A mass-conserving axisymmetric multiphase lattice Boltzmann method and its application in simulation of bubble rising

Abstract

In many lattice Boltzmann studies about bubble rising, mass conservation is not satisfactory and the terminal bubble rising shape or velocity is not so consistent with experimental data as those obtained through other CFD techniques. In this paper, based on the multiphase model (He et al., 1999 [1]), a mass-conserving axisymmetric multiphase lattice Boltzmann model is developed. In the model, a mass correction step and an effective surface tension formula are introduced into the model. We demonstrate how the macroscopic axisymmetric Cahn–Hilliard equation and Navier–Stokes equation are recovered from the lattice Boltzmann equations through Chapman–Enskog expansion. The developed model is applied to simulate the bubble rising in viscous fluid. The mass correction step in our scheme significantly improves the bubble mass conservation. The surface tension calculation successfully predicts the terminal bubble shapes and reproduces the effect of initial bubble shape. The terminal bubble rising velocities are very consistent with experimental and numerical data in the literature. Qualitatively, the wakes behind the bubbles also agree well with experimental data. This model is useful for predicting the axisymmetric two-phase flows.