An extended two-dimensional mathematical model of vertical ring furnaces
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I.
INTRODUCTION
R I N G furnaces are widely used in the aluminum industry for the baking of carbon electrodes. They can be of the horizontal or vertical type. The authors have acquired previously extensive experience in the mathematical modeling of the horizontal furnace, t~-4~ Furthermore, in 1990, a first model of the vertical furnace was elaborated5si The geometrical arrangement of this type of furnace is significantly different from that of the horizontal type. Figure t describes a typical fire train consisting of three fire ramps, three cooling and four preheat sections. The gas flow is from right to left, while the fire group equipment is moved one section ahead in the same direction at each fire cycle. Figure 2 gives the details of a section illustrating four different zones: the head wall and fire shaft, the underlid, the pit, and the tmderpit zones. The fuel combustion takes place in the fire shafts. The hot gases leave the fire shaRs, mix with infiltrated air, and exchange heat with the upper part of the furnace (lid) before they ftow down in more than a hundred separate vertical ducts along the brick holes which are uniformly distributed among the pits. In the pits, the gases exchange heat with the brick wails enclosing the coke covered anodes before reuniting in the underpit region. As they pass the pillars in the underpit region, they exchange heat with the solids before entering the next fire shaft downstream. While the electrodes are heated, volatiles (mainly tar, methane, and hydrogen) escape from the solid mass and enter the low pressure flue duet where they burn. The 1990 model was two-dimensional (2-D) (y and z in Figure 2). Assumption was made that the solid temperatures and the gas flow were uniform across a section of the furnace (along the transverse plane normal to the overall gas flow), and as a result, the model was unable to predict nonuniform baking in that direction. In this work, the model is improved by taking into account the variations in solid tern-
S. PETER, Research Professional, and A. CttARETTE and R.T. BUI. Proti~ssors of Engineering, are with the Department of Applied Sciences, University. of Quebec at Chieoutimi, Chicoutimi, PQ, Canada G7H 2BI. A. TOMSETT, Senior Research Scientist, Cornalco Research Center, Carbon Products. M.R.U., Thomastm,,-n 3074, Australia. V. POTOCNIK, Consultant, is with the Department of Reduction. Alean International Ltd., Jonquirre, PQ, Canada G7S 4K8. Manuscript submitted April 12, 1995. METALLURGICAL AND MATERIALSTRANSACTIONS a
peratures across the furnace considering three subcontrol volumes in the pit zone (extended 2-D + model). The effect of uneven gas flow distribution in these subcontrol volumes on anode temperatures is also determined. The same authors have published recently a three-dimensional (3-D) model of the vertical ring furnace, t6~ This model is very useful for the detailed description of a given section (the fourth preheat section was analyzed in the article); however, it cannot predict the behavior of the complete fire train
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