The Joule heat generated by current flow between electrodes in a resistance furnace not only melts and heats the charge but also induces mixing of the molten material. Increased mixing promotes improved chemical and temperature uniformity within the bath. This paper presents a novel approach to effectively optimizing electrode geometry in resistance furnaces. The method relies on a surrogate criterion derived exclusively from an electromagnetic submodel, which governs the process hydrodynamics. This criterion is based on the location of the Joule heat generation center in the bath. Its idea is to lower this center as much as possible while keeping it close to the vertical bath axis. Owing to this, the best conditions for the development of natural convection were obtained. The developed methodology was demonstrated through an application to a two-electrode furnace. The results showed that the influence of forced MHD convection is negligible in this furnace (with a Lorentz force of only about 0.0015 N/kg). The validation of the optimized geometry, derived using solely the electromagnetic submodel, was carried out using a full process model, including time-consuming hydrodynamic calculations. The proposed optimization methodology enabled a 10-fold increase in the average mixing velocity (from 0.0008 to 0.0084 m/s). The main significance of the presented study is the introduction of a surrogate criterion that allows for a multiple reduction in the time of numerical optimization of the mixing intensity in electrode resistance furnaces in comparison to the standard solution based on the flow velocity criterion determined from the hydrodynamic model.

Melting reactive metals and alloys, such as titanium, poses a significant challenge due to the risk of crucible damage and contamination of the molten material. Full levitation melting presents a promising solution; however, its application has largely been limited to small laboratory samples. This paper introduces a methodology for modeling (in a 2D axisymmetric domain) and optimizing a new large-scale levitation melting system and demonstrates its application to pure titanium. The system features a torus-shaped load positioned within a gutter-shaped coil. Numerical experiments using this approach confirm the feasibility of stable levitation for a substantial mass (2.6 kg) within a newly designed electromagnetic levitation system.

Electromagnetic levitation melting offers the opportunity for the energy-efficient processing of reactive and high-purity metals. This paper concerns a new levitator design that significantly expands the achievable mass of molten metal by processing a toroidal load within a device featuring an annular trough-shaped coil. However, this unconventional arrangement necessitates the optimization of the coil’s geometry and supply current to ensure the stable levitation of the charge. This paper discusses the methodology for such optimization, considering two variants of coil geometry modification. This developed methodology was initially validated using numerical simulation, based on a two-physics, coupled 2D process model, with a 2.6 kg titanium toroidal charge as an example.

Over the past several decades, numerous studies have been published on the topic of electric furnaces used in the reduction processes used for metallic slags

The importance of slag in metallurgy means that issues related to its physicochemical properties and the processes of its formation and movement on the surface of liquid metal are the subject of numerous studies. Two institutes of the Łukasiewicz Research Network have begun collaborating on observing the movement of slag on the metal surfaces using thermal imaging. The results obtained using this method will be used to improve numerical and physical models and optimize metallurgical processes. Initial tests of observing the movement of slag based on recording the change in the position of markers floating on the slag surface with a thermal imaging camera were performed in a laboratory electric arc furnace.

This paper addresses new optimization approaches for resistance furnaces with electrodes for processing molten slag. The thermal and hydrodynamic behavior of the melt is strongly influenced by the Joule heat distribution generated by the electric current flowing between the electrodes, making electrode geometry a key design variable affecting the final process conditions. The aim of this study is to combine two approaches: a surrogate criterion based on process physics and an additional high-level surrogate criterion generated by a Gaussian process. The solutions were validated using a full model of the slag melting process in a dual-electrode furnace, incorporating electromagnetic and hydrodynamic phenomena to evaluate the target criterion—slag mixing intensity. The results confirm the usefulness of the physics-based surrogate criterion, while also revealing limitations of the Gaussian-process layer under nonlinear geometric constraints. Further development of feasibility-aware acquisition strategies and validation on additional benchmark cases is required to establish its broader applicability.