Hydrodynamic and Mass transfer characterization at the oil water interface in a three phase model metallurgical ladle*

We investigate a three-phase flow inspired by the ladle metallurgical secondary refinement process. A container of water, modelling the molten metal, is topped by a thin layer of oil, modelling the slag. The system is agitated by the injection of air at the bottom, creating a bubble plume that merges into the air at the top of the system. Thymol, acting as a passive scalar, is dissolved from the water into the oil. We perform theoretical, numerical, and experimental studies of both the hydrodynamic and mass transfer properties of the system. A DNS is performed of the three-phase flow and the scalar transport equation modeling the dissolution of thymol is performed using a subgrid-scale SGS model.

At a critical flow rate, the hydrodynamic flow is governed by a combination of phenomena, where water is transported upward in a bubble plume, deviated outwards as it reaches the free surface in a radial jet, and deviated again under the oil film. The area of the water-air free surface where the water layer enters the oil layer is referred to as the open-eye and is a global measure used to measure the effect of flow rate on the ladle stirring time. The rising bubble plume akin is observed to follow a (Q/z)-1/3 scaling, where Q is the flow rate and z is the water height, similar to thermal plumes. The radial jet at the surface is compared to theory described for underwater blowouts. The size of the open eye is determined from a horizontal stress balance of gravity and inertia. A meniscus is demonstrated to develop both numerically and theoretically where a very thin oil layer stretches over the water, which affects the open eye size.

The mass transfer analysis is made difficult by the large Peclet number of the system, leading to thin concentration boundary layers for which the required number of grid points is prohibitive. We implement a subgrid scale (SGS) model to capture the thin boundary layers at the interface. We show that at lower flow rates where oil fragmentation is not present, the mass transfer is dominated by transfer in an annulus surrounding the open-eye, where the prediction of the mass transfer can be estimated from laminar boundary layer theory on at the oil-water interface.