针对裂变产额和半衰期的燃耗计算灵敏度和不确定度分析方法

基于广义微扰理论推导了裂变产额和半衰期的燃耗灵敏度系数理论模型,该模型考虑了原子核密度和中子通量的相互影响,并开发了燃耗计算中有效增殖因数和原子核密度等响应参数对核数据的灵敏度和不确定度分析程序。基于评价核数据中裂变产物独立产额的标准差数据,产生了针对压缩燃耗数据库的裂变产额协方差矩阵,以提高不确定度的计算精度。基于ENDF/B-Ⅶ.1数据库量化了UAM基准题TMI-1栅元无限增殖因数及重要裂变产物和重核的原子核密度由裂变产额和半衰期引入的不确定度。数值结果表明,对于栅元无限增殖因数,裂变产额和半衰期引入的不确定度很小;对于部分裂变产物的原子核密度,裂变产额和半衰期会引入较大的不确定度。     

基于抽样方法的燃耗计算核素积存量不确定度分析

基于抽样基本原理研究了应用于燃耗计算的不确定度分析方法,并开发了燃耗计算不确定度分析程序。基于评价核数据库ENDF/B-Ⅷ.0的裂变产额标准差和衰变常量标准差计算得到了衰变常量协方差矩阵和带相关性的裂变产额协方差矩阵,并结合SCALE6.2程序包的56群反应截面协方差数据库,对Takahama-3压水堆组件基准题中SF95-4样品进行不确定度分析。计算了反应截面、衰变常量和裂变产额不确定度引起的核素积存量的不确定度。计算结果表明,反应截面的不确定度是锕系核素积存量不确定度的主要来源,裂变产额和衰变常量的不确定度对部分裂变产物的积存量会引入较大的不确定度。但考虑裂变产额相关性后,裂变产额引起的不确定度显著降低。     

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。     

裂变产额的Zp模型评价方法及燃耗不确定度分析

裂变产额在核科学技术和核工程中有着重要的应用,发展可靠、高效的产额评价方法和相应燃耗计算不确定度分析方法,对于建立高质量的产额数据库具有重要的意义。本文根据裂变产物核衰变模式和衰变分支比,建立独立产额与累积产额的转换矩阵,用于Zp模型的扩展,使之适用于独立产额和累积产额的统一描述,并以此建立了用于产额统一评价的拟合程序ZpFit。把ZpFit程序应用于中子诱发235U裂变产物产额评价,获得了自洽的独立产额、累积产额和相应的协方差数据,并建立ENDF格式的中子诱发235U裂变的产额数据库。在此基础上,计算了UAM燃耗基准题的TMI 1栅元的kinf、重要核素原子核密度的不确定度,比对了本工作评价的产额数据和ENDF/B Ⅷ0评价库中产额数据传递给响应量的相对不确定度,结果基本一致,差异不大。     

基于不确定性与敏感性分析的FA300燃料棒燃耗限值研究

燃耗限值对于燃料棒的安全使用和设计改进均有重要意义,而FA300燃料棒的燃耗限值尚未有系统研究。不确定性与敏感性分析方法是燃耗限值研究的基础,工程上常用的极值分析法、蒙特卡罗法等均难以全面反映燃料棒性能分析中的不确定性与敏感性。本工作采用基于人工神经网络的响应面方法,对相应数学模型进行显式重构,在响应面上进行抽样统计获得不确定性信息;而对于特定形式的人工神经网络,通过简单的代数运算获得敏感性信息。基于这一方法的研究表明,FA300燃料棒的极限准则为包壳腐蚀及包壳应变。结合秦山一期加深燃耗组件随堆考验的检测结果,以及国际上相关使用经验,从燃料性能分析的角度给出FA300燃料棒的燃耗限值为55 000 MW•d/tU。     

基于经典微扰理论的特征值灵敏度和不确定度分析

核数据不确定度作为组件/栅元计算不确定度的重要来源,备受重视和研究。本文采用经典微扰理论,推导输运计算中keff对于核数据的灵敏度系数和不确定度的计算方法。基于ENDF/B-Ⅶ.1制作多群协方差数据库,并根据所采用的组件输运求解程序的截面模型对分反应道协方差矩阵进行归并。开发灵敏度和不确定度分析程序COLEUS,对传统压水堆燃料栅元进行计算分析。数值结果表明,栅元计算的keff对235 U每次裂变中子产额的扰动最为敏感,238 U俘获截面对keff不确定度的贡献最大。目前的核数据的不确定度会给keff带来0.4%~0.5%的不确定度。     

高阶预估-校正燃耗方法在压水堆组件计算中的应用

压水堆燃料组件输运燃耗耦合计算通常采用的是传统的预估-校正(PC)燃耗方法。然而,该方法本身的假设导致其存在一定的计算误差。为进一步提高燃耗计算的精度,本文针对传统的预估-校正燃耗方法的缺陷研究了改进的预估-校正燃耗方法,改进了对核反应率进行修正的高阶预估-校正燃耗方法,并在Bamboo-Lattice程序中进行了程序实现,对该方法进行了验证分析。结果表明:改进的预估-校正燃耗方法和高阶预估-校正燃耗方法在保证计算效率的前提下提高了燃耗计算的精度。     

Sensitivity Analysis of Fission Product Concentrations for Light Water Reactor Burned Fuel

The accurate prediction of fission product concentrations (FPCs) is necessary for application of the burnup credit to nuclear facilities. In order to specify important nuclear data for the accurate prediction of FPC, we extensively evaluate the sensitivities of FPC to nuclear data with the depletion perturbation theory. The target fission products are twelve important ones for the burnup credit, Mo-95, Tc-99, Rh-103, Nd-143, Nd-145, Sm-147, Sm-149, Sm-150, Sm-152, Cs-133, Eu-153, and Gd-155. The present study successfully specifies the important nuclear data both in a UO₂ cell and in a MOX cell. While the obtained sensitivities are mostly similar to each other between the UO₂ and MOX cells, large differences are observed in some cases, such as the Gd-155 concentration. It is clearly shown that such differences between the UO₂ and MOX cells come from differences in cumulative fission yields between U-235 and Pu-239 and differences in neutron flux energy spectra.     

钍增殖熔盐堆不同燃耗核数据不确定度分析

本文利用开发的耦合模块,将SCALE程序中的TRITON和TSUNAMI-3D模块相结合,针对1GWth钍增殖熔盐堆开展不同燃耗时期核数据引起的k_(eff)不确定度分析。结果表明:随着燃耗的增加,核数据引起的keff不确定度由0.49%增大到0.55%。初始时刻对k_(eff)不确定度影响最大的反应截面是232 Th(n,γ)(约0.35%),其次是233 U(n,f)和7 Li(n,γ)。随着燃耗的增加,~(135)Xe(n,γ)、~(143)Nd(n,γ)对k_(eff)不确定度的影响逐渐显著。各反应灵敏度系数分析表明,~(232)Th(n,γ)、~(233)U(n,f)和~7Li(n,γ)截面数据对k_(eff)不确定度影响较大,需重点改进。上述关键反应在0.02~0.5eV敏感性较强,需重点关注。     

蒙特卡罗燃耗计算程序MCNTRANS的开发与验证

本文介绍了开发的蒙特卡罗燃耗计算程序MCNTRANS。MCNTRANS的中子学计算参数直接采用MCNP5程序的反应率计算值,燃耗计算方法采用图论算法跟踪燃耗链,同时,对实际燃耗过程进行详细分析以提高计算精度与程序适用性,并使用预估 校正方法以获取较大的燃耗计算步长。程序计算结果通过OECD/NEA与JAERI燃耗基准题实验结果进行验证,并与其他程序的计算结果进行比较。结果表明,MCNTRANS程序在不同燃耗深度下的计算结果和实验值与其他程序的计算值符合较好,部分锕系核素与裂变产物的计算精度更高。     

基于最佳一致逼近多项式的燃耗计算方法研究

本文研究了一种基于最佳一致逼近多项式（MMPA）的燃耗计算方法求解燃耗方程。相比于切比雪夫有理近似方法（CRAM）和围道积分有理近似方法（QRAM）,MMPA方法只需一次矩阵求逆计算即可求解燃耗方程,且所有计算都是实数运算,具有数值稳定性好、求解效率高等优点。进一步研制了基于MMPA方法的点燃耗程序AMAC,并耦合蒙特卡罗输运程序OpenMC,采用衰变例题、固定辐照例题、OECD/NEA压水堆栅元燃耗基准题和沸水堆组件燃耗基准题进行验证,程序计算结果与实验值及各参考值吻合良好,初步验证了MMPA方法在理论和数值上的正确性和有效性。     

小破口失水事故最佳估算的不确定性和敏感性分析

本文采用RELAP5最佳估算程序对我国建造的先进热工水力试验（ACME）台架进行了小破口失水事故模拟,并开展了不确定性定量化评估,包括输入不确定性参数的选取、Wilks非参数统计方法的应用以及基于SNAP平台的不确定性传播计算,最后对计算结果进行了不确定性和敏感性分析。计算得到关键参数的95/95不确定性包络带,其中最小堆芯液位的下限仍保持在堆芯活性区以上,表明堆芯有95%的置信度未发生裸露。通过敏感性分析判别出对最小堆芯液位影响较大的输入不确定性参数。     

Approximate Calculation Method for Second Order Sensitivity Coefficient

A simple method has been developed for calculating the second order sensitivity coefficient of static and burnup-dependent core performance parameters. The method is applied to a small and a large fast breeder reactors. Changes in core performance parameters due to 10% cross section changes are compared with that predicted by the first and the second order sensitivity analyses. Numerical results reveal that the changes in breeding ratio, reaction rate ratio of the ²³⁸U capture to the ²³⁹Pu fission rate and burnup reactivity loss due to the 10% change in the ²³⁹Pu fission cross section and/or the ²³⁹Pu v-value show nonlinear behavior, and the second order sensitivity can predict the changes accurately.     

Fission Product Model for BWR Analysis with Improved Accuracy in High Burnup

A new fission product (FP) chain model has been studied to be used in a BWR lattice calculation. In attempting to establish the model, two requirements, i.e. the accuracy in predicting burnup reactivity and the easiness in practical application, are simultaneously considered. The resultant FP model consists of 81 explicit FP nuclides and two lumped pseudo nuclides having the absorption cross sections independent of burnup history and fuel composition. For the verification, extensive numerical tests covering over a wide range of operational conditions and fuel compositions have been carried out. The results indicate that the estimated errors in burnup reactivity are within 0.1Δk for exposures up to 100GWd/t. It is concluded that the present model can offer a high degree of accuracy for FP representation in BWR lattice calculation.     

Improvement of Monte Carlo Lattice Burnup Calculation Performance with the Correlated Sampling Method

For next generation reactor designs, which are attempting wide variations of assembly configurations, the flexibility Monte Carlo method holds is attractive, but still costly for repetitive design study works. This paper presents an advanced correlated sampling (ACS) method which was developed to speed up Monte Carlo lattice burnup calculations. The ACS method is the combination of the correlated sampling method and a pseudo-scattering technique. All burnup steps are considered as consecutive perturbed problems using the same neutron collision history, which is pre-calculated based on a selected unperturbed problem. Since neutron weights can be adjusted on every collision point, rather than along paths between them, the perturbed calculation is very fast and the neutron collision history is light enough to be stored in memory or physical storage, which is an indispensable feature for consecutive perturbed calculations. The presented theory shows that the ACS method has good potential to work for a wide range of neutron absorption variations, the dominant perturbation in the lattice burnup. In an example calculation on a BWR lattice, the ACS calculation results of 600,000 neutrons/step agree well with the independent Monte Carlo runs of 20,000,000 neutrons/step within 0.1%dk/k in terms of k_? throughout 95 steps (~50GWd/t). Average calculation time of neutron tracking with the former method is 3.4 s/step with 600,000 neutron histories on a single processor of an Alpha21164-600 MHz, and the speed-up factor against the Monte Carlo calculation turns out to be about 100.     

消息传递并行燃耗程序MCBMPI的栅元验证

程序采用模块化思想,其中输运部分采用MCNP5程序的消息传递并行版本MCNP5MPI,燃耗计算采用截断泰勒展开的矩阵指数法、TTA线性子链解析法和高斯-赛德尔迭代法三者相结合的燃耗求解方法,并行策略为对多燃耗区采用区域分解的MPI消息传递并行,完成了并行化蒙特卡罗燃耗程序MCBMPI的研制。整个程序系统仅由MCNP5MPI和燃耗程序组成,其中燃耗程序包含了对多燃耗区的区域分解并行功能、核素转换与衰变计算功能以及与MCNP5MPI的数据交换功能。并以压水堆栅元燃耗基准题对程序进行验证,验证结果表明:该程序可用于多燃耗区的并行燃耗计算,伴随计算机硬件性能的改善可显著提高计算效率。     

Adjoint Sensitivity and Uncertainty Analyses in Monte Carlo Forward Calculations

The adjoint-weighted perturbation (AWP) method, in which the required adjoint flux is estimated in the course of Monte Carlo (MC) forward calculations, has recently been proposed as an alternative to the conventional MC perturbation techniques, such as the correlated sampling and differential operator sampling (DOS) methods. The equivalence of the first-order AWP method and first-order DOS method with the fission source perturbation taken into account is proven. An algorithm for the AWP calculations is implemented in the Seoul National University MC code McCARD and applied to the sensitivity and uncertainty analyses of the Godiva and Bigten criticalities.     

基于CASMO5的燃耗历史对乏燃料反应性的影响计算

基于乏燃料贮存领域常用的锕系加裂变产物(APU-2)级燃耗信任制,应用二维组件燃耗计算程序CASMO5,计算了燃耗过程中功率密度和运行历史对乏燃料k∞的影响。结果表明:燃耗计算中,选择堆芯额定功率对应的平均功率密度,同时k∞附加0.002 3的包络裕度,运行历史选择循环内及循环间无停堆额定功率运行,同时k∞附加0.004 5的包络裕度,可满足燃耗信任制中包络性原则。     

基于CRAM的压水堆燃耗程序开发及验证

本文基于Cinder90燃耗数据库开发了燃耗求解程序MCRAM,并耦合MCNP程序对重要的锕系核素和裂变产物核素的反应截面进行了修正。以OECD/NEA乏燃料成分基准数据库中的Takahama-3压水堆燃料组件为基准题,对MCRAM程序的计算结果进行了验证,并与其他程序的计算结果进行了比较。结果表明,MCRAM程序对重要裂变产物和主要锕系核素的计算结果相对偏差小于5%,计算精度与ORIGEN2程序的相当。与此同时,同一例题的计算效率MCRAM较之MCNTRANS程序提高了近200倍。     

行波焚烧模式的理论分析与初步计算

行波焚烧模式是一种即时原位增殖焚烧模式。本工作从理论上进行初步分析,得出行波焚烧的物理图像。利用欧洲快堆计算程序ERANOS进行二维圆柱模型的方案分析,得到行波焚烧的基本物理特点。结果表明,行波堆在中子学上是可行的,且具有一些很好的物理特性。