Hybrid Multiphase CFD Solver for Coupled Dispersed/Segregated Flows in Liquid-Liquid Extraction

The flows in stage-wise liquid-liquid extraction devices include both phase segregated and dispersed flow regimes. As a additional layer of complexity, for extraction equipment such as the annular centrifugal contactor, free-surface flows also play a critical role in both the mixing and separation regions of the device and cannot be neglected. Traditionally, computional fluid dynamics (CFD) of multiphase systems is regime dependent—different methods are used for segregated and dispersed flows. A hybrid multiphase method based on the combination of an Eulerian multifluid solution framework (per-phase momentum equations) and sharp interface capturing using Volume of Fluid (VOF) on selected phase pairs has been developed using the open-source CFD toolkit OpenFOAM. Demonstration of the solver capability is presented through various examples relevant to liquid-liquid extraction device flows including three-phase, liquid-liquid-air simulations in which a sharp interface is maintained between each liquid and air, but dispersed phase modeling is used for the liquid-liquid interactions. 1. Introduction While multiphase flows present unique challenges for computational fluid dynamics (CFD) simulation, a host of solution methods exist for simulation of well categorized flows. For “dispersed” flows in which one phase is continuous and the other is distributed in fine droplets, one can use Lagrangian particle tracking for small phase fractions (less than ~10%) in which each individual fluid particle is followed through the fluid in response to local flow conditions. For high phase fraction dispersed flows, a multi-fluid Eulerian-Eulerian solution method with interphase mass and momentum transfer can be applied. For stratified flows in which the fluid phases have a clearly defined phase interface, free-surface capturing methods such as Volume of Fluid (VOF) can be employed. Real flows, such as those encountered in liquid-liquid extraction devices, are not so easily categorized and can span multiple flow regimes (both spatially and temporally). In theory, interface capturing methods could be used for direct simulation of dispersed flows given that a mesh spacing of ~10x smaller than the smallest droplet can be used; however, accurate physical capturing of droplet-droplet interactions requires yet finer mesh resolution or droplet coalescence is severely overpredicted. In practice such meshing—and the small timesteps required (on the order of ？s) for stable solution—is not feasible for realistic turbulent multiphase flows and will not be in the foreseeable future even