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

Stefano De Rosa; Jacob Maarek; Stéphane Zaleski

Home/Archive/arXiv

arXiv · 2509.05033

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

Stefano De Rosa·Jacob Maarek·Stéphane Zaleski

View original source ↗Read source document ↗Export metadata ↓

Abstract

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 P\'eclet 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.

Explore related subjects

physics.flu-dyn

Keep this discovery

BibTeX RIS

Stefano De Rosa, Jacob Maarek, Stéphane Zaleski. 2025-09-05. A multiscale numerical approach to investigate interfacial mass transfer in three phase flow: application to metallurgical bottom-blown ladles. https://arxiv.org/abs/2509.05033

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Correlative effects of induced magnetic field-buoyancy on reactive solute dispersion dynamics in couple-stress fluids

We investigate the dispersion of a reactive solute in a couple-stress fluid flowing between two parallel plates under the combined effects of pressure-driven flow, buoyancy, and an induced magnetic field. The model incorporates first-order heterogeneous reactions at both channel walls alongside a bulk reaction. Using Mei's multiscale homogenization technique accurate to third order, we develop a higher-order asymptotic formulation to determine the effective longitudinal dispersion coefficient and concentration field. Analytical predictions are complemented by Brownian dynamics simulations and finite-difference solutions, while the Aris method of moments quantifies transient mean displacement, spatial variance, and effective dispersivity. The hydrodynamic analysis reveals a singular branch in the velocity solution when the Hartmann number equals half the couple-stress parameter and identifies a characteristic quarter-power scaling between the Hartmann number and couple-stress parameter, separating couple-stress- and magnetically dominated regimes. The model recovers classical Taylor-dispersion behavior in the non-reactive Newtonian limit and agrees well with experimental measurements. Couple-stress rheology and magnetic damping suppress shear-induced dispersion, whereas buoyancy enhances dispersion through additional transverse velocity gradients. A distinct saturation regime of the dispersion coefficient emerges with an increasing couple-stress parameter, while unequal wall absorption induces persistent transverse asymmetry, and stronger absorption enhances solute removal near the source. Numerical and stochastic results validate the analytical framework while resolving higher-order concentration structures and particle-scale wall adsorption.

physics.flu-dyn↗

arXiv2026

DiffSWE2d: a differentiable Shallow Water Equations solver for end-to-end flood and tsunami modelling

Solving inverse and optimisation problems with traditional shallow water equations (SWE) solvers can be computationally expensive, particularly when gradients with respect to model inputs or parameters must be estimated through repeated forward simulations. In this paper, we introduce DiffSWE2d, an open-source differentiable shallow water equations solver for end-to-end flood and tsunami modelling implemented in PyTorch. By leveraging automatic differentiation, DiffSWE2d represents the time-marching physics as a differentiable computational graph, enabling gradients to be propagated directly through the numerical solver. We validate the solver against two established benchmark cases and demonstrate its application to tsunami waveform inversion, showing its ability to infer model inputs through gradient-based optimisation. DiffSWE2d provides a flexible framework for integrating physics-based hydrodynamic modelling with modern optimisation and machine learning methods. The source code and reproducible examples are publicly available at: https://github.com/ZhonghouXu/DiffSWE2d

physics.flu-dyn↗

arXiv2026

Low inertia limit of elasto-inertial turbulence

Pipe and channel flows of viscoelastic fluids display chaotic dynamics at unusually low speeds, a phenomenon referred to as elasto-inertial turbulence, EIT. First reported in experiments a century ago, recent theoretical studies and model computations predict a variety of scenarios for the phenomenon's origin, ranging from hoop stress modes to center modes and to Tollmien-Schlichting waves. Lacking experimental confirmation, the relevant scenario in actual flows of polymer solutions remains unknown. We here determine the transition threshold of EIT in pipe experiments, covering three decades in elasticity number. Across this entire parameter range, the transition features center mode structures at onset. Eventually the instability diverges at a lower inertia (upper elasticity) limit, which is a robust signature of this center mode scenario. Finally, we report the first experimental observation of a traveling wave in viscoelastic pipe flow, and the sequences of localized structures found, are in excellent agreement with a center mode traveling wave, the "arrowhead" solution, discovered in model simulations.

physics.flu-dyn↗