Shear driven two-phase flows in vertical cylindrical duct

Abstract

Experiments and numerical simulations were carried out for shear-driven two-phase flows in a confined volume of liquid under conditions of normal gravity. The geometry corresponds to a cylindrical liquid bridge surrounded by a concentric annular gas channel with external solid walls. The internal part consists of solid supports at the bottom and top, while the central part is a liquid zone filled with a viscous liquid and kept in its position by surface tension. Gas enters into the annular duct, flows between solid walls and upon reaching the liquid zone entrains initially quiescent liquid. The flow dynamics is governed by the Navier–Stokes equations in both fluids, which are numerically solved in the exact experimental geometry taking into account interface deformation by gravity. In the experiments 5 cSt silicone oil and air were used as test fluids and the flow was monitored by means of particle tracking velocimetry. The experiments were performed for unit aspect ratio (the ratio of liquid zone length to its radius), while the simulations of shear-driven flow were carried out for a wide range of parameters. A particular attention is focused on the effect of free surface shape and fluids viscosity contrast on the interfacial flow dynamics. The current study suggests a linear dependence between velocities of gas and liquid when the viscosity of the liquid is larger by two orders of magnitude than that of gas. Another relation is proposed when the fluids viscosity ratio, μ l / μ g , is less than 50.