基于切比雪夫有理逼近方法的蒙特卡罗燃耗计算研究与验证

燃耗计算在反应堆设计、分析研究中起着重要作用。相比于传统点燃耗算法,切比雪夫有理逼近方法(Chebyshev rational approximation method,CRAM)具有计算速度快、精度高的优点。基于超级蒙特卡罗核计算仿真软件系统SuperMC(Super Monte Carlo Simulation Program for Nuclear and Radiation Process),采用切比雪夫有理逼近方法和桶排序能量查找方法,进行了蒙特卡罗燃耗计算的初步研究与验证。通过燃料棒燃耗例题以及IAEA-ADS(International Atomic Energy Agency-Accelerator Driven Systems)国际基准题,初步验证了该燃耗计算方法的正确性,且IAEA-ADS基准题测试表明,与统一能量网格方法相比,桶排序能量查找方法在保证了计算效率的同时减少了内存开销。     

基于切比雪夫有理近似法的燃耗程序开发

基于切比雪夫有理近似法(CRAM)对燃耗方程进行求解,采用EAF数据库,开发了燃耗程序ABURN。计算了聚变堆第一壁活化例题和UO2燃料燃耗例题,并将ABURN程序的计算结果与欧洲活化程序FISPACT进行对比。结果表明,ABURN程序可达到FISPACT程序同等精度,并且由于采用了CRAM,程序在燃耗步设置方面具有高度的灵活性,初步验证了ABURN程序的可用性与准确性。     

CRAM在放射性核素存量计算中的应用

在反应堆中,组成材料的稳定核素经受强中子辐照后,会被活化成放射性核素。这些核素及其衰变产物对工作人员的职业辐照剂量具有重要贡献。为了更好地进行人员的辐射防护工作,需要对放射性核素的存量进行精确计算。相对于核素平衡方程的其它求解方法,切比雪夫有理逼近方法（Chebyshev Rational Approximation Method,CRAM）在计算精度和效率方面具有综合性优势。首先介绍了CRAM的基本理论,随后选取典型的例题进行了测试验证。与解析解对比的结果表明,采用CRAM进行中子辐照下的核素活化衰变计算能够取得不错的效果,但是用于核素长期衰变计算可能导致计算错误。针对此问题,将收缩乘方技术与CRAM相结合,取得了正确的计算结果,拓展了CRAM的适用范围。     

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。     

矩阵指数函数有理近似在点堆动力学中的应用

采用矩阵指数函数有理近似求解点堆动力学方程,研究了Padé近似、求积组有理近似(QRAM)和切比雪夫有理近似(CRAM)3种方法,并采用Richardson外推提高精度。计算结果表明,在大正反应性插入时,QRAM和CRAM的效果更好;外推后的Padé近似可能出现稳定性问题,其他2种方法稳定性较好。     

基于切比雪夫有理近似方法的点燃耗程序开发

基于切比雪夫有理近似方法（CRAM）开发了点燃耗求解程序。程序采用2套燃耗数据库,精细燃耗数据库和简化燃耗数据库,并将点燃耗程序与输运系统耦合。计算了定注量率辐照问题和衰变问题,以及JAEA轻水堆基准题,计算结果与国际知名程序对比。结果表明,程序在定注量率辐照问题和衰变问题的计算上,核子密度精度与ORIGEN2相当,单栅元和组件计算结果与HELIOS1.11以及参考解吻合良好。      

基于直接求导方法的中子活化计算不确定性研究

在中子活化计算中,由于输入核数据存在一定的固有不确定性,这将对计算结果产生一定的影响。而计算结果的不确定度对核设施源项分析、辐射屏蔽设计发挥着重要的作用。首先研究了用于不确定性分析的直接求导方法和Gear算法,随后进行了活化系数矩阵以及敏感性系数矩阵的构造,最后利用Gear算法同步求解活化方程组和敏感性方程组,得到核素存量对于核数据的敏感性系数,并结合核数据的相对不确定度得出核素存量的相对不确定度。将本工作研发的方法集成到中子活化程序ABURN中,并选取典型例题进行了测试验证。结果表明：ABURN程序对于核素存量及其敏感性系数与相对不确定度的计算结果,与解析解和欧洲活化程序FISPACT数值解的计算偏差很小,绝大部分偏差不超过0.2%,最大偏差不超过1%,说明此方法和程序具备了高精度分析核素存量的敏感性和不确定性的能力,能够为核设施辐射防护以及源项分析工作提供工具和数据支持。     

MMPA方法在多工况中子活化计算中的应用

反应堆内结构材料及回路中的腐蚀产物经过强中子辐照后会被活化成放射性核素,这些核素及其衰变产物是工作人员的主要辐照危害来源。因此,高效精确地计算这些放射性核素的存量对于反应堆屏蔽防护设计、放射性源项与废料管理等方面具有重要意义。本文研究了一种基于最佳一致逼近多项式(MMPA)的中子活化计算方法,相比于线性子链解析方法、指数欧拉方法等传统中子活化计算方法,该方法具有数值稳定性好、求解效率高且不需要单独处理短寿命核素的优点。进一步在自主研发的核素存量计算软件AMAC中研究并实现了基于MMPA方法的两种求解策略,并通过衰变工况、辐照工况、脉冲工况下的典型材料活化算例和针对大规模活化矩阵的算例初步验证了MMPA方法应用于多工况中子活化计算中的正确性和有效性。测试结果表明,该方法具有良好的计算精度和求解效率。     

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。     

基于R2S方法的反应堆结构材料活化剂量计算研究

反应堆结构材料在堆芯中子辐照下由于中子活化反应而产生大量的放射性核素,其衰变光子是反应堆停堆检修、换料、退役过程中工作人员职业照射剂量的重要来源。本文基于严格两步法（R2S）,研究了反应堆结构材料栅元活化计算方法,并基于蒙卡粒子输运程序（MCNP）与点活化计算程序（ORIGEN）建立了反应堆结构材料活化剂量计算软件（MOCA）。通过开发功能接口与数据接口程序实现输运程序与活化计算程序的自动耦合,进而实现“中子输运-活化分析-剂量计算”全自动耦合分析。利用M5包壳活化计算模型、不锈钢活化计算模型和NUREG/CR-6115压水堆模型对MOCA进行基准验证,证明了MOCA的正确性与可靠性。     

活化法区分浓缩铀与贫化铀数值模拟研究

铀材料的辐射探测方法是核查技术研究的重要内容,主动法是铀材料探测的有效方法之一.论文利用MCNP程序计算分析了活化法区分浓缩铀和贫化铀的可行性,研究表明通过铀材料的裂变率-慢化体厚度的关系曲线能够判断是贫化铀还是浓缩铀.计算分析了~(252)Cf和14MeV中子源在铀材料探测中的优缺点,结果表明~(252)Cf中子源优于14Mev中子源.最后从测量的角度,重点分析了探测对象--缓发γ射线和缓发中子,分析表明探测缓发中子优于缓发γ射线.     

基于SuperMC的ITER下窗口生物屏蔽插件屏蔽分析

在国际热核聚变实验堆(ITER)中,窗口生物屏蔽插件需为电子设备和工作人员提供必要的辐射屏蔽防护。基于中子学分析的生物屏蔽插件设计是ITER设计的重要内容。本文基于超级蒙卡核模拟软件SuperMC,在ITER大厅三维中子学模型中整合了ITER设计整合部门(DIN)最新设计的下窗口生物屏蔽插件模型,对四种下窗口生物屏蔽插件进行了屏蔽分析。分析结果显示,低温恒温器低温泵生物屏蔽插件中子屏蔽性能最好,室内监视系统生物屏蔽插件屏蔽性能最差;室内检视系统生物屏蔽插件停堆剂量率最小,环形低温泵生物屏蔽插件停堆剂量率最大。在SA2辐照方案下,停堆12天后,环形低温泵生物屏蔽插件处停堆剂量率超过规定限值20倍。分析结果表明,ITER下窗口生物屏蔽插件设计有待优化。     

Numerical Solutions of Discrete-Ordinate Neutron Transport Equations Equivalent to PL Approximation in X-Y Geometry

A numerical method for solving the steady-state one-velocity neutron transport equation in x-y geometry is presented. It is based on the concept of combining the spherical harmonics theory with the discrete-ordinate method. The validity of the method is illustrated by several numerical computations using the TWOTRAN-PLXY code, formulated by modifying the ordinary discrete-ordinate code TWOTRAN-(x, y).

Through numerical studies, it is shown that the present method is effective for obtaining solutions of high accuracy, as well as for eliminating the ray effects present in the ordinary discrete-ordinate method. As for the techniques for accelerating the convergence of the iterative solutions, it is proved that the Chebyshev device works well for the present method, while whole-system rebalancing is found to be less effective.     

Proposed Method of Measuring Thermal Diffusivity of a Small Specimen at Incandescent Temperatures

An evaluation was made of heat transfer tube failure propagation due to sodium-water reaction wastage in a sodium heated steam generator, by comparing an empirically derived wastage equation with leak detector responses.

The experimental data agreed well with the wastage equation even for different values of distance-to-nozzle diameter ratio, though the formula had been based on wastage data obtained for only one given distance. The time taken for failure propagation was estimated for a prototype steam generator, and compared with the responses characteristics of acoustic detectors and level gages. It was found that there exists a range of leak rate between 0.5 and 100g/sec, where the level gage can play a useful role in leak detection. The acoustic detector can be expected to respond more rapidly than the cover gas pressure gage, if noise is kept below ten times the value observed in an experimental facility, SWAT-2.     

桶装铀及超铀废物检测装置探测灵敏度的蒙特卡罗计算

基于桶装铀及超铀废物检测装置无源方式下中子总计数分析和有源方式下缓发中子计数分析的探测灵敏度表达式,运用蒙特卡罗方法计算了该装置对^240Pu和^235U的探测灵敏度,并对计算结果的可靠性进行了初步实验验证。     

New Uni-Resonance Approximation Technique for Reaction Rate of Higher Resonances in Activation Detectors

As a high efficiency solid sample analysis technique based on resonance ionization spectroscopy (RIS). Resonant Laser Ablation (RLA) is available. RLA combines Laser Ablation (LA) and RIS simultaneously with a single laser device. We have proposed the new dosimetry technique for a solid sample based on RLA.

We have attempted the detection of ²⁶Al (T _1/2: 7.2×10⁵yr) produced in the high purity Al irradiated by 14MeV neutrons at Fusion Neutronics Source (FNS). Japan Atomic Energy Research Institute. Some interference effects are observed in the trace element detection experiments. These interference effects interrupt the detection of ²⁶Al. In conclusion. it is difficult that ²⁶Al is recognized clearly. We have mainly discussed the origins and elimination methods of these interference effects to detect the trace elements produced by nuclear reactions.     

Improvement of the SPH Method for Pin-by-Pin Core Calculations

In this paper, improvement of the SPH method (the improved SPH method) is proposed. The SPH method is commonly used in pin-by-pin mesh core calculations to reduce cell-homogenization error. The investigation revealed that the normalization condition of the SPH factor in the conventional SPH method is not appropriate for multi-assembly calculations in which different assembly types are adjacent. Since the conventional normalization condition does not incorporate flux discontinuity between assemblies, cell homogenization error in assembly peripheral region becomes larger. In the improved SPH method, the SPH factor is divided by an averaged “cell-level” discontinuity factor obtained in each fuel assembly. Though the SPH factor is somewhat modified from the conventional value, no additional homogenization parameters (e.g. discontinuity factor) is necessary in core calculations. Test calculations were carried out in a simplified one-dimensional slab and two-dimensional PWR colorset geometries that simulate part of actual core geometry. The calculation results showed that the improved SPH method effectively reduce the cell-level homogenization error especially in assembly peripheral region. Since we can easily implement the improved SPH method by slight code modifications, it can be a promising candidate of the cell-homogenization method for pin-by-pin core calculations.     

Application of Multiband Method to Pin Cell Calculations

Abstract

In order to accurately calculate effective neutron cross sections in the resonance energy region, the multiband method has been applied to cell calculations. Cell calculations for UO² and MOX fuels of light water reactors have been performed and the results were compared with those of a continuous energy Monte Carlo code VIM and the conventional self-shielding method using the Dancoff factor.

The k∞values calculated by the multiband method agreed with those of the VIM calculations within 0.20% Δk for the UO² fuel cell and within 0.30% Δk for the MOX fuel cell, respectively, whereas the Dancoff factor method yielded about l.l%Δk errors for the two cells. The element- wise contribution to this error was investigated, and it was found that the effective microscopic cross sections, particularly those for the giant resonances of ²³⁸U, calculated by the multiband method were in good agreement with those of VIM. It was also found that interference effect between ²³⁸U and ²³⁵U resonances in the UO² fuel and that between ²³⁸U and ²³⁹Pu resonances in the MOX fuel made about 0.20%Δk contributions to k∞ in both fuel cells.