Flutter to tumble transition of buoyant spheres triggered by rotational inertia changes

Abstract

Heavy particles sink straight in water, while buoyant bubbles and spheres may zigzag or spiral as they rise. The precise conditions that trigger such path-instabilities are still not completely understood. For a buoyant rising sphere, two parameters are believed to govern the development of unsteady dynamics: the particle’s density relative to the fluid, and its Galileo number. Consequently, with these parameters specified, the opportunities for variation in particle dynamics appear limited. In contrast to this picture, here we demonstrate that vigorous path-oscillations can be triggered by modulating a spherical particle’s moment of inertia (MoI). For a buoyant sphere rising in a turbulent flow, MoI reduction triggers a tumble–flutter transition, while in quiescent liquid, it induces a modification of the sphere wake resulting in large-amplitude path-oscillations. The present finding opens the door for control of particle path- and wake-instabilities, with potential for enhanced mixing and heat transfer in particle-laden and dispersed multiphase environments.

Dynamics of heavy and buoyant underwater pendulums

“…It is well known that added mass coefficients m * a for oscillating cylinders depend on a variety of parameters, including the frequency of oscillation, distance to boundaries, free surfaces, etc. Most studies have focused on the case of cylinders near a free surface and for small oscillations (Dong 1978;Konstantinidis 2013;Koo & Kim 2015;Tatsuno & Bearman 1990;Mathai et al 2017Mathai et al , 2018. However, in complex situations with relative motions, curved trajectories and unsteady three-dimensional wakes with flow separation, m * a can deviate significantly from the two-dimensional potential flow added mass coefficient.…”

Bubbly and Buoyant Particle–Laden Turbulent Flows

“…When Rv increases, the rising spherical particle crosses the turbulent eddies at increasingly higher speeds, thus having little time to respond to the turbulent fluctuations. A third, not so obvious, influence was revealed experimentally in a recent study by Mathai et al (2018b), which hints that the observed path-instabilities are augmented by the particle's rotational motions Kinematics and dynamics of rigid buoyant spheres (Ξ ≈ 10) in a turbulent flow with Re λ ≈ 300. (a)-(c) Three dimensional trajectories of buoyant spheres for increasing Galileo number, Ga.…”

“…Although the mean forces on the particle can still be approximated, the instantaneous drag and lift can no longer be described using simplified coefficients. Furthermore, owing to the lightness of the particle, this regime paves way for a strong coupling between the unsteady wake dynamics and the particle motion, often resulting in vigorous path instabilities (Brücker 1999;Ern et al 2012;Mathai et al 2016bMathai et al , 2017Mathai et al , 2018bMougin and Magnaudet 2006). As reported in Risso (2017), there is, today, compelling evidence that the wakes and dynamics of isolated buoyant particles are remarkably robust to turbulent perturbations (Ford and Loth 1998).…”

“…(e) Reducing I * triggers a dramatic increase in the translational and rotational accelerations (see (e) and (f)). Drawings and figures are adapted from Mathai et al (2015Mathai et al ( , 2018b as well. To explain this, we revisit the Kelvin-Kirchhoff equations expressing linear and angular momentum conservation for a buoyant spherical particle:…”

Multi-phase wall-bounded turbulence

“…We find a skewness of the angular velocity between [−0.14, 0.24]. The kurtosis of the angular velocity lies in the range [34,40], which is much larger than the kurtosis of spheres of similar size ratios [109,110,111]. This can be attributed to the fact that for elongated ellipsoids the rotational inertia is typically much lower than the rotational inertia of similar-sized spheres [93].…”