Phase change modelling with flexible source-based kinetics for non-equilibrium transitions

Abstract

In this work, a modeling approach is developed to cope with the phase-change problems having deviations from equilibrium conditions. The mathematical model is based on continuity and enthalpy conservation equations. The core of the model is a source term of continuity which governs the rate of phase change. The formulation of the source term is originally proposed with an infinite series, i.e. an iterative rate-tuner, which accounts for both equilibrium and non-equilibrium phase changes. As the model tracks equilibrium transitions by the stand-alone rate-tuner, off-equilibrium paths are described by regulations of the rate-tuner. The model also resolves undercooling-superheating of phase change materials with a feature tackling nucleation-growth-transition using an interphase-detector-function. In order to evaluate the model, a computational program was developed from the equations discretized with finite volume method. The paper presents implementation of the code in three test problems; Test-case-I employs a typical Stefan problem, i.e. melting of an ice bar in equilibrium condition, which verifies the model with the exact solution. Test-case-II simulates the ice bar under periodic heating/cooling at its end, so that non-equilibrium melting/freezing arises at the end of the bar. Depths and fractions of the phase change are graphed versus the frequency of heating/cooling cycles and the rate-regulator parameter. A spectrum of kinetic behaviors is presented, depending on the rate-regulator parameter. Three kinetic behaviors are distinguished, namely; extremely fast (instantaneous equilibrium), intermediate (non-equilibrium) and extremely slow (bypassed, highly-restricted-rate). Finally, test-case-III deals with a non-equilibrium solidification in a real case (sodium-acetate-trihydrate) that exhibits undercooling and recalescence due to nucleation-growth kinetics. The model successfully predicted temperature history curves in comparison with experimental data. The model is a step toward enhancing our computational tools for non-equilibrium phase changes in advanced material processing like additive manufacturing, casting, welding, solidification and energy storage systems.