Mathematical modeling of a DC electric arc -: Dimension less representation of a DC arc

A mathematical model presented in previous publications is used to describe fluid flow, heat transfer and electromagnetic phenomena in the arc region of a Direct Current Electric Arc Furnace (DC-EAF). The effects of the arc current and the arc length on the arc characteristics and arc bath interactions are analyzed in a rather generalized way. This analysis leads to the conclusion that the arc behaves in such a way that when the arc shape (defined with the location of the 10 000 K isotherm) is plotted in the appropriate dimensionless form a unique arc expansion is achieved. This unique expansion (only restricted to arcs burned between graphite electrodes in air and outside the region where the arc jet impinges on the bath surface) gives the possibility to provide single dimensionless arc characteristics regardless the values of the arc current and arc length. These dimensionless correlations represent the main finding of this work and they allow means to estimate the important characteristics of the arc under different operational conditions without the need to run complex numerical calculation. The dimensionless characteristics of arc expressed in simple algebraic forms can be used for this purpose employing a pocket calculator.