Film Boiling and Water Film Ejection in the Secondary Cooling Zone of the Direct-Chill Casting Process
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THE direct-chill (DC) casting process, presented schematically in Figure 1, uses cooling water to remove heat from the molten metal. This heat removal occurs both indirectly through a water-cooled mold (primary cooling) as well as directly using cooling water jets (secondary cooling). The secondary cooling region can also be subdivided into two zones: an impingement point (IP), where the water jets hit the ingot or billet surface, and a water film free falling zone (FFZ) below this point. A significant portion of research work conducted on direct-chill casting nowadays is of a fundamental nature and focuses on the mathematical modeling of this process.[1] Mathematical models not only provide greater understanding of the DC casting process but also can help improve the design and control of this process. Thermal models, for instance, predict the temperature distribution in the cast product by solving a transient heat conduction problem. The thermal history within the billet or ingot is linked to the formation of defects such as hot tears and butt curl, as well as the microstructure development, the occurrence of segregation, and the surface quality. The first mathematical model of the DC casting process was developed in 1943 by Roth.[2] This analytical model calculated a heat balance to evaluate the temperature distribution in a billet as well as the sump depth. Subsequent attempts at modeling the DC casting process used finite-difference or finite-element ETIENNE CARON, formerly with the Department of Materials Engineering, University of British Columbia, Vancouver, BC, is now Postdoctoral Fellow, Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada. Contact e-mail: [email protected] MARY A. WELLS, Professor, is with the Department of Mechanical and Mechatronics Engineering, University of Waterloo. Manuscript submitted April 30, 2009. Article published online September 23, 2011. METALLURGICAL AND MATERIALS TRANSACTIONS B
approaches with increasing degrees of complexity. The accuracy of these numerical models was found to be related not to their ability to solve the governing partial differential equations but rather to the simplifying assumptions regarding the ingot geometry, the thermophysical properties of the cast material, and the external boundary conditions.[3] Precise knowledge of the boundary conditions is considered particularly important for the secondary cooling zone because the surface heat flux in this zone can experience significant variations. This research article discusses the importance of accurate boundary conditions for the secondary cooling zone. A literature review of previous research work summarizes the development of increasingly complex models for the secondary cooling. A finite-element model for the direct-chill casting of magnesium billets is then presented and used to simulate the process startup phase, during which defects are generally initiated. The relevance of the external boundary condition corresponding to secondary cooling is t
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