A Droplet Simulation on Motion Topology With Mass Transfer Using Moving Unstructured Mesh

A direct simulation code for a moving and dissolving droplet by using three-dimensional hybrid unstructured mesh was developed. The multi-phase flow field is discretised by a cell-centred finite volume ALE (arbitrary Lagrangian Eulerian) formulation. Based on the fractional step method, a semi-implicit scheme in time is used. Other numerical aspects of the present method are the method of Rhie and Chow (1983) for incompressibility, a third-order compact upwinding for convection term, and a second-order central difference for diffusion term. The mesh consists of tetrahedron prisms near interface for viscous boundary layer and tetrahedrons in the other part. The interface between the droplet and water moves along spines in the radial direction that satisfies its kinematic condition. The effect of interface tension is taken into account directly in solving the Poisson equation for pressure. This method is applied to the mass transfer from a rising droplet. The non-dimensional parameters to describe this phenomenon are the Schmidt number, the Reynolds number based on rise velocity and the Eo¨tvo¨s number relating the surface tension to the gravitational acceleration, and the Ohnesorge number relating the surface tension to viscous force. From the simulation results, we found that there are three regimes of the path topology of rising droplet, i.e. rectilinear, helical-zigzag and zigzag motion. These are categorized by the Reynolds and the Ohnesorge numbers. The mechanism of the trajectory morphology is elucidated by the relation to vertex shedding from the droplet.