A two-dimensional heat and fluid-flow model of single-roll continuous-sheet casting process
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I.
INTRODUCTION
B E C A U S E of large energy savings and reduced number of unit operations involved, which consequently lead to lower manpower and space requirements, the nearnet-shape casting of steel is rapidly moving toward the forefronts of technologies producing thin slabs, sheets, and strips of steels. Several of the near-net-shape casting processes, which have potential for commercial exploitation, are discussed elsewhere. ~-4~ One such process, generally referred to as the single-roll continuous-sheet/ strip casting process, is the subject of the present investigation, which aims at formulating a mathematical model based on fluid-flow, heat-transfer, and solidification considerations to quantitatively analyze the process and predict the effect of operating parameters on the process performance. The process under consideration, schematically shown in Figure 1, is described in detail elsewhere, t5,6,71In brief, the molten metal from a tundish flows on to a rotating hollow caster drum via a pool of molten metal, which is contained in the annular space between the concentric outer wall of the tundish and the rotating drum. The caster drum is quenched by water sprays from inside. As soon as the caster drum enters the molten pool, a skin of solidified metal is formed on its surface, which further grows in thickness during its sojourn in the metal pool. Heat is continuously extracted from the solidified sheet through the caster drum by water sprays. Chopra and Niessan were among the first investigators to model a single-roll sheet caster, t8j Their model involved a transient heat conduction equation which was solved using a control volume-based finite difference method. Using a simulation model, Pimputkar e t a / . [91 have shown that the sheet thickness is strongly affected M.R.R.I. SHAMSI, Graduate Student, and S.P. MEHROTRA, Professor and Head, are with the Department of Metallurgical Engineering, Indian Institute of Technology, Kanpur 208016, India. Manuscript submitted July 27, 1992. METALLURGICAL TRANSACTIONS B
by the rotational speed of the caster drum, melt pressure, metal head in the tundish, and the standoff distance between the tundish and the caster drum, while the orientation of the tundish nozzle, the superheat of melt, and the substrate temperature and material only have a marginal effect. A two-dimensional transient thermal model for the solidification of a sheet on moving substrates, in general, has been formulated by Papai and MobleyJ l~ Brimacombe and S amarsekera t~u have examined the heat extraction aspects of continuous casting of near-net-shape steel products from a fundamental standpoint. Some other aspects of sheet casting, relevant to a single-roll caster, have been reported elsewhere, t~2 151 Recently, Mehrotra and c o - w o r k e r s 15-7'16'17] starting with a simple overall enthalpy balance model, have come up with more rigorous mathematical models based on segmentwise heat-balance, solidification, and fluid-flow considerations. The model based on overall enthalpy balance takes in
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