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 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.

A Review of Models for Bubble Clusters in Cavitating Flows

“…The interaction between diluted bubble clusters and shock waves have been investigated in recent works by Maeda et al [140] comparing favoroubly for problems related to medical applications. Models based on similar ideas have been also proposed to investigate the attenuation of waves by bubble clusters to protect offshore structures and sealife [89] and problems related to hydrodynamic and ultrasonic cavitation [138] in regions where the gas/vapor phase can be considered disperse. One interesting observation of the results provided by these models is the prediction of significant pressure and velocity fluctuations that can be directly attributed to the heterogeneous distribution of the disperse phase in a given situation.…”

Modelling cavitation during drop impact on solid surfaces

“…However, such models are empirical and case dependent and thus, tuning is necessary. Alternatively, an Eulerian approach for the liquid and a Lagrangian method for the discrete bubbles based on the modified Rayleigh-Plesset equation has been employed in [111,112,113]. Apart from having a restricted validity for spherical bubbles, which is a strong assumption, such models significantly increase the computational cost.…”

Modeling Separation and Cavitation Behind a Blunt Body

“… is obtained from the space distribution and size information of the bubbles. The influence of each bubble is spread using a Gaussian distribution conserving the total bubble volumes [17]. Equations (2) and (3) are solved using the Eulerian flow solver 3DYNAFS-VIS © [18].…”