[论文解读] Numerical Predictions of Effective Thermal Conductivities for Three-dimensional Four-directional Braided Composites Using the Lattice Boltzmann Method

Wen‐Zhen Fang, Jian‐Jun Gou+3 more|arXiv (Cornell University)|Mar 30, 2015

Lattice Boltzmann Simulation Studies参考文献 36被引用 8

一句话总结

本研究提出一种采用非对角碰撞矩阵的多重松弛时间格子Boltzmann方法，用于预测三维四向编织复合材料的有效热导率，能够精确模拟各向异性、非均质微观结构中的热传导。该模型与热盘法实验数据高度吻合，并表明更高的纤维体积分数和更大的内部编织角度会提高横向热导率，但降低纵向热导率。

ABSTRACT

In this paper, a multiple-relaxation-time lattice Boltzmann model with an off-diagonal collision matrix was adopted to predict the effective thermal conductivities of the anisotropic heterogeneous materials whose components are also anisotropic. The half lattice division scheme was adopted to deal with the internal boundaries to guarantee the heat flux continuity at the interfaces. Accuracy of the model was confirmed by comparisons with benchmark results and existing simulation data. The present method was then adopted to numerically predict the transverse and longitudinal effective thermal conductivities of three-dimensional (3D) four-directional braided composites. Some corresponding experiments based on the Hot Disk method were conducted to measure their transverse and longitudinal effective thermal conductivities. The predicted data fit the experiment data well. Influences of fiber volume fractions and interior braiding angles on the effective thermal conductivities of 3D four-directional braided composites were then studied. The results show that a larger fiber volume fraction leads to a larger effective thermal conductivity along the transverse and longitudinal directions; a larger interior braiding angle brings a larger transverse thermal conductivity but a smaller one along the longitudinal direction. It is also shown that for anisotropic materials the periodic boundary condition is different from the adiabatic boundary condition and for periodic microstructure unit cell the periodic boundary condition should be used. Key words: effective thermal conductivities, anisotropic, multi-relaxation-time, lattice Boltzmann method, three-dimensional four-directional braided composites

研究动机与目标

• 开发一种稳健的数值模型，用于预测各向异性、非均质三维四向编织复合材料的有效热导率。
• 通过半格子划分方案，解决纤维与基体相之间内界面处的热流连续性问题。
• 利用基准解和热盘法实验数据对模型进行验证。
• 研究纤维体积分数和内部编织角度对横向与纵向热导率的影响。
• 明确在各向异性材料中，周期性微观结构单元胞的正确边界条件（周期性 vs. 绝热）。

提出的方法

• 采用具有非对角碰撞矩阵的多重松弛时间（MRT）格子Boltzmann模型，模拟各向异性非均质材料中的热传导。
• 应用半格子划分方案，确保不同材料相之间内界面处热流的连续性。
• 通过解析基准解和已有仿真数据对模型进行验证，以确认其准确性和稳定性。
• 在代表性体积元（RVE）上施加周期性边界条件，以真实反映复合材料的周期性微观结构。
• 通过在适当边界条件下求解热格子Boltzmann方程，实现对横向与纵向有效热导率的数值预测。
• 将仿真框架与热盘法实验测量结果相结合，用于模型验证。

实验结果

研究问题

• RQ1 MRT格子Boltzmann方法在预测具有各向异性组分的三维四向编织复合材料有效热导率方面，其准确性如何？
• RQ2 纤维体积分数对复合材料横向与纵向热导率有何影响？
• RQ3 内部编织角度如何影响横向与纵向方向的有效热导率？
• RQ4 在各向异性复合材料中，用于建模周期性微观结构的边界条件应为周期性还是绝热边界条件？
• RQ5 数值预测与热盘法获得的实验测量结果在多大程度上吻合？

主要发现

• 有效热导率的数值预测与热盘法获得的实验数据高度一致。
• 纤维体积分数的增加导致横向与纵向方向的有效热导率均提高。
• 较大的内部编织角度会提高横向热导率，但降低纵向热导率。
• 对于具有周期性微观结构的各向异性材料，必须使用周期性边界条件而非绝热边界条件，才能正确反映物理行为。
• 采用非对角碰撞矩阵的MRT格子Boltzmann模型在模拟复杂、非均质、各向异性复合材料中的热传导时，表现出高精度与高稳定性。