Research on the Few Group Cross-section Production Method for Heat Pipe Micro Reactors Based on Monte Carlo Code
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摘要: 为了提高热管微堆物理计算效率，基于栅元均匀化-堆芯输运计算两步法，从各向异性散射、燃料均匀化模型、泄漏修正、能群结构等方面，开展了基于蒙特卡罗程序的热管微堆输运计算所需少群截面制作方法研究。数值结果表明：采用输运修正、泄漏修正等方法，并且外围燃料采用专门的“燃料-反射层”均匀化模型，两步法计算得到的有效增殖因子（keff）偏差小于100pcm（1pcm=10−5），功率分布偏差小于3%，控制鼓总价值偏差小于5%，且堆芯输运计算代价比蒙特卡罗一步法全堆计算小2个量级。因此，本文研究的栅元均匀化-堆芯输运两步法满足工程设计的精度要求，同时大幅提高了热管微堆物理计算效率。Abstract: In order to improve the efficiency of the physical calculations of Heat Pipe Micro Reactors, based on the two-step method of cell homogenization-core transport calculation, this paper studies the few group cross-section production method for Heat Pipe Reactor core transport calculation by using the Monte Carlo (MC) code from the aspects of anisotropic scattering, fuel homogenization model, leakage correction and energy group structure. The numerical results show that using transport correction, leakage correction and other methods, and using a specialized "fuel-reflector" homogenization model for the peripheral fuel, the keff deviation obtained by the two-step core calculation is less than 100pcm (1pcm=10−5), the power distribution deviation is less than 3%, and the the control drum total worth deviation is less than 5%. Moreover, the core transport calculation cost is two orders of magnitude smaller than that of the Monte Carlo one-step full core calculation. Therefore, the two-step method of cell homogenization-core transport studied in this paper meets the accuracy requirements of engineering design and can greatly improve the efficiency of physical calculations of Heat Pipe Micro Reactors.
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图 7 不同燃料模型下的堆芯功率分布偏差
Figure 7. Bias of Core Power Distribution for Different Fuel Models
图 8 Case 4燃料模型下的堆芯功率分布偏差（泄漏修正后）
Figure 8. Bias of Core Power Distribution for Fuel Model of Case 4 (after Leakage Correction)
图 9 不同燃料模型下的堆芯功率分布偏差（9群）
Figure 9. Bias of Core Power Distribution for Different Fuel Models (Group 9)
表 1 能群结构
Table 1. Group Structure
总能群数 能群 上界/MeV 能群 上界/MeV 能群 上界/MeV 24群 8 0.4979 16 0.0091 24 0.0001 7 0.8209 15 0.0150 23 0.0003 6 1.3534 14 0.0248 22 0.0005 5 2.2313 13 0.0409 21 0.0007 4 3.6788 12 0.0674 20 0.0012 3 6.0653 11 0.1111 19 0.0020 2 10 10 0.1832 18 0.0034 1 19.6403 9 0.3020 17 0.0055 9群 3 0.8209 6 0.0091 9 0.0001 2 2.2313 5 0.0409 8 0.0005 1 19.64 4 0.1832 7 0.0020 
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表 2 各向异性散射对堆芯keff的影响
Table 2. Influence of Anisotropic Scattering on Core keff
算例 keff 计算偏差/pcm 参考解 1.11401 0阶 1.13344 1729 输运修正 1.11195 –185
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表 3 燃料模型对堆芯结果的影响
Table 3. Influence of Fuel Model on Core Results
算例 keff keff计算偏差/pcm keff模型
影响/pcm最大功率分布
偏差/%Case 1 1.11195 −185 −4.34 Case 2 1.11160 −216 −31 −4.39 Case 3 1.11333 −61 155 3.30 Case 4 1.11415 12 73 3.14
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表 4 泄漏修正对堆芯结果的影响
Table 4. Influence of Leakage Correction on Core Results
修正情况 算例 keff 偏差/pcm 泄漏修正
影响/pcm最大功率
分布偏差/%无泄漏修正 Case 1 1.11195 −185 −4.34 Case 2 1.11160 −216 −4.39 Case 3 1.11333 −61 3.30 Case 4 1.11415 12 3.14 泄漏修正 Case 1 1.11217 −165 20 −4.21 Case 2 1.11188 −192 24 −4.25 Case 3 1.11365 −32 29 2.95 Case 4 1.11430 27 15 2.89
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表 5 不同能群的堆芯结果
Table 5. Core Results for Different Energy Groups
能群 算例 keff keff计算偏
差/pcmkeff能群
影响/pcm最大功率
分布偏差/%24 Case 1 1.11217 −165 −4.21 Case 2 1.11188 −192 −4.25 Case 3 1.11365 −32 2.95 Case 4 1.11430 27 2.89 9 Case 1 1.11259 −127 38 −6.79 Case 2 1.11236 −148 44 −6.83 Case 3 1.11404 3 35 −4.45 Case 4 1.11471 63 36 −2.68
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表 6 ARI状态下的计算结果对比表
Table 6. Comparison of Calculation Results for Condition ARI
算例 keff keff偏差/
pcm控制鼓
价值/pcm控制鼓价
值偏差/%最大功率
分布偏差/%RMC 1.00783 10016 ARC-9群 1.01237 449 9630 −4% −2.797 ARC-24群 1.01131 344 9699 −3% −1.274
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表 7 单次堆芯计算代价
Table 7. Calculation Cost for Single Core Calculation
计算过程 能群 计算对象 计算代价/
核时单次总代
价/核时一步法堆芯输运计算 1/6堆芯 1.00×103 1.00×103 均匀化截面计算 24群 热管 2.73×102 3.30×103 燃料-中心 5.77×102 燃料-外围 3.88×102 基体 6.13×102 气隙 1.14×103 反射层 2.95×102 两步法堆芯输运计算 全堆芯 1.80×101 1.80×101 均匀化截面计算 9群 热管 2.70×102 2.75×103 燃料-中心 5.71×102 燃料-外围 3.89×102 基体 6.22×102 气隙 5.98×102 反射层 2.90×102 全堆芯 两步法堆芯输运计算 1.10×101 1.10×101
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