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 $\varGamma$ , the ratio of the particle density and fluid density, ranging from $0.37$ up to $0.97$ . At each $\varGamma$ the MOI was varied by shifting mass between the shell and the centre of the particle to vary $I^*$ (the particle MOI normalised by the MOI of a particle with the same weight and a uniform mass distribution). Helical paths are observed for low, and ‘three-dimensional (3-D) chaotic’ trajectories at higher values of $\varGamma$ . The present data suggest no influence of $I^*$ on the critical value for this transition $0.42<\varGamma _{{crit}}<0.52$ . For the ‘3-D 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 with earlier work. Rotational dynamics did not vary significantly between quiescent and turbulent surroundings, indicating that for the present configuration these are predominantly wake driven.

中文翻译：

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自由上升球体的动力学：惯性矩的影响

本研究的目的是阐明粒子惯性矩 (MOI) 对在静止和湍流流体中上升的球形粒子动力学的影响。为此，我们进行了不同密度比的实验 $\varGamma$ ，颗粒密度与流体密度之比，范围为 $0.37$ 取决于 $0.97$ . 在每一个 $\varGamma$ MOI 通过在壳和粒子中心之间移动质量来改变 $我^*$ （由具有相同重量且质量分布均匀的粒子的 MOI 归一化的粒子 MOI）。在较高的 $\varGamma$ . 目前的数据表明没有影响 $我^*$ 关于这一转变的临界值 $0.42<\varGamma _{{crit}}<0.52$ . 对于“3-D 混沌”上升模式，我们确定了粒子阻力系数减小的趋势（ $C_d$ ) 和振荡幅度随着增加 $我^*$ . 由于数据有限，目前尚不清楚螺旋机制中是否也存在类似的依赖性。对于所研究的所有情况，路径振荡仍然是有限的，并且没有遇到“直线”模式，这可能是与早期工作相比，目前允许更长的瞬态距离的结果。旋转动力学在静止和湍流环境之间没有显着差异，这表明对于目前的配置，这些主要是尾流驱动的。