Numerical study of the motion of a single elongated bubble in high viscosity stagnant liquids along pipelines

Abstract

Multiphase flow models involve more variables than available equations, thus closure relationships are required to solve the system of partial differential equations. In the Drift Flux Model, the mean drift velocity of the gas phase is estimate using the drift velocity closure relationship. This study investigates the motion of a single elongated bubble in high viscosity stagnant liquids in order to propose a comprehensive closure relationship for the bubble drift velocity. Different cases were run with inclination angles varying from 0° (horizontal direction) to 90° (vertical upward). OpenFOAM, an open source Computation Fluid Dynamics software, was used to numerically solve the two-phase incompressible flow problem. Drift velocities based on the movement of the bubble tip and the void fraction weighted averaged were compared to clarify the ambiguity in the drift velocity calculation and measurement. For horizontal pipe cases, the deformation of the bubble caused the drift velocity to be higher at the tip of the bubble than the drift velocity inside the bubble. For inclination angles more than 0°, the drift velocity at the tip is the same as inside the bubble. The closure relationship proposed is validated against experimental data in the literature. The results indicate that the closure relationship has a maximum 10% absolute average relative error for the viscosity range of 0.14–1.120 Pa·s, pipe size up to 0.152 m and pipe inclinations from 0° to 90°. The limitations of the closure relationship and potential enhancements for future studies are discussed.