DAKOTA法量化AP1000堆芯物理不确定性

应用DAKOTA程序中的超拉丁立方抽样方法开展AP1000堆芯物理关键参数的不确定性量化分析。分析结果表明:AP1000输入参数的不确定性对堆芯关键参数的不确定性影响较小,均未超过设计限值;全参数不确定性分析和敏感参数不确定性分析具有一定的等价性,可通过敏感性参数不确定性分析来获取AP1000堆芯关键参数的不确定性,提高分析计算效率。     

VVER机组LBLOCA始发严重事故工况下堆芯出口温度BEPU分析

最佳估算加不确定性（BEPU）方法目前广泛应用于核电厂设计基准事故（DBA）的分析。考虑到严重事故现象复杂及不确定性较大,BEPU方法在严重事故领域应用较少。堆芯出口温度（CET）是核电厂安全运行的重要监测参数,本文以VVER1000压水堆核电厂为研究对象,采用BEPU方法对大破口失水事故（LBLOCA）始发严重事故工况下包壳破裂对应的CET进行不确定性分析,并对输入参数进行敏感性分析。计算结果表明：气隙释放对应CET的单侧统计容忍限值（95/95）为430.85 ℃;CET对输入参数中的衰变热系数和包壳厚度较为敏感。     

压水堆部分堆芯参数敏感性分析

用估计严重事故原理的整体型第二代轻水堆电站风险评价工具MELCOR程序,以在建的岭澳核电站为对象,分析了压水堆部分堆芯参数的不确定性和敏感性。这些参数是燃料元件孔隙度,熔渣孔隙度,熔渣到下封头贯穿件的传热系数。把分析结果与相应的沸水堆参数的敏感性分析结果进行比较,发现核电站发生全厂断电事故时,事故进程对堆芯输入参数不敏感。     

不确定性分析在概率安全评价中的应用

分析了概论安全评价（PSA）中存在的完整性，模型假设条件及输入数据的不确定性和它们的来源。针对输入参数的不确定性，阐述了Risk Spectrum软件关于不确定性分析的原理，方法和误差因子的选取。对输入参数的不确定性进行定量计算后，得到13个初因和各工况的堆芯损坏频率的均值。介绍了表征不确定性的概率密度函数和累计密度函数曲线。     

氢气复合器算例数值模拟结果的不确定性分析和敏感性分析

在安全壳氢气分析中,由于输入参数具有不确定性,因此计算结果也具有不确定性。研究计算结果的变化范围,以及各输入参数对计算结果不确定性的贡献,在安全层面具有重要意义。为了对安全壳氢气复合器算例进行数值模拟,首先向计算流体力学程序HYDRAGON内添加复合器模型,然后选定燃爆转变因子和爆炸总能量及其相关的时刻量作为研究对象。对若干输入参数进行抽样后进行数值模拟。采用非参数统计方法,分析计算结果的不确定性,给出其变化范围。分析计算结果和输入参数之间的敏感性,筛选其不确定性出对计算结果影响较大的输入参数。     

基于抽样的敏感性分析方法在LBLOCA质能释放PIRT评级中的应用

基于随机抽样的非参量敏感性统计分析方法是一种有效的敏感性分析方法,通过计算热工水力分析程序多个抽样输入参数与输出参数之间的相关系数来评价各输入参数对输出参数影响的重要程度。通过耦合DAKOTA和WCOBRA/TRAC程序,开发了基于抽样的适用于非能动核电厂大破口失水事故质能释放的敏感性分析方法,该方法可全面定量评估各敏感性参数对计算结果的影响。计算结果表明：堆芯初始功率、燃耗、衰变热、安注箱初始水温、初始水体积、安注箱管道阻力系数、堆芯补水箱初始水温、喷放系数及破口阻力系数对破口质能释放具有显著影响。该分析结果可为大破口失水事故质能释放分析现象识别和重要度排序表评级提供定量依据。     

核电软件NESTOR堆芯功率分布计算不确定性研究

堆芯功率分布作为堆芯核设计的关键指标,其计算精度对于评价核电厂的安全性和经济性尤为重要。作为国内首套自主核电软件包,NESTOR软件的计算精度和适用性是其应用的基础。本文基于随机取样统计方法和误差传递理论,通过分析程序物理模型引入的不确定性和堆芯状态参数不确定性引入的不确定性,将两者联合起来得到最终功率分布计算的不确定性。结果表明:随机取样统计方法在核设计软件计算不确定性研究中是可行的,将堆芯功率分布拆分为组件内功率分布计算不确定性和组件功率计算不确定性分别分析,再由误差传递理论联合得到在95%置信度和95%概率下由程序物理模型引入的径向功率峰因子计算不确定性为±3.653%,由参数不确定性引入的径向功率峰因子计算不确定性为±0.964%。从而得出最终径向功率峰因子的计算不确定性为:±3.778%。与国外成熟工程核设计软件包的计算精度相当,为NESTOR核设计软件包的应用和验证奠定了基础。      

物性参数对氟盐球床堆传热模型不确定性和敏感性的影响分析

为了确保氟盐球床堆堆芯传热模型的预测能力满足安全限制,研究了氟盐冷却剂的物性参数对堆芯传热模型不确定度和敏感性的影响。采用统计学不确定性评估方法,将氟盐冷却剂物性参数（包括动力粘度、密度、比热容、导热系数）作为输入参数,选取经典传热关联式作为计算模型,分析了努赛尔数（Nu）的不确定性及其对物性参数的敏感性程度。结果表明,无论氟盐物性参数的概率分布为正态分布或均匀分布,计算得到的Nu的平均值非常接近,其分布形式都接近正态分布;同时发现,动力粘度是物性参数中对Nu影响最大的参数,并且呈负相关;导热系数对Nu的影响为负相关,密度和比热容对Nu的影响较小且均为正相关。      

静默式热管反应堆热工水力特性不确定性分析

基于不确定性分析软件DAKOTA和自编程热管反应堆单通道热工分析程序HEART,对静默式热管反应堆(NUSTER)稳态热工水力特性进行了不确定性分析。根据热管反应堆相关实验数据，选取运行功率、燃料热导率、气隙宽度、包壳厚度、热管蒸发段长度和基体厚度6个关键热工参数并确定其基准值与概率密度分布，通过大量重复性计算，获得了95%置信水平下热管蒸发段温度、热管冷凝段温度、燃料峰值温度、包壳峰值温度及基体温度的统计分布，并对各参数的不确定性对热管反应堆安全性的影响进行了分析。分析结果表明：热管蒸发段及冷凝段温度有0.67%的概率超过热管温度限值；由于热管反应堆堆芯为固态堆芯，传热以纯导热为主，输入变量的不确定性对不同目标参数的影响相同，燃料热导率的不确定性对5个目标参数的影响最为显著，且为负相关。本研究获得的结果可为热管反应堆的优化及其后续发展提供方向指引。     

压水堆大破口失水事故重要现象识别及数值计算不确定性量化分析研究

大破口失水事故是压水堆核电厂最重要的设计基准事故,对该事故的准确模拟可为提升反应堆功率提供重要支撑。本文采用最佳估算程序RELAP5对压水堆失水事故试验（LOFT）的实验工况FP-LP-2进行了模拟计算,并应用德国反应堆安全研究所（GRS）不确定性分析方法对计算结果进行不确定性量化和敏感性分析;给出了关键输出参数95%置信度的不确定性包络带,并分析了计算结果的不确定性变化趋势及原因。分析结果表明,对包壳峰值温度影响较大的重要现象包括堆芯衰变热、完整环路破口临界流喷放系数和燃料棒的热导率。本文研究确认了GRS方法的有效性,为改进现有核电站安全分析方法具有积极作用。      

典型压水堆小破口LOCA参数重要度排序表开发

现象识别排序表（PIRT）是反应堆热工水力分析的重要依据,传统PIRT的建立依赖于专家经验,因此缺乏专家经验时难以开展参数的识别工作。本文开展在缺乏专家经验时确定各输入参数重要度排序的研究,选定的工况为典型三回路压水堆（PWR）小破口失水事故（SBLOCA）。参考已有的SBLOCA PIRT,并基于基准计算结果,筛选和补充了可能对目标输出（FOM）具有影响的54个不确定性输入参数。使用一种优化矩独立全局敏感性分析方法计算得到了各输入参数对FOM的敏感性度量和重要度排序。将参数的重要度排序转换为Savage分数,按照Savage分数定性地将所有输入参数进行重要度分组,从而得到了SBLOCA的参数重要度排序表,为压水堆SBLOCA工况的参数排序提供了参考。     

Assessment study about the risk of Wilks’ formula for uncertainty quantification of design extension condition scenarios in prototype Gen-IV sodium fast reactor

Sensitivity analysis and uncertainty quantification using Wilks’ formula and Monte Carlo for Unprotected Loss of Flow (ULOF) and Unprotected Transient OverPower (UTOP) accidents of prototype Gen-IV sodium-cooled fast reactor were performed. Multi-dimensional analysis for reactor safety for liquid metal reactors code calculations were conducted while simultaneously varying the values of all uncertain parameters according to their distribution using parallel computing platform integrated for uncertainty and sensitivity analysis to obtain uncertainty bands for Figures of Merit (FOM) – coolant, fuel centerline, and cladding temperature at the hottest fuel rod. To specify the uncertainty range of the parameters for each accident scenario, literature survey and expert judgments were consulted. By the sensitivity analysis, the importance ranking of 25 parameters in model identification and ranking table based on phenomena identification and ranking table was identified. Through Monte Carlo calculation, 95% upper limit and 95% confidence level were obtained, and about 2% and 5% under-prediction (risk) of FOM of ULOF and UTOP accidents using Wilks’ formula were confirmed, respectively.     

Sampling based uncertainty analysis of station blackout in PSB VVER integral test facility

Best estimate accident analysis with uncertainty evaluation is being encouraged in the present licensing scenarios of nuclear power plants. This paper deals with uncertainty and sensitivity analysis for station blackout in PSB VVER integral test facility under the framework of coordinated research project of IAEA. Nodalization was developed using best estimate system code RELAP5/MOD3.2 and its steady state and transient level qualifications are achieved. Sampling based approaches are used to carry out uncertainty and sensitivity/importance analysis. The objective of the analysis is to get confidence for uncertainty methodology by comparing with the experimental results and extend its applicability to NPPs. Uncertainty analysis is carried out by selecting nine important input parameters with specified ranges and its uniform distributions. A design matrix of 45 × 9 is generated for variations of input parameters with the Latin Hypercube Sampling and 45 code runs were taken. Linear regression was also carried out to quantify the effect of each individual input parameter on output parameters in terms of standard rank regression coefficients. Uncertainty band in output parameters is defined between 95th and 5th percentile value. It is observed that most of the experimental values and code calculated reference values are lying within the uncertainty band. For most of the parameters, width of uncertainty band increases with transient progression time.     

keff uncertainty quantification and analysis due to nuclear data during the full lifetime burnup calculation for a small-sized prismatic high temperature gas-cooled reactor

To benefit from recent advances in modeling and computational algorithms,as well as the availability of new covariance data,sensitivity and uncertainty analyses are needed to quantify the impact of uncertain sources on the design parameters of small prismatic high-temperature gas-cooled reactors(HTGRs).In particular,the contribution of nuclear data to the keff uncertainty is an important part of the uncertainty analysis of small-sized HTGR physical calculations.In this study,a small-sized HTGR designed by China Nuclear Power Engineering Co.,Ltd.was selected for keff uncertainty analysis during full lifetime burnup calculations.Models of the cold zero power(CZP)condition and full lifetime burnup process were constructed using the Reactor Monte Carlo Code RMC for neutron transport calculation,depletion calculation,and sensitivity and uncertainty analysis.For the sensitivity analysis,the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance Characterization(CLUTCH)method was applied to obtain sensitive infor-mation,and the"sandwich"method was used to quantify the keff uncertainty.We also compared the keff uncertainties to other typical reactors.Our results show that 235U is the largest contributor to keff uncertainty for both the CZP and depletion conditions,while the contribution of 239Pu is not very significant because of the design of low discharge burnup.It is worth noting that the radioactive capture reaction of 28Si significantly contributes to the keff uncer-tainty owing to its specific fuel design.However,the keff uncertainty during the full lifetime depletion process was relatively stable,only increasing by 1.12％owing to the low discharge burnup design of small-sized HTGRs.These numerical results are beneficial for neutronics design and core parameters optimization in further uncertainty prop-agation and quantification study for small-sized HTGR.     

keff uncertainty quantification and analysis due to nuclear data during the full lifetime burnup calculation for a small-sized prismatic high temperature gas-cooled reactor

To benefit from recent advances in modeling and computational algorithms,as well as the availability of new covariance data,sensitivity and uncertainty analyses are needed to quantify the impact of uncertain sources on the design parameters of small prismatic high-temperature gas-cooled reactors(HTGRs).In particular,the contribution of nuclear data to the keff uncertainty is an important part of the uncertainty analysis of small-sized HTGR physical calculations.In this study,a small-sized HTGR designed by China Nuclear Power Engineering Co.,Ltd.was selected for keff uncertainty analysis during full lifetime burnup calculations.Models of the cold zero power(CZP)condition and full lifetime burnup process were constructed using the Reactor Monte Carlo Code RMC for neutron transport calculation,depletion calculation,and sensitivity and uncertainty analysis.For the sensitivity analysis,the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance Characterization(CLUTCH)method was applied to obtain sensitive infor-mation,and the"sandwich"method was used to quantify the keff uncertainty.We also compared the keff uncertainties to other typical reactors.Our results show that 235U is the largest contributor to keff uncertainty for both the CZP and depletion conditions,while the contribution of 239Pu is not very significant because of the design of low discharge burnup.It is worth noting that the radioactive capture reaction of 28Si significantly contributes to the keff uncer-tainty owing to its specific fuel design.However,the keff uncertainty during the full lifetime depletion process was relatively stable,only increasing by 1.12％owing to the low discharge burnup design of small-sized HTGRs.These numerical results are beneficial for neutronics design and core parameters optimization in further uncertainty prop-agation and quantification study for small-sized HTGR.     

先进压水堆熔融物堆内滞留参数不确定分析研究

压水堆核电厂在严重事故下将发生堆芯熔化事故而形成熔融池。形成熔融池的过程具有很大的不确定性,这影响到反应堆压力容器熔融物堆内滞留（IVR）策略的有效性。本工作以AP1000核电厂两层IVR模型为研究对象,对成功实施反应堆压力容器外部冷却（ERVC）的假想严重事故进行了熔融池参数不确定性分析,包括参数的敏感性分析和使用拉丁超立方抽样的概率分析。结果表明：衰变功率对IVR评价参数影响最大,应采取措施（如上堆腔注水）尽量延缓堆芯熔化的时间;熔融物中不锈钢的质量将对金属层参数造成较大影响,可考虑在压力容器内布置牺牲性材料来减小金属层的集热效应;氧化物层外压力容器失效的概率仅为1.2%,但金属层外压力容器失效的概率高达20%。本结果对今后IVR策略研究和设计具有一定的指导意义,同时也为压水堆核电厂安全评审提供理论支持。     

基于统计抽样的压水堆燃料组件性能分析不确定度量化研究

为能在给出数值模拟结果的同时提供置信区间,本文开展了压水堆燃料性能分析、组件燃耗和热工水力学分析计算的不确定度量化研究。采用西安交通大学自主开发的不确定度分析程序平台NECP UNICORN,分别耦合了轻水堆燃料性能分析程序FEMAXI、压水堆群常数计算程序NECP Bamboo Lattice和热工水力子通道程序CTF。首先针对不同物理过程的特点,分析需要考虑的不确定度来源。然后针对核数据协方差矩阵稀疏且不满秩的特点,应用COST方法以减少样本量。结果表明,对于燃料性能分析,边界条件、几何参数和材料性质对燃料中心温度有显著影响。对于燃耗过程,核数据和几何参数对特征值、功率分布、两群常数和核子密度的不确定度有显著影响。对于热工水力分析过程,边界条件、几何参数和模型系数对冷却剂温度和包壳温度的不确定度有较大影响。针对每种物理场,分别量化其输入输出参数的不确定度,对于后续量化复杂系统多物理耦合过程的不确定度具有重要意义。