A thermally coupled flow formulation with microstructural evolution for hypoeutectic cast-iron solidification

A thermally coupled incompressible flow formulation, including microstructu ral phase-change effects, is presented. The governing equations are written in the framework of the finite-element method using a generalized streamli ne operator technique. In particular, a hypoeutectic cast-iron microstructu ral model accounting for primary austenite and eutectic solidification is c onsidered. An inverse lever rule has been employed to describe the austenit e formation, while the eutectic (graphite and cementite) fractions are assu med to be governed by nucleation and growth laws. The application of this m ethodology in the area of casting solidification constitutes an original co ntribution of this work. Further, an enhanced staggered scheme is also prop osed in order to solve the resulting strongly coupled discretized equations . The analysis of a solidification problem, with particular interest in the influence of the natural convection on the microstructural formation, is p erformed. The numerical results obtained with the present formulation allow prediction of the flow patterns, volume-fraction distributions, and recale scences developed during the process.