Design and Multi-Objective Optimization Study of Liquid Lead-Supercritical Carbon Dioxide Heat Exchanger
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摘要: 为提高铅冷快堆主换热器的综合换热性能，本研究建立了以液态铅和超临界二氧化碳（S-CO2）为工质的螺旋盘管式主换热器的热工水力模型，采用MATALB语言编写了设计程序，并利用非支配排序遗传算法（NSGA-II）开展了对主换热器的换热面积和综合性能评价因子的多目标优化设计。结果表明，本文建立的优化设计方法可以在提高主换热器综合性能的同时，有效降低其换热面积。在主换热器的设计中，应优先考虑管外径、螺旋管层数以及第一层螺旋管数，以达到减小换热面积、提高综合换热性能的目的。Abstract: In order to improve the comprehensive heat transfer performance of the primary heat exchanger in lead-cooled fast reactors, the present study established a thermal-hydraulic model for a spiral-coil primary heat exchanger using liquid lead and supercritical carbon dioxide (S-CO2) as working fluids. A design code was developed in MATLAB language, and a multi-objective optimization design was conducted on the heat transfer area and comprehensive performance evaluation factor of the primary heat exchanger by employing the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The results showed that the optimization design method proposed in this paper can effectively reduce the heat transfer area of the heat exchanger and improve its comprehensive performance. In the design of the primary heat exchanger, priority should be given to the outer diameter of tubes, the number of spiral tube layers and the number of spiral tubes in the first layer, so as to reduce the heat exchange area and improve the comprehensive heat exchange performance.
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Key words:
- Lead-cooled fast reactor /
- Heat exchanger /
- Gene algorithm /
- Optimization design
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图 1 单根螺旋管示意图
H—换热管高度；Dk—第k层换热管螺旋直径；αk—第k层换热管的螺旋上升角
Figure 1. Schematic Diagram of a Single Spiral Tube
图 2 螺旋盘管式换热器结构示意图
do—管外径；di—管内径；ST—径向节距；SL—轴向节距；Din—中心柱直径；Dout—套筒内径
Figure 2. Schematic Diagram of Spiral Tube Heat Exchanger
图 3 换热器等功率分段模型示意图
T1,H—液态铅入口温度；T2,H—液态铅出口温度；T1,L—S-CO2入口温度；T2,L—S-CO2出口温度
Figure 3. Schematic Diagram of the Segmented Model at Equal Power
图 5 以管侧和壳侧综合性能评价因子为适应度函数的Pareto最优解集
Figure 5. Pareto Optimal Solution Set with Comprehensive Performance Evaluation Factors for Tube-side and Shell-side as Fitness Function
图 6 主换热器两侧表面换热系数的倒数随管外径的变化
Figure 6. Variation of the Reciprocal of Heat Transfer Coefficients on Both Sides of Heat Exchanger with the Outer Diameter of Tube
图 7 不同S-CO2入口温度下的Pareto最优解集
Figure 7. Pareto Optimal Set at Different Supercritical Carbon Dioxide Inlet Temperatures
图 8 优化变量对换热面积的敏感度
Figure 8. Sensitivity of Optimization Variables to Heat Exchange Area
图 9 优化变量对管侧综合性能评价因子的敏感度
Figure 9. Sensitivity of Optimization Variables to Comprehensive Performance Evaluation Factors of Tube Side
表 1 液态铅物性关系式
Table 1. Formulas for the Physical Properties of Liquid Lead
物性 关系式 密度ρ/(kg·m−3) ρ=11367−1.1944T 粘度μ/(Pa·s) μ=4.55×10−4exp(1069/T) 热导率λ/(W·m−1·K−1) λ=9.2+0.011T 比热容cp/
(J·kg−1·K−1)cp=175.1−4.961×10−2T + 1.985×
10−5T 2−1.524×106T −2−2.099 × 10−9T 3
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表 2 主换热器运行条件
Table 2. Operating Conditions of the Primary Heat Exchange
运行参数 具体参数 换热功率/MW 12.5 壳侧进出口温度/℃ 600/450 管侧进出口温度/℃ 360/560 壳侧压力/MPa 0.1 管侧压力/MPa 20 S-CO2质量流量/(kg·s−1) 51.3 液态铅质量流量/(kg·s−1) 571
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表 3 主换热器初步设计结果
Table 3. Preliminary Results of Primary Heat Exchanger
设计变量 设计值 换热管外径/mm 8 换热管内径/mm 6.6 径向节距/mm 10 轴向节距/mm 10 螺旋管层数 45 换热管数 1800 中心柱直径/mm 100 套筒内径/mm 1016 第一层螺旋管头数 18 平均螺旋上升角 14.3° 换热面积/m² 112.7
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表 4 优化变量取值范围
Table 4. Variable Range for Optimization
变量 取值范围 换热管外径/mm 8≤do≤25 径向节径比（ST/do） 1.25≤（ST/do）≤1.6 轴向节径比（SL/do） 1.25≤（SL/do）≤1.6 第一层螺旋管头数（M0） 10≤M0≤20 螺旋管层数（N） 40≤N≤70 中心柱直径/mm 100≤Din≤500
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