Finite element analysis of solidification of aluminum with natural convection

Abstract

It is well known that A segregation similar to that found in steel castings is the result of an upward flow of inter-dendritic liquid. The liquid steel rises because the density of the liquid in contact with the solid decreases with temperature decrease. The inter-dendritic liquid steel is thus lighter than the bulk liquid steel. Channels or A segregates are formed because the rising liquid steel must move towards the hotter center of the casting. As the temperature increases, the inter-dendritic liquid can dissolve the solid and a channel is formed. Once formed, a channel continues to grow, producing the well-developed A segregate in the final casting. Thus, detailed information during solidification in the presence of natural convection is of importance. Because of the non-linearity and complexity of the problem, analytic solutions of the solidification of pure metals and alloys are limited. In order to understand the interaction of fluid flow in solidifying system, a two-dimensional finite-element program which can be applied for solving the solidification of pure metals and alloys, including the effects of natural convection in liquid, was developed using a temperature-recovery scheme. Two numerical examples demonstrate the accuracy and the capability of the program developed.