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

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 $\varGamma$ , 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.

Wake-induced dynamics of anisotropic particles in homogeneous and shear flows

“…This transition from one Str mode to the other is found to occur, for the present Ga = 200 and I * = 1, between Γ = 0.1 and Γ = 0.2. This density ratio-dependent behaviour is known from previous studies on rising and settling bodies (Namkoong et al, 2008;Horowitz and Williamson, 2010b;Mathai et al, 2017;Auguste and Magnaudet, 2018;Will and Krug, 2021a). Note that the low Strouhal number regime here, as in literature, corresponds to larger amplitude path oscillations and the higher Strouhal number to smaller amplitudes.…”

“…Similar density ratio-related transitions in the regime of motion have also been observed for spheres Horowitz and Williamson (2010a); Auguste and Magnaudet (2018); Will and Krug (2021a). Similarly to the mass density ratio also, the rotational Moment of Inertia (MOI) was investigated as a relevant parameter governing the dynamics of rising and settling 2D cylinders in the numerical work by (Mathai et al, 2017) as well as experimentally for spheres (Will and Krug, 2021a). The effects of Γ and MOI will both be investigated in this work as individually relevant parameters, as well as how they affect the dynamics induced by COM offset.…”

“…For the case of freely rising and settling 2D cylinders, a critical mass density ratio was encountered, marking the threshold between limited coupling between particle dynamics and the wake for high Γ and large amplitude path oscillations and a modification of the vortex shedding frequency for low Γ Williamson, 2006, 2010b). Similar density ratio-related transitions in the regime of motion have also been observed for spheres Horowitz and Williamson (2010a); Auguste and Magnaudet (2018); Will and Krug (2021a). Similarly to the mass density ratio also, the rotational Moment of Inertia (MOI) was investigated as a relevant parameter governing the dynamics of rising and settling 2D cylinders in the numerical work by (Mathai et al, 2017) as well as experimentally for spheres (Will and Krug, 2021a).…”

Path Instabilities of a Freely Rising or Falling Sphere

“…Even in the absence of such an offset, Mathai et al (2018) highlighted the influence of the moment-ofinertia on the rotational sphere dynamics: hollow spheres with a thin axisymmetric shell, which are often used in experimental studies for investigating the low 𝜌 range, may exhibit a different behaviour than homogeneous spheres with the same mass but a correspondingly lower moment-of-inertia (by a factor of approximately 5/3) as considered in numerical simulations. However, recent experiments by Will and Krug (2021a) showed no influence of the moment-of-inertia on the transition between the 3D chaotic and spiralling regime (in both quiescent and turbulent flow) and indicated only a weak effect on the drag coefficient (which increased slightly with decreasing moment-of-inertia in their experiments).…”

Silica Supraparticles with Self‐Oscillatory Vertical Propulsion: Mechanism & Theoretical Description

“…[ 41 ] However, experimentally we did not observe that tumbling of particles had any significant effect on the particle movement, different to rising spheres of varying density, which may exhibit complex motion. [ 42 ] However, in our case the particle movement is dominated by moving in z ‐direction and lateral motion, that could for instance arise from convection, obviously can be neglected (Figure S1, Supporting Information). In summary, apparently, the translational inertia and being well under conditions of laminar flow stabilizes the linear motion of the particles.…”