Modeling Macrosegregation during Direct-Chill Casting of Multicomponent Aluminum Alloys
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MACROSEGREGATION modeling became a working instrument thanks to the pioneering work of Flemings et al. in the 1960s.[1] The main mechanism behind macrosegregation is now well understood, i.e., the transport of segregated alloying elements at the scale of a casting by the relative movement of liquid and solid phases. The most widely used macrosegregation models are single domain methods, based on either volume averaging technique[2,3] or mixing theory,[4] in which the rigid solid phase usually is treated as highly viscous fluid (pseudo-fluid concept). Recently, Beckermann[5] gave a good review of macrosegregation modeling, emphasizing the applications of macrosegregation models in various industrial casting processes. Our research work is intended to enable the application of macrosegregation modeling in the industrial direct-chill (DC) casting process by implementing an efficient method to access the phase diagram data and by taking full advantage of the features provided by the commercial CFD software, CFX-5,* such as unstruc* CFX is a trademark of Ansys, Inc., Canonsburg, PA.
tured meshing and parallel computing. Over the last decade, several articles have been published with an attempt to extend the application of macrosegregation models to ternary alloys,[6,7,8] because
Q. DU, Postdoctor and D.G. ESKIN, Senior Scientist are with the Netherlands Institute for Metals Research, 2628CD Delft, the Netherlands. Contact e-mail: [email protected] L. KATGERMAN, Professor, is with the Delft University of Technology, 2628CD Delft, the Netherlands. Manuscript submitted April 20, 2006. 180—VOLUME 38A, JANUARY 2007
the local solidification path can be changed dramatically by the addition of alloying elements. Krane and Incropera concluded that the continuum mixture equations of ternary alloys were essentially the same as those for a binary alloy, differing only in the addition of a second species Eq. [6] They also found in their simulation results on the lever-rule type solidification of a ternary Pb-Sb-Sn alloy that macrosegregation of the solutes was altered significantly from the familiar patterns of the binary systems when the alloy composition was close to the monovariant lines of the ternary phase diagram. If the secondary solidification occurred deep in the mushy zone, the resulting microsegregation had only small effects on the final redistribution of solute.[7] The addition of a second alloying element may also change the flow velocity through the solutal buoyancy term, and therefore may alter the final macrosegregation pattern. It remains, however, unclear if this effect is important in DC casting of aluminum alloys. The extension to multicomponent alloys with a ‘‘real’’ phase diagram is of great industrial interest but requires a special strategy. The difficulty in solving the set of equations for multicomponent alloys originates from the demand to have an easy and quick access to the phase diagram information. To solve this problem, indirect coupling with a CALPHAD type of software, namely, the mapping technique, has been implem
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