A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets
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UCTION
THE aluminium industry produces extrusion billets and rolling-sheet ingots by the direct-chill (DC) casting process. However, a number of defects such as cold shuts, melt runout, segregations, butt curl, butt swell, center cracks, and cold cracks may occur. Quality requirements are increasing and the process is being continuously improved with respect to ingot quality as well as casting recovery. Mathematical modeling is used to understand the basic mechanisms of the process and to interpret casting experiments; in the present article, the ALSIM model is presented. A sketch of the DC semicontinuous casting process is shown in Figure 1. Initially, the starting block is positioned inside the mold and the liquid metal is poured into the open mold from the top. A solidified shell is formed over the starting block and along the mold wall. As soon as the solidified shell is strong enough to embay the molten metal inside, the starting block is lowered. As the ingot emerges from the mold, the water impinges directly on the cast surface. After some distance, e.g., 1 m for a commercial-size sheet ingot, a nearly steady-state regime (the stationary period) is established for the thermal field. Several models for the heat and fluid flow in continuous casting have been reported in the literature. The modeling of the flows in the stationary period has been investigated by various authors, as well as the effects of macrosegregation, surface segregation, and grain transport.[1–10] The dynamic heat and fluid flow, in two-dimensional start-up calculations, has been studied in References 11 through 13. In this article, the evolution of the three-dimensional heat and fluid flows in the start-up period of sheet ingot casting with a metal distributor are described. Experience from casting has shown that many defects, like center cracks and surface cracks, initiate during the startup and may develop
throughout the whole process. In this early stage of the process, the ingot is chilled both from the starting block and from the water film, and, in addition to the fluid flow, the geometry of the starting block as well as the development of the boiling process in the water film are crucial for the prediction of the early thermal field. When the water first impinges on the ingot surface, the temperature is very high and film boiling may be present for a casting length of several centimeters, as reported in References 13 through 15. Section II of this article concerns the formulation of the mathematical model, and, in Sections III and IV, a detailed description of the boundary conditions is given. An effective numerical method suitable for three-dimensional dynamic fluid flows with a solidification term is presented in Section V, and, in Section VI, the results are given from the case study. II.
MATHEMATICAL MODEL
The model for the heat and fluid flows is based on the continuum-mixture model for the solid-liquid material, as derived by Bennon and Incropera.[16] In this model, the solid velocity is prescribed as opposed to a calculatio
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