Parameters Sensitivity Analysis and Optimization of High-Temperature Heat Pipe for Heat Pipe Reactor
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摘要: 热管堆用高温热管的设计是存在约束的多目标优化问题，本文旨在实现高温热管的快速多目标设计优化。针对高温热管，考虑干道、槽道、丝网、烧结等吸液芯，基于改进热阻网络法，采用非支配遗传算法Ⅱ对热阻和毛细质量流量进行优化。结果表明，热管性能与工质和吸液芯有关，圆形和矩形干道采用工质钾更佳，三角槽和烧结纤维采用工质钠更佳；钠热管中热阻性能优劣依次为环形干道、丝网、矩形槽、烧结颗粒、烧结纤维、三角槽、圆形干道、矩形干道，流量性能优劣依次为环形干道、丝网、烧结颗粒、矩形槽、矩形干道、圆形干道、三角槽、烧结纤维；在800~950 K范围内，工作温度提升导致除环形干道外热阻减小89.9%以上，流量增加320.8%以上，环形干道中热阻减小93.5%，但流量减小8.8%。本研究可为核反应堆高温热管设计优化提供参考，提升高温热管性能。Abstract: The design of high-temperature heat pipe for heat pipe reactor is a multi-objective optimization problem with constraints. This paper aims to achieve rapid multi-objective design optimization of high-temperature heat pipe. For high-temperature heat pipe, main line, channel, wire mesh, sintering and other wicks are considered. In this paper, based on the improved thermal resistance network method, the non-dominant genetic algorithm II is used to optimize the thermal resistance and capillary mass flow. The results show that the performance of the heat pipe is related to the working medium and the wick. The working medium potassium is better for round and rectangular main lines, and the working medium sodium is better for triangular grooves and sintered fibers; For thermal resistance in sodium heat pipe, the ranking is in the order of circular main line, wire mesh, rectangular groove, sintered particles, sintered fiber, triangular groove, circular main line and rectangular main line; for flow, the ranking is in the order of circular main line, wire mesh, sintered particles, rectangular groove, rectangular main line, circular main line, triangular groove, sintered fiber. In the range of 800~950 K, the increase of working temperature results in the reduction of thermal resistance by more than 89.9% except for the annular main line, flow increase by more than 320.8%. In the annular main line, the thermal resistance is reduced by 93.5%, but the flow is reduced by 8.8%. This study can provide reference for the design optimization of high-temperature heat pipe of nuclear reactor, and for improving the performance of high-temperature heat pipe.
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图 2 热管的热阻网络
Rwi,z—dz长度内吸液芯的轴向热阻；Rwi,e/c—蒸发段/冷凝段的吸液芯径向热阻；Rwa,e/c—蒸发段/冷凝段的吸液芯径向热阻；Rwa,z—dz 长度内管壁的轴向热阻；Rv—蒸气热阻；T—温度
Figure 2. Thermal Resistance Network of Heat Pipe
图 3 吸液芯结构示意图
W—槽宽；Dis—槽间距；D—直径；ri—环形干道内半径；ro—环形干道外半径；Df—纤维直径；Dg—槽深；Dp—颗粒直径；ψ—三角槽的1/2角度
Figure 3. Structure Diagram of Wick
图 6 不同吸液芯结构下热阻-负毛细质量流量多目标优化
Figure 6. Multi-objective Optimization of Thermal Resistance-Negative Capillary Mass Flow with Different Wick Structures
图 7 不同吸液芯结构下的热阻和负毛细质量流量
Figure 7. Thermal Resistance and Negative Capillary Mass Flow with Different Wick Structures
图 8 工作温度对钠热管热阻和负质量流量的影响
Figure 8. Influence of Working Temperature on Thermal Resistance and Negative Mass Flow of Sodium Heat Pipe
表 1 吸液芯结构特征参数
Table 1. Characteristic Parameters for Wick Structures
吸液芯结构 rcap Dh ε K 圆形干道 D/2 D 1 D2/32 矩形干道 $ \dfrac{{WDg}}{{W + Dg}} $ $\dfrac{{2WDg}}{{W + Dg}}$ 1 $\dfrac{ {D_{_{\text{h}} }^{^{\text{2} }} } }{ {2{F_{_{ {\text{RA} }} } } } }$ 环形干道 ro−ri 2(ro−ri) 1 $\dfrac{ {D_{_{\text{h} }}^{^{\text{2} }} } }{ {2{F_{_{ {\text{AA} }} } } } }$ 矩形槽 W $ \dfrac{{4WDg}}{{W + 2Dg}} $ $\dfrac{W}{ { {D_{_{ {\text{is} }} } } } }$ $\dfrac{ {\varepsilon D_{_{\text{h} }}^{^{\text{2} }} } }{ {2{F_{_{ {\text{RG} }} } } } }$ 三角槽 $\dfrac{W}{{\cos \psi }}$ $W\cos \psi $ $\dfrac{W}{ {2{D_{_{ {\text{is} }} } } } }$ $\dfrac{ {\varepsilon D_{_{\text{h} }}^{^{\text{2} }} } }{ {2{F_{_{ {\text{IG} } }} } } }$ 丝网 $\dfrac{{W + D}}{2}$ $\dfrac{\varepsilon }{{1 - \varepsilon }}D$ $1 - \dfrac{ {1.05{\text{π } }N_{_{\text{mesh} }} D} }{4}$ $\dfrac{ { {D^{^2}}{\varepsilon ^{^3}} } }{ {122{ {\left( {1 - \varepsilon } \right)}^{^2}} } }$ 烧结颗粒 $0.21{D_{_{\text{p} }} }$ $\dfrac{ {2\varepsilon } }{ {3\left( {1 - \varepsilon } \right)} }{D_{_{\text{p} }} }$ 0.27~0.66 $\dfrac{ {D_{\text{p} }^{^{\text{2}} }{\varepsilon ^{^3}} } }{ {150{ {\left( {1 - \varepsilon } \right)}^{^2}} } }$ 烧结纤维 $\dfrac{ { {D_{_{\text{f} }} } }}{ {2\left( {1 - \varepsilon } \right)} }$ $\dfrac{\varepsilon }{ {1 - \varepsilon } }{D_{_{\text{f} }} }$ 0.6~0.9 FSF Nmesh—丝网目数；FSF、FAA、 FRA、FIG、FRG关系式详见文献[16] 
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表 2 液态金属高温热管设计参数
Table 2. Design Parameters of Liquid-metal Heat Pipe
参数 参数值 参数 参数值 工作温度/K 900 热管长度/m 2.0 最大承受压力/MPa 2 蒸发段长度/m 0.5 工作角度 0°（水平） 冷凝段长度/m 1.0 传热功率/kW 1 管壳外径/mm 30
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表 3 选取钠作为工质时不同吸液芯结构性能比较
Table 3. Comparison of Performance of Various Wick Structures with Sodium as the Working Fluid
性能参数 性能排序 热阻 环形干道>丝网>矩形槽>烧结颗粒>烧结纤维>三角槽>圆形干道>矩形干道 毛细质量流量 环形干道>丝网>烧结颗粒>矩形槽>矩形干道>圆形干道>三角槽>烧结纤维 热阻可行范围 烧结纤维>烧结颗粒>三角槽>矩形槽>圆形干道>矩形干道>丝网>环形干道 毛细质量流量可行范围 丝网>烧结颗粒>矩形槽>矩形干道>圆形干道>三角槽>烧结纤维>环形干道
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