Development and Preliminary Verification of OpenMC-PARCS Two-step Criticality and Burnup Calculation Model for Fast Reactors
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摘要: 快堆因具有能谱硬、共振现象复杂等特点而无法直接采用压水堆计算模型进行中子学分析。蒙特卡罗（MC）方法使用连续能量中子截面，能够准确模拟快堆中的共振干涉现象，得到精度较高的均匀化少群截面。本文研究了基于MC方法和三角形多项式展开节块（TPEN）方法的OpenMC-PARCS快堆两步法临界和燃耗计算模型，并且以OpenMC一步法计算结果为参考，利用钠冷快堆基准题MET-1000对假设微观截面不变的燃耗计算方案进行初步验证。初始稳态计算时，OpenMC-PARCS两步法堆芯有效增殖因子（keff）偏差约为−104pcm（1pcm=10−5），径向功率分布偏差不大于1%；燃耗计算时，堆芯keff与参考解的最大偏差为591.2pcm，大部分主要核素核子密度偏差不大于1%。初步验证结果表明，OpenMC-PARCS两步法模型有望用于大型金属快堆核设计和燃料管理。
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关键词:
- 钠冷快堆 /
- 蒙特卡罗（MC）方法 /
- 三角形多项式展开节块（TPEN）方法 /
- 两步法 /
- 燃耗计算
Abstract: Fast reactors cannot directly use PWR calculation models for neutronics analysis due to their hard spectra and complex resonance phenomena. Monte Carlo (MC) method utilizes continuous-energy neutron cross-sections, which can accurately simulate resonance interference phenomena in fast reactors, yielding highly precise homogenized few-group cross-sections. This paper, based on MC method and the Triangle-based Polynomial Expansion Nodal (TPEN) method, investigates an OpenMC-PARCS two-step method of criticality and burnup calculation for fast reactors. Based on the OpenMC one-step method calculation results, a preliminary validation of the assumed constant microscopic cross-section burnup calculation scheme is conducted using the sodium-cooled fast reactor benchmark problem MET-1000. In the initial steady-state calculation, the deviation of the core effective multiplication factor (keff) using the OpenMC-PARCS two-step method is −104pcm (1pcm=10−5), and the deviation in the radial power distribution is no greater than 1%. During burnup calculations, the maximum deviation of the core keff from the reference solution is 591.2pcm, while most major nuclide number density deviation is no greater than 1%. The preliminary validation results indicate that the OpenMC-PARCS two-step method model can be used for large metallic fast reactor core design and fuel management. -
图 3 OpenMC-PARCS快堆两步法稳态计算过程
Figure 3. OpenMC-PARCS Fast Reactor Two-step Steady-state Calculation Process
图 4 OpenMC-PARCS快堆稳态与燃耗计算流程图
Figure 4. OpenMC-PARCS Fast Reactor Steady-state and Burnup Calculation Flowchart
图 7 非均匀两圈超组件模型（左）和等效均匀两圈超组件模型（右）
Figure 7. Non-uniform Two-ring Supercell Model (Left) and Equivalent Uniform Two-ring Supercell Model (Right)
图 9 OpenMC计算得到的MET-1000 1/6 堆芯径向功率分布
Figure 9. The Radial Power Distribution of MET-1000 1/6 Core Obtained from OpenMC Calculations
图 10 OpenMC-PARCS计算得到的MET-1000 1/6 堆芯径向功率分布
Figure 10. The Radial Power Distribution of MET-1000 1/6 Core Obtained from OpenMC-PARCS Calculations
图 11 MET-1000 1/6堆芯径向功率相对偏差
Figure 11. MET-1000 1/6 Core Radial Power Relative Deviation
图 12 MET-1000堆芯轴向功率分布及相对偏差
Figure 12. Axial Power Distribution and Relative Deviation of the MET-1000 Reactor Core
图 14 OpenMC一步法和OpenMC-PARCS两步法之间主要核素核子密度的相对偏差
Figure 14. Relative Deviation of the Nuclear Density of Major Nuclides between OpenMC and OpenMC-PARCS
表 1 MET-1000堆芯名义工作条件
Table 1. Nominal Operating Conditions of MET-1000 Reactor Core
参数名 参数值 反应堆功率/MW 1000.0 冷却剂温度/℃ 432.5 结构平均温度/℃ 432.5 燃料平均温度/℃ 534.0 
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表 2 由ECCO-33群简化的24群能群结构
Table 2. 24-group Energy Group Structure Simplified from ECCO-33
能群序号 能量上界/MeV 能量下界/MeV 能群序号 能量上界/MeV 能量下界/MeV 1 1.964033×101 1.000000×101 13 4.086771×10−2 2.478752×10−2 2 1.000000×101 6.065307×100 14 2.478752×10−2 1.503439×10−2 3 6.065307×100 3.678794×100 15 1.503439×10−2 9.118820×10−3 4 3.678794×100 2.231302×100 16 9.118820×10−3 5.530844×10−3 5 2.231302×100 1.353353×100 17 5.530844×10−3 3.354626×10−3 6 1.353353×100 8.208500×10−1 18 3.354626×10−3 2.034684×10−3 7 8.208500×10−1 4.978707×10−1 19 2.034684×10−3 1.234098×10−3 8 4.978707×10−1 3.019738×10−1 20 1.234098×10−3 7.485183×10−4 9 3.019738×10−1 1.831564×10−1 21 7.485183×10−4 4.539993×10−4 10 1.831564×10−1 1.110900×10−1 22 4.539993×10−4 3.043248×10−4 11 1.110900×10−1 6.737947×10−2 23 3.043248×10−4 1.486254×10−4 12 6.737947×10−2 4.086771×10−2 24 1.486254×10−4 1.000010×10−11
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表 3 堆芯反应性效应计算结果
Table 3. Core Reactivity Calculation Results
堆芯参数 OpenMC OpenMC-PARCS 偏差/pcm ${k_{{\text{eff}}}}$（提棒工况） 1.030524±0.00003 1.029484 −104±3 ${k_{{\text{eff}}}}$（插棒工况） 0.867201±0.00003 0.866372 −82.9±3 $\Delta {\rho _{{\mathrm{CR}}}}$/pcm 16332.3±6 16311.2 −21.1±6 $\Delta {\rho _{{\mathrm{Doppler}}}}$/pcm −354.9±9 −401.9 −47±9 $\Delta {\rho _{{\mathrm{Na}}}}$/pcm 2308.4±6 1553.1 −755.3±6
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表 4 不同燃耗计算模型花费的计算时间
Table 4. Computational Time Spent by Different Burnup Calculation Models
计算模型 组件阶段计算时间/核时 堆芯阶段计算时间/核时 总计算时间/核时 OpenMC随机
体积计算OpenMC生成
均匀化群常数OpenMC生成微观
燃耗计算参数库接口程序+PARCS堆芯
扩散计算+组件燃耗计算OpenMC一步法① 7464.4 OpenMC-PARCS两步法② 0.028 221.573 559.028 0.614 781.24 注：①OpenMC一步法执行MC全堆输运计算，直接统计总计算时间；②OpenMC-PARCS两步法分阶段统计计算时间。
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