Interface Tracking Simulation of Drops Rising through Liquids in a Vertical Pipe Using Three Coordinate Systems

Abstract

Interface tracking simulations of single drops rising through a vertical pipe are carried out using three coordinate systems, i.e. cylindrical, general curvilinear and Cartesian coordinates, to investigate the effects of coordinate system and spatial resolution on the accuracy of predictions. Experiments of single drops in a vertical pipe are also conducted to obtain experimental data for comparisons with simulations. The drop shape observed are spheroidal and deformed spheroidal at low values of the diameter ratio, Λ, of the sphere-volume equivalent diameter of a drop to the pipe diameter, whereas they take bullet-shapes at large Λ. The conclusions obtained are as follows: (1) the effects of coordinate system on drop shape are small at low Λ. At large Λ, the effects are also small for drops in a low viscosity system, whereas non-physical shape distortion takes place when the Cartesian coordinates are used with low spatial resolution for drops in a high viscosity system, and (2) the drop terminal velocity and the velocity profile in the liquid film between a bullet-shaped drop and a pipe wall are well predicted using all the coordinate systems tested even at low spatial resolution.