Fast Numerical Optimization of Electrode Geometry in a Two-Electrode Electric Resistance Furnace Using a Surrogate Criterion Derived Exclusively from an Electromagnetic Submodel

The Joule heat generated by current flow between electrodes in a resistance furnace not only melts and heats the charge but also induces mixing of the molten material. Increased mixing promotes improved chemical and temperature uniformity within the bath. This paper presents a novel approach to effectively optimizing electrode geometry in resistance furnaces. The method relies on a surrogate criterion derived exclusively from an electromagnetic submodel, which governs the process hydrodynamics. This criterion is based on the location of the Joule heat generation center in the bath. Its idea is to lower this center as much as possible while keeping it close to the vertical bath axis. Owing to this, the best conditions for the development of natural convection were obtained. The developed methodology was demonstrated through an application to a two-electrode furnace. The results showed that the influence of forced MHD convection is negligible in this furnace (with a Lorentz force of only about 0.0015 N/kg). The validation of the optimized geometry, derived using solely the electromagnetic submodel, was carried out using a full process model, including time-consuming hydrodynamic calculations. The proposed optimization methodology enabled a 10-fold increase in the average mixing velocity (from 0.0008 to 0.0084 m/s). The main significance of the presented study is the introduction of a surrogate criterion that allows for a multiple reduction in the time of numerical optimization of the mixing intensity in electrode resistance furnaces in comparison to the standard solution based on the flow velocity criterion determined from the hydrodynamic model.