Mathematical modeling of a direct current electric arc: Part I. Analysis of the characteristics of a direct current arc

Abstract

A mathematical model is used to describe fluid-flow, heat-transfer, and electromagnetic phenomena in the arc region of a direct current electric arc furnace (DC EAF). Based on those model results, a detailed physical analysis of the arc was performed, where the numerical computations help to explain the arc structure, its behavior, and the highly coupled relationship among their main physical variables. This analysis leads to the conclusion that the arc behaves in such a way that all the arc characteristics are controlled by the expansion of the arc, which is the main feature used to physically describe the arc behavior. The arc expansion is evident from the arc shape, which is defined as the region where conduction of electricity takes place. The arc shape is clearly seen in several contour fields presented in this work, such as the current density, the magnetic flux density, the electric conductivity, the electric potential, and the temperature fields. The results of this article focus on process analysis, to provide insight into the inter-relationship among the arc variables, and to establish physical grounds to subsequently explore dimensionless analytical representations to describe the arc behavior.