Modeling of fluid flow and heat transfer in the plasma region of the dc electric arc furnace
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I.
INTRODUCTION
ELECTRIC arc furnace steelmaking is responsible for approximately 45 pct of the steel produced in the United States. This figure is likely to grow in coming years with the advent o f tighter economic and environmental constraints facing other types of furnaces. Electric arc steelmaking consumes about 500 kWh/ton of steel produced and is responsible for the consumption of 1.6 X 109 kWh of energy annually. As with most industrial processes, the ultimate goal of an electric furnace shop is to maximize production while minimizing cost. This means maximizing the energy input to the steel. If an average sized company can decrease its electrical energy consumption, a significant saving can be achieved. Most of the existing electric arc furnaces are operated with alternating current (ac). There is renewed interest in direct current (dc) furnaces, t91 The dc arc furnaces provide reduced graphite and power consumption, lower noise, and greater reduction of flicker effects. To assess the performance characteristics of a typical dc electric arc furnace, a mathematical model was developed based on the equations of conservation of mass, momentum, and energy and the Maxwell equations of the electromagnetic field. The mathematical model is solved numerically to calculate the velocity and temperature distributions in the plasma region and heat transfer from the arc to a rigid anode surface. The model was applied to obtain quantitative results on the relative importance of the various modes of heat transfer from the electric arc to the anode surface. Three important aspects addressed by the present model are as follows: (1) generation of the high-velocity, high-temperature cathode jet; (2) interaction of this jet with the anode surface, i.e., heat
F. QIAN, Graduate Student, and B. FAROUK, Professor, are with the Mechanical Engineering and Mechanics Department, and R. MUTHARASAN, Professor, is with the Chemical Engineering Department, Drexel University, Philadelphia, PA 19104. Manuscript submitted December 27, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS B
and momentum transfer across the plasma metal interface; and (3) energy efficiency of the electric arc furnace. Unlike previous studies, t121 in this article we do not assume or use empirical estimates of arc shapes. Instead, the arc shape is a result of solving governing equations. Maxwell equations are solved by introducing the electrical potential and by considering electrical conductivity to be a function of temperature. A rigid anode surface is considered for ease of analysis. II.
BACKGROUND
Szekely and McKelligetB3~ developed a mathematical representation for fluid flow and heat transfer in the cathode region of high-intensity carbon arcs through the simultaneous calculation of simplified forms of the Maxwell equations, the turbulent Navier-Stokes equations, and the differential thermal energy balance equation. The shape of the electric arc radius was considered to be known to simplify the analysis. The predicted electric fields were compared with semi
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