Collective Behavior of Clusters of Free-to-Move Cylinders in the Wake of a Fixed Cylinder

Abstract: We study the collective behavior of clusters of cylinders placed in the wake of a fixed cylinder and free to move in a direction perpendicular to that of the incoming flow, with no structural damping or stiffness. We keep the Reynolds number, defined based on the cylinder diameter, at 100 and consider five different configurations for the initial positions of the cluster cylinders: linear, rectangular, V-shaped, triangular, and circular. In each configuration, we consider progressively increasing number of cylinders in the cluster. We show that overall, the cylinders tend to form final linear configurations, in which, after their transition, the cylinders form one or more lines. Some free-to-move cylinders might take the lead position in some of these linear formations depending on the initial configuration. These steady-state positions are achieved when the mean value of lift that acts on the cylinders becomes negligible. As a byproduct of these reconfigurations, the overall drag force that acts on the collection of cylinders reduces at their final steady-state locations in comparison with their original configurations. The complicated wakes that are observed in the fixed counterparts of these configurations are replaced by a series of vortex rows in the wake of separate lines of cylinders. Reducing the mass ratio allows the cylinders to oscillate about their mean displacement paths, but their transient paths and their final steady-state positions are not affected significantly by the decrease in the mass ratio.