Skin and Proximity Effects in Electrodes and Furnace Shells
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A review of two-dimensional (2D) analytical models of skin and proximity effects in large industrial furnaces with three electrodes arranged in an equilateral triangle is given. The models cover three different cases: one electrode only, three electrodes where two are approximated by line currents, and induced shell currents where all electrodes are approximated by line currents. The first two models show how the skin and proximity effects depend on electrode material properties and size, and the distance between the electrodes. The third model shows how the strength of the induced shell currents will depend on electrode position and furnace size. These models are compared to numerical studies including distributed electrodes and shell currents. The analytical models are accurate when induced shell currents can be disregarded. However, strong shell currents may have a significant impact on the current distribution within the electrodes. This electrode-shell proximity effect competes with the electrode-electrode proximity effect. Finally, the 2D models have been compared with three-dimensional (3D) case studies of large industrial furnaces. In 3D, the shell currents are significantly smaller than what are predicted by the 2D models, but they are sufficiently strong to cause a significant correction of the electrode current density. https://doi.org/10.1007/s11663-019-01651-8 The Author(s) 2019
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INTRODUCTION
IN many metal-producing units, the energy needed for the primary reactions are delivered by electric currents through large electrodes. Examples of such units are slag resistance furnaces and electric arc furnaces, used in the production of steel, ferroalloys, calcium carbide and silicon.[1,2] Typically, three-phase alternating current (AC) circuits using three or more electrodes are used, operating at the grid frequency of 50 or 60 Hz. Correct and stable operation of the electrodes is of crucial importance for successful and cost-effective operation of the furnace.[3,4] Detailed understanding of current densities, thermal conditions and mechanical stresses is needed to address electrode problems such as electrode breakages and electrode consumption.[5–7] Also, for designing the furnace and for understanding its process, the current-carrying capabilities and sizing of the electrode play an important role.[8–10] EGIL VA˚LANDSMYR HERLAND is with NORCE Norwegian Research Centre AS, Universitetsveien 19, 4630 Kristiansand, Norway and also now with Elkem ASA Technology, Fiska˚veien 100, 4621 Kristiansand, Norway. MANUEL SPARTA and SVENN ANTON HALVORSEN are with NORCE Norwegian Research Centre AS. Contact e-mail: [email protected] Manuscript submitted January 28, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS B
The electrodes are made of electrically conductive graphite or baked carbon material, and their main function is to carry the electric currents needed for powering the chemical reactions of the process. Although direct current (DC) furnaces can be found in the industry, most units use AC current, and in AC ele
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