Mathematical Modeling of a DC Electric Arc-Dimensionless Representation of a DC Arc

Abstract

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.

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

“…Some of these results have been published previously. [10] The analysis and Fig. 1-Arc shape expressed in dimensionless form.…”

“…Here, only a brief summary of these fitted expressions are presented since they were published elsewhere. [10] As mentioned previously, Table I shows a summary of some dimensionless correlations used to describe in a rather general way some of the most important arc characteristics. A detailed explanation of each equation and the methods used to obtain these correlations can be found in Reference 10, and the List of Symbols in this article can be consulted to understand the meaning of each variable included in the table.…”

“…The work presented here is based on the model presented in Part I and it builds upon preliminary dimensionless correlations presented elsewhere, [10] in an attempt to provide simple analytical means to describe the behavior of DC EAF systems, regarding both the arc region and the arc-bath interactions. The correlations are the results of many simulations carried out using the model presented in Part I of this series of the article.…”

Dimensionless representation of the column characteristics and weld pool interactions for a DC argon arc

“…The arc shape can then be expressed as: The value of the offset is z = 0.9310 R c , which can be expressed as the rule of thumb that the vertex of the parabola lies inside the electrode at a depth equal to the radius of the cathode area. Several authors have proposed similar arc shapes by a quadratic behaviour of the arc radius as a function of the axial distance [17,24], but Equation (2) describing the arc radius has not been proposed before.…”

General expressions for heat distribution, pressure, and current density in argon welding arcs

“…Ramírez-Argáez et al [18] developed an Electric Arc Furnace (EAF) dimensionless representation in a steelmaking process with simple equations. The physics of both arcs (welding and EAF) are almost the same, but the flow regime of the arcs in EAF is turbulent, while in welding, the flow regime is laminar.…”