A mathematical model for surface segregation in aluminum direct chill casting

A two-dimensional mathematical model for the development of macrosegregation at and close to the ingot surface during direct chill (DC) casting of aluminum rolling sheet ingots is presented. The model accounts for macrosegregation caused by exudation of interdendritic melt and macrosegregation associated with solidification shrinkage. Equations for the conservation of energy, solute, momentum, and mass during the stationary phase of the process are solved numerically by a finite-element method. The solution domain corresponds to a vertical cross section at the middle of the longest side of the slab. The main simplifications in the modeling concept are to assume that the solid in the mushy zone moves with the casting speed, and that the alloy is binary and solidifies according to the lever rule. The thickness and solute concentration of the surface layer and the macrosegregation close to the surface are calculated, and modeling results are compared to measurements on full-scale castings.