A coupled level-set and volume-of-fluid method for the buoyant rise of gas bubbles in liquids

Abstract

This paper investigates some fundamental aspects of rising gas bubbles in stagnant Newtonian liquids using a coupled level-set and volume-of-fluid (CLSVOF) method. The coupled method not only calculates the geometric properties (normal and curvature) of the bubble surface accurately but also satisfies compliance of mass conservation very well. The method solves a single set of governing equations for both phases using variable transportive properties on a fixed Eulerian two-dimensional mesh in axisymmetric coordinates. We computed the terminal shapes and Reynolds numbers (Re) of isolated gas bubbles rising in stagnant liquids for low to high Eötvös number (Eo < 340) and Morton number (M < 44). In addition, the drag co-efficients for a single bubble rising in liquid with M ⩾ 10−4 are computed. The rise and shape of two co-axial gas bubbles with same size in stagnant liquid and the evolution history of the bubble coalescence process are examined. Furthermore, the mechanisms of bubble-bursting at a free surface and formation of liquid jets are also studied qualitatively. The computational results are compared with the experimental results available in literature. It is observed that the predicted results are in good agreement with experimental counterpart. Finally, the formation of gas bubbles from a submerged orifice in quiescent and co-flowing liquids for low Reynolds number flows is discussed where the viscosity ratio of liquid to gas is about 16, 474.