Mathematical modeling of a direct current electric Arc:: Part II:: Dimensionless representation of a direct current arc

A mathematical model presented in Part I of this work is used to describe fluid-flow, heat-transfer, and electromagnetic phenomena in the arc region of a direct current electric arc furnace (DCEAF). From the analysis of the system, the effects of the arc current and the arc length on the arc characteristics and arc bath interactions can be represented analytically in a rather generalized way, based on the finding that the arc shape is unique (defined with the location of the 10,000 K isotherm) when plotted in the appropriate dimensionless form. This dimensionless arc expansion (only restricted to arcs burned between graphite electrodes in air and outside the region where the are jet impinges on the bath surface) gives the possibility to derive a unique arc description regardless of the values of the arc current and arc length. Dimensionless correlations representing the relationships among important arc characteristics and arc-bath interactions are derived in this work. These expressions may be used to estimate process variables without the need to run complex numerical calculation.