Calculation of Source Terms for Water-cooled Fusion Reactor Based on Deviation Effect Nuclide Screening Method
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摘要: 活化腐蚀产物是水冷聚变堆正常运行过程中主要的放射性源项，一般采用解析方法求解，但解析方法无法在满足精度要求的同时提高计算效率。本文提出一种基于定量化偏离效应分析的核素筛选方法，以放射性活度和剂量率2个参数定义偏离效应指标，通过分析偏离效应指标，筛选出满足接收准则的核素，以确定计算所需要的目标核素，这种分析方法既能满足精度需求，又能提高计算效率。将该核素筛选方法应用于国际热核聚变实验堆（ITER） 限制器-外包层水冷回路 （LIM-OBB）的活化腐蚀产物源项分析，并与此问题下的高精度基准解进行对比。结果表明，57Co、58Co、55Fe、51Cr等主要活化腐蚀产物核素的比活度计算结果相对于基准解的偏差均控制在1.5%以内；应用核素筛选方法后的计算效率相对于基准解的计算效率提高了279倍。Abstract: The activated corrosion products are the main radioactive source terms in the normal operation of water-cooled fusion reactor, and are generally solved by analytical methods, but analytical methods cannot improve the calculation speed while meeting the accuracy requirements. In this paper, a nuclide screening method based on quantitative deviation effect analysis is proposed, which defines the two parameters of radioactivity and dose rate as deviation effect indicators. By analyzing the deviation effect indicators, nuclides meeting the acceptance criteria are screened to determine the target nuclides required for calculation. This analysis method can not only meet the accuracy requirements, but also improve the calculation efficiency. This nuclide screening method is applied to the source term analysis of activated corrosion products in the International Thermonuclear Experimental reactor (ITER) limiter-outer cladding water-cooled loop (LIM-OBB), and compared with the high-precision benchmark solution under this issue. The results show that the relative deviations of the specific activity calculation results of important activated corrosion product nuclides such as 57Co, 58Co, 55Fe, and 51Cr compared with the benchmark solution are all controlled within 1.5%; The calculation efficiency of the nuclide screening method is 279 times higher than that of the benchmark solution.
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表 1 LIM-OBB水冷回路的运行参数
Table 1. Operating Parameters of LIM-OBB Water Cooling Circuit
参数名 参数值 辐照区流速/ (m·s−1) 1~6 非辐照区流速/(m·s−1) 3~5 辐照区温度/℃ 174 非辐照区温度/℃ 140 冷却剂密度/ (kg·m−3) 9.10×102 中子注量率/ (m−2·s−1) 2.58×1017 流经辐照区的时间/ s 2 流经非辐照区的时间/ s 26 过滤器流量/(kg·s−1) 2.55 过滤因子/ % 50 
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表 2 LIM-OBB水冷回路中腐蚀产物及活化腐蚀产物的比活度计算结果
Table 2. Specific Activity Calculation Results of Specific Activity of Corrosion Products and Activated Corrosion Products in LIM-OBB Water Cooling Circuit
腐蚀产物（CPs）总质量 辐照区/kg 非辐照区/kg 冷却剂/kg 氧化层 沉积层 氧化层 沉积层 离子 微粒 20.48 0.71 29.09 1.45 6.42×10−3 4.48×10−3 活化腐蚀产物总比活度 辐照区/(Bq·m−2) 非辐照区/(Bq·m−2) 冷却剂/(Bq·m−3) 氧化层 沉积层 氧化层 沉积层 离子 微粒 1.04×1012 6.06×1010 4.07×105 2.85×1010 2.40×109 7.01×109
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表 3 LIM-OBB水冷回路中活化腐蚀产物主要核素的比活度
Table 3. Specific Activity of Main Nuclides of Activated Corrosion Products in LIM-OBB Water Cooling Circuit
核素 辐照区核素比活度/(Bq·m−2) 非辐照区核素比活度/(Bq·m−2) 冷却剂/(Bq·m−3) 氧化层 沉积层 氧化层 沉积层 离子 微粒 53Fe 1.57×1010 5.46×108 7.54×10−1 5.63×104 3.62×107 9.96×107 53Fem 5.08×109 1.77×108 6.75×10−2 5.03×103 1.17×107 3.23×107 55Fe 1.98×1011 1.96×1010 2.11×105 1.48×1010 4.57×108 1.47×109 59Fe 4.19×108 2.24×107 1.30×102 9.17×106 9.67×105 2.79×106 57Co 8.43×1010 7.27×109 7.28×104 5.07×109 1.95×108 6.08×108 58Co 5.18×1010 3.16×109 2.35×104 1.64×109 1.20×108 3.52×108 58Com 3.41×1010 1.19×109 9.36×101 6.98×106 7.86×107 2.16×108 60Co 8.96×108 9.12×107 9.91×102 6.98×107 2.06×106 6.69×106 60Com 7.75×109 2.70×108 4.18×10−1 3.12×104 1.78×107 4.93×107 57Ni 2.15×1010 7.63×108 2.38×102 1.77×107 4.97×107 1.37×108 63Ni 3.61×107 3.79×106 4.16×101 2.95×106 8.33×104 2.72×105 51Cr 3.47×1011 1.63×1010 6.93×104 4.98×109 8.01×108 2.28×109 55Cr 1.88×109 6.55×107 3.43×10−2 2.56×103 4.34×106 1.19×107 54Mn 3.32×1010 2.93×109 2.97×104 2.07×109 7.68×107 2.41×108 56Mn 2.10×1011 7.33×109 1.68×102 1.25×107 4.85×108 1.34×109
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表 4 基于核素筛选方法得到的活化腐蚀产物主要核素的比活度及相对于高精度基准解的相对偏差
Table 4. Specific Activity of Main Nuclides of Activated Corrosion Products Obtained Based on Nuclide Screening Method and Their Relative Deviation from High-precision Benchmark Solution
核素 辐照区 非辐照区 冷却剂 氧化层 沉积层 氧化层 沉积层 离子 微粒 比活度/
(Bq·m−2)相对偏
差/%比活度/
(Bq·m−2)相对偏
差/%比活度/
(Bq·m−2)相对偏
差/%比活度/
(Bq·m−2)相对偏
差/%比活度/
(Bq·m−3)相对偏
差/%比活度/
(Bq·m−3)相对偏
差/%53Fe 1.57×1010 0 5.47×108 −0.18 7.54×10−1 0 5.63×104 0 3.62×107 0 9.96×107 0 53Fem 5.08×109 0 1.77×108 0 6.75×10−2 0 5.04×103 −0.20 1.17×107 0 3.23×107 0 55Fe 1.98×1011 0 1.95×1010 0.51 2.10×105 0.47 1.47×1010 0.68 4.57×108 0 1.47×109 0 59Fe 4.19×108 0 2.24×107 0 1.30×102 0 9.17×106 0 9.67×105 0 2.79×106 0 57Co 8.43×1010 0 7.27×109 0 7.30×104 −0.27 5.05×109 0.39 1.95×108 0 6.08×108 0 58Co 5.18×1010 0 3.17×109 −0.32 2.35×104 0 1.64×109 0 1.20×108 0 3.52×108 0 58Com 3.41×1010 0 1.19×109 0 9.36×101 0 6.98×106 0 7.86×107 0 2.16×108 0 60Co 8.94×108 0.22 9.06×107 0.66 9.89×102 0.20 6.90×107 1.15 2.06×106 0 6.67×106 0.30 60Com 7.75×109 0 2.71×108 −0.37 4.18×10−1 0 3.12×104 0 1.79×107 −0.56 4.93×107 0 57Ni 2.15×1010 0 7.65×108 −0.26 2.38×102 0 1.77×107 0 4.96×107 0.20 1.37×108 0 63Ni 3.60×107 0.28 3.76×106 0.79 4.15×101 0.24 2.91×106 1.36 8.31×104 0.24 2.71×105 0.37 51Cr 3.47×1011 0 1.63×1010 0 6.93×104 0 4.98×109 0 8.01×108 0 2.28×109 0 55Cr 1.88×109 0 6.56×107 −0.15 3.43×10−2 0 2.56×103 0 4.34×106 0 1.19×107 0 54Mn 3.32×1010 0 2.93×109 0 2.97×104 0 2.06×109 0.48 7.67×107 0.13 2.41×108 0 56Mn 2.10×1011 0 7.35×109 −0.27 1.68×102 0 1.25×107 0 4.85×108 0 1.34×109 0
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表 5 基于核素筛选方法的比活度计算结果和高精度基准解对比
Table 5. Comparison of Results Based on Nuclide Screening Method and High-precision Benchmark Solution
核素种类 活化腐蚀产物比活度 计算时间 辐照区/(Bq·m−2) 非辐照区/(Bq·m−2) 冷却剂/(Bq·m−3) 氧化层 沉积层 氧化层 沉积层 离子 微粒 筛选后核素（数百种） 1.04×1012 6.06×1010 4.07×105 2.85×1010 2.40×109 7.01×109 4.5 min 全部核素（数千种） 1.11×1012 6.34×1010 4.12×105 2.90×1010 2.56×109 7.47×109 21 h 筛选后核素放射性贡献/% 93.7 95.6 98.8 98.3 93.7 93.9 — “—”——无此项
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