基于分形理论的相变储热拓扑优化结构的换热特性分析

Analysis of heat transfer characteristics in phase change thermal storage with optimized structure based on fractal theory

采用变密度的拓扑优化方法,对不同肋片体积分数的管壳式相变蓄热器进行结构优化,并分别对拓扑优化分岔肋片进行分形特征分析、分形几何重构和放热特性分析。结果表明:不同的肋片体积分数对于优化结果有一定影响,随着肋片体积的增加,拓扑形态逐渐由一级分岔转变为二级分岔。相较于光管模型,体积分数φ为5%、7.5%、10%、12.5%和15%的拓扑优化肋片模型完全凝固时间分别缩短了90.9%、94.9%、95.6%、95.9%和96.3%。拓扑优化后的分岔肋片为分形结构,优化结构的分形维数和模型放热速率呈正相关。结合分形理论重构的分形肋片模型和拓扑优化肋片模型的分形维数和放热速率相差不大,表明重构的分形肋片虽结构简单,但保持了传热的高效性。

A topology optimization method with variable density was used to optimize the structure of shell-and-tube phase change accumulators with different fin volume fraction.The topology-optimized bifurcated fins were subjected to fractal characterization,fractal geometrical reconstruction and exothermic property analysis.The study indicates that the optimization results are affected by the fin volume fraction,and the topology morphology changes from primary bifurcation to secondary bifurcation as the fin volume increases.The complete solidification time of the topology-optimized fin model is reduced significantly compared to the light pipe model,with reductions of 90.9%,94.9%,95.6%,95.9%,95.9%and 96.3%for fin volume fraction of 5%,7.5%,10%,12.5%and 15%,respectively.The bifurcated fins optimized for topology are fractal structures.The exothermic rate of the model is positively correlated with the fractal dimension of the optimized structure.The reconstructed fractal fin model,which combines fractal theory and the topology-optimized fin model,has a fractal dimension and exothermic efficiency that do not differ much,indicating that the reconstructed fractal fin maintains high heat transfer efficiency despite its simple structure.