Numerical Simulation of Single Drops in a Vertical Pipe Using Various Coordinate Systems

The effects of the diameter ratio λ (= d/D, where d and D are the diameters of a drop and a pipe, respectively), the Morton number M and the viscosity ratio κ (= μ_d/μ_c, where μ is the viscosity and the subscripts d and c are the dispersed fluid particle and the continuous phase, respectively) on terminal velocities and shapes of single drops rising through stagnant liquids in a vertical pipe are investigated experimentally. Then, the drops in the pipe are simulated using a volume tracking method with various coordinate systems, i.e., three-dimensional (3D) cylindrical coordinates, 3D general curvilinear coordinates and 3D Cartesian coordinates. Predicted velocities and shapes of the drops using three coordinate systems are compared with the measured data to examine the effects of coordinate systems on the accuracy of prediction. As a result, (1) The velocity ratio V_T/V_T0 (V_T and V_T0 are the terminal velocity in a pipe and infinite liquid, respectively) decreases as λ increases, and it depends not only on λ but also on M and κ, (2) Good predictions for the terminal velocities and shapes of drops are obtained not only with cylindrical coordinates and curvilinear coordinates but also with Cartesian coordinates, provided that the spatial resolution is high, (3) When the spatial resolution is low, effects of coordinate systems on a drop shape are larger for Cartesian coordinate systems than for cylindrical coordinate and general curvilinear coordinate systems, and (4) Errors in predicted drop velocities are not so large even with very low spatial resolution.