A multiscale numerical approach to investigate interfacial mass transfer in three phase flow: application to metallurgical bottom-blown ladles

We use direct numerical simulation (DNS) to investigate mass transfer between liquid steel and slag during a metallurgical secondary refinement process through two reduced-scale water experiments, which reproduce the dynamics seen in an industrial bottom-blown ladle. A container is filled with water and topped by a thin layer of oil, representing the molten steel and slag, respectively. The system is agitated by a bubble plume that impinges on the oil layer and forms an open-eye. A tracer species, dissolved in the water, acts as a passive scalar that is progressively absorbed into the oil layer. Both the hydrodynamics and mass transfer in the system are studied and compared with experiments from the literature of different size and geometry. The numerical simulation of mass transfer is challenging due to the high Péclet number, leading to extremely thin species boundary layers at the interface. Resolving the boundary layer is prohibitive even with adaptive grid techniques. A subgrid-scale (SGS) boundary layer model corrects the scalar transport equation, allowing us to solve convection-dominated transport on relatively coarse grids. The hydrodynamics is investigated, and we analyze how the resultant flow field governs mass transport. The numerical results recover two flow regimes: a quasi-steady regime at low flow rates with small deformations of the oil-water interface and an atomizing regime at large flow rates. Interfacial species transport is determined to be dominated in an annulus surrounding the open eye caused by a shear layer at the oil-water interface. It is observed that we achieve grid-independent macroscopic quantities that match relatively well with those observed in experiments, allowing use of simulation techniques as a complementary tool going forward.

💡 Research Summary

This paper presents a multiscale numerical modeling study aimed at investigating interfacial mass transfer in a system relevant to metallurgical bottom-blown ladles. To overcome the challenges of high-temperature, opaque industrial experiments, the authors use a scaled-down three-phase water-oil-air system, mimicking the steel-slag-gas interactions. The primary innovation lies in addressing the computational hurdle posed by the extremely high Péclet number (≈10^5), which results in species boundary layers at the interface that are too thin to be resolved directly on a feasible computational grid.

The research builds upon two existing experimental campaigns: a conical ladle by Kim & Fruehan and a cubic ladle by Joubbert et al. Simulations are performed using the open-source Basilisk platform, which employs a Volume-of-Fluid (VOF) method to capture the interfaces between water, oil, and air, solving the incompressible Navier-Stokes equations.

The core methodological advancement is the development and implementation of a multiscale modeling approach. While the large-scale turbulent flow is resolved using Direct Numerical Simulation (DNS), the mass transfer across the thin species boundary layer is handled by a Subgrid-Scale (SGS) boundary layer model. This model corrects the scalar transport equation, allowing for accurate prediction of interfacial mass fluxes on relatively coarse grids without artificially increasing the species diffusivity—a common but uncertain practice in prior studies.

Key findings from the simulations include the identification of two distinct flow regimes depending on the gas injection rate: a quasi-steady regime with minimal interface deformation at low flow rates, and an atomizing regime with significant slag (oil) fragmentation at high flow rates. Analysis reveals that the most intense interfacial mass transfer occurs in an annular region surrounding the “open eye” (the area cleared of the top layer by the bubble plume), driven by high shear at the oil-water interface.

Crucially, the multiscale simulations demonstrate grid independence for macroscopic quantities such as the global mass transfer rate (expressed as a Sherwood number) and the open-eye area. The numerical results show favorable agreement with experimental data from both referenced studies, despite differences in ladle geometry and scale. The study concludes that this validated multiscale numerical framework provides a computationally efficient and accurate complementary tool to experiments for analyzing interfacial transport in complex multiphase systems like gas-stirred ladles, offering significant potential for process understanding and optimization.