Abstract: In this paper, a direct numerical simulation model coupled with gas and two layers of liquid with different densities is developed to study the dynamics of rising bubbles in a two-layer stratified environment. Based on the level set method with 5th-order weighted essentially non-oscillatory (WENO) and 3rd-order Runge-Kutta scheme, a numerical method coupling multiple level set functions is proposed to capture both the gas-liquid interface and each liquid surface, as well as calculating both the density and viscosity on the interface. The method proposed is verified by comparing with the available numerical simulation results. Besides, this model is employed to study the motion of a rising bubble in a two-layer fluid involving water and oil, which provides detailed flow structures in a complex environment. The results suggest that compared with the movement in a uniform environment, the water column induced by pressure difference is easier to break at the bottom when a bubble rises against a two-layer stratified background. The increase of liquid thickness above the bubble can extend the time that the bubble stays in the underwater deformation stage, and can lead to a flatter bottom of the bubble.

Key words: bubble, stratified fluids, level set method, numerical simulation