复杂多孔介质中固液相变的格子Boltzmann方法及模拟

This project is aimed at constructing a set of complete and efficient lattice Boltzmann models and methods for the simulation of solid-liquid phase change, which can be used to realize the accurate simulation and rapid prediction of solid-liquid phase change problem in complicated porous media. The main work includes: (1) developing a lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator for the convection-diffusion equation, which can deduce the macroscopic convective-diffusion equation precisely without any deviation term by Chapman-Enskog analysis; (2) studying the efficient treatment of latent-heat source term to avoid the iteration procedure of enthalpy, which is further used to form the lattice Boltzmann model for the temperature field simulation; (3) exploring the realization method of no-slip velocity boundary condition at the solid-liquid phase interface with the mushy zone and moving feature, and further combining the lattice Boltzmann model for the athermal fluid flows with the above lattice Boltzmann model for the temperature field to constitute a complete lattice Boltzmann model for the solid-liquid phase change simulation; (4) studying the coupling method between the coarse grid and fine grid when both temperature field and velocity field are calculated by multi-grids to realize the adaptive mesh refinement simulation of the solid-liquid phase change, which can further increase the simulation accuracy and reduce the computation cost; (5) based on the lattice Boltzmann model and method developed above, the simulation research will be made on the solid-liquid phase change in the complicated porous media, and effects of the pore structure, porous frame, phase change core materials on the phase change characteristics will be analyzed. Simulation results can serve as theoretical principles for the design and development of porous phase change materials with high performance.

本项目旨在构建一套完整高效的用于固液相变模拟的格子Boltzmann模型和方法，实现复杂多孔介质中固液相变的精确模拟和快速预测。内容包括：构建对流扩散方程的多松弛时间格子Boltzmann模型，通过Chapman-Enskog分析可精确恢复对流扩散方程而不带偏差项；进一步研究潜热源项的高效处理方法，避免焓值迭代，以构建温度场模拟的LBM模型。在无热流动LBM模型基础上，探索具有糊状区域和移动界面特征的固液相界面处无滑移边界条件的实现方法，并结合温度场LBM模型，构建完整的固液相变模拟的格子Boltzmann模型。探索温度场、速度场同时采用局部网格加密时粗细网格间的数据耦合方法，实现固液相变模拟的自适应网格算法，以提高精度、减小计算量。基于上述构建的模型和方法，开展复杂多孔介质中固液相变的LBM模拟，探索孔隙结构、多孔载体、相变芯材的影响规律，为高性能多孔复合相变材料的研制开发提供理论依据。

固液相变具有广泛而重要的工程应用背景，传统CFD方法在处理复杂多孔介质固液相变问题时存在困难，而格子Boltzmann(LB)方法的介观物理背景使其处理该问题具独特优势。本项目采用理论分析与数值模拟相结合的方法，开展了固液相变LB模型和方法的研究，取得以下主要成果：(1)鉴于固液相变温度场控制方程的基本框架为对流扩散方程，对现有对流扩散方程LB模型进行研究，发现其偏差项产生的根本原因为恢复对流项对恢复扩散项的干扰；在此基础上，通过改进松弛矩阵并确定相应的平衡态矩函数，构建了全新的对流扩散方程多松弛时间LB模型，消除了现有模型中存在的偏差项。(2)提出将固液相变非线性潜热源项吸收到时变项中，进一步引入总焓分布函数并确定相应的平衡态分布函数，构建了全新的固液相变LB模型(即总焓LB模型)，成功避免了焓值迭代计算和线性方程组求解，显著提高了计算效率。(3)提出了可精确实现糊状相界面处及固相内部速度无滑移条件的体积LB格式，避免了非物理虚假流动；通过引入参考比热容并改进平衡态分布函数，巧妙处理了相界面处变物性非稳态耦合传热；揭示了相界面处数值扩散形成机制并提出了消除手段。(4)从保证Chapman-Enskog展开方程网格无关性的介观新角度，直接在矩空间导出了粗细网格间完整的信息耦合方程；通过引入指示函数，设计了逐次加密多块网格的自适应生成策略，率先实现了固液相变的自适应网格加密LB模拟，兼顾了模拟精度和效率。(5)运用本项目构建的固液相变LB模型和方法，结合GPU高性能计算，开展了复杂多孔介质中固液相变的孔隙尺度模拟，揭示了多孔介质结构、导热系数、孔隙率和孔密度等对其相变传热特性的影响规律，为新型高效复合相变材料的设计开发提供理论和科学指导。项目迄今发表论文45篇，其中SCI论文20篇，EI论文23篇；培养毕业博士生2人、硕士生5人；项目负责人入选Elsevier中国高被引学者。

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