超级均匀化方法在压水堆堆芯Pin-by-pin计算中的应用与研究

在压水堆堆芯Pin-by-pin计算中,采用超级均匀化（SPH）方法作为均匀化技术,对燃料组件传统SPH因子进行计算,生成了Pin-by-pin等效均匀化参数。针对存在中子泄漏现象的反射层组件,研究了与空间泄漏相关的SPH方法,在保证反应率守恒的基础上,同时保证各栅元各能群的中子泄漏率守恒,解决了存在中子泄漏时SPH因子迭代计算的不收敛问题,生成了反射层组件的等效均匀化参数。基于KAIST基准题,分析了压水堆堆芯Pin-by-pin计算中应用SPH因子的堆芯计算精度。数值结果表明,与传统组件均匀化计算方法相比,应用SPH方法的压水堆堆芯Pin-by-pin计算的计算精度更高。     

基于连续能量蒙特卡罗的快中子反应堆均匀化截面计算方法研究

快堆确定论两步法通常由组件均匀化截面计算和堆芯扩散/输运计算共同组成,已广泛应用于快堆工程设计与分析领域。基于连续能量精细几何的蒙特卡罗均匀化截面计算方法可为先进快堆提供高精度均匀化群常数。本文简要综述了蒙特卡罗生成的均匀化截面与堆芯扩散/输运计算结合的发展现状与技术趋势。介绍了蒙特卡罗体积通量均匀化方法和超级均匀化等效修正方法,提出了蒙特卡罗通量矩均匀化方法。以MET-1000金属燃料快堆数值对标为例,针对堆芯扩散计算,对控制棒使用超级均匀化等效修正方法,将堆芯扩散计算的控制棒价值高估从13.5%减小到0.35%,并提高了功率分布预测精度;针对堆芯输运计算,定量解析了误差原因,提出了蒙特卡罗通量矩均匀化方法,可减小MET-1000堆芯输运计算的反应性误差698 pcm。本文中适用于快堆扩散及堆芯输运计算的蒙特卡罗均匀化截面生成方法针对先进非均匀布置快堆、小型快堆等新型堆芯,与不同堆芯求解器的结合有待进一步发展与验证。同时,蒙特卡罗生成快堆均匀化截面还有许多问题需要深入研究,如不连续因子修正、基模修正、历史效应处理方法等。     

基于凤凰快堆寿期末控制棒提棒实验的SARAX程序系统确认

寿期末控制棒提棒实验是在法国钠冷快堆Phenix(凤凰快堆)退役之前开展的最后一次实堆测量实验,实验中测量了低功率状态下的控制棒价值和满功率状态下的径向功率分布。本实验采用西安交通大学开发的快堆中子学计算程序系统SARAX进行建模和计算,其计算过程采用基于点截面的超细群方法进行能谱计算,采用超级均匀化(SPH)因子方法进行组件均匀化计算,以及采用多群中子输运节块方法进行堆芯计算,最终计算了实验中4个临界状态的有效增殖因子、控制棒价值、堆芯反应性系数及功率分布等参数。计算结果表明:SARAX的计算结果与实验值吻合较好,计算精度优于传统的快堆物理计算程序,可以用于钠冷氧化物混合燃料(MOX燃料)快堆的核设计。     

环形燃料超临界水冷堆中子学计算方法研究

基于先进组件程序HELIOS和堆芯节块法程序SIXTUS,研发了超临界水冷堆（SCWR）的中子学计算程序FENNEL-N,并通过与蒙特卡罗程序对比分析了其用于环形燃料超临界水冷堆计算的精度。组件验证结果表明：制作多群数据库的压水堆能谱与超临界水冷堆能谱的差异是导致计算误差的主要原因。堆芯验证结果表明：传统的组件均匀化方法在计算超临界水冷堆时会引入较大误差。应用FENNEL-N程序对组件均匀化方法进行了研究,结果表明,采用优化的组件参数少群结构能减少堆芯能谱变化对精度的影响,采用超组件模型计算组件参数可考虑反射层对组件参数的影响。采用新的组件均匀化方法后,FENNEL-N的计算精度满足了预概念设计需求。     

蒙特卡罗方法在快堆组件参数计算中的应用

在快中子反应堆中,中等核素的散射共振现象以及空间耦合效应较为明显。为解决此问题,使用基于蒙特卡罗方法的Open MC程序产生少群快堆组件参数,传递给基于确定论方法的堆芯程序进行混合计算。采用二维径向-轴向坐标几何的等效堆芯作为产生组件参数的计算模型。数值结果表明,该方法很好地解决了结构材料在高能区的散射共振现象;同时混合计算的相对误差均小于1%,可应用于快堆的稳态计算。     

基于数字化反应堆物理计算程序SHARK的一步法输运计算方法研究

为建立基于数字化反应堆技术的新一代反应堆物理计算方法,实现数字化反应堆高保真建模、高分辨率高精度计算,基于数字化反应堆物理计算程序SHARK,开展了一步法输运计算方法研究,建立并比较了二维/一维方法及准三维特征线输运方法;基于空间区域分解及粗网有限差分(CMFD)的大规模并行加速技术,实现了棒状堆芯及板状堆芯的全堆规模一步法输运计算。数值结果与蒙特卡罗程序基准解相比,特征值偏差小于100pcm(1pcm=10^-5),最大棒功率、板功率偏差小于3%,验证了SHARK程序一步法输运计算方法具有良好计算精度,能够适用于棒状、板状堆芯等多应用场景。     

超级等效方法研究

在广义等效理论(GET)和超级均匀化方法(SPH)的基础上,提出同时满足反应率、界面流和组件特征值守恒,且不显式使用等效因子的超级等效方法(SPE)。在蒙特卡罗组件均匀化中应用SPE,将该方法植入蒙特卡罗组件均匀化程序MCMC,并通过C5G7基准题进行验证。验证分析表明:SPE等效均匀化群常数堆芯计算精度更高,适应性更广。     

SPH等效均匀化方法研究

SPH等效均匀化方法是一种通过调整截面参数使得均匀化前后反应率保持守恒的均匀化方法。近年来,由于计算机硬件条件的飞速发展和对更高精度堆芯分析能力的要求,基于Pin-by-Pin的全堆芯计算越来越受到业界的关注。SPH均匀化方法不需要保存额外的均匀化参数(不连续因子),是栅元均匀化的首选方法之一。本文研究了SPH因子的求解方法及其应用,证明了在组件层面上SPH修正后均匀的扩散计算能够完全恢复非均匀输运计算结果。本文对由UO2燃料和MOX燃料组成的Colorset问题进行了检验,数值结果表明,与传统的通量-体积权重的均匀化方法相比,基于SPH均匀化方法的细网计算可以更好的预测控制棒价值和燃料棒功率分布。     

DRAGON&DONJON程序在MSR中堆芯燃耗计算的适用性

DRAGONDONJON组件-堆芯"两步法"程序通过合理简化,理论可适用于任何堆芯与工况。使用蒙特卡罗方法 RMC(Reactor Monte Carlo code)、MCNP(Monte Carlo Neutron Particle transport code)程序验证DRADON程序是否能够承担快/热谱型熔盐堆(Molten Salt Reactor,MSR)焚烧TRU、Th U燃料燃耗计算。选出熔盐增殖堆(Molten Salt Breeder Reactor,MSBR)与熔盐锕系元素再循环和嬗变堆(Molten Salt Advanced Reactor Transmuter,MOSART)堆型进行比较,同时分别利用RMC程序验证DRAGON程序组件燃耗计算的准确性,利用MCNP程序验证DRAGON程序组件均匀化方法以及DONJON程序截面调用和程序全堆扩散的准确性。结果表明,组件燃耗计算中,TRU和Th U燃料满足燃耗计算要求;堆芯临界计算中,快/热谱堆芯计算误差均小于0.001。证明DRADON程序可以胜任快、热谱型MSR焚烧TRU、Th U燃料的物理计算任务。     

液态金属冷却快堆堆芯物理分析软件LoongSARAX的验证与确认

NECP-SARAX是西安交通大学核工程计算物理实验室自主开发的先进反应堆中子学分析计算系统。在此基础上,西安交通大学针对液态金属冷却快堆的堆芯物理工程设计与安全审评,定制开发了LoongSARAX。为了实现LoongSARAX的工程应用,规范性、系统性的验证与确认是该过程的重要一环。为此,本文针对LoongSARAX验证与确认研究,在搜集整理国际上关于液态金属冷却快堆物理计算基准题的基础上,建立了其验证与确认矩阵,并将程序分成不同模块,分别进行了模块验证、子系统验证和系统确认,范围涵盖冷却剂为钠和铅的快堆,如JOYO、ZPPR17A等。程序验证与确认表明LoongSARAX程序对于液态金属冷却快堆具有较高的计算精度,同时针对中国实验快堆(CEFR)开展了不确定度量化研究。结果表明,在99%置信度下,有效增殖因数计算结果的不确定度有90%的概率落在[-389 pcm, 300 pcm]以内。     

热管式空间反应堆燃耗计算研究

针对热管式空间反应堆,基于OpenMC程序产生均匀化截面参数,并由确定论快堆分析程序SARAX进行堆芯输运及燃耗计算。以蒙特卡罗程序（MCNP）的输运计算结果以及MVP程序的燃耗计算结果作为参考解,通过对比稳态输运计算和燃耗计算的结果,证明了耦合的OpenMC和SARAX程序系统对于空间堆中子学分析和燃耗分析的适用性和高效性。为热管式空间反应堆的设计分析提供了参考。      

Reconstruction of cell homogenized macroscopic cross sections for analyzing fast and thermal coupled cores using the SRAC system

A fast and thermal neutron coupled core adopts blanket fuel assemblies with zirconium hydrides in the core for negative coolant void reactivity. Conventional neutronics calculation methods have been developed for analysis of a fast core or thermal core, in which the coarse-group macroscopic cross sections of fuel assemblies are prepared without including the effect of the surrounding fuel assemblies. However, such methods are not adequate for analyzing fast and thermal neutron coupled cores where the intra-assembly and inter-assembly heterogeneity effects must be precisely taken into account. Recently, a concept of reconstruction of cell homogenized macroscopic cross sections has been proposed to take into account effects of inter-assembly heterogeneities on macroscopic cross sections used in the reactor core analysis and successfully applied based on a Monte Carlo method. In the present study, a reconstruction method of cell homogenized coarse-group macroscopic cross section for analyzing fast and thermal coupled cores is developed based on a deterministic neutronics calculation code system, SRAC. Three types of fixed source calculations for unit assembly cell geometry are performed independently of the specific core layouts and their results are combined with the results of core analysis to produce cell homogenized coarse-group macroscopic cross sections. Numerical results show that the heterogeneity effects can be adequately reflected in the reconstructed macroscopic cross sections with the proposed method. When the number of energy groups is small, the proposed method gives poor results in the transitional energy groups from resonance to thermal energy. Therefore, it is necessary to increase the number of energy groups in this energy range.     

Reconstruction method of homogenized cross sections

The reconstruction method of homogenized cross sections in the direct response matrix method has been developed. In this reconstruction method, homogenized cross sections, which take into consideration the influences of neighboring fuel assemblies, can be reconstructed with the response relationship of incoming neutron partial currents and neutron production rates. Calculations for heterogeneous multi fuel assembly systems were done to verify the developed method. The thermal energy group fuel assembly cell-averaged homogenized cross sections reconstructed by this method agreed with those evaluated by the direct calculation of the whole system using the Monte Carlo method within 0.2%. The effect using the reconstructed fuel assembly cell-averaged homogenized cross sections in a conventional core analysis code using cross sections homogenized in a fuel assembly cell was also investigated. The results obtained showed that the analysis accuracy of k-infinity can be improved by using the cross sections reconstructed by the method. Because almost no influences on the analysis accuracy could be found related to the divided numbers of the surfaces and the angles, and the response relationship with neutron production rates of fuel rods or a fuel assembly cell-averaged neutron production rate, this reconstruction method is applicable to a conventional core analysis code using homogenized cross sections in a fuel assembly cell.     

Bamboo-Lattice程序多群截面数据库的改进

本文基于ENDF/B-Ⅶ.0核评价数据库,利用核数据加工处理程序NJOY及LATTICE_PRE为Bamboo-Lattice程序研制了一套改进后的多群截面数据库NECL2.0。基于基准题和数值分析的结果表明：采用NECL2.0数据库计算得到的燃料组件的k_inf、裂变率分布、少群均匀化截面与参考解均吻合很好;考虑银铟镉共振对k_inf的计算精度可提高近1000 pcm,与参考解相比最大裂变率相对偏差从-0.97%降低到-0.53%;考虑包壳锆的共振对k_inf的计算精度可提高约60 pcm。     

反应堆堆芯先进中子学模拟软件SCAP-N研发

堆芯中子学计算是反应堆设计分析的基础,为提高堆芯中子学计算的模拟分辨率与计算精度,开发了反应堆堆芯先进中子学模拟软件(SCAP-N)。该程序首先根据轴向特征对堆芯进行分层,并逐层进行二维堆芯非均匀输运计算,再采用超级均匀化方法(SPH)获得栅元等效均匀化截面,最后进行三维堆芯逐棒(pin-by-pin)输运计算,获得堆芯有效增殖因子与精细棒功率分布。为提高程序计算效率,采用分布式/共享式(MPI/OPENMP)混合并行方式对程序进行了并行化开发。利用虚拟反应堆(VERA)系列基准例题及美国先进非能动压水堆(AP1000)启动物理试验实测数据对程序进行了测试验证。结果表明,相比于商用核设计程序系统,SCAP-N程序采用的逐棒输运技术能够提高堆芯中子学的计算精度。与同类型高精度中子学程序相比,SCAP-N具有更高的计算效率,可进一步提高核电厂的经济性及运行灵活性。     

超级均匀化方法用于球床氟盐冷却高温堆扩散计算

球床氟盐冷却高温堆的控制棒位于侧反应射层内,存在无裂变中子源且受堆芯泄漏谱强烈影响的强吸收体区域扩散计算难题。超级均匀化方法(Super Homogenization,SPH)被用于对氟盐球冷却床堆侧反射层中控制棒区域的强吸收体进行等效均匀化处理,同时堆芯除控制棒区域外采用谱修正方法(Spectra Modification,SM),将输运计算的结果作为基准进行验算。结果表明,SM-SPH模型能有效地计算球床氟盐冷却高温堆反射层控制棒价值及通量分布,并且较常规的SPH方法能更好地处理棒间干涉效应。     

Accuracy of nuclear design of fast and thermal neutron coupled core by SRAC

Supercritical-pressure light water cooled fast reactor adopts the blanket fuel assemblies with depleted uranium fuel and zirconium hydride layer in the core for negative coolant void reactivity. Thermal neutrons are generated in the core of fast reactor. It is called “fast and thermal neutron coupled core”. The purpose of the present study is to examine the accuracy of assembly and core calculations including preparation of the macroscopic cross sections with the SRAC code system for “fast and thermal neutron coupled core” in comparison with the Monte Carlo codes, MVP and MVP-BURN. Accuracy of the neutron multiplication factor and coolant void reactivity calculation has been evaluated in four types of cores of different fractions of the blanket fuel assembly with zirconium hydride rods. The conventional analysis is based on the macroscopic cross sections which are prepared with infinite lattice. The conventional SRAC calculation underestimates the neuron multiplication factor for all types of cores. Other findings are that the conventional SRAC calculation overestimates coolant void reactivity for the cores without zirconium hydride rods, and underestimates coolant void reactivity for the core of all blanket fuel assemblies having zirconium hydride rods. To overcome these problems, it has been proposed that the macroscopic cross sections of seed fuel assembly are prepared with the model that a seed fuel assembly is surrounded by blanket fuel assemblies in order to take into account the effects of the surrounding fuel assemblies. Evaluations show that accuracy of the neutron multiplication factor by the SRAC calculation can be improved by the proposed method.     

CAP1400数值反应堆系统关键技术研究及示范应用

本文系统介绍了“大型先进压水堆及高温气冷堆核电站”国家科技重大专项课题“CAP1400数值反应堆关键技术研究”的主要研究成果。课题首先分别开发了基于确定论方法和蒙特卡罗方法的高保真堆芯物理计算程序,然后开发了pin by pin先进子通道分析程序和基于精细网格的燃料棒性能分析程序,以此为基础建立了物理 热工 燃料性能多物理耦合的CAP1400数值反应堆系统。利用国际基准题VERA、AP1000启动物理实验参数对数值反应堆系统进行了验证和确认,并进一步实现了CAP1400大型先进压水堆的启动物理参数、循环模拟分析和部分功率能力分析的示范应用。数值结果表明,所开发的数值反应堆关键分析软件具有很高的计算精度,可直接服务于CAP1400的设计验证、物理启动和运行支持。     

快堆用蒙特卡罗多群数据库制作方法研究

Based on the discrete angle method, a Monte Carlo multi-group cross section generation program MGXSMC was developed. This program can read the cross section data from an input file or read the cross section from a library in a specified format to generate the multi-group cross section for MCNP or RMC. The corresponding index file list can be automatically generated. The two-dimensional two-group IAEA pressurized water reactor (PWR) benchmark and lead-based fast reactor (RBEC-M) benchmark were used to verify the cross section library generated by the MGXSMC program. The calculation results show that the difference between the calculated result of the P5 order approximate multigroup section and the continuous point cross section is 24 pcm (1pcm = 10-5), and the difference of the keff result calculated by the P0 order approximate multigroup section and the continuous point section is large. This shows that the method and the program developed for the Monte Carlo Group Section Library are correct. At the same time, the neutron anisotropic scattering has a large impact on the calculation results of the lead-based fast reactor. Therefore, when the Monte Carlo Group Section library is produced, the neutron scattering angle data should be added.     

快堆用蒙特卡罗多群数据库制作方法研究

基于离散角方法,开发了蒙特卡罗多群数据库生成程序MGXSMC,该程序可以实现从输入文件读取截面数据或者从指定格式的截面库中读取截面,产生可供蒙特卡罗程序MCNP或RMC计算的数据库,并且可自动生成相应的索引文件列表。采用二维两群不带反射层的国际原子能机构(IAEA)压水堆(PWR)基准题和铅基快堆(RBEC-M)基准题对MGXSMC程序加工产生的核数据进行验证,计算结果表明,采用P₅阶近似多群截面与连续点截面计算的有效增殖系数(k_eff)结果相差24 pcm(1pcm=10^-5),而采用P₀阶近似多群截面与连续点截面计算的k_eff结果相差较大。由此说明蒙特卡罗多群数据库的制作方法和所开发的程序是正确的,同时,中子各向异性散射对铅基快堆计算结果影响较大,故制作蒙特卡罗多群数据库时应加入中子散射角数据。