This dissertation describes research conducted to apply the Fractional Step Method to finite-element simulations of directional solidification. The Fractional Step Method (FSM) is also referred to as a projection method and as a splitting method, and has been applied commonly to high Reynolds number flow simulations. However, it is less common for low Reynolds number flows, such as occur in an alloy undergoing directional solidification (DS). The FSM offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and velocity components. The FSM provides significant benefits for predicting flows in a DS alloy, since other methods presently employed are not computationally efficient. Previously, the most suitable finite-elements based methods for predicting flow in a DS alloy has been the penalty method for two-dimensional simulations and Galerkin least-squares (GLS) for three-dimensional simulations. The penalty method and GLS have the disadvantage that they require the coupled solution of the velocity components. The FSM allows decoupled iterative solution of the finite element equations, thereby greatly increasing the efficiency of the method, both in terms of memory and CPU requirements. Numerical simulations are now commonly used to predict macrosegregation in directionally solidified (DS) castings, which are used in jet and spacecraft engines. In particular, the finite-element simulations can predict the existence of "channels" within the processing mushy zone and subsequently "freckles" within the fully processed solid, which are known to result from macrosegregation. This macrosegregation is a direct result of thermosolutal convection of the melt during the solidification process. Freckles cause strong material non-uniformities in the castings that are therefore scrapped. The phenomenon of thermosolutal convection in an alloy undergoing DS is explained, along with applications for DS alloys. Next, the momentum and continuity equations for a binary alloy undergoing DS, and the application of the FSM to these equations are presented, along with characteristics of the FSM that make its application to DS challenging. Finally, results of applying the FSM to simulations of DS in a binary alloy are given for two-dimensional and three-dimensional geometries, including performance improvements over methods previously applied.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/280329 |
| Date | January 2003 |
| Creators | Westra, Douglas G. |
| Contributors | Heinrich, Juan C. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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