固定网格尖界面数值解法解决三相球形Stefan问题
Fixed-grid sharp-interface numerical solutions to the three-phase spherical Stefan problem
AI总结：
本文提出固定网格尖界面方法解决三相球形Stefan问题，验证了纳米粒子相变中动能项的重要性。
摘要：
许多金属制造过程涉及相变现象，包括熔化、沸腾和汽化。这些现象往往同时发生。理解相变现象的典型一维模型是Stefan问题。有大量的文献讨论了两相Stefan问题的解析解，该问题仅描述相变材料（PCMs）的熔化或沸腾，具有一个移动界面。文献中通常忽略密度变化引起的额外流体流动，以简化Stefan问题的数学表达。在我们最近的工作[1]中，我们提供了三相Stefan问题的解析和数值解，该问题描述了在笛卡尔坐标系中同时发生熔化、固结、沸腾和冷凝的现象。我们的当前工作基于之前的成果，解决了一个更具挑战性的问题：在有限尺寸粒子中的三相Stefan问题的球坐标系解。该系统有三个移动界面：熔融前沿、沸腾前沿和与大气接触的外边界。尽管无法找到该问题的解析解，但我们使用固定网格尖界面方法，以二阶时空精度求解控制方程。利用小时间解析解，我们预测了模拟开始时三个相的温度（合理准确的估计）以及界面位置和速度。我们的数值方法通过重现Font等人[2]的双相纳米粒子熔化结果进行了验证。最后，我们通过数值求解三相Stefan问题来展示相变过程中小尺寸（纳米）粒子的动能项的重要性。相比之下，这些效应在大尺寸（微米及以上）粒子中会减弱。
英文摘要：
Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the Stefan problem. There is a large body of literature discussing the analytical solution to the two-phase Stefan problem that describes only the melting or boiling of phase change materials (PCMs) with one moving interface. Density-change effects that induce additional fluid flow during phase change are generally neglected in the literature to simplify the math of the Stefan problem. In our recent work [1], we provide analytical and numerical solutions to the three-phase Stefan problem with simultaneous occurrences of melting, solidification, boiling, and condensation in Cartesian coordinates. Our current work builds on our previous work to solve a more challenging problem: the three-phase Stefan problem in spherical coordinates for finite-sized particles. There are three moving interfaces in this system: the melt front, the boiling front, and the outer boundary which is in contact with the atmosphere. Although an analytical solution could not be found for this problem, we solved the governing equations using a fixed-grid sharp-interface method with second-order spatio-temporal accuracy. Using a small-time analytical solution, we predict a reasonably accurate estimate of temperature (in the three phases) and interface positions and velocities at the start of the simulation. Our numerical method is validated by reproducing the two-phase nanoparticle melting results of Font et al. [2]. Lastly, we solve the three-phase Stefan problems numerically to demonstrate the importance of kinetic energy terms during phase change of smaller (nano) particles. In contrast, these effects diminish for large particles (microns and larger).
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