Effects of confinement on bubble dynamics in a square duct

In this paper, we simulate the effects of confinement on three-dimensional bubble dynamics in a square duct. A systematic study of three confinement ratios, four Bond numbers and two Morton numbers has been conducted. A GPU implemented VOF numerical algorithm on a Cartesian collocated grid with an improved method to handle the surface tension force has been developed. A three-dimensional geometry construction method with a piecewise linear interpolation scheme for approximating the interface segments is used to compute the interface shape and liquid volume flux from the cell faces. The Navier-Stokes equations are solved with a space-time second-order accurate fractional step numerical scheme. The surface tension force is treated as a pressure gradient and an additional Poisson equation is solved. Transient and steady state bubble deformations, rise velocities and aspect ratios are presented.