Modelling and simulation of ingot solidification with the open-source software Code-Saturne

In order to address the issue of macro-segregations in large industrial ingots, a solidification model has been recently developed in Code-Saturne, the general purpose open-source Computational Fluid tablDynamics (CFD) software developed and released by EDF R&D. This model is a liquid-solid mixture model inspired from the pioneer work of Bennon and Incropera, including mass, momentum, energy and species conservation equations. In particular, the energy conservation equation is formulated with the temperature variable, the thermosolutal convection is accounted for through the Boussinesq approximation and the interdendritic flow in the mushy zone is governed by the Darcy's law. Furthermore, a rigid solid phase is assumed and classical microsegregation models are used featuring lever-rule or Gulliver-Scheil assumptions. At the discrete level, a first-order upwind scheme is implemented with a SIMPLEC approach to solve the velocity-pressure coupling. The other couplings involving temperature and concentration fields are efficiently solved performing sub-loops with a PISO-like approach. The overall scheme is mainly implicit with additional treatments to ensure the equilibrium between the hydrostatic pressure gradient and the buoyant forces, and to deal properly with solid zones. The segregation predictions offered by the model are validated against both academic test case and industrial ingot configurations. A convergence study is also led focusing on time step and mesh size sensitivities.