Buoyancy driven bubbly flows: role of meso-scale structures on the relative motion between phases in bubble columns operated in the heterogeneous regime

TL;DR

This study investigates how meso-scale structures like clusters and voids influence bubble motion in heterogeneous bubble columns, revealing that these structures significantly affect relative velocities and flow dynamics.

Contribution

It introduces a novel analysis of meso-scale structures' role in bubble dynamics using Vorono"i tessellations and links structure size and concentration to relative velocities.

Findings

Bubbles in clusters move up to 3.5 times faster than terminal velocity.

Meso-scale structures significantly influence bubble velocities.

The relative velocity scales as (gDε)^{1/2}.

Abstract

The hydrodynamics of bubble columns in the heterogeneous regime is investigated from experiments with bubbles at large particle Reynolds numbers and without coalescence. The void fraction field $\varepsilon$ at small scales, analyzed with Vorono\"i tessellations, corresponds to a Random Poisson Process (RPP) in homogeneous conditions but it significantly differs from a RPP in the heterogeneous regime. The distance to a RPP allows identifying meso-scale structures, namely clusters, void regions and intermediate regions. A series of arguments demonstrate that the bubble motion is driven by the dynamics of these structures. Notably, bubbles in clusters (respectively in intermediate regions) are moving up faster, up to 3.5 (respectively 2) times the terminal velocity, than bubbles in void regions those absolute velocity equals the mean liquid velocity. Besides, the mean unconditional relative velocity of bubbles is recovered from mean relative velocities conditional to meso-scale structures, weighted by the proportion of bubbles in each structure. Assuming buoyancy-inertia equilibrium for each structure, the relative velocity is related with the characteristic size and concentration of meso-scale structures. By taking the latter quantities values at large gas superficial velocities, a cartoon of the internal flow structure is proposed. Arguments are put forward to help understanding why the relative velocity scales as $(gD\varepsilon)^{1/2}$ (with $D$ the column's diameter and $g$ gravity's acceleration). The proposed cartoon seems consistent with a fast-track mechanism that, for the moderate Rouse numbers studied, leads to liquid velocity fluctuations proportional to the relative velocity. The potential impact of coalescence on the above analysis is also commented.