Numerical study of liquid-gas and liquid-liquid Taylor flows using a two-phase flow model based on Arbitrary-Lagrangian-Eulerian (ALE) formulation

The liquid-gas and liquid-liquid Taylor flows in circular capillary tubes are numerically studied using a mathematical model developed in the frame of Arbitrary-Lagrangian-Eulerian (ALE), where the interface is tracked so that the important interfacial curvature and forces for Taylor flow can be accurately estimated. It is found that for liquid-gas Taylor flow, thin film thickness predicted by the present numerical model agrees very well with the benchmark experimental data both in visco-capillary and visco-inertia flow regimes. Thin film thicknesses decreases first and then increases as Reynolds number (Re) increases at relatively large capillary numbers (Ca). With the increase of Ca, classical pressure drop correlations become inaccurate, because of strong internal circulation inside liquid slug, the appearance of waves at rear meniscus, as well as the deviation from semi-spherical shape of head meniscus. For liquid-liquid flow, when Ca is small, thin film thickness correlations for liquid-gas flow can be used since the disperse phase has negligible effects, while when Ca is relatively large, the viscosity ratio and density ratio of continuous phase to disperse phase become two additional influencing factors. The larger are the viscosity ratio and the density ratio, the thicker is the film thickness. Different from stagnant thin film in liquid-gas flow, the flow in thin film of liquid-liquid flow is not stagnant and has a large contribution to pressure drop. The numerical model developed in this study is shown to be a powerful and accurate tool to study both the liquid-gas and liquid-liquid Taylor flows.