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。     

压水堆燃耗数据库的制作与验证

基于评价数据库ENDF/B-Ⅷ.0和EAF-2010研制了一套适用于CINDER90程序的压水堆用燃耗数据库,该数据库包含中子反应截面、衰变数据和裂变产额数据3部分。中子反应截面的加工分为两步,首先采用Inverted Stack算法和CRECTJ6程序将EAF 2010库的截面分支比融入ENDF/B Ⅷ0库全套中子评价数据,然后用NJOY2016程序处理成63群截面。衰变数据和裂变产额数据分别由MF8/MT457和MF8/MT454数据加工得到,裂变产额数据共包含36个裂变核的60组产额数据。以SFCOMPO 20中Takahama 3压水堆燃料组件为基准题,对研制的燃耗数据库进行了验证。结果表明,本文制作的燃耗数据库的方法是正确的,对于某些核素,如242Amm,制作的数据库比自带库的计算结果更接近实验值。     

Uncertainty analyses of decay heat summation calculations using JENDL,JEFF, and ENDF files

The uncertainty analyses of decay heat calculation were carried out using major evaluated nuclear data files, JENDL, JEFF, and ENDF. The uncertainties were obtained from the sensitivity of individual fission product nuclide to the decay heat summation calculation. The summation calculation was performed for a burst fission. The sensitivities derived from the analyses were for decay energy, fission yield, and decay constant among the nuclear data included in the summation calculation. The uncertainties of the calculations at 0.1 s after a fission burst are ～10% for JENDL and ～8% for JEFF and ENDF and those at 10⁴ s are less than 2% for all cases. The main differences came from the different adoption of the energy uncertainty. The sensitivity analysis can be used to improve the decay data for decay heat calculation.     

基于精细燃耗历史及精细燃耗链的球床高温气冷堆燃耗不确定性分析

球床高温气冷堆的燃料管理具有燃料球多次通过堆芯的特点,使得燃料元件经历的燃耗历史十分复杂。球床高温气冷堆堆芯物理设计程序VSOP可以提供燃料元件的精细燃耗历史,但仅包含少量燃耗链和核素种类。而清华大学自主开发的燃耗计算程序NUIT可实现精细燃耗计算,且包含完整燃耗链和核素信息,但不具备精细燃耗历史跟踪功能。本文基于NUIT,结合VSOP提供的球床高温气冷堆精细燃耗历史,开发了球床高温气冷堆堆芯的精细燃耗计算功能,搭建了带有精细燃耗历史模拟和精细燃耗链核素的燃耗分析流程,并实现燃耗不确定性分析功能。在此基础上研究了裂变产额不确定性对球床高温气冷堆燃耗计算不确定性的贡献,并与VSOP的计算结果进行对比。计算分析结果显示,基于NUIT的精细燃耗计算结果和VSOP的燃耗计算结果得到了相互验证,且可以得到更多的核素浓度信息,该计算结果是开展球床高温气冷堆衰变热不确定性研究的基础。     

基于蒙特卡罗方法的IVR熔融池内热源时序模型构建及分析

堆内熔融物滞留（IVR）作为反应堆严重事故的关键缓解策略,目前已广泛应用于新一代压水堆（PWR）。针对IVR的有效性,如熔融池内对流、下封头传热、壁面临界热流密度（CHF）的估算等研究,是该领域数年来的热点。针对上述问题,国内外先后开展了数起实验,如COPO、BALI、SEMICO、COPRA等,并基于实验结果展开了大量数值模拟,以探索IVR下的传热规律,为其性能及设计提供参照。本文基于中子物理蒙特卡罗程序RMC对压力容器下封头熔融池模型进行了细网格建模及材料填充,并通过燃耗/衰变热计算DEPTH程序构建了熔融池内热源时序模型。研究结果显示,该模型能体现熔融池内热源变化趋势,得到的时序数据对IVR的进一步研究有重要意义。     

铅基快堆RBEC-M燃耗库制作方法研究及验证

      提出了一套新的方法流程，用来处理和生成燃耗计算所需的数据。利用核数据处理程序NJOY处理评价数据库ENDF-B-Ⅶ.1生成33群的MATXS格式库，再根据具体问题中的材料信息，经截面处理程序MGGC处理得到相关核素的微观、宏观截面，经自编写的处理模块Triso对其进行格式转化、合并，最终得到提供给燃耗计算程序使用的ISOTXS库文件，其中一般核素以微观截面的形式表示，裂变产物以类似宏观截面的伪裂变产物形式表示。对铅冷快堆基准题900 MW RBEC-M进行了计算，采用REBUS-3进行燃耗计算，对比了结果中的有效增殖系数k_eff随燃耗的变化趋势、功率分布以及中子能谱，最终结果与参考报告较为符合，初步验证了这一系列燃耗库制作流程的可行性。      

Validation of a new continuous Monte Carlo burnup code using a Mox fuel assembly

The reactivity of nuclear fuel decreases with irradiation (or burnup) due to the transformation of heavy nuclides and the formation of fission products. Burnup credit studies aim at accounting for fuel irradiation in criticality studies of the nuclear fuel cycle (transport, storage, etc…). The principal objective of this study is to evaluate the potential capabilities of a newly developed burnup code called “BUCAL1”. BUCAL1 differs in comparison with other burnup codes as it does not use the calculated neutron flux as input to other computer codes to generate the nuclide inventory for the next time step. Instead, BUCAL1 directly uses the neutron reaction tally information generated by MCNP for each nuclide of interest to determine the new nuclides inventory. This allows the full capabilities of MCNP to be incorporated into the calculation and a more accurate and robust analysis to be performed. Validation of BUCAL1 was processed by code-to-code comparisons using predictions of several codes from the NEA/OCED. Infinite multiplication factors (k_∞) and important fission product and actinide concentrations were compared for a MOX core benchmark exercise. Results of calculations are analysed and discussed.     

基于WIMS-D库燃耗数据的更新与基准验证

随着AP1000等新一代压水堆的发展,燃耗深度在不断提高,平均卸料燃耗深度提高到60 GW d·t-1。然而,传统使用的WIMS69群和XMAS172群WIMS-D格式多群常数库,其能群结构存在共振峰重叠,核素种类较少,裂变产物产额的偏差较大,并且伪裂变产物中包含的核素种类较多而导致152Gd、160Gd、159Tb、160Tb等重要核素无法得到精确处理等问题。因此,本文主要针对AP1000等新一代反应堆的设计以及运行特点,基于ENDF/B-VII.1库,并且在现有基础上针对WIMS-D库中的伪裂变产物、裂变产物燃耗链以及裂变产物产额等燃耗数据进行更新,再通过NJOY程序开发了SHEM281群WIMS-D格式多群常数库。通过DRAGON程序挂载该WIMSD281库,对其进行临界和燃耗两方面基准验证。计算结果表明,该数据库的计算结果与基准值符合较好,精度较高,结果可靠,可初步用于压水堆的相关计算。     

Uncertainty quantification of neutron multiplication factors of light water reactor fuels during depletion

Nuclear data-induced uncertainties of infinite neutron multiplication factors (k_∞) during fuel depletion are quantified in a single cell and a 3×3 multi-cell including burnable absorbers. Uncertainties of reaction cross sections, fission yields, decay half-lives and decay branching ratios provided in the JENDL libraries are taken into account. Hundred percent uncertainties are assumed to nuclear data to which uncertainty information are not provided in JENDL. Uncertainties propagation calculations are carried out with the adjoint-based procedure, and required sensitivity profiles of k_∞ with respect to these nuclear data are efficiently calculated by the depletion perturbation theory. Covariance matrices for fission yields and decay data in a simplified burnup chain are successfully generated by the stochastic-based procedure. k_∞ uncertainties of about 0.6% during fuel depletion are obtained, and it is shown that actinoids reaction cross sections are dominant contributors. Nuclide-wise decomposition of the uncertainties and observation of component-wise sensitivity profiles provide physical interpretations. By virtue of the adjoint-based procedure, several parametric surveys are also conducted. Contributions of uncertainties in fission products (FPs) nuclides are quantified, and important nuclides and energy ranges are identified for further evaluation of nuclear data of FP nuclides. Effect of cooling period on k_∞ uncertainties is also discussed.     

Sources: A code for calculating (alpha,n), spontaneous fission,and delayed neutron sources and spectra

SOURCES is a computer code that determines neutron production rates and spectra from (alpha, n) reactions, spontaneous fission, and delayed neutron emission due to the decay of radionuclides in homogeneous media, interface problems, and three-region interface problems. The code is also capable of calculating the neutron production rates due to (alpha, n) reactions induced by a monoenergetic beam of alpha particles incident on a slab of target material. The (alpha, n) spectra are calculated using an assumed isotropic angular distribution in the center-of-mass system with a library of 107 nuclide decay alpha-particle spectra, 24 sets of measured and/or evaluated (alpha, n) cross sections and product nuclide level branching fractions, and functional alpha particle stopping cross sections for Z < 106. Spontaneous fission sources and spectra are calculated with evaluated half-life, spontaneous fission branching, and Watt spectrum parameters for 44 actinides. The delayed neutron spectra are taken from an evaluated library of 105 precursors. The code outputs the magnitude and spectra of the resultant neutron sources. It also provides an analysis of the contributions to that source by each nuclide in the problem.     

聚变-裂变混合能源堆球模型中子学对算研究

利用蒙特卡罗程序和自主开发的蒙特卡罗-燃耗耦合程序MOCouple-s,对北京应用物理与计算数学研究所提出的聚变-裂变混合能源堆球模型进行了对算研究。对初始时刻及各燃耗时刻下的有效增殖因数、能量倍增因子、氚增殖比、中子源强度等堆芯参数进行了比较,结果总体符合较好。对寿期末重要核素的成分进行了详细比较,除个别核素外,偏差很小,表明所采用的计算程序与核参数库一致性良好。对核参数库的选择、铀水体积比等对燃耗计算结果的影响进行敏感性分析,并对外中子源驱动的次临界堆芯的燃耗计算进行详细讨论,提出可行的燃耗计算基准。     

Effect of fission products yield library on the calculation of the nuclide composition of the fuel in sodium-cooled fast reactors

The calculation of the composition of irradiated fuel for different degrees of burnup is a basic problem in the analysis of nuclear-radiological safety of objects holding spent fuel assemblies. The yield of fission products is one of the important initial indicators in burnup calculations. Methods for compiling libraries of fission products yield on the basis of the ENDF/B up-to-date evaluated nuclear data files are described. The nuclide composition of uranium oxide and uranium-plutonium-zirconium metal fuel in sodium-cooled fast reactors is analyzed by means of high-precision calculations performed with different fission product yields libraries using different computer codes MONTEBURNS–MCNP5–ORIGEN2 and the results are presented.     

Neutron energy dependence of delayed neutron yields and its assessments

Incident neutron energy dependence of delayed neutron yields of uranium and plutonium isotopes is investigated. A summation calculation of decay and fission yield data is employed, and the energy dependence of the latter part is considered in a phenomenological way. Our calculation systematically reproduces the energy dependence of delayed neutron yields by introducing an energy dependence of the most probable charge and the odd–even e?ect. The calculated fission yields are assessed by comparison with JENDL/FPY-2011, delayed neutron activities, and decay heats. Although the fission yields in this work are optimized to delayed neutron yields, the calculated decay heats are in good agreement with the experimental data. Comparison of the fission yields calculated in this work and JENDL/FPY-2011 gave an important insight for the evaluation of the next Japanese evaluated nuclear data library (JENDL) .     

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。     

双约束核素筛选与燃耗链压缩算法研究

在进行反应堆燃耗计算时,由于评价核数据库中各核素反应截面、寿命差异大,因此形成的燃耗矩阵规模大、刚性强。为降低燃耗矩阵规模、改善矩阵病态程度,有必要研究适用于多种堆芯设计研发需求的燃耗链压缩算法,并形成压缩燃耗链和数据库。首先建立了核素筛选标准,根据各个核素对中子吸收率和重要核素核子密度的贡献率对核素重要性进行排序筛选,研究了基于中子吸收率和重要核素产量贡献率的双约束燃耗链压缩算法,并完成相关程序模块的开发。通过对Kylin-2程序数据库压缩的计算分析,验证了该燃耗链压缩算法的可行性。采用压缩数据库可使其在保持原有计算精度的基础上大幅减少计算时间、提高计算效率;通过燃耗链压缩算法的研究与压缩数据库的实现,为从评价数据库出发制作压缩数据库提供了技术支撑。      

强中子场裂变产物中子核反应网络方程研究

本文建立了考虑中子参加反应的裂变产物中子反应及衰变的网络方程,选用求解一阶线性刚性微分方程组的Gear方法,开发了可计算任意裂变产物核数量在不同中子场强度和中子谱下随时间变化的核反应网络方程计算系统FIRENEQ,并配套了裂变产物产额和衰变数据库FPYDDL及裂变产物核中子反应截面数据库FPNCDL。检验结果表明,计算结果正确,程序可靠。利用该程序系统,研究了裂变产物核数量在不同中子场、不同诱发中子能量下随时间的变化。     

Fission Product Model for BWR Lattice Calculation Code

A benchmark calculation of full fission product was performed for thermal reactor application using an isotope transmutation code DCHAIN based on 185 nuclides with revised nuclear data library. The fission product model for BWR lattice calculation was studied and tested with the benchmark results, and a model containing 45 explicit nuclides and one pseudo nuclide was selected as a reasonably best model to predict the burn up reactivity with high precision for practically all types of fuel and reactor operating conditions. The evaluated thermal cross section and resonance integral for the pseudo nuclide are σ_2,200 = 2.6b and.RI = 10.6b, combined with the pseudo fission yield values of 1.3898, 1.3233, 1.3675 and 1.2773 for fissions from ²³⁵U, ²³⁸U, ²³⁹Pu and ²⁴¹Pu, respectively. The present results are believed as equally applicable to PWR lattice calculation.     

Propagation of statistical and nuclear data uncertainties in Monte Carlo burn-up calculations

Two methodologies to propagate the uncertainties on the nuclide inventory in combined Monte Carlo-spectrum and burn-up calculations are presented, based on sensitivity/uncertainty and random sampling techniques (uncertainty Monte Carlo method). Both enable the assessment of the impact of uncertainties in the nuclear data as well as uncertainties due to the statistical nature of the Monte Carlo neutron transport calculation. The methodologies are implemented in our MCNP–ACAB system, which combines the neutron transport code MCNP-4C and the inventory code ACAB.     

熔岩玻璃体核素衰变热功率的计算

温度是影响熔岩玻璃体溶解速度的关键因素,为此,本文计算了核试验后10~300 000d内熔岩玻璃体中核素衰变热功率,评估了核素衰变热功率对熔岩玻璃体的温度和溶解速度的影响程度。采用了国际原子能机构给出的100kt TNT当量地下核试验产生的、半衰期大于1a的放射性核素含量,利用其中裂变产物核素137 Cs的含量推算累积裂变产额大于0.1%、半衰期为1d~1a的短寿命裂变产物核素的含量。分析了各核素的放射性衰变特点,采用ENDF/BⅦ库中核素衰变辐射的平均α能量、平均电子能量和平均电磁辐射能量计算各核素在熔岩玻璃体内因衰变而沉积的能量。计算结果表明:核素衰变热功率呈分段幂函数衰减;在10~2 000d、2 000~60 000d和60 000d之后的时段内,衰变热功率分别主要源于短寿命裂变产物核素、长寿命裂变产物核素和锕系元素。核素衰变热功率对熔岩玻璃体的温度和溶解速度的影响不大,1 000d后影响非常小。