摘要：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.
