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

TL;DR

This study reveals that rotational effects and center-of-mass offset significantly influence the dynamics of rising and settling cylinders, inducing resonance modes that alter trajectories and increase drag, with implications for understanding particle-fluid interactions.

Contribution

The paper introduces a systematic analysis of how center-of-mass offset affects cylinder dynamics, highlighting the emergence of resonance modes and their dependence on key parameters, which was not previously well understood.

Findings

Resonance modes cause larger translational and rotational amplitudes.

Center-of-mass offset as small as a few percent can induce resonance.

Resonance increases drag coefficient by over two times.

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 timescale, 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, and Centre-Of-Mass offset (COM) systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibit 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 moment of inertia. Remarkably, depending on the input parameters, resonance can be observed for centre-of-mass offsets as small as a few percent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter.