Mathematical modeling of D.C. electric arc furnace operations

Abstract

A fundamental study of the Direct Current Electric Arc Furnace (DC-EAF) for steel-making has been carried out through the development of a rigorous mathematical model. The mathematical representation involves the simultaneous solution of Maxwell's equations for the electromagnetic fields, and the turbulent fluid flow and heat transfer equations. In solving the arc and bath regions it was assumed ( and justified) that the arc-bath interactions are dominated by the behavior of the arc. In contrast to previous modeling investigations, this work relaxes some critical assumptions and provides a more realistic and comprehensive representation of the system. This work also examines and compares the relative merits of alternative electromagnetic and turbulence formulations, and addresses the role of induced currents and compressibility effects in the representation of the arc. Furthermore, due allowance was made to represent and analyze the effect of gas injection, the presence of a slag layer in the bath and changes in anode configuration at the bottom of the reactor. Because of a lack of experimental information on actual or pilot plant DC-EAF systems, different aspects of the model were validated using several sources of experimental data reported in the literature for related systems. These included measurements on welding arcs, laboratory scale high-intensity carbon arcs, electromagnetically driven metallic systems, and ladle metallurgy physical models. It was found that, in general, the agreement between measurements and predictions was good. A detailed analysis was carried out to examine the effect of process parameters (e.g., arc current, arc length, bath dimensions, anode arrangements, etc) on the behavior of the furnace (e.g., heat transfer to the bath, heating efficiency, mixing times in the bath, etc). Predictions from the arc model show that all the arc characteristics are strongly coupled and that the arc physics is governed by the expansion of the arc. From a parametric study it was found that when the arc region (defined by the 10,000 K isotherm) is plotted in dimensionless form, a universal shape for the arc can be defined, regardless of the values of arc current or arc length. This universality was restricted to the range of conditions analyzed in this thesis, to arcs struck between graphite cathodes in air, and does not include the jet impingement region on the bath surface. This common arc expansion behavior suggested the universal nature of other arc characteristics. Universal maps of temperature, magnetic: flux density, and axial velocity are also reported in terms of simple analytical expressions. The practical effects of the two main process parameters of the arc region,. i.e. the arc current and the arc length, were analyzed. It was found that increasing the arc length significantly increases the arc resistance and, consequently, the arc power, although this behavior reached asymptotic values at larger arc lengths. Increasing the arc current, however, does not affect the arc voltage. Thus, it is found that increasing the arc power increases the amount of energy transferred into the bath, but the heat transfer efficiency decreases. Therefore, the shorter the arc the more efficient is the heat transfer to the bath. It is also recognized that heat transfer from the arc to the bath is controlled by convection, although radiation can become an important mechanism, especially for large arc lengths. Results of the bath model indicate that, in the absence of inert gas stirring and with no slag present in the system, electromagnetic body forces dominate and are responsible for the fluid flow patterns in the system. The effects of the arc determine the distributions of temperature and other mixing characteristics in the bath. The bath model was used to evaluate the effect of the main process parameters and design variables on mixing, refractory wear, temperature stratification, and heat transfer efficiency. An increase in the arc length is detrimental to mixing but increases the rate of heating in the melt as a result of the increased arc power. Increasing arc current improves mixing and the heat transferred to the bath, but is likely to be detrimental to the life of the bottom refractory. The results also suggest that high furnace aspect ratios (taller and thinner arc furnaces) are highly recommended because an increase in the aspect ratio increases mixing, prevents refractory wear, and promotes arc heating efficiency. The arc configuration in the furnace can be changed to control fluid flow patterns in the bath to meet specific needs, such as better mixing, or to prevent refractory wear. The presence of a top layer of slag reduces mixing and increases overall liquid temperatures. Injection of gases through the bottom in eccentric operations generates complex flow patterns that improve mixing in regions away from the symmetry axis. It is the author's belief that this model is a useful tool for process analysis in the DC-EAF. It has the capability to address many issues of current and future concern and represents one component of a fundamental approach to the optimization of DC-EAF operations.