Mathematical modelling of macrosegregation in binary alloys induced by convection - Assunção Junior, Milton de Oliveira (2021)
The occurrence of macrosegregation in ingot casting can actuate to depletion of the products final quality. Such defect can be described as a severe variation on macroscopic scale of chemical species that compose the alloy, whilst large ingots can also be severely affected by shrinkage cavity along the center line. The prediction of its occurrence via computational simulations has yet to be improved. This thesis provides: a 2D mathematical model for the formation of the shrinkage cavity using mass balance, and energy conservation with latent heat as source term, able to numerically verify the efficiency of apparatus currently used in the industry to reduce the cavity depth; a 2D macrosegregation model with a single-domain formulation including momentum, heat, mass and solute conservation, that reproduces results available in the literature; lastly, a novel 1D macrosegregation model undergoing shrinkage is presented, consisting of three distinct regions bounded by three moving interfaces, for which a similarity solution valid for small times was obtained and validated against numerical data, serving as initial condition to the non-similar problem used to draw some guidelines that can, in some circumstances, reduce the standard deviation on the initial solute concentration by up to 40%.