A hybrid method to generate few-group cross sections for fast reactor analysis

The accuracy of fast reactor core calculation is usually determined by the accuracy of self-shielded few-group cross sections. To further improve the accuracy of cross section generation, a hybrid method is proposed. In the hybrid method, the Monte-Carlo method is used to deal with the resonance effect in both the resolved and unresolved resonance range. The self-shielded ultrafine-group total, fission and elastic scattering cross sections are tallied by the Monte-Carlo method. The scattering transfer matrices are then generated in a synthesis way by using the tallied elastic scattering cross sections and a problem-independent elastic scattering function. The angular flux moments for the group condensation are calculated in an explicit deterministic way. Several tests are done to verify the hybrid method. The results show that the hybrid method avoids the disadvantages of both the traditional deterministic method and the pure Monte-Carlo method. It is a more accurate method to generate the few-group cross sections for fast reactor cores.     

On the use of the Serpent Monte Carlo code for few-group cross section generation

Serpent is a recently developed 3D continuous-energy Monte Carlo (MC) reactor physics burnup calculation code. Serpent is specifically designed for lattice physics applications including generation of homogenized few-group constants for full-core core simulators.     

NAPTH: Neutronics analysis code system for the fusion–fission hybrid reactor with pressure tube type blanket

The fusion–fission hybrid reactor is considered as a potential path to the early application of fusion energy. A new concept with pressure tube type blanket has recently been proposed for a feasible hybrid reactor. In this paper, a code system for the neutronics analysis of the pressure tube type hybrid reactor is developed based on the two-step calculation scheme: the few-group homogeneous constant calculation and the full blanket calculation. The few-group homogeneous constants are calculated using the lattice code DRAGON4. The blanket transport calculation is performed by the multigroup Monte Carlo code. A link procedure for fitting the cross sections is developed between these two steps. An additional procedure is developed to calculate the burnup, power distribution, energy multiplication factor, tritium breeding ratio and neutron multiplication factor. From some numerical results, it is found that the code system NAPTH is reliable and exhibits good calculation efficiency. It can be used for the conceptual design of the pressure tube type hybrid reactor with precise geometry.     

Expression of Few-Group Effective Microscopic Cross Sections in BWR Burnup Calculations

A practical method is proposed to express few-group effective microscopic cross sections for BWR burnup analysis. A set of few-group cross sections is prepared for an infinite square lattice of fuel rods as a function of the ratios of number density of nuclides such as ²³⁵ U, ²³⁸U and ²³⁹Pu, and the water quantity around a fuel rod. Spatial variation of few-group cross sections in the fuel assembly is taken into account by adjusting the water quantity around a fuel rod.

Numerical studies show that the present method can evaluate effective few-group cross sections within the accuracy of 3% in comparison with a two-dimensional integral transport calculation.     

NECP-Atlas中屏蔽数据库制作模块的开发与验证

在核数据处理程序NECP-Atlas中开发了屏蔽数据库制作模块Shield_calc,该模块先利用NECP-Atlas产生问题无关的MATXS格式细群中子、光子截面数据库;然后采用超细群方法、Bondarenko迭代方法进行共振自屏计算,获得有效自屏截面;最后,基于1维反应堆模型采用NECP-Hydra进行输运计算获得应用堆型的典型权重谱,将细群屏蔽数据库归并为宽群屏蔽数据库NECL-SHILED。利用Shield_calc模块,基于与BUGLE-B7相同的评价核数据库ENDF/B-Ⅶ.0,制作了47群中子、20群光子的NECL-SHILED,并与BUGLE-B7进行了对比,数值结果显示NECL-SHILD与BUGLE-B7计算结果吻合较好,验证了Shield_calc模块具有较高的精度。      

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.     

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。      

Recent activities in the field of nuclear waste management and environmental science

The multiband method has been applied to analyses of critical experiments related to the high-conversion core at the Kyoto University Critical Assembly in order to accurately treat the resonance self-shielding in heterogeneous cells. Three-band parameters were generated using the self-shielding table installed in the SRAC code, and used to calculate the cell-averaged cross sections. The k _∞ values calculated by this method have been compared to those by the VIM Monte-Carlo calculation, the SRAC fine group calculation, Dancoff factor method and/or Tone's method self-shielding calculation. The k∞ values calculated by the present method agree with those by the VIM calculation within 0.3%Δk for all the cases considered.     

Extension of Askew's Coarse Mesh Method to Few-Group Problems for Calculating Two-Dimensional Power Distribution in Fast Breeder Reactors

A few-group coarse mesh method has been developed for the calculation of power distribution in 2-dimensional geometry of a fast breeder reactor by extending Askew's one-group coarse mesh method. This method employs modified macroscopic cross sections including group-dependent corrections for coarse meshes of one point per hexagonal assembly and can be easily incorporated into conventional diffusion codes.

Results obtained in few-group 2-dimensional test cases on a prototype fast breeder reactor indicate that this method is as accurate as fine mesh calculations with six mesh points per assembly and the computing time is about ¼ of that of fine mesh calculations.     

The pseudo-resonant-nuclide subgroup method based global–local self-shielding calculation scheme

The pseudo-resonant-nuclide subgroup method (PRNSM) based global–local self-shielding calculation scheme is proposed to simultaneously resolve the local self-shielding effects (including spatial self-shielding effect and the resonance interference effect) for large-scale problems in reactor physics calculations. This method splits self-shielding calculation into global calculations and local calculations. The global calculations obtain the Dancoff correction factor for each pin cell by neutron current method. Then an equivalent one-dimensional (1D) cylindrical problem for each pin cell is isolated from the lattice system by preserving Dancoff correction factor. The local calculation is to perform self-shielding calculations of the equivalent 1D cylindrical problem by the PRNSM. The numerical results show that PRNSM obtains accurate spatial dependent self-shielded cross sections and improves the accuracy of dealing with the resonance interference over the conventional Bondarenko iteration method and the resonance interference factor method. Furthermore, because both global and local calculation is linearly proportional to the size of problems, the global–local calculation scheme could be applied to large-scale problems.     

全陶瓷微密封燃料有效多群截面计算方法研究

全陶瓷微密封（FCM）燃料是一种弥散颗粒燃料。由于弥散颗粒燃料存在双重非均匀性，传统的确定论方法及蒙特卡罗方法皆难以处理这种双重非均匀效应以获得有效多群截面。本文基于超细群方法建立FCM燃料的有效多群截面计算方法。为描述燃料棒内TRISO颗粒的非均匀性，在共振能量段，通过采用超细群方法求解包含TRISO颗粒的一维球模型得到超细群缺陷因子，通过超细群缺陷因子修正所有核素的超细群截面即可将颗粒和基质均匀化。由于TRISO颗粒在热能区也存在较强的自屏效应，在热能区，利用穿透概率及碰撞概率等价得到多群缺陷因子，通过多群缺陷因子修正所有核素的多群截面将燃料和基质均匀化。均匀化后的FCM燃料组件即可视为普通压水堆燃料组件进行共振计算。利用丹可夫修正因子等价得到FCM燃料组件各燃料棒的等效一维棒模型，对一维棒模型求解超细群慢化方程从而得到共振能量段的有效自屏截面。数值结果表明，该方法能有效处理FCM燃料的双重非均匀性，得到精确的有效自屏截面。     

SARAX-FXS程序针对非均匀快堆堆芯计算中的改进及应用

SARAX-FXS程序是基于确定论方法,适用于快谱堆芯组件能谱、均匀化参数计算的程序。由于快堆中组件空间自屏的非均匀效应不可忽视,本文将基于一维圆柱、平板几何的碰撞概率方法加入SARAX-FXS模块,并以等效一维模型计算组件的均匀化参数。为保证能群归并前后的核反应率守恒,在组件计算中引入超级均匀化(SPH)因子修正截面。采用快堆基准题MET-1000对程序的计算结果进行验证,结果表明,与参考解相比,SARAX-FXS的一维计算模块具有较高的精度,特征值计算相对偏差在100~200pcm之间。堆芯计算结果显示,引入SPH因子可提高特征值计算的精度约300pcm,功率分布的均方根误差可从约3%下降至约1%。     

Optimization treatment of point-wise nuclear data in Monte Carlo criticality and burnup calculations

The Monte Carlo codes used for neutron transport calculations are always time consuming, a large proportion of which is possessed by the treatment of continuous-energy cross sections. In this paper, two companion methods are developed for the optimization treatment of point-wise nuclear data, the first of which is called Computational-Expense Oriented (CEO) method based on the unionized energy grid approach and reconstructs only the computationally expensive cross sections in neutron transport simulation, and the other of which is called energy bin (EB) method, a companion of CEO method when the reaction rate tallies for MC-coupling burnup calculation are performed. These two methods are implemented in the code RMC, a Monte Carlo (MC) code used for reactor analysis, and tested on fast reactor core and BWR assembly problems. The numerical results show that CEO method, in comparison with reconstructing all cross sections under the unionized grid, requires the sharply decreased computer memory while achieving almost the same computational efficiency, and EB method can optimize the processing of nuclide-specific energy grid search and thus effectively reduce the total search number while requiring very small computer memory.     

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.     

Use of the local Pu-239 concentration as an indicator of burnup spectral history in DYN3D

Codes for reactor core calculations use few-group cross sections (XS) which depend on local burnup, given in terms of the energy produced per fuel mass (MWd/kgHM). However, a certain burnup value can be reached under different spectral conditions depending on moderator density and other local parameters. Neglecting these spectral effects, i.e. applying the summary-burnup value only, can cause considerable errors in the calculated power density.     

Study on double heterogeneity effect of Pu-rich agglomerates in mixed oxide fuel using cross section homogenization method for particle-dispersed media

A cross section homogenization method for media containing randomly and uniformly dispersed particles, which was originally developed by Shmakov et al., has been applied to MOX fuels containing Pu-rich agglomerates. This method (Shmakov’s method), which is incorporated into a continuous-energy Monte Carlo code MCNP, has been applied to lattice calculations of an infinite MOX fuel rod array. Shmakov’s method can accurately reproduce the criticality calculation results for an explicit heterogeneous arrangement of Pu-rich agglomerates. A correction factor that Shmakov’s method defines to obtain an effective microscopic cross section provides a proper quantitative indication of the double heterogeneity of MOX fuels containing Pu-rich agglomerates. The correction factors exhibit an obvious double heterogeneity effect of Pu-rich agglomerates dispersed in MOX fuel pellets. The effective microscopic cross sections of plutonium isotopes in MOX fuels containing Pu-rich agglomerates are significantly reduced due to the self-shielding effect as compared to the homogeneous MOX fuel model. However, the double heterogeneity effect of Pu-rich agglomerates on k_eff seems to be unexpectedly minor because the underestimate of the reaction rates in the resonance energy range is offset by the overestimate of the reaction rates in the thermal energy range.     

连续能量核数据敏感性分析及其在AP1000中的应用

AP1000是典型的第三代核电技术,对AP1000反应堆进行核数据的敏感性分析是不确定度量化分析的基础,对AP1000后续的安全分析有重要作用。本文基于反复裂变几率方法在蒙特卡罗前向计算中求解共轭通量,并根据一阶微扰理论得到keff对核数据的灵敏度系数。针对反复裂变几率方法普遍存在占用内存大的问题,采用稀疏矩阵的存储方式降低内存。针对计数效率低、统计涨落大的问题,采用重叠块法提高计数效率。通过在蒙特卡罗程序NECP-MCX中开发连续能量核数据敏感性分析功能模块,并对AP1000进行连续能量核数据灵敏度系数的计算,得到了对keff的灵敏度系数影响较大的核数据,同时将计算结果与MCNP6进行了比较。结果表明,NECP-MCX和MCNP6的计算结果吻合较好。     

基于抽样方法的特征值不确定度分析

核数据是反应堆物理计算的基础数据,研究其不确定度对反应堆物理计算引入的不确定度,对提高反应堆的安全性和经济性具有重要意义。本文基于抽样理论研究了反应堆物理计算不确定度分析的方法,研发了不确定度分析程序UNICORN。基于ENDF/B-Ⅶ.1评价数据库,使用NJOY程序开发了多群协方差数据库。采用UNICORN程序和多群协方差数据库对三哩岛燃料棒和基准题RB31的k∞进行了不确定度分析,得到核数据库中各分反应道截面的不确定度对k∞造成的不确定度。结果表明:238 U(n,γ)截面对三哩岛燃料棒k∞造成的不确定度最大,相对不确定度达0.4%左右;协方差数据库的不同来源会对不确定度分析结果造成一定影响。     

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。     

快堆伪裂变产物截面和角分布的计算

为满足我国示范快堆研究的需要并解决以往伪裂变产物截面数据偏小的问题,需重新研制一种制作伪裂变产物数据的方法,为制作多个裂变核的伪裂变产物全套中子数据提供基础。本文用浓度加权求和的方法计算伪裂变产物截面、微分截面和双微分截面。在挑选核素的过程中提出贡献法,即利用裂变率加权产额和吸收截面(反应道MT=27)得到产物核对反应堆的贡献值,从而量化了挑选核素的过程,提高了计算的准确性。最后以CENDL_NP库为主要数据来源,TENDL库数据为补充,制作出了一套~(235) U的伪裂变产物截面数据,通过与以往计算结果比较证明了上述方法的优越性和实用性。