Topology Optimization of Fins for Rapid Heat Storage and Release in Triangular-Inside Tube Units
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摘要:
针对传统相变蓄热器传热速率低的问题，提出了一种内三角管式的蓄热器，并基于拓扑优化原理，以强化换热为目的，对其进行肋片设计，重构了拓扑结果，进而提取其拓扑特征重新设计肋片，分析了不同肋片设计对传热能力的影响。结果表明：内三角管式蓄热器相比传统圆管式蓄热器，蓄放热性能大大提高；安装拓扑重构肋片的蓄热器可以使蓄、放热时间缩短，传热效率提高；在蓄热过程中，分叉的拓扑特征可以提高自然对流作用；在放热过程中，安装拓扑重构肋片的蓄热器(火 积)耗散更小，可逆性更好，换热效率更高。
Abstract:A triangular-inside tube accumulator was proposed to solve the problem of low heat transfer rates of traditional phase change accumulators. Based on the topology optimization, the fins were designed for the purpose of enhancing heat transfer, and the topological results were reconstructed, with the topological characteristics extracted to redesign the fin configuration, and the heat transfer capacities of different fin configurations analyzed. The results show that, the triangular-inside tube accumulators have significant advantages of heat storage and release performances over the traditional circular tube accumulators; the accumulators with topologically reconstructed fins can shorten the heat storage and release time and improve the heat transfer efficiency; in the heat storage process, the bifurcated topology characteristics can improve the natural convection; during the heat release process, the accumulators with topologically reconstructed fins are less entransy dissipative, more reversible and more efficient.
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图 1 相变蓄热器物理模型简图 (单位：mm)
Figure 1. Physical model diagrams of phase change accumulators (unit: mm)
图 2 模型验证：(a) 网格无关性验证；(b) 时间步长验证；(c) 模拟与实验结果对比
Figure 2. Model validations: (a) the mesh assessment; (b) the time step assessment; (c) the comparison with experiment results
图 3 蓄热（左）和放热（右）过程拓扑优化结果
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同。
Figure 3. Topology optimization results of thermal storage (left) and release (right) processes
图 4 肋片重构和特征肋片设计（单位： mm）
Figure 4. The fin reconstruction and the characteristic fin design (unit: mm)
图 5 熔化过程中的液相和温度分布
Figure 5. Liquid fractions and temperature distributions in the melting process
图 6 液相分数和平均Nu数在熔化过程中的变化：(a) 液相分数；(b)
$\overline {Nu} $ Figure 6. Changes of the liquid fraction and the average Nu number in the melting process: (a) the liquid fraction; (b)
$\overline {Nu} $ 
图 7 平均速度区域监测示意图
Figure 7. Schematic diagram of the regional monitoring of average velocities
图 8 区域平均速度变化对比： (a) 区域I的平均速度；(b) 区域O的平均速度
Figure 8. Comparison of regional average velocity changes: (a) the average velocity in zone I; (b) the average velocity in zone O
图 9 凝固过程中的液相和温度分布
Figure 9. Liquid fractions and temperature distributions in the solidification process
图 10 液相分数和平均Nu数在凝固过程中的变化：(a) 液相分数β；(b)
$\overline {Nu} $ Figure 10. Changes of the liquid fraction and the average Nu number in the solidification process: (a) the liquid fraction β; (b)
$\overline {Nu} $ 
图 11 凝固过程中的总(火 积)耗散
Figure 11. Total entransy dissipations in the solidification process
表 1 物性参数表
Table 1. The physical property parameter table
parameter RT82 Cu solid density ${ { {\rho _{\text{s} } } } / {( { {\text{kg} } \cdot { {\text{m} }^{ { { - 3} } } }} )} }$ 950 8 978 liquid density ${ { {\rho _{\text{l} } } } / {( { {\text{kg} } \cdot { {\text{m} }^{ { { - 3} } } } } )} }$ 770 heat capacity at constant pressure ${{{c_p}} /{( {{\text{J}} \cdot {\text{k}}{{\text{g}}^{{{ - 1}}}} \cdot {{\text{K}}^{{{ - 1}}}}} )}}$ 2 000 381 latent heat ${{{L_{\text{p}}}} / {( {{\text{J}} \cdot {\text{k}}{{\text{g}}^{{{ - 1}}}}} )}}$ 176 000 phase change temperature interval $ {{{T_{{\text{pc}}}}} / {{{\text{K}}^{{{ - 1}}}}}} $ 350.15 ~ 358.15 thermal conductivity ${\lambda /{( {{\text{W}} \cdot {{\text{m}}^{{{ - 1}}}} \cdot {{\text{K}}^{{{ - 1}}}}} )}}$ 0.2 387.6 dynamic viscosity ${\mu / {( {{\text{kg}} \cdot {{\text{m}}^{{{ - 1}}}} \cdot {{\text{s}}^{{{ - 1}}}}} )}}$ 0.034 99 thermal expansion coefficient $ {\alpha /{{{\text{K}}^{{{ - 1}}}}}} $ 0.001 
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表 2 肋片设计参数表
Table 2. The fin design parameter table
model number number of fins fin thickness d/mm fin proportion η/% model 3 – – 4.72 model 4 24 0.4 4.60 model 5 24 0.4 4.56 model 6 24 – 4.75 model 7 24 0.8 9.12
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