Modeling fluid interactions with the rigid mush in alloy solidification
Macrosegregation is a casting defect characterized by long range composition differences on the length scale of the ingot. These variations in local composition can lead to the development of unwanted phases that are detrimental to mechanical properties. Unlike microsegregation, in which compositions vary over the length scale of the dendrite arms, macrosegregation cannot be removed by subsequent heat treatment, and so it is critical to understand its development during solidification processing. Due to the complex nature of the governing physical phenomena, many researchers have turned to numerical simulations for these predictions, but properly modeling alloy solidification presents a variety of challenges. Among these is the appropriate treatment of the interface between the bulk fluid and the rigid mushy zone. In this region, the non-linear and coupled behavior of heat transfer, fluid mechanics, solute transport, and alloy thermodynamics has a dramatic effect on macrosegregation predictions. This work investigates the impact of numerical approximations at this interface in the context of a mixture model for alloy solidification. First, the numerical prediction of freckles in columnar solidification is investigated, and the predictive ability of the model is evaluated. The model is then extended to equiaxed solidification, in which the analogous interface is the transition of free-floating solid particles to a rigid dendritic network. Various models for grain attachment are investigated, and found to produce significant artifacts caused by the discrete nature of their implementation on the numerical grid. To reduce the impact of these artifacts, a new continuum grain attachment model is proposed and evaluated. The differences between these models are compared using uncertainty quantification, and recommendations for future research are presented.
Krane, Purdue University.
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