Solidification and Macrosegregation in Aluminum Alloys on Uneven Surfaces

"Solidification of metal aluminum and aluminum alloys is modeled on uneven surfaces characterized by sinusoidal curves. Wavelengths and amplitudes of these sinusoidal surfaces are varied to study their effects on processes like solidification, macro-segregation and inverse segregation. Solidification and macro-segregation are modeled using a slightly modified form of a stabilized finite element method developed recently to model high Rayleigh number solidification and porous media flows. For pure metal solidification, the effect of varying amplitudes and wavelengths is observed in heat transfer, fluid-flow ~nd phase change processes. The relative importance of shrinkage driven flow and solutal convection on the redistribution of solute for an alloy solidifying in a rectangular cavity is compared. The analysis is then extended by modifying one of the surfaces to a sinusoid. In this case the effects of varying amplitudes and wavelengths are studied in heat transfer, fluid flow, phase change, macro-segregation and inverse segregation processes.1 IntroductionTransport phenomenon during solidification of alloys is a major cause ofcasting defects such as segregation, micro-voids, hot tears, porosity, internal and surface cracks. Heat flow across metal and mold surfaces directly affects the phase change process and plays an important role in determining freezing conditions within the metal. In alloys, natural convection and shrinkage play an important role in determining the final solute redistribution, macrosegregation and evolution of solid macromorphology. Surface unevenness plays an important role during the early stages of solidification. It influences the heat transfer rate and fluid flow in the melt, which in turn affect the morphology and shape of the solid-liquid interface. The effect of surface unevenness on solute redistribution is important during solidification of alloys, where solute driven flow in the mushy zone is prominent. Thevik and Mo in [7] and [8] used a one dimensional model for studying surface segregation and macrosegregation in alloys under the influence of exudation and solidification shrinkage. Air-gap formation in their model was expressed through a variable convective heat transfer coefficient at the boundary. Tsai et al. in [3] and [4] have modeled macrosegregation in an aluminum-copper alloy driven by shrinkage and solutal convection. They used a single domain model based on mixture theory and solved the transport equations using finite difference methods. Our aim is to model solidification of aluminum followed by macrosegregation and inverse segregation in aluminum-copper alloys on uneven surfaces by finite element methods. These surfaces are modeled as sinusoids characterized by amplitudes, ?s and wavelengths, As, By varying As and ?s, changes in heat transfer, fluid flow, phase-change and macrosegregation are studied."