耦合刚体运动与二元相变：一种尖锐水平集/嵌入边界方法

中文摘要 AI 辅助

我们开发了一种用于自由移动固体颗粒进行纯熔化或二元熔化的尖锐界面方法。水平集表示在长距离平移和旋转过程中保持颗粒几何形状，而嵌入边界公式在欧拉笛卡尔网格上尖锐地施加流体动力学、热和溶质条件。液体温度和溶质浓度通过保守的移动切割单元离散化推进，而固体温度通过几何一致的保守示踪剂传输。流体动力学载荷、刚体运动和相变在每个物理时间步内迭代耦合。该方法针对刚体运动、规定运动的纯熔化和二元熔化以及具有自由颗粒运动的完全耦合熔化进行了逐步验证。它再现了已建立的参考解，并捕捉了熔化球体的尾流诱导旋转以及三维扁椭球的同时平移、旋转和热溶质熔化。作为最终应用，对漂浮冰盘的模拟揭示了热对流不稳定性、几何约束和熔化如何共同决定其自发运动，其中相变通过演化的颗粒几何形状反馈到不稳定性上。额外的测试确立了长时间几何保真度、局部标量守恒和几何一致固体温度传输的重要性。所得到的框架为强耦合移动体相变问题提供了一种尖锐且保守的方法。

英文摘要

We develop a sharp-interface method for freely moving solid particles undergoing pure or binary melting. A Level-Set representation preserves the particle geometry during long-distance translation and rotation, while an embedded-boundary formulation imposes hydrodynamic, thermal and solutal conditions sharply on a Eulerian Cartesian mesh. Liquid temperature and solutal concentration are advanced with a conservative moving-cut-cell discretization, whereas the solid temperature is transported through a geometry-consistent conservative tracer. Hydrodynamic loads, rigid-body motion and phase change are coupled iteratively within each physical time step. The method is validated progressively for rigid-body motion, prescribed-motion pure and binary melting, and fully coupled melting with free particle motion. It reproduces established reference solutions and captures wake-induced rotation of a melting sphere and the simultaneous translation, rotation and thermosolutal melting of a three-dimensional oblate ellipsoid. As a final application, simulations of a floating ice disc reveal how thermoconvective instability, geometric confinement and melting jointly determine its spontaneous motion, with phase change feeding back on the instability through the evolving particle geometry. Additional tests establish the importance of long-time geometrical fidelity, local scalar conservation and geometry-consistent solid-temperature transport. The resulting framework provides a sharp and conservative approach for strongly coupled moving-body phase-change problems.

发表机构

• State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University（西安交通大学航天学院机械结构强度与振动国家重点实验室）

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