基于拼接裂变矩阵的燃耗计算方法研究

为了实现高效率的输运-燃耗耦合计算,本文基于拼接裂变矩阵理论提出了一种新的燃耗计算方法。拼接裂变矩阵方法使系统的裂变矩阵可以通过预先计算的数据库获得,再根据计算模型的实际工况,按照终点区域性质进行拼接。裂变矩阵数据库采用蒙特卡罗固定源计算得到,堆芯计算也不需要蒙特卡洛模拟,因此可避开耗时的临界计算。本文采用新的燃耗计算方法计算了一个典型两组件模型燃耗600有效满功率天（EFPD）的有效增殖因子和裂变源分布,结果表明燃耗-富集度复合修正比例可将裂变源均方根误差控制在0.7%以下,证明该算法的可行性。     

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。     

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。     

多群蒙特卡罗程序MCMG的开发与基准校验

基于连续能量蒙特卡罗程序MCNP开发了多群蒙特卡罗程序MCMG.利用由栅元程序WIMS产生的随燃耗变化的多群宏观均匀化截面取代连续能量点截面,大大提高了程序的计算速度,同时也解决了蒙特卡罗程序不能进行燃耗计算等问题.针对输运修正引起的自散射截面导致的负概率抽样现象,提出了一种非负修正方法,并用基准计算验证了该方法的正确性.     

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。     

基于CITATION-ORIGEN2球床堆平衡态计算程序的实现

基于确定论中子扩散软件CITATION和点燃耗软件ORIGEN2,编写了球床堆分析程序COBBLE,以实现指定燃料球加载策略下的球床堆平衡态燃耗计算。COBBLE程序采用谱区能谱修正方法,通过迭代求解得到球床堆堆芯平衡态参数。本文选取简化的球床模块高温气冷堆(PBMR)堆芯进行建模,计算其功率分布及燃耗分布,并使用基于蒙特卡罗方法的球床堆燃耗计算程序PBRE进行了验证与分析。结果表明,COBBLE程序适用于球床堆的平衡态燃耗计算。     

基于RMC的蒙特卡罗燃耗计算氙振荡抑制方法研究

蒙特卡罗燃耗计算模型为中子输运弱耦合系统时,计算结果会出现数值振荡,从而引入较大误差,甚至导致计算终止。蒙卡燃耗计算中出现的数值振荡主要由堆内的裂变毒物氙驱动,所以如何有效抑制氙振荡是蒙卡燃耗计算研究的内容之一。强制平衡氙方法在各燃耗步功率保持恒定时有很好的抑制效果,但在小步长变功率燃耗计算时,所得的计算结果存在显著偏差。目前,国际主流的反应堆基准题提出了变功率燃耗计算的需求,为抑制小步长变功率燃耗计算的氙振荡,在堆用蒙卡程序RMC中开发了通用平衡氙方法。本文介绍RMC中主要采用的平衡氙方法,包括强制平衡氙方法和通用平衡氙方法。对数值验证的计算结果进行分析和比较,结果表明通用平衡氙方法能有效抑制定功率及小步长变功率蒙特卡罗燃耗计算的氙振荡现象。     

基于计数器数据分解的RMC全堆燃耗计算研究

内存不足是蒙特卡罗方法大规模输运模拟的关键问题。对于反应堆燃耗分析,需在输运过程中统计大量反应截面数据,计算机内存限制了燃耗计算规模。本文基于反应堆蒙特卡罗程序(RMC),利用数据分解方法对计数器数据并行存储,并与点燃耗并行耦合,实现计数器数据分解和燃耗数据分解的综合并行方法。对全堆基准题进行数值测试,结果表明综合并行方法可明显降低计算内存,验证了数据分解对蒙特卡罗大规模燃耗分析的有效性。     

堆用蒙卡程序燃耗计算功能开发

堆用蒙卡程序(RMC)是由清华大学工程物理系REAL实验室自主开发的用于反应堆物理分析的中子输运蒙卡程序,本文主要介绍其燃耗计算功能的开发与验证。RMC的燃耗计算功能具有的特点:内部耦合ORIGEN,相比于外耦合方式,更加灵活和高效;使用基于能谱的单群截面统计方法,可在保证精度的前提下,显著提高计算效率;采取预估修正和中点近似等多种燃耗步策略,减小大燃耗步长时的计算误差。通过计算压水堆栅元、沸水堆组件、快堆等一系列基准题和算例,验证了RMC燃耗计算的正确性和速度优势。     

COSINE软件包组件计算程序LATC的燃耗计算模块开发与验证

燃耗计算是反应堆组件参数计算程序的核心功能之一,其计算精度直接影响堆芯物理计算精度。本文系统研究了组件参数计算程序中燃耗计算方法,建立了燃耗计算理论模型,给出了能有效解决燃耗方程刚性的数值方法,根据此方法编制了LATC程序的燃耗计算模块并进行了数值验证。计算结果表明,该燃耗计算模块精度较高,在大燃耗步、深燃耗下仍可得到合理可信的结果。     

Analysis of Core Physics Experiments on Fresh and Irradiated PWR UO2 Fuels in the REBUS Program

Critical experiments of two cores each loaded with fresh 5 × 5 test PWR-type fuel rods of ²³⁵U enrichment of 3.8 wt% or irradiated 5 × 5 test rods of rod average burnup of 55 GWd/t in the REBUS program were analyzed using diffusion, transport, and continuous-energy Monte Carlo calculation codes coupled with nuclear data libraries based on JENDL-3.2 and JENDL-3.3. Biases in effective multiplication factors k _eff's of the critical cores were about ?1:2%Δk for the diffusion calculations (JENDL-3.2), ?0:5%Δk for the transport calculations (JENDL-3.3), and ?0:5 and 0.1%Δk for the Monte Carlo calculations (JENDL-3.3 and JENDL-3.2, respectively). The measured core fission rate and Sc- or Co-activation rate distributions were generally well reproduced using the three types of calculation. The burnup reactivity determined using the measured water level reactivity coefficients was ?2:35 ± 0:07Δk/kk′. The calculated result of the Monte Carlo calculations agreed with it; however, the diffusion and transport calculations overestimated the absolute value by about 7%, which would be mainly attributed to the errors in the calculation of the reactivity caused by changing the fuel compositions from fresh fuel to irradiated fuel.     

Analysis of core physics experiments on irradiated BWR MOX fuel in the REBUS program

Critical experiments were performed in the REBUS program on a core loaded with a test bundle including 16 irradiated BWR-type MOX rods of average burnup of 61 GWd/t. The experimental data were analyzed using diffusion, transport, and continuous-energy Monte Carlo calculation codes coupled with nuclear data libraries based on JENDL-3.2 or JENDL-3.3. Biases in effective multiplication factors of the critical cores were ?1.0%Δk for the diffusion calculations (JENDL-3.2), ?0.3%Δk for the transport calculations (JENDL-3.3), and 0.2%Δk for the Monte Carlo calculations (JENDL-3.2). The measured core fission rate and co-activation rate distributions were generally well reproduced using the three types of calculations. The burnup reactivity determined using the measured water level reactivity coefficients was ?2.41 ± 0.08%Δk/kk’, which also agreed with the results of the three type of calculations within the measurement and calculation errors. The most probable isotopic inventories in the irradiated MOX rods was tentatively obtained by using the ratios of the calculation to chemical assay data on a pellet sample, and the burnup reactivity was reanalyzed to split the calculation error into those due to the inventory and reactivity calculations. This approach showed that the inventory calculation error compensated the reactivity calculation error.     

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。     

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.     

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。     

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.     

复杂燃料成分的多核素共振干涉计算方法研究

共振干涉现象广泛存在于反应堆系统中,是影响共振计算精度的重要因素之一。当前提出的干涉因子方法,其计算效率难以适用于燃耗过程中的复杂燃料成分。基于改进的伪核素理论与超细群慢化方程求解程序,提出了一种针对实际压水堆燃耗过程的快速共振干涉计算方法。对于燃耗过程中的复杂燃料成分,在均匀问题和压水堆栅元几何下进行了共振自屏分析。结果表明,该方法的计算精度与严格的超细群计算及蒙特卡罗方法相当,效率上优于干涉因子方法,适用于压水堆燃耗过程中的快速共振计算。     

Two practical methods for unionized energy grid construction in continuous-energy Monte Carlo neutron transport calculation

A considerable speed-up in continuous-energy Monte Carlo neutron transport calculation can be achieved by using the same unionized energy grid for all point-wise reaction cross sections. This speed-up results from the fact that time-consuming grid iteration is reduced to minimum, and if the unionized grid is constructed by combining the grids of all nuclides, there is no loss of data or accuracy in the calculation. The drawback of this approach is that computer memory is wasted for storing a large number of redundant data points. Memory usage may become a problem, especially in burnup calculation, in which the irradiated materials consist of several hundred actinide and fission product nuclides. The grid size easily increases to over 1 million points, requiring tens of gigabytes of memory for storing the cross section data. This paper presents two practical methods for reducing the memory demand, while trying preserve the accuracy of the original data. The calculation routines are included in the PSG2/Serpent Monte Carlo reactor physics burnup calculation code and the methods are tested in a BWR assembly burnup calculation.     

Effect of error propagation of nuclide number densities on Monte Carlo burn-up calculations

As a result of improvements in computer technology, the continuous energy Monte Carlo burn-up calculation has received attention as a good candidate for an assembly calculation method. However, the results of Monte Carlo calculations contain the statistical errors. The results of Monte Carlo burn-up calculations, in particular, include propagated statistical errors through the variance of the nuclide number densities. Therefore, if statistical error alone is evaluated, the errors in Monte Carlo burn-up calculations may be underestimated. To make clear this effect of error propagation on Monte Carlo burn-up calculations, we here proposed an equation that can predict the variance of nuclide number densities after burn-up calculations, and we verified this equation using enormous numbers of the Monte Carlo burn-up calculations by changing only the initial random numbers. We also verified the effect of the number of burn-up calculation points on Monte Carlo burn-up calculations. From these verifications, we estimated the errors in Monte Carlo burn-up calculations including both statistical and propagated errors. Finally, we made clear the effects of error propagation on Monte Carlo burn-up calculations by comparing statistical errors alone versus both statistical and propagated errors. The results revealed that the effects of error propagation on the Monte Carlo burn-up calculations of 8 × 8 BWR fuel assembly are low up to 60 GWd/t.     

Development of a practical Monte Carlo based fuel management system for the Penn State University Breazeale Research Reactor (PSBR)

A practical fuel management system for the he Pennsylvania State University Breazeale Research Reactor (PSBR) based on the advanced Monte Carlo methodology was developed from the existing fuel management tool in this research. Several modeling improvements were implemented to the old system. The improved fuel management system can now utilize the burnup dependent cross section libraries generated specifically for PSBR fuel and it is also able to update the cross sections of these libraries by the Monte Carlo calculation automatically. Considerations were given to balance the computation time and the accuracy of the cross section update. Thus, certain types of a limited number of isotopes, which are considered “important”, are calculated and updated by the scheme. Moreover, the depletion algorithm of the existing fuel management tool was replaced from the predictor only to the predictor-corrector depletion scheme to account for burnup spectrum changes during the burnup step more accurately. An intermediate verification of the fuel management system was performed to assess the correctness of the newly implemented schemes against HELIOS. It was found that the agreement of both codes is good when the same energy released per fission (Q values) is used. Furthermore, to be able to model the reactor at various temperatures, the fuel management tool is able to utilize automatically the continuous cross sections generated at different temperatures. Other additional useful capabilities were also added to the fuel management tool to make it easy to use and be practical. As part of the development, a hybrid nodal diffusion/Monte Carlo calculation was devised to speed up the Monte Carlo calculation by providing more converged initial source distribution for the Monte Carlo calculation from the nodal diffusion calculation. Finally, the fuel management system was validated against the measured data using several actual PSBR core loadings. The agreement of the predicted core excess reactivities and the measured values is found to be good considering the measurement uncertainties.