Kinematics and dynamics of freely rising spheroids at high Reynolds numbers

TL;DR

This study experimentally explores how geometrical anisotropy affects the rising behavior of buoyant spheroids at high Reynolds numbers, revealing six distinct regimes with unique dynamics based on aspect ratio.

Contribution

It systematically characterizes the influence of particle shape on rise dynamics and identifies six regimes with distinct motion patterns at high Reynolds numbers.

Findings

Six regimes of rise dynamics identified based on aspect ratio.

Distinct motion patterns such as tumbling, zig-zag, flutter, and helical trajectories.

Drag coefficient varies with shape, especially in extreme geometries.

Abstract

We experimentally investigate the effect of geometrical anisotropy for buoyant ellipsoidal particles rising in a still fluid. All other parameters, such as the Galileo number $Ga \approx 6000$ and the particle density ratio $\Gamma \approx 0.53$ are kept constant. The geometrical aspect ratio, $\chi$, of the particle is varied systematically from $\chi$ = 0.2 (oblate) to 5 (prolate). Based on tracking all degrees of particle motion, we identify six regimes characterised by distinct rise dynamics. Firstly, for $0.83 \le \chi \le 1.20$, increased rotational dynamics are observed and the particle flips over semi-regularly in a "tumbling"-like motion. Secondly, for oblate particles with $0.29 \le \chi \le 0.75$, planar regular "zig-zag" motion is observed, where the drag coefficient is independent of $\chi$. Thirdly, for the most extreme oblate geometries ($\chi \le 0.25$) a "flutter"-like behaviour is found, characterised by precession of the oscillation plane and an increase in the drag coefficient. For prolate geometries, we observed two coexisting oscillation modes that contribute to complex trajectories: the first is related to oscillations of the pointing vector and the second corresponds to a motion perpendicular to the particle's symmetry axis. We identify a "longitudinal" regime ($1.33 \le \chi \le 2.5$), where both modes are active and a different one, the "broadside"-regime ($3 \le \chi\le 4$), where only the second mode is present. Remarkably, for the most prolate particles ($\chi = 5$), we observe an entirely different "helical" rise with completely unique features.