一种一致且守恒的相场方法用于六方程模型可压缩多相流

中文摘要 AI 辅助

在本研究中，一致且守恒的相场方法被扩展到用于可压缩多相流的六方程模型。仅基于守恒定律和热力学第二定律，首先推导了带有相场机制的六方程模型。除了满足伽利略不变性和还原一致性外，该模型具有通用性，可容纳任意数量的相，并支持不同形式的相场机制。分析了通过压力松弛实现的等压封闭以及所提出模型的不可压缩极限。推导和分析识别出由相场机制产生的额外项，这些项在以往研究中缺失。一致且守恒的数值方法经过适度修改后被适配到所提出的六方程模型，保留了界面平衡条件、守恒性以及结合不同相场机制（具有界保持性）的灵活性和鲁棒性。作为求解六方程模型的新组成部分，压力松弛和压力-温度松弛均在一般多相设置中进行了理论分析，并证明了这两种松弛的热力学容许解的存在性和唯一性。进行了多种两相可压缩流基准测试以验证该方法，并与精确解取得了良好的一致性。

英文摘要

In the present study, the consistent and conservative Phase-Field method is extended to the six-equation model for compressible multiphase flows. Based solely on the conservation laws and the second law of thermodynamics, the six-equation model with the Phase-Field mechanism is first derived. In addition to satisfying Galilean invariance and consistency of reduction, the model is general to admit an arbitrary number of phases with different formulations of the Phase-Field mechanism. The isobaric closure by the pressure relaxation and the incompressible limit of the proposed model are analyzed. The derivation and analysis identify additional terms arising from the Phase-Field mechanism, which are absent from previous studies. The consistent and conservative numerical approach is adapted to the proposed six-equation model with moderate modifications, retaining the interfacial equilibrium condition, conservation, and flexibility and robustness of incorporating different formulations of the Phase-Field mechanism with bound preservation. As the new component of solving the six-equation model, both the pressure and pressure-temperature relaxations are theoretically analyzed in a general multiphase setup, with a proof of the existence and uniqueness of a thermodynamically admissible solution for these two relaxations. Various two-phase compressible flow benchmarks are performed to demonstrate the method, and good agreement with exact solutions is achieved.

发表机构

• South China University of Technology（华南理工大学）

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