Bubble–bubble interaction effects on dynamics of multiple bubbles in a vortical flow field

Bing Cui,Baoyu Ni,Qigang Wu

doi:10.1177/1687814016631708

Abstract

Bubble–bubble interactions play important roles in the dynamic behaviours of multiple bubbles or bubble clouds in a vortical flow field. Based on the Rayleigh–Plesset equation and the modified Maxey–Riley equation of a single bubble, bubble–bubble interaction terms are derived and introduced for multiple bubbles. Thus, both the Rayleigh–Plesset and modified Maxey–Riley equations are improved by considering bubble–bubble interactions and then applied for the multiple bubbles entrainment into a stationary Gaussian vortex. Runge–Kutta fourth-order scheme is adopted to solve the coupled dynamic and kinematic equations and the convergence study has been conducted. Numerical result has also been compared and validated with the published experimental data. On this basis, the oscillation, trajectory and effects of different parameters of double-bubble and multi-bubble entrainment into Gaussian vortex have been studied and the results have been compared with those of the cases without bubble–bubble interactions. It indicates that bubble–bubble interactions influence the amplitudes and periods of bubble oscillations severely, but have small effects on bubble trajectories.

Highlights

Cavitation and gas bubbles entrainment into a vortical flow field is always of great importance, because of its either useful applications or undesirable effects, in chemical engineering,[1] hydraulic engineering,[2] marine and ocean engineering[3,4] and so on
Hsiao and Pauley[6] studied the cavitation inception in a tip vortex flow through the spherical Rayleigh–Plesset (RP) bubble dynamics equation coupled with the bubble motion equation
Most previous researchers studied the multiple bubbles entrainment into vortex flow using the same method as the single bubble and just increased the number of equations directly

Summary

Introduction

Cavitation and gas bubbles entrainment into a vortical flow field is always of great importance, because of its either useful applications or undesirable effects, in chemical engineering,[1] hydraulic engineering,[2] marine and ocean engineering[3,4] and so on. Hsiao and Pauley[6] studied the cavitation inception in a tip vortex flow through the spherical Rayleigh–Plesset (RP) bubble dynamics equation coupled with the bubble motion equation. Hsiao and Chahine[9] applied spherical and nonspherical bubble dynamic models to study the cavitation inception, deformation and the scaling of the bubble in a vortex flow. Most previous researchers studied the multiple bubbles entrainment into vortex flow using the same method as the single bubble and just increased the number of equations directly. Hsiao and Chahine[17] simulated the acoustic pressure generated by cavitation inception in a tip vortex flow in water containing a realistic bubble nuclei size distribution through the spherical bubble dynamics model directly. Substituting equation (10) into equation (8) and considering gas density rb ’ r=820, one can obtain the simplified bubble motion differential equation as dubi dt g

CD 4 Ri ðuw ubiÞjuw ubij

À eÀj ð12Þ

Findings

Conclusion