Experimental Validation of Continuum Mixture Model for Binary Alloy Solidification

Abstract

Experiments were performed with binary metal alloys to validate a continuum mixture model for alloy solidification. Ingots of two compositions, Pb-20%Sn and Pb-40%Sn, were cast in a permanent mold, and the solidification process was simulated. Temperature histories were measured during casting, and composition profiles were found in the solidified ingot. Dendritic arm spacings were found from optical micrographs of the alloy microstructure and used to determine a constant in the Blake-Kozeny submodel for the mushy zone permeability in the liquid-solid interaction term of the momentum equations. Scaling analysis from a previous work and a large uncertainty in the permeability constant suggested that predictions of the composition are extremely sensitive to the choice of a permeability model. Three simulations of each casting were performed using the permeability constant as a parameter, and measured temperatures and compositions were compared with predictions based on different model constants. In the region of the liquidus interface, where all of the significant advection of solute takes place, the results suggest that the Blake-Kozeny model based on measured dendritic arm spacings significantly underpredicts the resistance of the dendritic array to fluid flow.