Computational study of the interaction of freely moving particles at intermediate Reynolds numbers

Motivated by our interest in understanding collective behaviour and self-organization resulting from hydrodynamic interactions, we investigate the two-dimensional dynamics of horizontal arrays of settling cylinders at intermediate Reynolds numbers. To simulate these dynamics, we develop a direct numerical simulation based on the immersed interface method. A novel aspect of our method is its ability to efficiently and accurately couple the dynamics of the freely moving objects with the fluid. We report the falling configuration and the wake pattern of the array, and investigate their dependence on the number of particles, $n$, as well as the initial inter-particle spacing, ${d}_{0} $. We find that, in the case of odd-numbered arrays, the middle cylinder is always leading, whereas in the case of even-numbered arrays, the steady-state shape is concave-down. In large arrays $n\geq 5$, the outer pairs tend to cluster. In addition, we analyse detailed kinematics, wakes and forces of three settling cylinders. We find that the middle one experiences a higher drag force in the presence of neighbouring cylinders, compared to an isolated settling cylinder, resulting in a decrease in its settling velocity. For a small initial spacing ${d}_{0} $, the middle cylinder experiences a strong sideway repulsive force, the magnitude of which increases with decreasing ${d}_{0} $. During the fall, the left and right cylinders rotate outwards and shed vortices in anti-phase.