Finite element modeling of macrosegregation coupled with shrinkage cavity in steel ingots using arbitrary Lagrangian-Eulerian model

Shrinkage cavity has significant influence on macrosegregation in steel ingots. An arbitrary Lagrangian-Eulerian (ALE) model based on volume averaging method is developed to predict the coupled formation progress of macrosegregation and shrinkage cavity during solidification of steel ingots. The combined effect of thermal-solutal convection and solidification shrinkage on macrosegregation is considered in the model. A specially designed mesh update algorithm is proposed to consider the formation of shrinkage cavity. The streamline-upwind/Petrov-Galerkin (SUPG) stabilized finite element algorithm is adopted to solve the conservation equations. Two solution methods for the energy conservation equation are proposed, i.e. the temperature-based solver and enthalpy-based solver. A Pb-48wt.%Sn solidification benchmark is used for validation. Then, the ALE model is applied to a Fe-3.6wt.%C industrial steel ingot. The formation progress of macrosegregation coupled with shrinkage cavity is predicted. By comparison with the predictions of the finite element model and finite volume model, the effect of shrinkage cavity formation on macrosegregation is investigated. Results show that the formation of shrinkage cavity can significantly change the segregation region and segregation degree at the hot top. It is demonstrated that the ALE model can predict the coupled formation of macrosegregation and shrinkage cavity in steel ingots.