Solidificación de Aleaciones Binarias con Fase Eutéctica: un Esquema Implícito Basado en la Formulación de Entalpía

Abstract

A numerical scheme to model the solidification of a binary alloy that undergoes a eutectic reaction during the phase change is presented. The method combines a continuum mushy zone model with a regularization of the eutectic front, being the fraction ofliquid the regularization variable. In particular, the scheme is also efficient for the case of solidification of a pure metal. Employing a Newton-Raphson linearization, temperature, phase enthalpies and concentrations, and fraction of liquid, are computed simultaneously for each time step, with no need of external iterations of explicit type. The phase diagram of the alloy is used implicitly in the scheme to compute the fraction of liquid, avoiding ad hoc temperature vs. fraction of liquid relations. The metllod is robust and allows an efficient implementation of enthalpy functions that depend on both temperature and concentration. A calculation is presented to study the effect of considering different enthalpy functions for the pri mary solid and the eutectic solid on the advancing speed of the eutectic front.