Dynamics of a deformable bubble swarm at high Reynolds number: An interface-resolved direct numerical simulation

We perform interface-resolved direct numerical simulations of deformable bubble swarms in a high-Reynolds-number wobbling regime (Reb≈434, Eo=3) to investigate the interplay between collective motion, bubble clustering, and bubble-induced turbulence over a wide range of void fractions (ϕ=2%–16%). To overcome the challenge of numerical coalescence in the volume-of-fluid method, we extend a previously developed short-range repulsive force model to swarm simulations, enabling the robust simulation of long-duration, close-interaction dynamics. Our primary finding is a striking non-monotonic dependence of the mean swarm rise velocity on the void fraction. At low void fractions (ϕ≤4%), the swarm velocity is enhanced relative to an isolated bubble, driven by the formation of persistent, vertically-aligned chain-like structures. This clustering, sustained by the negative lift force on deformable bubbles in wake-induced shear, provides a low-drag configuration. In contrast, at higher void fractions (ϕ≥8%), intense multi-bubble interactions disrupt these coherent structures, leading to a collective hindrance effect that suppresses the rise velocity. This transition in dynamics is directly mirrored in the statistics of the liquid-phase pseudo-turbulence. At low void fractions, vertical clustering leads to a strong anisotropic suppression of velocity fluctuations, fundamentally altering the horizontal velocity probability density functions to a single-slope exponential decay. As the void fraction increases, the flow transitions toward a more isotropic, Gaussian-like state. Finally, across all void fractions, the kinetic energy spectra universally exhibit a k−3 scaling law at sub-bubble scales, while the energy at large scales is dictated by the dominant collective structure. These results provide new fundamental insights into the structural and statistical properties of dense, high-Reynolds-number bubbly flows.