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.

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.

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.

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In order to simulate the mold filling and solidification of the outer shell of large work rolls being cast by horizontal centrifugal casting, the shallow water equations were adopted to solve the 2D average flow dynamics of the melt spreading inside the cylindrical mold. The model accounts for centrifugal force, Coriolis force, shear force, gravity and convective and diffusive energy transport. The solidification front was tracked by fulfilling the Stefan condition. Radiative and convective heat losses were included from both, the free surface and the outer wall of the mold. By introducing a stochastic factor to account for the irregular filling jet behavior an uneven spreading of liquid from the center of the mold towards the extremities was predicted. Thus, the formation of the first solid layer also happens unevenly. However, when the mold is covered everywhere with a solid layer, the solidification rate decreases and further filling increases the height of the liquid layer. With increase liquid height the amplitude of the free surface waves also increases.

Two mathematical approaches have been compared for modeling the electrical behavior (e.g., electric/current density field) of an electrolyte. The first approach uses the traditional Ohmic method (Laplace equation) based on the assumption of a uniform concentration of ions in the electrolyte. The second approach utilizes the ionic transport method that takes into account the effect of electrochemical transport/reaction of ions assuming a quasi-electro neutral bulk for the electrolyte. For the latter, the PoissonNernst-Planck (PNP) equations are employed to include impacts of the non-uniformity of the concentration of ions on the electrical pattern of the electrolyte. Demonstratively, a 2D case was studied. It comprises two unequally sized electrodes, which are separated by the electrolyte. Findings show that the electrical behavior of the electrolyte remains unchanged using an Ohmic approach, regardless of variations in operational parameters such as applied voltage and electrode polarity. In contrast, the electrical behavior in response to the operational parameters is found to be significantly influenced using the ionic transport approach. Therefore, Ohm's law is invalid in the bulk of an electrolyte, when a non-uniform concentration field of ions exists. Ultimately, the obtained results helped to propose an explanation on a commonly observed phenomenon (melt rate-polarity relationship) during the DC operation of the electroslag remelting (ESR) process.

Field structures including electromagnetic, concentration of ions, and flow fields in an ESR-like process composed of a graphite crucible containing a molten slag, air, and an iron electrode are computed. Both CaF 2-(mass pct 2) CaO and CaF 2-(mass pct 2) Al 2 O 3 slags are examined. Tertiary current distribution is calculated. Therefore, polarization overpotential and Faradic reactions at metal-slag interface are considered using Tafel law, whereas transport of ions in the bulk of slag is determined through Nernst-Planck equations. The main goal is to shed light on the invisible phenomena such as magnetohydrodynamics caused by transport of ions, electrical conductivity of CaF 2-based slag using additives (e.g., CaO or Al 2 O 3), and the role of complexation of ions (e.g., AlO 3À 3) in the molten slag applied to the ESR. An explanation is given for the observation of higher oxygen content in the metal using Al 2 O 3 than that using equivalent amount of CaO in the CaF 2-based slag of a DC-operated ESR.