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Dynamics of electromagnetic forces rejecting arcs from verticals in a three-phase arc furnace
Abstract
Knowledge of the nature and behavior of forces acting on an arc is important when designing furnaces, controlling and automating their work. The effect of electromagnetic arc blowing has a negative effect on technical and economic indicators of the furnace, since the arc is removed from dimples in metal and slag. Radiation of the arc on walls and arch increases. And the effective power absorbed by the metal decreases. For this and a number of other tasks, it is necessary to know the dynamic behavior of the arc, which is largely determined by the instantaneous values and directions of the individual forces and the resultant force. The paper discusses the behavior of an electromagnetic force acting on an arc column from currents flowing through a liquid metal and currents flowing through other parallel arcs and graphitized electrodes in a three-phase AC arc furnace. It was assumed that the arcs burn perpendicular to the surface of the metal bath (their axes coincide with the axes of the electrodes) and effective value of the linear currents in different phases is the same. A mathematical model is proposed for calculating the instantaneous values and directions of the main electromagnetic forces acting on arcs in a three-phase arc furnace, allowing to reveal the nature of arcs dynamic behavior. A computer program has been created that makes it possible to visualize the behavior of a hodograph of forces acting on an arc. Hodographs of forces acting on the arc from the currents flowing through the melt are shown; they are ellipses lying in a horizontal plane. The resulting force deflecting an arc is also an even harmonic function with a frequency twice as high as the industrial frequency of the current. Its hodograph is an ellipse lying in a horizontal plane, the big semi-axis of which makes an angle of 20 – 80° with a line connecting the center of decay of the electrodes and the electrode axis.
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Results
of analytically studied effect of electromagnetic blowing and the slag height
on the arc efficiency are stated. An arc is blown from under an electrode
toward the furnace walls under an electromagnetic force, arc radiation on the
wall and roof increase and effective output, absorbed by the metal decreases.
EAF (electric arc steel melting furnace) with independently powered arcs,
eliminating its electromagnetic blowing is proposed. When arcs are powered
independently, its efficiency increases significantly, and specific energy consumption
decreases.
The effect of electromagnetic blowing and the slag layer height on the arc efficiency is analytically studied. An arc is blown from under an electrode toward the furnace walls under an electromagnetic force. The arc efficiency of a 100-t high-power electric arc furnace changes from 0.47 to 0.76 when the slag height increases from 0 to 550 mm.
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.
AC electric arc furnaces (EAFs) highly reduce power quality of the network by generating disturbances such as flicker and harmonics. These disturbances are due to the nonlinear electromagnetic and thermal field behaviors of the AC arcs. Analysis of these nonlinear behaviors is required for improving power quality in the network. This paper presents a three-dimensional finite element modeling of the electromagnetic fields in an AC three-phase electric arc furnace. The model includes the electrodes, arcs and molten bath. Current density, voltage and magnetic field intensity in the arcs, molten bath and electrodes are predicted as a result of applying the three-phase AC voltages to the EAF. This model does not consider the instantaneous geometry of the arc, instead a constant geometry, which is adjacent to the geometry of a DC arc with a DC current equal to the RMS value of the current waveform, is considered. Electromagnetic field of the AC arc in the time-domain is also modeled using the three-dimensional finite element method.
Use of twin-electrode DC arc furnaces for the purposes of smelting is a growing trend in the research being performed at Mintek. Even though twin-electrode furnaces add complexity to aspects of the mechanical design of the furnace roof and electrode mechanisms (as well as power supply configurations and control systems), the design and operational advantages gained in moving to dual electrodes are significant.Some small-scale testwork on a twin-electrode furnace was performed at Mintek in late 2003, with the aim of enabling direct observation of the plasma arcs and their interactions both with each other and the molten slag bath beneath them. Still and video photography of the twin arcs was performed. The results are presented here, along with some theoretical exploration.The arc trajectory is shown to follow a circular path, with the radius of curvature being directly proportional to the electrode separation, and approximately independent of electrical variables such as current.The influence of the arc deflection on the true arc length, and the dependence of arc voltage on electrode height have been calculated.
Purpose
The purpose of this paper is to present a 3D finite element model of the electromagnetic fields in an AC three‐phase electric arc furnace (EAF). The model includes the electrodes, arcs, and molten bath.
Design/methodology/approach
The electromagnetic field in terms of time in AC arc is also modeled, utilizing a 3D finite element method (3D FEM). The arc is supposed to be an electro‐thermal unit with electrical power as input and thermal power as output. The average Joule power, calculated during the transient electromagnetic analysis of the AC arc furnace, can be used as a thermal source for the thermal analysis of the inner part of furnace. Then, by attention to different mechanisms of heat transfer in the furnace (convection and radiation from arc to bath, radiation from arc to the inner part of furnace and radiation from the bath to the sidewall and roof panel of the furnace), the temperature distribution in different parts of the furnace is calculated. The thermal model consists of the roof and sidewall panels, electrodes, bath, refractory, and arc. The thermal problem is solved in the steady state for the furnace without slag and with different depths of slag.
Findings
Current density, voltage and magnetic field intensity in the arcs, molten bath and electrodes are predicted as a result of applying the three‐phase AC voltages to the EAF. The temperature distribution in different parts of the furnace is also evaluated as a result of the electromagnetic field analysis.
Research limitations/implications
This paper considers an ideal condition for the AC arc. Non‐linearity of the arc during the melting, which leads to power quality disturbances, is not considered. In most prior researches on the electrical arc furnace, a non‐linear circuit model is usually used for calculation of power quality phenomena distributions. In this paper, the FEM is used instead of non‐linear circuits, and calculated voltage and current densities in the linear arc model. The FEM results directly depend on the physical properties considered for the arc.
Originality/value
Steady‐state arc shapes, based on the Bowman model, are used to calculate and evaluate the geometry of the arc in a real and practical three‐phase AC arc furnace. A new approach to modeling AC arcs is developed, assuming that the instantaneous geometry of the AC arc at any time is constant and is similar to the geometry of a DC arc with the root mean square value of the current waveform of the AC arc. A time‐stepping 3D FEM is utilized to calculate the electromagnetic field in the AC arc as a function of time.
This paper presents a 3D numerical modeling of electromagnetic and thermal fields in three-phase electric arc furnaces. The thermal effect of the foamy slag is studied in the first part of the paper. The Joule power density is calculated with an AC electromagnetic analysis and is transferred to the steady state thermal problem as heat source. The second part of the paper presents a numerical analysis of new electromagnetic stirring methods.
The two most likely causes of electromagnetic instability in
electric furnace arcs are shown to be the kink and the fire-hose
instabilities. Stabilization by an externally imposed axially magnetic
field is analyzed, and experimental results are presented demonstrating
stabilization of a small, pulsed test arc by this method
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