Modelling of Electric Arcs for Industrial Applications, a Review

Electric arcs are a necessary heat source in many industrial processes that take place in Submerged Arc Furnaces (SAFs). Arcs exhibit non-linear electrical characteristics and behave in a complex manner. Therefore, an improved understanding of their behaviour enables better control of furnace operation. Modelling of industrial arcs is a multiphysics process that involves simultaneously solving several coupled physical phenomena, such as electromagnetics, fluid dynamics and heat transfer, including a radiative heat transfer from the plasma arc. Coupling fluid dynamics and electromagnetics is known as Magnetohydrodynamics (MHD). There are also simpler approaches to arc modelling, either based on simplified physical principles or empirical behaviour. A number of MHD models for electric arcs have been presented in the literature, but most of them involve simplifications such as axial-symmetry to reduce the simulation time, pertain to currents much lower than for industrial arcs, focus on DC arcs rather than arcs carrying AC current or do not have the plasma properties of the actual gas in the furnace. In a recently started project, the ambition is to create a full-scale 3D MHD model for an industrial AC arc at the conditions to be found in Si-metal furnaces. As much can be learned from previous arc modelling, this paper will review different arc modelling approaches and develop a classification framework to categorize the modelling methods, both the more intricate MHD models as well as the simpler modelling approaches. Among the available simplified models, one will be selected and coupled with a submerged arc furnace electrical circuit model. The complete circuit model parameters such as resistances and inductances are updated using a 3D submerged arc furnace that has been developed in ANSYS Maxwell using an eddy current solver.