Rising and settling 2-D cylinders with centre-of-mass offset

Abstract

Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in situations when mass eccentricity, and thereby a new pendulum time scale, is introduced to the system. We employ two-dimensional simulations to study the motion of a single cylinder in a quiescent unbounded incompressible Newtonian fluid. This allows us to vary the Galileo number, density ratio, relative moment of inertia (MOI) and centre-of-mass (COM) offset systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibits a resonance mode, during which the coupling via the Magnus lift force causes a positive feedback between translational and rotational motions. This mode results in vastly different trajectories with significantly larger rotational and translational amplitudes and an increase of the drag coefficient easily exceeding a factor two. We propose a simple model that captures how the occurrence of the COM offset induced resonance regime varies, depending on the other input parameters, specifically the density ratio, the Galileo number and the relative MOI. Remarkably, depending on the input parameters, resonance can be observed for COM offsets as small as a few per cent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter.