三区非均匀栅元X-Y几何块方法中子输运计算

基于中子积分输运理论,应用综合界面流和碰撞几率技巧的块方法,导出了处理三区非均匀栅元结构的二维（Ｘ－Ｙ）几何多群中子输运问题的数值模型。即对于由若干栅元组成的按Ｘ－Ｙ几何排列的堆芯结构,对每一类栅元剖分为圆柱形元件（如燃料棒、控制棒、可燃毒物棒等）、包壳和慢化剂三个均匀区,用碰撞几率（ＣＰ或ＰＩＪ）方法计算各区的中子通量分布;对于相邻栅元用ＤＰ１近似的中子流来耦合;因此,块方法具有精度高、速度快、能灵活处理各种几何问题的优点,是目前动力堆组件计算最有前途的方法之一。基于块方法基本理论,发展了三区栅元模型,导出了计算方法,编制了ＦＯＲＴＲＡＮ计算机程序。为验证其精度和适用性,对两个例题进行了计算,并与其它程序的计算结果进行了比较,证明功率分布和本征值均符合较好。     

Analysis of VIP-BWR reactor core physics experiments on UO2 and MOX mockup fuel assemblies - part 2: analysis with SIMULATE5

Analysis of the three test cores in the VIP-BWR program was performed in a two-dimensional geometrical model with CASMO5 coupled with the JENDL-4.0-based neutron data library, and reported in the previous paper. Following the study, interpretation of the experiments were carried out in a three-dimensional geometrical model with SIMULATE5 for the code validation study. The nuclear libraries for the SIMULATE5 calculations were generated with CASMO5 with the JENDL-4.0-based neutron data library. The effective multiplication factors of the critical cores ranged from 0.9983 to 1.0023 with measurement uncertainties of 0.0003 to 0.0004 (one σ). The root mean squares of (the calculated/the measured-1) for the fission rates at the core-mid plain of all the measured fuel rods were about 3% for the three cores. It was noticed that the calculations underestimated the fission rates of the UO₂ fuel rods and overestimated those of the MOX fuel rods for the test cores loaded with MOX fuel rods, which was consistent with trends in the preceding analysis studies of the VIP-BWR program and other MOX core experiments, and the biases were confirmed in the calculation results of power distributions in MOX-fueled light water reactor cores.     

超临界水冷快堆增殖因子敏感性初步研究

从长远观点来看,超临界水冷快堆（SCFWR）的增殖性能是一个重要问题,由于超临界水堆中冷却剂密度仅相当于当前沸水堆（BWR）的1/3,加之稠密性栅格布置,SCFWR具有增殖的潜力。为了探究SCFWR的增殖性问题,利用基于多群三维细网有限差分中子扩散方程的堆芯核计算方法,设计不同的算例,分别计算了堆芯冷却剂流型、不锈钢和ZrH_1.7的利用、堆型布置、棒径大小、MOX燃料中PuO₂的份额、堆芯燃耗深度及堆芯尺寸等因素对SCFWR增殖性能的影响。计算结果表明,增大堆芯转换比的途径有：采用对流式流型、加入ZrH_1.7层、采用合适的堆芯布置、增加棒径、提高MOX燃料中PuO₂的份额及增大堆芯尺寸而减少中子泄漏等。从而为提高SCFWR的转换比提供了可参考的依据路线。     

Conceptual Design Study of 180 MWt Small-Sized Reduced-Moderation Water Reactor Core

Conceptual design of a Small-sized Reduced-Moderation Water Reactor (S-RMWR) core, which has the thermal output of 180 MW, the conversion ratio of 1.0 and the void reactivity coefficient of negative value, has been constructed. S-RMWR is a technology demonstration reactor which also conducts material and fuel testing for commercial use of Reduced-Moderation Water Reactor (RMWR) in large-scale power plants. It has a very tight triangular fuel rod lattice and a high coolant void fraction. The RMWR core axially has two short and flat uranium plutonium mixed oxide (MOX) regions with an internal blanket region in between, in order to avoid a positive void reactivity coefficient. The MOX regions are sandwiched between upper and lower blanket regions, in order to increase a conversion ratio.

In this small reactor core, leakage of neutrons is expected to be larger than in a large core. Therefore, a core design concept different from that for a large core is necessary. Core burnup calculations and nuclear and thermal-hydraulic coupled calculations were performed in the present study with SRAC and MOSRA codes. MVP code was also used to obtain control rod worth. Because of its large neutron leakage, keeping the void reactivity coefficient negative is easier for S-RMWR than RMWR. Thus, the heights of MOX region can be taller and the plutonium enrichment can be lower than in RMWR. On the other hand, to achieve the conversion ratio of 1.0, radial blanket and stainless steel reflector assemblies are necessary, whereas they are not needed for RMWR.     

Ultra-fine-group resonance treatment using equivalent Dancoff-factor cell model in lattice physics code GALAXY

In order to achieve highly accurate resonance calculations with short computation time , a new ultra-fine-group resonance calculation method is developed. The ultra-fine-group method has a limitation in practical design applications of large and complicated geometries in fuel assembly level due to its long computation time. Therefore, we developed an enhanced one-dimensional (1D) cylindrical pin-cell model to achieve both high calculation accuracy and short computation time. In the enhanced 1D cylindrical pin-cell modeling, moderator radius is adjusted to preserve each fuel pellet's Dancoff factor obtained in the exact 2D fuel lattice arrangement. We call this model the ‘equivalent Dancoff-factor’ cell model. This model can accurately consider heterogeneity effects in PWR fuel assemblies and can represent effective cross sections obtained by the ultra-fine-group calculations in the complicated 2D square lattice arrangements. The present method is implemented with Mitsubishi Heavy Industries, Ltd. lattice physics code GALAXY. From the comparisons of neutron multiplication factors and pin power distributions between GALAXY and a continuous-energy Monte Carlo code, applicability of the present method to lattice physics calculations is confirmed. Application of GALAXY with the present method achieves high accuracy with short computation time in normal operations and accident conditions including low moderator density conditions.     

On the influence of spatial discretization in LWR-burnup calculations with HELIOS 1.9 – Part II: Mixed oxide (MOX) fuel

Cell and burnup calculations are the basis for all deterministic static and transient 3D full core calculations for different operational states of the reactor. The arising differences in the integral transport solution (neutron flux and k_inf) for different discretization strategies during the burnup of mixed oxide (MOX) fuel due to different spatial discretization are demonstrated. The influence of different discretization strategies on the calculation of homogenized few group cross-sections is investigated. The influence of the discretization strategies on the calculation time is evaluated.     

Application of wavelets scaling function expansion method in resonance self-shielding calculation

The wavelets expansion method is widely used in various fields due to its powerful ability to simulate the oscillating functions. This method is applied to discretize the energy variable of neutron angular flux within the resonant energy range. Meanwhile, the conventional multi-group method is applied in fast and thermal energy ranges. This coupled method can obtain the problem-dependent continuous-energy neutron flux spectrum within the resonant energy range. The method of characteristics (MOC) is employed as a space-variable solver in this paper to keep the powerful capability of dealing with the complex geometry problems. A pressurized water reactor (PWR) fuel cell problem with UO2 fuel (UOX) and mixed oxide fuel (MOX), and a cylindrical cluster fuel problem are calculated by utilizing this coupled method. Results of these problems are all in good agreement with the results of the Monte Carlo statistical transport code MCNP. It is concluded that this is a valuable method to solve the resonance self-shielding calculation problems in a complex geometry, and it is promising to be applicable for realistic reactor problems.     

基于MOX燃料组件的177混合堆芯装料方案数值研究

通过计算华龙一号（HPR1000）压水堆平均卸料燃耗得到乏燃料中钚（Pu）同位素的含量,以此成分比例来设计铀钚混合氧化物（MOX）燃料。采用离散型燃料组件设计,通过不同Pu含量的MOX燃料棒离散型布置来降低与UO₂燃料组件间的功率梯度。采用程序MCNP和COSLATC模拟堆芯功率分布和热中子注量率分布,采用分区分层的低泄漏装料方案,降低不同燃料组件间的功率梯度,展平堆芯的功率分布。在不考虑可燃毒物的前提下,利用3种Pu含量的MOX组件将混合堆芯的功率峰因子控制在1.77左右,明显优于原堆芯的功率峰因子,为国产三代压水堆引入MOX燃料提供了具有参考价值的装料方案。      

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.     

A sensitivity analysis of thermal lattices kinetic parameters with respect to the spectral weighting function using ultrafine BN method

Accurate calculation of kinetic parameters is of utmost importance in the safety analysis of a nuclear reactor. In the current paper, two approaches are investigated to evaluate these parameters in energy phase space. In the first approach, these parameters are derived from an energy-continuous form of the forward and adjoint transport equations and then integrals with respect to the energy variable are replaced by weighted summations over the energy groups, while in the second approach these parameters are extracted from the multi-group forward equation and its associate adjoint equation in which their multigroup constants are weighted by forward spectrum. The difference of weighting functions in these two approaches would naturally lead to different values for the kinetic parameters. This paper mainly compares the outcome of these two approaches in calculating kinetic parameters for two main types of thermal critical lattices: Mixed Oxide (MOX) and Uranium Oxide (UOX) using ultrafine B_N method. The results show that calculations which are based on using the forward weighted spectrum for generating the kinetic parameters underestimate prompt neutron generation time in both thermal lattices, while effective delayed neutron fraction is overestimated in UOX thermal lattice and underestimated in MOX one.     

Kinetic parameters of a low enriched uranium fuelled material test research reactor at end-of-life

The kinetic parameters at end-of-life of a material test reactor fuelled with low enriched uranium fuel were calculated. The reactor used for the study was the IAEA’s 10 MW benchmark reactor. Simulations were carried out to calculate core excess reactivity, neutron flux spectrum, prompt neutron generation time and effective delayed neutron fraction. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It was observed that in comparison with the beginning-of-life values, at end-of-life, the neutron flux increased throughout the core, the prompt neutron generation time increased by 3.68% while the effective delayed neutron fraction decreased by 0.35%.     

Cell geometry effect on equilibrium state of nuclear reactors

The effects of the cell configuration on core performance for a liquid sodium cooled MOX fuel type fast reactor and a PWR type thermal reactor are investigated. In this study our equilibrium cell iterative calculation system (ECICS) are used in order to obtain consistent neutron spectra, one-group constants and nuclide number densities at the nuclear equilibrium state. The fuel pellet diameter and the pin pitch are changed to evaluate their core characteristics. The distinction of reactors at the equilibrium state appears clearly by means of the change in the cell geometrical design.     

Neutron Anisotropic Scattering Effect in Heterogeneous Cell Calculations of Light Water Reactors

A study on the anisotropic scattering effects in heterogeneous square cells of light water reactors has been performed using the characteristics method. It was found that the effects of the anisotropic scattering were relatively large for the MOX fuel cell because of the large neutron current from the moderator to the fuel region and the k _inf value by the P₀ calculation became 0.10–0.16% larger than that by the P₅ calculation. With the transport correction, the k _inf difference from the P₅ calculation became even larger than that from the P₀ calculation and the k _inf value by the transport correction became 0.18–0.25% larger than that by the P₅ calculation for the MOX fuel cell. The transport corrected self-scattering cross sections of the moderator region become smaller than the non-transport corrected ones and the angular flux distribution becomes more anisotropic with the transport correction. Therefore, more neutrons toward the moderator region between the fuel pellets can slow down to the lower energy region with the transport correction. As a result, the k _inf value by the transport correction becomes larger than that by the P₀ calculation, which is opposite effect to that by the P₅ calculation.     

高温气冷堆和轻水堆超铀元素管理特性研究

乏燃料中长寿命锕系元素对环境造成长期潜在危害,本文研究球床高温气冷堆不同燃料循环中超铀元素的产生和焚烧特性。在250 MW球床模块式高温气冷堆示范电站HTR-PM铀钚循环的乏燃料中提取铀和钚作为核燃料,设计了PuO₂和MOX燃料元件,将新设计的燃料元件重新装入与HTR-PM相同结构和尺寸的堆芯,分别形成纯钚燃料循环和MOX燃料循环。采用高温气冷堆物理设计程序VSOP,研究了高温气冷堆一次通过燃料循环和不同闭式燃料循环的超铀元素焚烧特性,并与轻水堆燃料循环结果进行比较和分析。结果表明：高温气冷堆一次通过燃料循环超铀元素生成率约为轻水堆的1/2;高温气冷堆闭式燃料循环能有效嬗变超铀元素。     

Comparison of FBTR hybrid core and Mark-II (carbide) core design and neutron irradiation in invessel shields

Fast Breeder Test Reactor (FBTR) in Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam, India is presently operating with a combination of Mark-I (PuC 70% and UC 30%) and Mark-II (PuC 55% and UC 45%) fuels. Recently it became necessary to review the type of fuel for the FBTR core due to the use of oxide fuel for the PFBR under construction at Kalpakkam. A full Mark-II core was earlier designed to take the reactor to higher power. An alternate strategy of having hybrid core with Mark-I fuel at the centre and MOX fuel at the periphery was also studied. MOX subassemblies have a fissile column length of 43 cm which is higher than Mark-I subassemblies (32 cm). The lower position of these subassemblies is closer to the grid plate and therefore there was a concern on the grid plate fluence below the MOX fuel. It is interesting to compare the dose rates to the grid plate in the two above design as the doses determine reactor life. Many 2-D R-Z transport calculations were carried out for FBTR including all regions of interest like borated graphite and carbon steel in the top shield and vault concrete to obtain 175 group neutron flux distribution in Vitamin J structure with IGC-S3 self shielded cross-section set. The radiation damage to grid plate below MOX part is found to be less than that below Mark-I part of hybrid core in spite of longer fissile column length. Similar behaviour is seen for helium production as well. Comparison showed that the difference in fluence in the grid plate region is less than 3% between the two core designs.     

Development and verification of a nodal approach for solving the multigroup SP3 equations

The core model DYN3D which has been developed for three-dimensional analyses of steady states and transients in thermal reactors with quadratic or hexagonal fuel assemblies is based on nodal methods for the solution of the two-group neutron diffusion equation. Loading cores with higher content of MOX fuel, the increase of the fuel cycle length, and the consideration of new reactor types are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P₃ (SP₃) approximation of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. The method described in the paper is verified with pinwise calculations of a steady state of the OECD/NEA and US NRC PWR MOX/UO₂ Core Transient Benchmark. The used 16-group cross section library was generated for DORT calculations with homogenized pin cells. Two different approximations of the diffusion coefficient which occurs in the within-group form of the SP₃ equations are investigated. Using the transport cross section for the calculation of the diffusion coefficient gives much better results than those obtained with the removal cross section. The improvement of the results in comparison to a pinwise diffusion calculation is shown. The results are compared with the DORT and the heterogeneous reference solution of the code DeCART. Concerning the SP₃ calculation using the diffusion coefficient based on the transport cross section (DYN3D-SP3-TR) the deviations of the eigenvalue k_eff and the assembly powers from the transport solutions of DORT and DeCART are in the same order as those between the two transport solutions themselves. The improvement of the DYN3D-SP3-TR results in comparison to the diffusion calculation is presented. As the DYN3D-SP3-TR and DORT calculations are performed with homogenized pin cells, the pin powers of the two calculations are closer to each other than to the pin powers of the DeCART solution. To estimate the contribution of higher flux-moments, the ratio of the second flux moment to the zeroth flux moment is investigated along a horizontal row of pins. It is shown that it is low in the fuel assemblies with small peaks at the water channels. Considering the baffle and the water reflector regions higher values are obtained in the fast neutron groups.     

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.     

Homogenization-free reactor core analysiswith general first collision probabilities method

The C5G7 MOX Benchmarkfor current codes has been proposed as a basis to test the ability of current transport codes to teat reactor core problems without spatial homogenization. This is a seven-group form of the C5G7 MOX fuel assembly problem specified by Cavarec et.al. There are four fuel assemblies, two contain UO₂ fuel elements and two contain MOX fuel elements. Seven group cross sections for different kinds of fuel (three enrichment of MOX and UO₂), the guide tubes, the fission chambers and moderator are given. Thus this benchmark is just a mathematical test that allows testing the accuracy of the neutron transport equation solution with different methods and codes. In this paper the General First Collision Probabilities Method (GFCPM) is used to analyze the two-dimensional configuration of this benchmark. A linear flux approximation is used in the reflector. Different calculation schemes in the reflector region have been used. The output results, K_eff and the pin powers have been analyzed. The convergence of the results has been analyzed both as a function of the subdivision scheme of the reflector region and of the number of points in the calculation scheme for general first collision probabilities. Comparison has been carried out for K_eff and pin powers both with the reference results (external convergence) and with the results of different approximations of GFCPM (internal convergence).     

Accuracy of criticality calculations made using current nuclear data libraries for MOX fuelled fast critical assemblies

Criticality calculations have been made for a set of ten mixed plutonium–uranium oxide (MOX) fuelled fast critical assemblies using the current nuclear data libraries, JEFF-3.1, JEFF-3.1.1, JENDL-3.3 and ENDF/B-VII.0. The results obtained using the different libraries are compared and conclusions drawn concerning the accuracy of criticality calculations made for MOX fuelled fast reactors.     

Hafnium clad fuels for fast spectrum BWRs

We show that by use of hafnium cladding, a fast neutron spectrum is achievable in the top of uprated BWRs. Monte Carlo calculations have been made for Hf clad inert matrix nitride and low fertile MOX fuels, with fuel segments located in the upper part of an uprated BWR, where the coolant void fraction exceeds 70%. The nitride fuel results in the hardest neutron spectrum, but the low fertile MOX fuel still yields fission probabilities for even neutron number nuclides similar to those of sodium cooled reactors. The inert matrix nitride fuel configuration yields high burning rates, permitting to stabilise TRU inventories with less than 50% BWR cores of the here suggested type in the power park. The core with low fertile MOX fuel is less efficient, but still a zero net producer of TRU. Fuel and coolant temperature feedbacks are affected by introduction of absorbing elements in the fuel, but remain within acceptable ranges for the low fertile MOX fuel. Although control rod worths are reduced, shutdown margins are sufficient to ensure sub-criticality in cold conditions. From a materials point of view, the behaviour of hafnium clad MOX fuel would be similar to zircalloy clad MOX fuel already used extensively in nuclear industry. Thus, if dynamic stability of the core can be ensured, the here proposed fuel may be considered as a low cost solution for transmutation of minor actinides on industrial scale.