| This dissertation presents a mathematical model which is capable of predicting the fluid flow and heat and mass transfer during solidification process of binary alloys. The governing differential equations, including the continuity, momentum, energy, and species equations, are derived based on the continuum model, in which the liquid phase, mushy zone and solid phase are treated as a single region with continuously changing properties, and hence, there is no need to track the phase interfaces explicitly. The SIMPLEC algorithm is used to solve the set of fully coupled partial differential equations. The model has been used to study: (a) the formation of macrosegregation in an ingot with cross-section change; (b) the formation of macrosegregation in an aluminum-copper alloy cooled from one side; (c) the formation of macrosegregation in an iron-carbon alloy cooled from one side; and (d) the formation of macrosegregation in an aluminum-copper alloy solidifying in a sand mold.;It is found that generally shrinkage-induced flow is dominant in the mushy zone and that natural convection caused by thermal and solutal gradients is strong in the bulk liquid region. Shrinkage-induced flow may cause inverse segregation on the cooling surfaces, positive segregation in the dead-end corners of a casting and negative segregation in the under-riser region. Natural convection is responsible for the solute transport in the liquid region, which may cause macrosegregation inside the casting. The effects of shrinkage-induced flow are more significant in the alloys with wide mushy zone, such as aluminum-copper alloy. The density difference between the two constituents in an alloy has major influence on the fluid flow and the formation of macrosegregation. For a casting with a mold, the inverse segregation, under-riser segregation and shrinkage caused segregation similar to a V-shape have been found. The results are in good agreement with the phenomena found in foundry practices. |
