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摘要:
为强化翅片管式储能系统的传热速率和相变材料域的温度均匀性，基于带惩罚的固体各向同性材料方法，以两种分形结构和对应翅片体积分数为参数，采用月桂酸为相变材料，进行了拓扑优化设计，并对比研究了拓扑优化的强化导热效果和温度均匀性。研究表明：壁面温度20 ℃时，拓扑优化有更好的导热效果，比分形优化分别减少21.18%和12.68%的总凝固时间，相变材料温度最高降低了7.33 ℃和4.30 ℃，平均降低了0.98 ℃和3.85 ℃；拓扑优化也具备更好的温度均匀性，相变材料平均方差分别为对应分形的33.38%和72.13%；壁温偏离拓扑的设计参数时，其热性能也基本未发生改变。以上结果传导为翅片设计提供了一定参考。
Abstract:In order to improve the temperature uniformity of the phase change material domain and the heat transfer rate of the finned tube energy storage system, two types of fractal structures and their corresponding fin volume fraction were used as design parameters, and lauric acid was used as the phase change material to carry out topology optimization design. This was done using the Solid Isotropic Material with Penalty method. The thermal conductivity enhancement and temperature uniformity of topology optimization are compared. The findings indicate that the topology optimization has a better thermal conductivity impact and can shorten the overall solidification time by 21.18% and 12.68%, respectively, when the wall temperature is 20 ℃. The phase change material temperature is reduced by 7.33 ℃ and 4.30 ℃, 0.98 ℃ and 3.85 ℃ on average. At the same time, the topology optimization also has better temperature uniformity, and the average variance of phase change material is 33.38% and 72.13% of the corresponding fractal, respectively. When the wall temperature deviates from the design parameters of the topology, the thermal performance does not change. This study provides some reference for fin design.
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图 1 拓扑优化的几何尺寸和设计域确定示意
Figure 1. Schematic diagram of geometry size and design domain determination for topology optimization
图 2 树状分形的各级尺寸示意
Figure 2. Schematic diagram of dimensions at each level of a tree fractal
图 4 拓扑优化结果（ri=15 mm, ro=60 mm）
Figure 4. Topology optimization results (ri=15 mm, ro=60 mm)
图 5 拓扑优化结果（ri=10 mm, ro=30 mm）
Figure 5. Topology optimization results (ri=10 mm, ro=30 mm)
图 6 网格无关性验证和时间步长无关性验证
Figure 6. Grid independent verification and time step independent verification
图 8 拓扑优化和Huang的分形优化液相质量分数云图(左半)和温度云图(右半)
Figure 8. Liquid fraction contour (left half) and Temperature contour (right half) of topology optimization and Huang’s fractal optimization
图 9 拓扑优化和Huang分形优化的液相分数对比
Figure 9. Comparison diagram of liquid fraction between topology optimization and Huang's fractal optimization
图 10 拓扑优化和Huang分形优化的PCM温度方差与温度对比
Figure 10. Comparison diagram of σPCM2 and TPCM between topology optimization and Huang's fractal optimization
图 11 拓扑优化和Luo的分形优化液相质量分数云图(左半)和温度云图(右半)
Figure 11. Liquid fraction contour (left half) and temperature contour (right half) of topology optimization and Luo’s fractal optimization
图 12 拓扑优化和Luo分形优化的液相分数对比
Figure 12. Comparison diagram of liquid fraction between topology optimization and Luo's fractal optimization
图 13 拓扑优化和Luo分形优化的PCM温度方差与温度对比
Figure 13. Comparison diagram of σPCM2 and TPCM between topology optimization and Luo's fractal optimization
图 14 拓扑和分形优化在不同壁面温度下的液相质量分数
Figure 14. Liquid fraction of topological and fractal optimization at different wall temperatures
图 15 拓扑和分形优化在不同壁面温度下的PCM温度方差
Figure 15. σPCM2 of topological and fractal optimization at different wall temperatures
表 2 材料热物性参数
Table 2. Thermal properties of material
ρ/（kg∙m−3） cp/（kJ∙kg−1∙℃−1） k/（W∙m−1∙℃−1） L/（kJ∙kg−1）
（月桂酸）Tm/℃
（月桂酸）月桂酸 铝 月桂酸 铝 月桂酸 铝 1007 (固)/862(液)2730 1.7(固)/2.4(液) 0.896 0.22(固)/0.147(液) 167 178 42～48 
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