基于理论的传热结构拓扑优化

doi:10.11949/0438-1157.20191079

摘要/Abstract

摘要：

以理论为基础，分析了在含有内热源的二维稳态导热问题中的耗散。并以此为目标函数，通过密度法建立拓扑优化模型并用全局移动渐近线（GCMMA）开展拓扑优化研究。对比分析了以最小耗散以及最小熵产得到的拓扑优化构型在传热性能上的异同。然后，以最小耗散为优化目标，进一步分析了不同高导热材料体积占比下最优传热拓扑结构。结果表明，最小耗散以及最小熵产得到的拓扑优化构型结构相似，均可大幅增加传热性能，系统的平均温度均可降低9℃以上。而对于传热结构来说，综合考虑优化效果以及成本，20%的体积占比是一个较优值，在此占比下，优化后的耗散仅为优化前的8.7%。基于理论的传热结构拓扑研究为肋片的结构设计以及传热强化提供了理论指导。

关键词: 传热, 耗散, 熵, 优化设计

Abstract:

Based on entransy theory, the entransy equilibrium equation for two-dimensional steady heat conduction with internal heat source is derived, and the entransy dissipation in this heat conduction process is analyzed. Then, taking entransy dissipation as the objective function, the thermal conductivity of the material as the design variable, the topology model is built with solid isotropic microstructure with penalization method, the model is solved by globally convergent method of moving asymptotes. The entropy generation is also applied as the objective function to compare with the entransy dissipation. The results show that both of minimum entransy dissipation and minimum entropy generation lead the similar heat transfer structure during the optimal process, the topology structure extends outward gradually as the iteration goes on and tends to be optimal, the average temperature can be decreased by 9℃. Finally, the topology structures with different high conductive material fraction are compared under the objective function of minimum entransy dissipation, the results indicate that the entransy dissipation decreases under different volume ratios of high thermal conductive material. Considering the optimization effect and cost, with the high conductive material fraction of 20%, the entransy dissipation of optimal structure can be reduced to 8.7%.

Key words: heat transfer, entransy dissipation, entropy, optimal design

中图分类号:

TH 124

张庭玮, 李斌, 翟晓强. 基于理论的传热结构拓扑优化[J]. 化工学报, 2020, 71(S1): 31-37.

Tingwei ZHANG, Bin LI, Xiaoqiang ZHAI. Topology optimization on heat conduction based on entransy theory[J]. CIESC Journal, 2020, 71(S1): 31-37.

图/表 8

图1 传热模型

Fig.1 Heat transfer model

表1 模型参数

Table 1 Parameters of model

参数	数值
外径R	1 m
壁温T_b	273.15 K
高热导率k_high	237 W·m^-1?K^-1
体积占比γ	0.2
权重因子q	0.5
内径r	0.3 m
初始温度T_ini	293.15 K
低热导率k_low	2.4 W·m^-1?K^-1
惩罚因子p	5
热源 $Q ˙$	100 W·m^-3

表1 模型参数

Table 1 Parameters of model

参数	数值
外径R	1 m
壁温T_b	273.15 K
高热导率k_high	237 W·m^-1?K^-1
体积占比γ	0.2
权重因子q	0.5
内径r	0.3 m
初始温度T_ini	293.15 K
低热导率k_low	2.4 W·m^-1?K^-1
惩罚因子p	5
热源 $Q ˙$	100 W·m^-3

图2 基于最小耗散的传热拓扑结构

Fig.2 Topology structure of heat conduction based on minimum entransy dissipation

图3 基于熵产最小的传热拓扑结构

Fig.3 Topology structure of heat conduction based on minimum entropy generation

图4 温度分布等值图

Fig.4 Isothermal line of temperature

图5 不同目标函数下平均温度随迭代次数的变化

Fig.5 Variation of average temperature under different objective function

图6 不同体积占比下的拓扑结构

Fig.6 Topology structure under different volume fraction

图7 优化前后的耗散

Fig.7 Entransy dissipation before and after optimization

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