Multiple-relaxation-time lattice Boltzmann method for three dimensional free-surface flows with multi-bubble model

Abstract

Flow with bubbles is a commonly occurring phenomenon in nature and industrial applications. This study provides a multi-bubble model for the free surface lattice Boltzmann method (FSLBM) which can be used to simulate fluid flow with bubbles as well as their splitting and merging processes. FSLBM neglects the flow of gas and considers only the gas pressure, and thus simplifies the gas-liquid two-phase flow to a single-phase free surface. The compression of the bubble will influence its pressure and lead to movement, splitting, or merging processes within the bubble flow. The multi-bubble model considers the evolution of bubble's pressure by enhancing the model for free surface which simulates the behavior of gas-liquid interface inside the liquid. The Smagorinsky subgrid-scale model (SGS) and the more advanced multiple-relaxation-time (MRT) collision model is used for high Reynolds number. In this study, a bubble algorithm to handle the bubble splitting and merging without incurring significant computational costs is provided. The verification and analysis of this model are given by a comparison between both analytical solution and an experiment. Therefore, the multi-bubble as an extension of FSLBM can be used to solve a wider range of two-phase flow problems more efficiently, such as bubble formation, metal foaming process, and development in chemical reactors.