Numerical simulation of bubble rising in viscous liquid

Abstract

An improved numerical algorithm for front tracking method is developed to simulate the rising of a bubble in quiescent viscous liquid due to buoyancy. In the new numerical algorithm, volume correction is introduced to conserve the bubble volume while tracking the bubble’s rising and deforming, and volume flux conservation based SIMPLE algorithm is adopted to solve the Navier–Stokes equation for fluid flow using finite volume method. The new front tracking algorithm is validated systematically by simulating single bubble rising and deforming in quiescent viscous liquid under different flow regimes. The simulation results are compared with the experimental measurement in terms of terminal bubble shape and velocity. The simulation results demonstrate that the new algorithm is robust in the flow regimes with larger ranges of Reynolds number ( Re < 200), Bond number ( Bo < 200), density ratio ( ρ l/ ρ b < 1000) and viscosity ratio ( μ l/ μ b < 500). The new front tracking algorithm is also applied to investigate bubble rising and deforming behaviour in the various flow regimes of “air bubble/water solution” system under effects of Reynolds number, Bond number, density ratio, viscosity ratio as well as the bubble initial shape, which have been explored previously by experiments. The predicted bubble shape and terminal velocity agree well with the experimental results. Hence, the new modelling algorithm expands the conventional front tracking method to more realistic and wider applications.