Dynamics of freely rising spheres: the effect of moment of inertia

TL;DR

This study investigates how the moment of inertia influences the rising behavior of spherical particles in fluids, revealing that higher MOI affects trajectory complexity and drag, with minimal impact from surrounding turbulence.

Contribution

It provides experimental insights into the role of particle MOI on trajectory modes, drag, and oscillations during particle rise in quiescent and turbulent fluids.

Findings

Helical and 3D chaotic trajectories observed depending on density ratio

No influence of MOI on the transition point between trajectory modes

Decreasing drag coefficient with increasing MOI in chaotic regime

Abstract

The goal of this study is to elucidate the effect the particle moment of inertia (MOI) has on the dynamics of spherical particles rising in a quiescent and turbulent fluid. To this end, we performed experiments with varying density ratios $\Gamma$, the ratio of the particle density and fluid density, ranging from $0.37$ up to $0.97$. At each $\Gamma$ the MOI was varied by shifting mass between the shell and the center of the particle to vary $I^*$ (the particle MOI normalised by the MOI of particle with the same weight and a uniform mass distribution). Helical paths are observed for low, and `3D chaotic' trajectories at higher values of $\Gamma$. The present data suggests no influence of $I^*$ on the critical value for this transition $0.42<\Gamma_{\textrm{crit}}<0.52$. For the `3D chaotic' rise mode we identify trends of decreasing particle drag coefficient ($C_d$) and amplitude of oscillation with increasing $I^*$. Due to limited data it remains unclear if a similar dependence exists in the helical regime as well. Path oscillations remain finite for all cases studied and no `rectilinear' mode is encountered, which may be the consequence of allowing for a longer transient distance in the present compared to earlier work. Rotational dynamics did not vary significantly between quiescent and turbulent surroundings, indicating that these are predominantly wake driven.