On the numerical prediction of channel segregation. (September 2016) - Plotkowski, A.; Krane, M.J.M.
Highlights: Investigated numerical nature of freckles in a model of columnar solidification. Describe the formation of channels as a function of numerical noise. Conclude that freckle predictions are not reliable for coarse grids. Suggest convergence criterion that minimizes freckle appearance. Abstract: The prediction of freckles in a numerical model of alloy solidification was critically evaluated through a series of simulations of the cylindrical static casting of aluminum alloy 7050. Artificial numerical constrains in the number of iterations per time step were used to exaggerate the formation of freckles for ease in understanding the mechanism behind channel initiation and propagation. It was found that initial protrusions at the solidification front caused by instabilities in the solution to the highly non-linear governing equations cause a feedback loop in the solid fraction, momentum, and composition fields that allows channels to initiate and propagate. Unfortunately, the initial instabilities in models of this type are limited to the length scale of the numerical grid rather than the dendrite arm spacing which produces such variation in their physical counterparts. For macroscale simulations where excessive grid refinement is not computationally viable, it is recommended that freckle formation be suppressed by the application of an appropriate convergence criterion and the minimization of numerical noise originating from convergence residuals.