压水堆核电站活化产物源项计算程序CPAP的开发

活化产物为压水堆核电站中主要辐射源,有必要对其建立分析手段。分析了压水堆核电站堆芯外材料中活化产物源项的产生途径,建立了压水堆核电站堆芯外材料中活化产物源项的计算模型,并分别基于矩阵指数法和切比雪夫有理近似法求解所建立的计算模型。开发了具有良好人机界面的计算程序CPAP,并采用典型材料活化例题与国外同类软件进行了对比测试。测试结果表明:CPAP程序对于测试算例的计算结果与国外同类软件的计算结果之间的偏差在工程可接受的范围内。CPAP程序具有人机界面友好以及求解器可选的优点,可广泛应用于压水堆核电站的设计、运行和退役阶段。     

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Super MC(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。     

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。     

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。     

基于高阶CRAM的燃耗程序开发与验证

本文基于高阶切比雪夫有理近似方法（CRAM）研制了点燃耗程序ICRAM，并内耦合于蒙特卡罗输运程序OpenMC，形成了一套燃耗计算分析程序OPICE。与传统部分分式分解（PFD）形式的CRAM相比，高阶不完全局部分解（IPF）形式的CRAM具有数值稳定性好、计算精度高和步长包容性更好等特点，满足高保真燃耗计算发展的需求。为提高耦合计算精度，OPICE采用了预估-校正和子步法两种耦合策略，支持纯衰变、定通量和定功率3种计算模式。通过OECD/NEA压水堆栅元燃耗基准题和快堆燃耗基准题的验证，程序计算结果与实验值及各参考值吻合良好，初步验证了OPICE的正确性与有效性。     

微观燃耗方程求解方法研究与数值验证

研究分析了求解燃耗方程的多种计算方法,包括泰勒级数展开(Taylor)方法、Pade近似(Pade)方法、尺度平方(Scale)方法、特征值(Eig)方法、切比雪夫有理近似(Cram)方法、拉格朗日插值(Lagrange)方法、牛顿插值(Newton)方法、范德蒙矩阵方法和子空间(Krylov)方法,比较分析了各算法在计算效率和计算精度的优劣,最终确定了Cram方法为求解燃耗方程的优选算法。采用Cram方法开发完成了燃耗方程的求解程序,并进行了基准题的验证。结果表明,开发完成的燃耗方程求解程序具有较高的计算精度。     

水冷聚变堆主回路活化产物源项计算分析

水冷聚变堆中结构材料活化腐蚀产物和冷却剂活化产物是正常运行工况下的最主要放射性来源,也是反应堆运行及维护过程中工作人员辐照剂量的直接来源。本文使用CATE V2.1程序对国际热核聚变实验堆(International Thermonuclear Experimental Reactor,ITER)LIM-OBB(Limiter-Out-Board Baffle)冷却回路的活化腐蚀产物和水活化产物进行模拟计算,并根据CATE模拟得到的放射性活度通过点核积分程序分别计算正常运行1.2 a及停堆15 d的剂量率。计算结果表明,反应堆运行期间冷却剂活化产物比活度和剂量率远大于结构材料活化腐蚀产物,而停堆后冷却剂活化产物迅速衰变完,结构材料的活化腐蚀产物成为比活度和剂量率的主要来源。     

Computational tracking of BN-600 operation

Computational tracking of BN-600 operation is described. The high quality of computational tracking is largely due to the nature of a fast reactor, in this case BN-600. Unlike reactors with a thermal neutron spectrum, in a fast reactor, because the prompt and delayed fission neutrons as well as the absorbed neutrons are almost in the same energy range as the fast neutrons, a computational cell can be confidently homogenized and the reactor is strongly coupled to the neutron field. These are the reasons why the behavior of the reactor can be successfully predicted by means of computational programs which are based on the diffusion approximation neglecting the anisotropy of the interaction of the neutrons and the heterogeneity of the medium.     

A Method for Measuring Absolute Reactor Power through Neutron Fluctuation

A new principle is presented for obtaining absolute reactor power by processing the random fluctuation of neutron flux based on the stochastic nature of nuclear reactions. The required combination of instruments to carry out experiments is described, and experimental results obtained in a swimming pool reactor are reported. The power spectral density of the output current of an ion chamber located near the reactor core is determined by reactor kinetic parameters such as delayed neutron yield, life time, ν (mean number of neutrons generated per fission) and counter efficiency as well as by the total number of neutrons in the core, which is a measure of absolute power.

Using either logarithmic amplifier or reactivity meter, absolute reactor power can be measured without any information about detector efficiency. This method has such merits as easiness and simplicity in operation, ability to measure absolute power in the range 0.01～100 W where other methods are inapplicable, and negligible effect of changes in core configuration or in detector position.

The results of actual reactor experiments with this method proved to agree fairly well with those of absolute measurement by gold foil activation.     

JFNK求解高温气冷堆中子扩散问题的预处理方法研究

预处理方法是非线性求解方法JFNK中效率和数值收敛特性的关键。基于包括活性区、石墨反射层和外围含硼碳砖在内的高温气冷堆堆芯中子扩散本征值问题，对JFNK求解过程中的预处理环节进行了研究。根据矩阵元素的物理性质简化得到不同的近似雅克比矩阵，使用线性预处理方案ILU、SIPLU进行了预处理，并对其预处理效果、矩阵稀疏性、预处理时间等参数进行了分析。结果表明，块雅克比型近似阵是对原雅克比矩阵的较好近似，其能够在保留各中子能群内部耦合关系的前提下，构造结构简单、适用性强的近似雅克比矩阵。对于此类高温气冷堆中子扩散问题，选取SIPLU方法能获得性能良好的预处理矩阵，达到高效JFNK计算。     

Sub-critical reactor kinetics analysis using incomplete gamma functions and binomial expansions

Point reactor kinetics equations with one group of delayed neutrons are solved analytically to determine the neutron population as a function of time for any ramp reactivity insertion in the presence of external neutron source using prompt jump approximation. With the time dependent neutron population the other important kinetic parameters such as the reactor period also can be derived. Analytical solutions are available in the literatures for any ramp reactivity insertion into a critical reactor without considering the source term. Analytical solutions available in the literature by considering the source term also to study sub-critical reactor kinetics. But such a solutions either uses constant source approximation which under predicts the solution, or the available solution is not useful for all kind of sub-critical reactivity and external ramp reactivity insertion combination due to the computer precision incompatibility. In the present work, analyses are carried out to determine the reactivity boundary to which the existing results can converge to a true solution, beyond where the precision incompatibility arises. A new series solution is recommended in the region where existing solution converges to false solution due to precision incompatibility.     

Refinement of the method of homogenization of a heterogeneous reactor

Conclusions We have described the basic features of the step-by-step method of obtaining the finite-difference equations describing the neutron distribution in a heterogeneous reactor.It is proposed to devote further study to an analysis of the approximation to which the method should be limited in most actual situations, what further microdistributions of neutrons within a reactor cell should be found, and what accuracy is required in their calculation.Translated from Atomnaya Énergiya, Vol. 43, No. 4, pp. 247–253, October, 1977.     

Improvement of Neutron Source Introduction Method for Absolute Measurements of Low Reactor Power

The neutron source introduction method was applied to absolute measurements of low reactor power at the Static Experiment Critical Facility STACY. To obtain the effective neutron source intensity more accurately, which is a key parameter for the source introduction method, the neutron source is newly defined as fission neutrons from the first fission reaction caused by neutrons emitted from the external neutron source. To obtain the newly defined effective neutron source intensity, the probability that a neutron from the external neutron source causes a fission reaction is calculated using the Monte Carlo code MCNP. This calculation took into consideration the three-dimensional complicated core structures. Furthermore, the fission reaction distribution, fundamental mode forward and adjoint flux distribution in a critical state were calculated using the three-dimensional transport code THREEDANT. Following the principle of the neutron source introduction method, an external neutron source was inserted near the STACY core tank and the reactor power was measured. The reactor powers by the neutron source introduction method were in good agreement with the ones from the analyses of the FP activity generated by high power operation.     

Development and Validation of Burnup Code Based on High-order Chebyshev Rational Approximation Method

Based on high-order Chebyshev rational approximation method (CRAM), a point-burnup code named ICRAM was developed and internally coupled to Monte Carlo code OpenMC, forming a burnup calculation and analysis program OPICE. Compared with the traditional partial fraction decomposition (PFD) form of CRAM, the high-order incomplete partial fractions (IPF) form of CRAM has the characteristics of good numerical stability, high calculation accuracy and better step tolerance, etc., which meets the needs of high-fidelity burnup calculation development. In order to improve the accuracy of coupling calculations, two coupling strategies including prediction-correction method and sub-step method were implemented in OPICE. Three different calculation modes were supported by OPICE to execute the decay, constant flux and constant power calculations. By calculating the OECD/NEA burnup benchmark and fast reactor burnup benchmark, the calculation results of OPICE are in good agreement with the experimental data and each reference value. The correctness and validity of OPICE are verified preliminarily.