A Comprehensive 3D Mathematical Model of the Electroslag Remelting Process

A comprehensive 3D mathematical model was proposed to predict the electromagnetic field, the multiphase flow field, the temperature field, and the pool profile of an industrial electroslag remelting (ESR) system. Especially, the metal droplets formation and falling in the slag pool during the ESR process are taken into account using the volume of fluid method. In addition, the electromagnetic and solidification phenomena are modeled using the magnetic vector potential method and the enthalpy-porosity method, respectively. The predicted results were found to be in good agreement with experimental measurements, regarding the magnetic flux density, the pool profile, the energy consumption, and the melt rate. And the model developed in the present work has been proved to be a powerful tool to provide a useful insight into the multi-physical phenomena in the ESR system. The results show that the Joule heating is mainly distributed in the slag pool due to the lower electrical conductivity of slag, and provides the thermal energy for melting the electrode. The molten metal on the conical electrode surface is washed away by the Lorentz force and the gravity force and gradually accumulates at the electrode tip. When the drop at the electrode tip reaches the critical size, the small droplets form due to the necking effect and depart from the conical electrode tip. In the slag pool, there are two axisymmetric vortexes with downward flows under the conical electrode tip, where the Lorentz force and the falling droplets are dominant, and another two axisymmetric vortexes with downward flows near the mold surface, where the thermal buoyancy is dominant. However, in the metal pool, there are only two vortexes with downward flows at the solidification front, where a high thermal gradient exists. The slag is significantly hotter and more uniform than the metal, because of an abundant of Joule heating and intensive turbulence in the slag pool. The molten metal is directionally solidified in the water cooling copper mold and the pool profile is a shallow U-shape for the industrial scale ESR process with the ingot diameter of 360 mm, when the applied current density and frequency are 8000 A and 50 Hz, respectively.