Development and Application of Structural Method for Uncertainty Evaluation of Constitutive Models
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摘要: 最佳估算加不确定性（BEPU）方法被国际原子能机构（IAEA）推荐用于核电厂安全分析，目前已成为核电厂执照申请的主流方法。典型BEPU方法依赖于最佳估算程序将输入参数的不确定性传播至输出，而程序本构模型的不确定性则往往没有得到适当考虑。本研究提出了一种结构化方法用于评价程序本构模型的不确定性，基于该方法对本构模型按照特征进行分类，针对不同模型类型采用不同评价方法。本研究使用的模型评价方法包括前向方法中的非参数曲线估计法以及反向方法中的贝叶斯校准法和覆盖率校准法，此外还包含替代模型的构建方法。使用该结构化方法量化了失水事故中重要模型的不确定性，并将量化的模型不确定性通过抽样计算传播至包壳峰值温度。结果表明，抽样计算值和实验值均小于保守计算值，考虑了模型不确定性后的传播计算结果能够很好地包络实验值，且考虑模型不确定性后能够有效增加安全裕量。Abstract: The best estimate plus uncertainty (BEPU) analysis is recommended by IAEA for safety analysis of nuclear power plants, and has become the mainstream method for license application of nuclear power plants. Typical BEPU method relies on the best estimation program to propagate the uncertainties of input parameters to the output, while the uncertainties of the program constitutive model are often not properly considered. In this study, a structural method is proposed to evaluate the uncertainties of program constitutive model. Based on this method, constitutive models are classified according to characteristics, and different evaluation methods are adopted for different model types. The model evaluation methods used in this study include the non-parametric curve estimation method in the forward method and the Bayesian calibration method and coverage calibration method in the reverse method, as well as alternative model construction methods. The structural method is used to quantify the uncertainties of important models in LOCA, and the quantified model uncertainties are transmitted to the peak cladding temperature through sampling calculation. The results show that both the sampling calculation values and the experimental values are smaller than the conservative calculation value, and the propagation calculation results after considering the model uncertainties can well cover the experimental values, and the safety margins can be effectively increased after considering the model uncertainties.
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图 1 独立模型和非独立模型示意图
Figure 1. Schematic Diagram of Independent Model and Dependent Model
图 4 LOFT工况保守参数输入计算结果
Figure 4. Calculation Results of Conservative Parameter Input for LOFT Condition
图 5 LOFT工况考虑所有输入不确定性计算结果
Figure 5. Calculation Results for LOFT Condition with All Input Uncertainties Considered
图 6 LOFT工况不考虑模型不确定性计算结果
Figure 6. Calculation Results for LOFT Condition without Model Uncertainties Considered
表 1 LOCA重要本构模型不确定性评价总结表
Table 1. Summary of Uncertainty Evaluation of LOCA Important Constitutive Model
编号 模型 不确定性乘子修正参数 乘子95%区间 乘子分布 1 包壳氧化模型 氧化层厚度 (0.6392, 1.0850) 正态 2 CHF模型 AECL-UO查询表计算CHF (0.7735, 1.6703) 正态 PG-CHF关系式计算CHF (0.6353, 1.1159) 正态 3 膜态沸腾换热模型 膜态沸腾液相换热系数 (0.5911, 2.4546) 对数正态 膜态沸腾气相换热系数 (0.4741, 1.8750) 对数正态 4 再淹没模型 再淹没膜态沸腾液相换热系数 (1.1011, 1.7496) 对数正态 再淹没膜态沸腾气相换热系数 (0.4051, 0.9007) 对数正态 再淹没两相界面阻力系数 (0.4784, 1.0050) 对数正态 5 夹带模型 夹带液滴份额 (0.6696, 1.6230) 正态 6 CCFL模型气相截距 Wallis-Kutateladze关系式系数 （0.64, 0.88） 均匀 7 相界面冷凝模型 相界面冷凝换热系数 (0.5167, 2.1949) 正态 8 临界流模型 Henry-Fauske模型计算临界流量 (0.7607, 1.2559) 正态 9 燃料棒储热模型 温度小于1800 K时UO2体积热容 (0.98, 1.02) 正态 温度大于1800 K时UO2体积热容 (0.87, 1.13) 正态 温度小于2000 K时UO2热导率 (0.9, 1.1) 正态 温度大于2000 K时UO2热导率 (0.8, 1.2) 正态 10 衰变热模型 衰变功率或衰变功率曲线 (0.92, 1.08) 正态 11 气隙导热模型 气隙导热模型等效气隙尺寸 (0.8, 1.2) 正态 12 破口背压模型 最佳估算安全壳程序计算值 (0.9, 1.1) 均匀 实验测量曲线 (0.85, 1.15) 均匀 
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