Electroslag remelting (ESR) is widely used for the production of high-value-added alloys such as special steels or nickel-based superalloys. Because of high trial costs and the complexity of the mechanisms involved, trial-and-error-based approaches are not well suited for fundamental studies or for optimization of the process. Consequently, a transient-state numerical model has been developed that accounts for electromagnetic phenomena and coupled heat and momentum transfers in an axisymmetrical geometry. The model simulates the continuous growth of the electroslag-remelted ingot through a mesh-splitting method. In addition, solidification of the metal is modeled by an enthalpy-based technique. A turbulence model is implemented to compute the motion of liquid phases (slag and metal), while the mushy zone is described as a porous medium the permeability of which varies with the liquid fraction, thus enabling accurate calculation of solid/liquid interaction. The coupled partial differential equations (PDEs) are solved using a finite-volume technique. The computed results are compared to the experimental observation of an industrial remelted ingot; the melt pool depth and shape, in particular, are investigated, in order to validate the model. These results provide valuable information about the process performance and the influence of the operating parameters. In this way, we present an example of a model used as a support in analyzing the influence of the electrode fill ratio.

A Comprehensive Model of the Electroslag Remelting Process: Description and Validation

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.

Review on Modeling and Simulation of Electroslag Remelting

A transient three-dimensional finite-volume mathematical model has been developed to investigate the coupled physical fields in the electroslag remelting (ESR) process. Through equations solved by the electrical potential method, the electric current, electromagnetic force (EMF), and Joule heating fields are demonstrated. The mold is assumed to be conductive rather than insulated. The volume of fluid approach is implemented for the two-phase flow. Moreover, the EMF and Joule heating, which are the source terms of the momentum and energy sources, are recalculated at each iteration as a function of the phase distribution. The solidification is modeled by an enthalpy-porosity formulation, in which the mushy zone is treated as a porous medium with porosity equal to the liquid fraction. An innovative marking method of the metal pool profile is proposed in the experiment. The effect of the applied current on the ESR process is understood by the model. Good agreement is obtained between the experiment and calculation. The electric current flows to the mold lateral wall especially in the slag layer. A large amount of Joule heating around the metal droplet varies as it falls. The hottest region appears under the outer radius of the electrode tip, close to the slag/metal interface instead of the electrode tip. The metal pool becomes deeper with more power. The maximal temperature increases from 1951 K to 2015 K (1678 °C to 1742 °C), and the maximum metal pool depth increases from 34.0 to 59.5 mm with the applied current ranging from 1000 to 2000 A.

A General Coupled Mathematical Model of Electromagnetic Phenomena, Two-Phase Flow, and Heat Transfer in Electroslag Remelting Process Including Conducting in the Mold

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.

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A Dynamic Mesh-Based Approach to Model Melting and Shape of an ESR Electrode

In the ESR process, it is very difficult to make experimental observations of the phenomena occurring within the molten slag. At present, the state of the process is solely evaluated from the variation of the measured electric variables. The present paper proposes the use of 3D numerical model to explore the complex coupling existing between the electrodynamics and the phase distribution during the process. The droplet formation during melting of an electrode under the action of a strong DC current is simulated with a multiphase-magnetohydrodynamic approach. A volume-of-fluid approach is used for the interface tracking, and the potential formulation is used to determine the electric and magnetic fields. The Lorentz force and the Joule heating are recalculated at each time step as a function of the phase distribution. The evolution of the electric resistance of the system during the droplet formation and departure is reported. The results are compared with the measurements made in experimental and industrial-scale ESR processes. Two values of metal/slag interfacial tension of 1 and 0.1 N m � 1 are explored. The effects of the control system as well as the presence of a horizontal magnetic field are also investigated. These results open the possibility to link online the voltage signal variation with real physical phenomena happening during the process.

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Simulation of the Electric Signal During the Formation and Departure of Droplets in the Electroslag Remelting Process

The paper is based on the development and use of a mathematical model that simulates the electroslag remelting (ESR) operation. The model assumes axisymmetrical geometry and steady state. Maxwell equations are first solved to determine the electromagnetic forces and Joule heating. Next, coupled fluid flow and heat transfer equations are written for the two liquids (slag and liquid metal). Thek-e model is used to represent turbulence. The system of coupled partial differential equations is then solved, using a control volume method. Using the operating parameters as inputs, the model calculates the current density, velocity, and temperature throughout the fluids. This paper is concerned with fluid flow and heat transfer in the slag phase. After being validated by comparing its results with experimental observation, the model is used to evaluate the influence of operating variables, such as the fill ratio, and the thermophysical properties of the slag.

A. Jardy

Papers

Magnetohydronamic and thermal behavior of electroslag remelting slags