The gas-assisted fluid flow expelled in front of a long bubble in a circular tube

This study investigates the steady-state flow field in a circular tube filled with a viscous fluid expelled by a long gas bubble. We use a finite difference method with successive over-relaxation in the computation of the viscous flow field. An empirical bubble profile is employed to simplify the computation of the interface shape between the gas and the viscous fluid. By varying the ratio of the bubble width to the diameter of the circular tube (A), the numerical simulation shows three fluid flow patterns: the complete bypass flow, the recirculation flow and the transient flow. The transient flow is only observed in a limited lambda range of root 1/2 < lambda < 0.7143 and isn't clearly discussed in the previous studies. The variation of vorticity also is observed by the various sizes of lambda.