Modeling of an Ensemble Averaged Electric Arc in a Laboratory-Scale Electric Arc Furnace
This work, which is done in the framework of the SisAl Pilot EU project, presents the use of the COMSOL Multiphysics® software for simulating an ensemble averaged electric arc in a laboratory-scale electric arc furnace. The SisAl Pilot project aims at optimising the silicon production in Europe by recycling materials and using a carbon-emission friendly technology. The silicon production experiments are conducted on laboratory and pilot scales in different types of furnaces, including electric arc furnaces (EAF). Besides experimental work, the process optimisation also relies on the numerical modelling. The present model simulates the furnace preheating and the initial slag melting in a laboratory-scale EAF, in which a DC electric arc operates between a graphite cathode and the anode formed by a thin layer of slag at the bottom of the graphite crucible. The main difficulty is associated with modelling the heat source due to the electric arc operation. There are various complex physical processes involved in the arc, including the plasma physics, induced high-velocity gas flow, and radiant and convective heat transfer towards the electrodes and the crucible. The channel-arc model is a commonly used approach for a simplified 0D simulation of the electric arc behaviour in a variety of applications. Being used in this model, it estimates the temperature and gas velocity in the arc column. At each moment in time, this 0D model provides an instantaneous spatial distribution of heat sources in the furnace relative to an immediate arc position. Additional modelling complication stems from the fact that the instantaneous electric arc is constantly changing its position on a very short time scale by jumping from one place to another. On average, it occupies the whole space under the graphite cathode. Thus, an ensemble averaging of the arc position is performed to obtain integral expressions of the averaged arc radiation and of the averaged Lorentz force that drives the gas flow in the plasma region. These integrals are evaluated in part analytically, and in part numerically. The experimentally measured electric potential difference and dissipated power are used as model input parameters. The following COMSOL® physics interfaces are employed in this model: Heat Transfer in Solids and Fluids with phase change, Turbulent Flow k-ε model in gas and liquid slag phases, Surface-to-Surface Radiation, Electric Currents to simulate the Joule effect in electrically conducting materials, Deformed Geometry to simulate variable electric arc shape, and Global and Domain ODEs to compute quantities associated with the ensemble averaging of the electric arc. A bidirectional coupling of all the interfaces is present due to multiple interdependencies. The averaging of the arc position helps to deconcentrate and redistribute heat sources, which results in plausible material temperatures and demonstrates the expected initial slag melting. The model can be further used to optimize furnace operation in terms of predicting possible thermal damages or heat losses and increasing the raw material melting efficiency. The presented ensemble averaging approach can be applied to other electric arc problems with a similar geometry.
