考虑液固相变的热-气-液-固流动的一致守恒相场模型
A consistent and conservative Phase-Field model for thermo-gas-liquid-solid flows including liquid-solid phase change
摘要：
本文建立了一个自洽的、守恒的相场模型来研究具有液固相变的热-气-液-固流动。所提出的模型推导出的一致性条件的帮助下，并准确地减少到一致的和保守的相场方法的不可压缩两相流，虚拟域Brinkman惩罚（FD/BP）方法的流体-结构的相互作用，和相场模型的凝固的纯材料。它尊重质量守恒，明确定义各个相的体积分数，因此捕获由于相变引起的体积变化。当没有固相时，动量守恒，但当固相出现时，由于固体边界处的无滑移条件，动量发生变化。所提出的模型还保存了能量，保持温度平衡，并且是伽利略不变量。提出了一种新的连续表面张力力来限制其在气液界面的贡献，并从卡门-Kozeny方程修改的拖曳力，以减少固体速度为零。通过对插值函数进行物理修改，解决了在凝固的原始相场模型中引发相变的问题。建立了相应的相容格式求解该模型，数值结果与解析解及已有的实验和数值结果吻合较好。两个具有广泛的材料特性和复杂的动力学具有挑战性的问题进行了演示所提出的模型的能力。
英文摘要：
In the present study, a consistent and conservative Phase-Field model is developed to study thermo-gas-liquid-solid flows with liquid-solid phase change. The proposed model is derived with the help of the consistency conditions and exactly reduces to the consistent and conservative Phase-Field method for incompressible two-phase flows, the fictitious domain Brinkman penalization (FD/BP) method for fluid-structure interactions, and the Phase-Field model of solidification of pure material. It honors the mass conservation, defines the volume fractions of individual phases unambiguously, and therefore captures the volume change due to phase change. The momentum is conserved when the solid phase is absent, but it changes when the solid phase appears due to the no-slip condition at the solid boundary. The proposed model also conserves the energy, preserves the temperature equilibrium, and is Galilean invariant. A novel continuous surface tension force to confine its contribution at the gas-liquid interface and a drag force modified from the Carman-Kozeny equation to reduce solid velocity to zero are proposed. The issue of initiating phase change in the original Phase-Field model of solidification is addressed by physically modifying the interpolation function. The corresponding consistent scheme is developed to solve the model, and the numerical results agree well with the analytical solutions and the existing experimental and numerical data. Two challenging problems having a wide range of material properties and complex dynamics are conducted to demonstrate the capability of the proposed model.
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