Spherical bubble dynamics in a bubbly medium using an Euler–Lagrange model

Abstract

For applications involving large bubble volume changes such as in cavitating flows and in bubbly two-phase flows involving shock and pressure wave propagation, the dynamics, relative motion, deformation, and interaction of bubbles with the surrounding medium play crucial roles and require accurate modeling. We present in this paper a fundamental study of the dynamic oscillations of a “primary” bubble in a bubbly mixture using a two-way coupled Euler–Lagrange model. It addresses a simplified spherical configuration while using the full three-dimensional code. A main objective of the study is to investigate how the dynamics of a “primary” bubble is affected by the presence of a surrounding bubbly medium and how it differs from its behavior in a pure liquid. This helps elucidate the physics at play for this relatively simple configuration. The model simulates the mixture as a continuum and solves the corresponding Navier Stokes equations with grids moving with the interface of the primary bubble wall. The surrounding microbubbles are tracked in a Lagrangian fashion accounting for their volume evolution. The two-way coupling between the bubbly medium and the primary bubble dynamics is realized through the local density of the mixture obtained from the tracking of the microbubbles and the determination of their volumes and spatial distribution.The simulations clearly indicate that the surrounding microbubbles absorb energy emitted from the primary bubble during its oscillations. This results in a reduction of the maximum radius and the period of oscillations of the primary bubble as compared to the dynamics in the pure liquid. Also, accounting for the dynamics of the field bubbles brings out the presence in the two-phase medium of a phase shift between density and pressure distributions. Such a shift is not captured by two-phase homogeneous medium models. These effects increase with increase in the mixture void fraction and in the initial bubble sizes in the mixture. The numerical observations are found to be in good qualitative agreements with previously published experimental data (Jayaprakash et al., 2011) investigating spark generated bubble dynamics in a bubbly medium.