Extended cross-section adjustment method to improve the prediction accuracy of core parameters

An extended cross-section adjustment method has been developed to improve the prediction accuracy of target core parameters. The present method is on the basis of a cross-section adjustment method which minimizes the uncertainties of target core parameters under the conditions that integral experimental data are given. The present method enables us to enhance the prediction accuracy better than the conventional cross-section adjustment method by taking into account the target core parameters, as well as the extended bias factor method. In addition, it is proved that the present method is equivalent to the extended bias factor method when only one target core parameter is taken into account. The present method is implemented in an existing cross-section adjustment solver. Numerical calculations verify the derived formulation and demonstrate an applicability of an adjusted cross-section set which is specialized for the target core parameters.     

Development of a “best representativity” method for experimental data analysis and an application to the critical experiments at the Toshiba NCA facility

For nuclear critical experiments, it is essential to certify similarities of the experiment with the objective of the actual reactor conditions or actual reactor equipment. To judge the applicability of the experimental data, the concept of a “representativity factor” has recently been adopted in the critical experiment field, particularly for fast breeder reactors and future reactor studies. In this study, we extended this concept to the design of a light water reactor system. We developed a new numerical evaluation method and a calculation system. The method is based on a linear combination of the sensitivity coefficient vector of an experiment in which the representativity factor to the target system is maximized to utilize experimental data effectively. Simultaneously, using the measurement data of critical experiments, the method enables us to evaluate calculation errors caused by errors or uncertainties of physical parameters. The derivation of the new calculation method is explained first. We then qualify it with a sample calculation, presenting numerical results for three kinds of critical experiments conducted at the Toshiba Nuclear Critical Assembly facility. Finally, the results are compared with those of an extended bias factor method to clarify the performance of the new method.     

Generalized Bias Factor Method for Accurate Prediction of Neutronics Characteristics

A generalized bias factor method is proposed to improve the prediction accuracy of neutronics characteristics of a target core. The generalized bias factor method uses conventional bias factors calculated for several critical assemblies. The weighting factors for individual bias factors are determined to minimize the variance of neutronic characteristics of the target core. Numerical calculations are performed to investigate the uncertainty reductions of neutronics characteristics for a tight-lattice core. Though the uncertainty is not remarkably reduced for k_eff , that for the reaction rate ratio of ²³⁸U capture/²³⁹Pu fission is remarkably reduced: For example, the uncertainty reduction of the reaction rate ratio in the upper core is 0.871 for the present method, and 0.657 for the conventional bias factor method.     

燃耗数据库基准检验方法研究

燃耗数据库基准检验方法对于研制高准确度的燃耗数据库至关重要。本文以TAKAHAMA 3压水堆辐照后检验实验中SF95样品的建模为例，研究了建模要素对燃耗计算的影响，确定了燃耗实验建模的方法，开展了燃耗信用制研究感兴趣的锕系和裂变产物核素积存量计算值与实验值的比对。比对结果显示，主锕系核素计算偏差小于2%，大部分次锕系核素偏差小于10%，大部分重要裂变产物核素偏差小于5%。本文还对125Sb积存量随燃耗深度变化规律进行了理论分析，确认了破坏性放化实验测量结果存在缺陷，并进一步获得了125Sb积存量的修正值，使计算偏差从接近170%下降到20%以内。本次研究表明，燃耗数据库基准检验研究不仅需发展适当的燃耗实验建模方法，还需对实验数据进行适当的评价。     

燃耗信任制下燃耗计算对临界计算的偏差及不确定度的研究

为量化燃耗信任制中燃耗计算传递给临界计算的不确定度,本文基于参数统计法对燃耗计算的核素偏差及偏差不确定度展开分析,并以蒙特卡罗（MC）抽样方法计算的kinf不确定度为基准,比较不同抽样方法对临界计算不确定度的影响。结果表明,核素偏差与偏差不确定度是随样品燃耗变化的分段函数。对于临界计算,拉丁超立方抽样（LHS）方法与MC抽样方法的kinf不确定度计算结果吻合较好,且LHS方法可考虑参数间的相关性,计算结果更真实,可进一步提升电厂的经济性。     

Bias factor method using random sampling technique

Toward the practical use of the bias factor method for actual light water reactor core analyses, the bias factor method using the random sampling technique is newly proposed. The bias factor method is one of the correction methods using information of E/C values in existing measurable systems, to reduce biases and uncertainties of predicted core characteristics parameters. By the aid of the random sampling technique, our proposed bias factor method can be carried out using only forward calculations without any adjoint calculations, and can easily take into account burnup and thermal-hydraulic feedback effects, which are difficult points in the practical application to actual core analyses. Although the statistical error due to the random sampling technique is inevitable in the proposed method, the statistical error can be simply quantified by the resampling technique such as the bootstrap method. As one of the feasibility studies, effectiveness of the proposed method is verified through a numerical experiment which virtually simulates a typical equilibrium pressurized water reactor core. In this verification problem, it is clarified that E/C values of control rod worth at the beginning of cycle under the hot zero power condition are useful information to reduce biases and uncertainties of predicted assembly-wise power distributions during operation of hot full power.     

Prediction Uncertainty Analysis of Neutronic Properties of Fast Breeder Reactor by Use of Sensitivity-Based Methodology

The prediction accuracies of key neutronic characteristics including burnup properties evaluated with use of the sensitivity-based methodology have been reviewed for a fast breeder reactor. The bias factor method, the cross section adjustment method and the combined method are used to evaluate the prediction accuracies. The calculation method of sensitivity coefficients used in the uncertainty analysis is discussed. The three methods are compared from the theoretical and numerical points. For the numerical comparison, they are applied to a 1,000 MWe fast breeder reactor. The prediction uncertainties are within the range of 0.7~1.0% for k_eff , 3~5% for control rod worth, 1~2% for ²³⁹Pu fission rate distribution, 12% for burnup reactivity loss and 1.5% for breeding ratio. These values are much smaller than those predicted without any integral data.     

中国实验快堆热工参数的自适应BP神经网络预测方法研究

中国实验快堆（CEFR）堆芯的热工参数是否超出限值是评价反应堆安全运行的标准。本文针对燃料包壳最高温度预测问题，通过堆芯子通道分析程序COBRA生成数据样本后，开发基于BP神经网络自适应算法的智能预测程序，对于特定的单盒组件，仅需给出堆芯进口功率和流量，即可实现燃料包壳最高温度的快速准确预测。结果表明，与COBRA相比，在大规模重复性计算的场景下，自开发程序能节约大量计算时间和算力，提高燃料包壳设计和CEFR运行时的操作效率。实验分析得出BP神经网络方法的最大相对误差不超过6%，平均预测相对误差不超过3%，计算效率提升至原程序的300倍，网络模型的预测精度高，且易推广至实验快堆其他参数预测，具有很大的应用前景。     

Research on Adaptive BP Neural Network Prediction Method for Thermal Parameters of China Experimental Fast Reactor

Whether the thermal-hydraulic parameters of China Experimental Fast Reactor (CEFR) core exceed the limit is the standard for evaluating the safe operation of the reactor. For the maximum temperature prediction problem of fuel cladding, after generating the data samples by the core sub-channel analysis code COBRA, an intelligent prediction code based on adaptive BP neural network algorithm was developed in the paper. For a specific single-box component, only the core inlet power and mass flow rate were required to achieve fast and accurate prediction of the fuel cladding maximum temperature. Compared with COBRA, in the scenario of large-scale repetitive calculation, self development code can save a lot of calculation time and rescource, and improve the operating efficiency of fuel cladding design and CEFR operation. The experimental analysis shows that the maximum relative error of BP neural network method is less than 6%, the average prediction relative error is less than 3%, and the calculation efficiency is improved to 300 times of the original code. So the prediction accuracy of the network model is high, and self development code is easy to apply to other parameter predictions of the experimental fast reactor.     

The Corrected Simulation Method of Critical Heat Flux Prediction for Water-Cooled Divertor Based on Euler Homogeneous Model

An accurate critical heat flux(CHF) prediction method is the key factor for realizing the steady-state operation of a water-cooled divertor that works under one-sided high heating flux conditions.An improved CHF prediction method based on Euler's homogeneous model for flow boiling combined with realizable k-ε model for single-phase flow is adopted in this paper in which time relaxation coefficients are corrected by the Hertz-Knudsen formula in order to improve the calculation accuracy of vapor-liquid conversion efficiency under high heating flux conditions.Moreover,local large differences of liquid physical properties due to the extreme nonuniform heating flux on cooling wall along the circumference direction are revised by formula IAPWSIF97.Therefore,this method can improve the calculation accuracy of heat and mass transfer between liquid phase and vapor phase in a CHF prediction simulation of water-cooled divertors under the one-sided high heating condition.An experimental example is simulated based on the improved and the uncorrected methods.The simulation results,such as temperature,void fraction and heat transfer coefficient,are analyzed to achieve the CHF prediction.The results show that the maximum error of CHF based on the improved method is 23.7%,while that of CHF based on uncorrected method is up to 188%,as compared with the experiment results of Ref.[12].Finally,this method is verified by comparison with the experimental data obtained by International Thermonuclear Experimental Reactor(ITER),with a maximum error of 6% only.This method provides an efficient tool for the CHF prediction of water-cooled divertors.     

本构模型不确定性评价结构化方法开发及应用

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。      

MC-MC耦合计算方法在核电厂中子屏蔽设计中的应用

中子屏蔽精细化设计是三代堆型核电厂区别于二代堆的主要辐射防护设计特征之一,其设计优劣直接影响了辐射场内设备寿命及功率运行期间可能进入的工作人员的辐射安全。为了精确、快速、有效解决大尺度复杂厂房中子屏蔽计算难题,提出了将MC-MC耦合计算应用于解决核电厂大型复杂计算模型的中子屏蔽设计方法。通过与欧洲第三代压水堆技术方案(CEPR)设计结果对比表明,计算结果偏差小于15%,满足工程屏蔽设计误差要求,证明该方法的正确性与可行性。该方法已应用于国内某三代堆型核电厂反应堆厂房中子屏蔽设计。     

六边形套管型燃料堆芯核设计专用程序试验验证

采用六边形套管型燃料堆芯（HCTFR）7个零功率物理试验方案的试验数据对核设计程序（CELL+CPLEV2）的计算精度进行工程验证。验证结果表明,7个临界试验方案的临界棒位有效增殖因子（k_eff）计算偏差均在±0.8%以内,与试验结果符合较好,控制棒价值和停堆深度计算偏差也都在可接受范围内,表明CELL+CPLEV2程序具有较高的计算精度和可靠性,可用于HCTFR的核设计。      

稳定蒸汽浸没射流冷凝传热系数评价

为分析稳定蒸汽浸没射流的传热特性,对3类典型冷凝传热系数开展评价。结果表明:平均传热系数实验值精度主要受界面面积计算模型影响,由冷凝驱动势和蒸汽质量流速表征的传统半经验关系式在不同孔径下的预测偏差较大,新增排放孔径为独立拟合变量的纯经验关系式适用范围更广且误差在±30%以内;界面传热系数的预测精度主要受汽羽微观参数取值的影响;由压力振荡主频表征的无量纲传热系数在低池水过冷度下与实验值偏差较大,关系式中纳入汽羽贯穿长度后,预测趋势与实验值类似。      

弥散颗粒型燃料特征线方法输运计算研究

弥散颗粒型燃料的中子输运问题因其特有的随机性和双重非均匀性难以直接使用现有输运方法进行求解。Sanchez-Pomraning方法借助更新方程,对特征线方法进行改进,使其能应用于弥散颗粒型燃料的输运计算中。本文对二维圆柱形弥散颗粒燃料输运问题进行了计算,数值结果表明：程序在不同颗粒填充率、不同颗粒尺寸、燃料颗粒与毒物颗粒共存的问题下均能保证较好的计算精度,反应性特征值绝对偏差大多低于100 pcm,仅在QUADRISO毒物颗粒填充时绝对偏差达到163 pcm。本文方法能满足弥散颗粒型燃料的输运求解要求,为新型燃料的设计研究工作提供了可靠的结果。     

基于多次碰撞源的屏蔽计算方法研究

离散纵标（SN）方法在求解过程中将空间变量和角度变量进行离散，空间变量和角度变量的离散误差控制对保证计算精度至关重要。本文基于射线追踪研究了多次碰撞源方法，通过计算在选定区域内粒子发生多次碰撞的通量密度，将孤立源等效为计算模型内的分布源进行离散纵标输运计算。选取自设屏蔽问题及Kobayashi基准题进行测试验证并对结果进行分析。数值结果表明，自设屏蔽问题中多次碰撞源方法较首次碰撞源方法能有效缓解二次射线效应问题；Kobayashi基准题计算结果与基准值相对误差的均方根小于3%。多次碰撞源方法有效地减弱了离散误差，提高了屏蔽计算的准确性与可靠性。     

基于决策树的堆芯物理参数预测研究

反应堆堆芯核设计涉及大量方案的搜索与详细计算，缩短方案搜索时间有利于提高核设计效率。数据挖掘技术通过对大量数据进行学习与模式识别，可实现核设计方案物理参数的快速预测，更快地筛选出可行的备选堆芯方案。本文基于数据挖掘的决策树4种算法：C4.5、RepTree、Random Forest及Random Tree，在计算时以燃料富集度、含可燃毒物燃料棒数量及含量作为自变量，以寿期内k_eff不均匀系数偏差（KUCD）、径向功率不均匀系数偏差（RPNCD）、径向中子通量不均匀系数偏差（RFNCD）、堆芯寿期（CL）作为目标函数，构成目标函数符合度（CPF），利用大量已知核设计参数的组件及堆芯设计方案作为数据挖掘训练集，构建数据挖掘模型，并用于对未知核设计参数的组件方案集合（测试集）进行CPF快速预测。结果表明，4种算法利用训练集构建数据挖掘模型的时间在0.6 s以内，各算法的交叉验证精度均在0.7以上，其中C4.5算法对CPF预测精度最高；对测试集方案的核设计参数预测中，单个方案的预测时间均在0.9 s以内，而Random Forest算法对CPF等于4的预测效果最好。     

基于正向蒙特卡罗计算的自动源偏倚方法在屏蔽计算中的应用

反应堆屏蔽计算是粒子输运数值计算的难点问题之一。由于仅有少量处于堆芯外围组件的高能中子能到达屏蔽层外，如果对源粒子采用无偏抽样，大量的计算时间用于模拟无用的源粒子，计算效率很低。偏倚抽样是提升蒙特卡罗模拟计算效率的重要途径，包含源偏倚、输运偏倚和碰撞偏倚等。MCNP程序的权窗发生器可为输运偏倚和碰撞偏倚提供参数，但不包含源偏倚。本文利用正向蒙特卡罗计算权窗发生器产生的重要性函数，生成源偏倚参数以及与之匹配的权窗系数，在屏蔽计算中取得了很好的效果。本文的方法与MCNP的权窗功能完全兼容，使用方便。     

蒙特卡罗临界计算能量偏倚的最佳源偏倚方法

使用堆用蒙特卡罗程序RMC进行临界计算时采用了传统的裂变源迭代法，即每代源中子按照真实物理过程产生、存库和再抽样。传统裂变源迭代法的计算代之间存在较大的相关性，导致了方差低估计现象，同时总体方差未实现最优化。为实现源中子在空间和能量上的最佳分布，并消除方差低估计现象，提出了能量偏倚的最佳源偏倚方法。该方法基于最佳分层抽样法，结合香农熵诊断和组统计方法，对源中子的空间和能量进行偏倚，实现了全局减方差的计算效果。在RMC程序中开发了能量偏倚的最佳源偏倚方法，并对典型压水堆组件进行测试，计算结果证明了该方法的正确性和有效性。     

γ射线自吸收修正因子精确计算方法研究

对具有一定几何尺寸的样品进行γ谱分析时,样品自身对γ射线的吸收影响对核素含量的精确测量。本文在对比国内外关于自吸收修正因子计算方法的基础上,分析了被广泛采用的简化计算模型存在的问题及对修正结果的影响。基于混合蒙特卡罗模拟的思想,提出了自吸收修正因子的精确计算模型,并使用FORTRAN程序进行了随机抽样和积分计算,得到精确的自吸收修正因子。通过加标样品及不同质量标准源的对比测量,将精确计算模型与简化计算模型和无源效率校准软件计算结果进行了对比分析。结果表明,简化计算模型过高评估了自吸收干扰,而精确计算模型计算结果与实验测量结果及无源效率校准软件计算结果具有较好的一致性,相对偏差不大于5%。最后针对核电厂周围环境中主要关注的γ核素,使用精确计算模型得到了不同γ核素在土壤中的自吸收修正因子。