Non-linear matrix correlation for multiphase temperature-composition coupling in modeling of solidification and macrosegregation.

• Reassessment on the mathematical modeling of solidification and macrosegregation. • Phase-change kinetics via a source-based transport tracking deviations from equilibrium. • Multiphase equilibria and solute mass balance integrated by non-linear programming (NLP). A reassessment was done on the state-of-the-art mathematical description of solidification to cope with the critical issues about the restricting assumption of equilibrium and uncertainties in the composition fields. Two hypotheses were suggested: (1) A phase fraction field that involves phase-change kinetics would be expressed via a source-based transport equation that tracks deviations of temperature and composition from equilibrium. (2) Local multiphase equilibria and solute mass balance can be integrated by a Non-Linear Programming (NLP) strategy to form a consistent correlation between temperature, composition, and phase fraction fields. Accordingly, a mathematical model was presented based on volume-averaged mass, momentum, energy, and species transports for a general three-phase binary alloy solidification. A new Multiphase-Thermodynamic-Coupling (MTC) was proposed based on NLP to link the phase diagram with the transport equations. The model was tested numerically through two benchmarks of directional solidification of an Al-Cu alloy. The proposed approach resulted in a lever-rule-like final solution with deviations from equilibrium during the iterations and near the chill boundary. The computed macrosegregation profile showed agreement with a semi-analytical solution (0.3 % error) and available experimental data (1.5 % error). The distributions of Phase-Change-Rate (PCR) were obtained in the form of bell-shaped curves. The proposed MTC approach provided an extendable formulation that allows one to read a phase diagram directly and run source-based phase-change-kinetics which can deviate from equilibrium. [Display omitted] [ABSTRACT FROM AUTHOR]