Coupled electro-thermal-flow model for very long electric arcs

A mathematical model that couples the electrical potential in the arc with the resulting thermal and flow fields has been developed to describe the behaviour of the arc plasma in a DC electric arc furnace. The set of conservation equations, along with a potential equation for the electric field, were solved using the PHOENICS software package. Key aspects of the modelling problem, necessary to achieve a stable and meaningful numerical solution for the long DC electric arc, are evaluated. These aspects involve convergence issues as well as the treatment of the nonlinearities. Particular attention was given to the selection and adjustment of several under-relaxation factors.