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

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.