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.

中文翻译：

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使用灵活的基于源的动力学进行非平衡转变的相变建模

摘要 在这项工作中，开发了一种建模方法来处理偏离平衡条件的相变问题。数学模型基于连续性和焓守恒方程。该模型的核心是控制相变率的连续源项。源项的公式最初是用无限级数提出的，即迭代速率调谐器，它考虑了平衡和非平衡相变。当模型通过独立的速率调谐器跟踪平衡转变时，非平衡路径由速率调谐器的规则描述。该模型还解决了相变材料的过冷-过热问题，其特征是使用相间检测器功能解决成核-生长-转变问题。为了评估模型，根据有限体积法离散化的方程开发了一个计算程序。论文给出了代码在三个测试题中的实现；Test-case-I 使用了一个典型的 Stefan 问题，即平衡条件下冰棒的融化，它用精确的解来验证模型。测试案例-II 模拟冰棒末端周期性加热/冷却，从而在棒末端出现非平衡熔化/冻结。相对于加热/冷却循环的频率和速率调节器参数绘制了相变的深度和分数。根据速率调节器参数，呈现了一系列动力学行为。区分三种动力学行为，即；极快（瞬时平衡）、中间（非平衡）和极慢（绕过，高度限制率）。最后，测试案例 III 处理真实案例（醋酸钠三水合物）中的非平衡凝固，由于成核-生长动力学表现出过冷和再辉。与实验数据相比，该模型成功地预测了温度历史曲线。该模型是朝着增强我们在先进材料加工（如增材制造、铸造、焊接、凝固和储能系统）中的非平衡相变计算工具迈出的一步。