Numerical Simulation On Marcosegregation Formation During Binary Alloy Solidification Processes With Effect Of Shrinkage

Macrosegregation is an inevitable defect in solidification process,which has great influence on ingot qualities.Its formation is mainly due to the solute redistribution in front of the solid/liquid interface and the solute flow in mushy zone.Among various causing factors,solidification shrinkage and thermo-solutal buoyancy induced flow is the most important one for solute flow during solidification.The former is induced by the difference of solid/liquid phase density and the later directly results in the variation of the local density in the melt.In this paper,a macroscopic model coupling fluid flow,heat transfer and solute transport was developed for binary alloy solidification process in order to investigate the influence of solidification shrinkage and thermo-solutal buoyancy on macrosegregation,An additional source term related to solidification shrinkage is added in momentum equation.A Fortran code based on finite volume method was developed for modeling the solidification of binary alloys such as Pb-48wt%Sn alloy et al.The results show that,(1)Considering separately the influence of solidification shrinkage and thermo-solutal buoyancy on alloy solidification,the segregation induced by thermo-solutal buoyancy is more serious than the one by solidification shrinkage.(2)The segregation profile induced by both solidification shrinkage and thermo-solutal buoyancy is more serious.(i)For Pb-48wt%Sn alloy,in the case that the cavity is cooled down from the left lateral side,the thermo-solute buoyancy drives the melt flow clockwise in liquid zone,the solidification shrinkage,however,enhances the interdendritic flow.(ii)The macrosegregation becomes more serious under the larger solidification shrinkage ratio and the solute expansion coefficient and the smaller thermal expansion coefficient.(iii)The direction of buoyancy depends on the sign of thermal and solutal expansion coefficients,especially dominated by their magnitudes.In present,the cavity is cooled down from the left lateral side.When the thermal and solutal buoyancies are in the same direction,the convection in liquid zone is counterclockwise;otherwise,the thermal/solutal buoyancy in large magnitude determines the convection direction of the melt.(iv)In the cases of Al-7wt%Si alloy and Fe-0.1wt%C alloy,cooled at left lateral side of the ingot,the melt flows anticlockwise in liquid zone.Thus forms negative segregation in the upper left of ingot and positive segregation in the lower right of ingot.(3)For Pb-48wt%Sn alloy,the influence of riser size on the solute flow is small and can be ignored.(4)Two numerical treatments for the decrease of volume due to shrinkage are studied.Free surface descent method has to deal with the moving surface with a moving grid system,which,is difficult to handle the irregular change of the grid numbers near surface.However,riser feeding method alters the total mass in ingot,and the inflow from riser also changes the internal flow pattern in ingot which further changes the solute distribution.(5)Enhancing the heat transfer increases the flow in melt,speeds up the moving of mushy zone and shortens the time for solute to immigrate along with the inter-dendritic flow.Thus the macrosegregation caused by either solidification shrinkage or thermo-solutal buoyancy becomes weaker.The influence of solidification shrinkage on segregation is still minor to that of thermo-solutal buoyancy.(6)The parameter study shows that,the larger the secondary dendrite arm spacing and the smaller the dynamic viscosity,the less the flow resistance and consequently the more serious the macrosegregation,The similar phenomena can be obtained with or without consideration of solidification shrinkage.