The Electroslag Remelting (ESR) is an advanced technology for the production of high quality materials, for example, hot work tool steels or nickel base alloys. In the past years, several models are developed aiming to predict the way in which the operational parameters affect the structure and chemical composition of the final ESR ingot. Proper modeling of this process depends on the ability of the model to predict the Multiphysics resulting from the complex coupling between many physical phenomena. This review includes the main findings starting from the 1970's, with a special focus on the results obtained in the period of 1999-2017. The difficulties related to the poorly known physical properties of ESR slags are discussed. Then, the main achievements in the field of electromagnetism, fluid flow, heat transfer, and solidification are also summarized. The review finishes by presenting the special topics representing the actual scientific frontiers, such as the physics of mold current, the importance of multiphase phenomena, and the difficulties in predicting the electrode melting rate.

This paper presents a numerical method to investigate the shape of tip and melt rate of an electrode during electroslag remelting process. The interactions between flow, temperature, and electromagnetic fields are taken into account. A dynamic mesh-based approach is employed to model the dynamic formation of the shape of electrode tip. The effect of slag properties such as thermal and electrical conductivities on the melt rate and electrode immersion depth is discussed. The thermal conductivity of slag has a dominant influence on the heat transfer in the system, hence on melt rate of electrode. The melt rate decreases with increasing thermal conductivity of slag. The electrical conductivity of slag governs the electric current path that in turn influences flow and temperature fields. The melting of electrode is a quite unstable process due to the complex interaction between the melt rate, immersion depth, and shape of electrode tip. Therefore, a numerical adaptation of electrode position in the slag has been implemented in order to achieve steady state melting. In fact, the melt rate, immersion depth, and shape of electrode tip are interdependent parameters of process. The generated power in the system is found to be dependent on both immersion depth and shape of electrode tip. In other words, the same amount of power was generated for the systems where the shapes of tip and immersion depth were different. Furthermore, it was observed that the shape of electrode tip is very similar for the systems running with the same ratio of power generation to melt rate. Comparison between simulations and experimental results was made to verify the numerical model.

A full 3D simulation of an industrial scale electroslag remelting (ESR) process (f 750 mm ingot) is performed, and results are verified by experiment. A typical non-axis symmetry flow pattern and temperature field in the slag region is demonstrated. A statistical analysis of the turbulent flow in the slag and melt pool is performed to quantitatively characterize the transient behavior of the flow. By comparing the 3D calculation with a 2D axis-symmetrical calculation, we find that the predicted shape of melt pool (profile of the solidifying mushy zone of the ingot) are quite similar, leading to the conclusion that a 2D calculation is sufficient to solve the melt pool profile of the ingot.

Electrochemical reactions always occur at the electrode–slag and slag–metal melt interfaces during the electroslag remelting (ESR) process. However, those reactions together with the ion transport phenomenon in the molten slag region are still poorly understood. A numerical model considering both the ion transport and the electrochemical reactions is demanding. For this purpose, a numerical model is proposed. The ion transport is modeled by solving the Poisson–Nernst–Planck (PNP) equations, while the kinetics of the reaction at the slag–metal interface is modeled with the well‐known “Butler–Volmer” formula. Demonstratively, a one‐ dimensional case is calculated: a DC electric current is applied to a molten multi‐ion slag (CaF2–FeO) between the anode and the cathode. The modeling results show that the redox reaction occurs only for the ferrous ion (Fe2+), not for other ions at low current density (<2 kA m−2), which was verified experimentally. We also find that formation of ferric iron (Fe3+) or discharge of calcium at large current density (>5 kA m−2) may not take place, although some researchers have proposed such a hypothesis. Therefore, further research steps are suggested to verify this point so that the model is fully applicable for the industrial ESR process.

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