First, experimental result validated the hard-sphere model and soft- sphere model. Three collision models are introduced to simulate the motion of spheres in suspension, and the analyses of wakes and velocities show that: in a non-concentrated suspension containing only one sphere or two spheres, the motion is independent of the collision model chosen because the behavior of spheres here is mainly controlled by the long-range hydrodynamic forces, and the effect of the short-range interactions taking place at near contact is insignificant. By contrast, results are different for the concentrated suspension: the sedimentation of 25 spheres in a three-dimensional vertical tube are simulated using three different collision models, and the velocities and wakes are not similar any more. The result demonstrates that in a concentrated suspension, the short-range interactions affect the motion significantly.Three collision models are based on different principles. The function of simple repulsive force used in the original DLM/FD method is not only related to the distance of two spheres but also affected by the collision parameters which are not physical. For the soft-sphere model, at the lower Reynolds number, the function of short-range force has physical meaning, and the force is only related to the separation and the particle velocities. Compared to the repulsive force model, rotation is considered when the collision happens and the particles touch or even overlap. For the hard-sphere model, the momentum exchange between two colliding particles is considered instead of the forces. Post-collision velocities of the particles are determined from the system momentum and energy conservation or loss, which brings...