Effect of domain size on grid convergence in numerical models of alloy solidification

When a multi-component alloy solidifies the redistribution of solute components leads to the formation of segregation patterns. One common form of patterns is the formation of high solute segregation channels, which can have thickness dimensions from several to tens of mm. Many numerical casting models have the ability to predict the formation of these channels. The problem, however, is that the grid size in such calculations can have a significant influence on the shape, size, number, and location of these channels. With this lack of grid convergence results it is not possible to formulate a phenomenological understanding of the segregation processes. Recently, working with an Al-4.5%Cu binary alloy solidifying in a small side cooled cavity 40x40 mm we have shown that it is possible to arrive at grid independent predictions of channels once the grid size falls below ~ 0.3 mm. Clearly, however, such a cavity size is well below that that might be used in industrial and even laboratory settings. Here our task is to see if similar grid independent results can be obtained with simulations on a larger grid size of 76x76mm. Our results indicate that although grid resolution is approached with a grid size of ∼0.3 mm it has still not been fully achieved. Thus indicating that the expected increase in fluid flow in the larger cavity produces more and finer channels which are harder to numerically resolve.