Congregation of particles on a plane boundary due to the flow induced by an oscillating sphere

Abstract

The complex flow-field associated with a spherical structure oscillating adjacent to a solid boundary is significant in ocean engineering. The dynamic interaction between the flow induced by an oscillating sphere and the boundary is evident not only in terms of flow-field deformation around the structures but also on the boundary in the form of shear stress modifications. The present study aims to understand the influence of a plane boundary on the shear stress distributions and particle motion near the boundary induced by the flow due to a submerged sphere oscillating in a viscous fluid. Experiments are conducted using a non-intrusive flow visualization technique, and three-dimensional direct numerical simulations are used to link the time-mean results of the experiments to the simulated Lagrangian particle drift on the plane boundary. The dye tracer in the experiments and the Lagrangian particles in the simulation congregate at the same location. This stagnation location coincides with a ring of zero mean shear stress centered on the point on the plane boundary through which the axis of oscillation of the sphere passes. This ring of zero mean stress is termed the congregation zone. The radius of the particle congregation zone is investigated as a function of the sphere oscillating amplitude, Reynolds number, and the distance between the center of the sphere and the plane boundary. Furthermore, a systematic power scaling law is established for the radius of the congregation zone from the control parameters.