Bubble shape oscillations in a turbulent environment

TL;DR

This study uses direct numerical simulations to analyze bubble shape oscillations in turbulent flows, modeling interface deformations as stochastic oscillators and revealing increased dissipation and pressure fluctuation characteristics.

Contribution

It introduces a stochastic linear oscillator model for bubble interface modes in turbulence and quantifies the effects of turbulence on bubble deformation dynamics.

Findings

Natural frequency matches Rayleigh frequency in quiescent flow

Dissipation increases 15-fold due to boundary layer effects

Pressure fluctuations exhibit exponential tails and eddy timescales

Abstract

We investigate bubble deformations in an homogeneous and isotropic turbulent flow by means of direct numerical simulations of a single bubble in turbulence. We examine interface deformations by decomposing the local radius into the spherical harmonics base. We show that the linear dynamics of each mode, (for low Weber number), can be modeled by a forced stochastic linear oscillator. We measure the coefficients of the model directly from the modes' statistics. We find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, dissipation increases by a factor 15 compared to the quiescent case, at $Re_\lambda = 55$. This enhanced dissipation originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the integration of pressure over the bubble surface, is independent on bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. Eventually, we investigate the pressure modes' statistics in the absence of bubbles and compare them to the effective forcing statistics. We show that both fields share the same pdf, characterized by exponential tails, and a characteristic timescale corresponding to the eddy turnover time at the mode scale.