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

A thermally coupled incompressible flow formulation, including microstructural phase-change effects, is presented. The governing equations are written in the framework of the finite-element method using a generalized streamline operator technique. In particular, a hypoeutectic cast-iron microstructural model accounting for primary austenite and eutectic solidification is considered. An inverse lever rule has been employed to describe the austenite formation, while the eutectic (graphite and cementite) fractions are assumed to be governed by nucleation and growth laws. The application of this methodology in the area of casting solidification constitutes an original contribution of this work. Further, an enhanced staggered scheme is also proposed 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 performed. The numerical results obtained with the present formulation allow prediction of the flow patterns, volume-fraction distributions, and recalescences developed during the process.