In the exploiting and processing of submarine energy, such as natural gas, petroleum and combustible ice, it is always accompanied with multi-phase flow of large density and viscosity ratio, like bubbly flows. The essential mentioned subjects are bubbles rising in the viscous medium, the coupling effects among rising bubbles. In this paper, SPH method is used to simulate the interaction between two bubbles, where the focusing problem is the interface between gas and liquid. The multiphase flow characteristics are greatly influenced by surface tension and viscous force especially when the characteristic length scales are relatively small. As many experiments in previous literatures indicate, the rising bubbles are often followed by a long tail which greatly affects the shape and motion path of a single bubble and bubble groups. Though Boundary Element Method (BEM) may be well used to simulate the movement and deformation of a single bubble, there are still many challenges in simulating the bubble interactions like coalescing and bouncing. The traditional Smoothed Particle Hydrodynamics (SPH) method was well employed in simulating moving boundary and large deformation problems in single-phase problems, but in the ocean engineering, the density and viscosity ratio at the gas-liquid interface may be up to nearly 1000 and 100 respectively, which will always cause unphysical penetrations and pressure fluctuations at the gas-liquid interface. The present improved SPH algorithm based on volume approximation can guarantee the continuous conditions at the gas-liquid interface. Through a staggered particle distribution and an appropriate re-mesh, the process of rising, pulsing and jet of a single bubble is simulated, which agree well with that of experiments in the existing literatures. Besides, the trails of the rising bubble and interactions among bubbles are studied. On these bases, the coalescing and bouncing of two bubbles posited at different directions are simulated, which are consistent well with the experiment carried out in previous literatures. The present studies aims to provide a reference for the industrialized productions.

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