A Simple Model of the Mold Boundary Condition in Direct-Chill (DC) Casting of Aluminum Alloys
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THE direct-chill (DC) casting process has been used for the production of large ingots and billets of nonferrous alloys since the mid-1930s.[1] This process is still in widespread use in the aluminum industry because of its simplicity and robust nature. A schematic of the DC casting process is shown in Figure 1. The molten aluminum is poured into a water-cooled mold whose bottom is closed initially by a starter block. The primary cooling from the mold starts to solidify the molten metal, thereby forming the initial solid shell of the ingot. The starter block is then withdrawn steadily at the casting speed pulling down with it the solid shell. Once the shell exits the bottom of the mold, it is cooled rapidly by a direct spray of water that extracts most of the heat from the ingot. This direct water spray is called secondary cooling. The casting process continues until an ingot with a desired height is produced. Numerous analytical and numerical models have been proposed to help develop a quantitative understanding of the DC casting process.[2–5] The accuracy of these AMIR R. BASERINIA, Postdoctoral Fellow, H. NG, Research Assistant, and D.C. WECKMAN and M.A. WELLS, Professors, are with the Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada. Contact e-mail: [email protected] S. BARKER, Metallurgist, and M. GALLERNEAULT, Director of Research, are with the Novelis Global Technology Centre, Kingston, ON K7L 3N6, Canada. Manuscript submitted May 14, 2011. Article published online April 13, 2012. METALLURGICAL AND MATERIALS TRANSACTIONS B
models is constrained primarily by the accuracy of the external thermal boundary conditions applied to the primary and secondary cooling regions. In the primary cooling region, initially a high rate of heat extraction is observed when the molten metal comes in direct contact with the mold. The rate of heat extraction, however, decreases dramatically as the primary solid shell grows and pulls away from the mold wall because of thermal contraction and air gap formation between the ingot surface and the mold wall.[2,4,6–8] If the air gap becomes too large, then remelting of the shell may occur, leading to undesirable liquid metal exudation and inverse segregation or in extreme cases, a dangerous liquid metal breakout.[1] Therefore, it is crucial to account for the air gap effect in any primary mold cooling model. The effect of air gap formation on the primary mold cooling boundary condition has been quantified by experimental measurements. Vreeman et al.[5] used experiments to measure the mold boundary conditions, whereas others have inferred a heat-transfer coefficient that provided a reasonable correlation between numerical predictions and experimental measurements of the shell thickness.[9–12] When modeling the DC casting process, however, it is preferred to have a predictive model of the air gap effect on the primary cooling rather than relying on the experimental measurements. The main challenge in formulating a predictive air gap mod
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