Adsorption Behavior of Americium on Granulated Zirconium Phosphate

The investigation on the characteristics of void reactivity coefficients for the high-conversion-type core of the FLWR (HC-FLWR) concept for MA recycling has been performed. Void reactivity coefficients are the major restrictions for the core design of HC-FLWR for MA recycling, because the loaded MA makes void reactivity coefficients worse. Therefore, it is important to investigate the characteristics of void reactivity coefficients as a mechanism of reactor physics. Thus, in this study, the investigation of void reactivity coefficients has been performed using the exact perturbation calculations. In the exact perturbation theory, the reactivity is related to the variation in the cross section, and divided into scattering, leakage, absorption, and fission terms. Then, the worsening of the void reactivity coefficient caused by the MA loading mainly via the scattering term is found. Moreover, the void reactivity coefficient becomes better via the scattering term for the smaller fuel rod diameter, and via the leakage term for the lower core height. In addition, the 100% void reactivity coefficient, which is the restriction for the core design of HCFLWR for MA recycling, cannot be negative only by using the effect of the scattering term by reducing the fuel rod diameter. Therefore, the mechanism of achieving the negative 100% void reactivity coefficient by using the effect of the leakage term through the core height reduction is quantitatively verified.     

Monte Carlo calculations on vector supercomputers using GMVP

A multigroup general purpose Monte Carlo code GMVP has been developed. The vectorization algorithm is based on a stack-driven zone selection method. GMVP can treat repeated rectangular and hexagonal lattices together with combinatorial geometry which is quite useful to achieve a high gain by vectorization. The performance of the code was evaluated by solving various types of problems. In addition, the continuous energy code is under development and the performance is compare with conventional codes. The code was installed on other four different supercomputers to investigate portability and computer dependence of code performance.     

Decoding of Thermal Data in Fleischmann & Pons Paper

A uranium-free fast reactor was simulated at FCA in order to examine the prediction accuracy for sodium void effect of plutonium burning fast reactors. Material sample worth for plutonium and B4C was also measured to compare its prediction accuracy with that for the sodium void reactivity worth. It was found that an axial distribution of plutonium sample worth and the central B₄C sample worth for various kinds of ¹⁰B enrichment were precisely calculated by the conventional calculation method for fast reactors with 70-group structure. The sodium void reactivity worth was, however, poorly predicted especially for the non-leakage term. This discrepancy seems to be caused by the peculiar energy breakdown of the non-leakage term in the uranium-free fast reactor.     

大型MOX燃料快堆钠空泡反应性微扰理论研究

钠空泡反应性效应是钠冷快堆核设计和安全分析的重要内容。本文基于多群节块扩散法,采用微扰理论推导出钠空泡反应性的计算方法,对1 000 MWe钠冷快堆MOX燃料堆芯的总钠空泡反应性、空间分布、物理分项进行了计算。结果表明,钠空泡反应性主要来源于中子泄漏的增加和能谱的硬化,两者一正一负,且空间分布规律相反,导致钠空泡反应性具有强烈的空间依赖性;对于所计算的MOX燃料堆芯钠空泡反应性高达3 $左右。计算和分析结果阐明了钠空泡反应性的产生机理和分布规律,可为低钠空泡的设计提供参考。     

Sodium Void Reactivity Worth Calculations for Fast Critical Assemblies without Whole-Lattice Homogenization

In the present paper, we calculate the sodium void reactivity worth of fast critical assemblies without whole-lattice homogenization in order to reduce errors associated with lattice homogenization. Firstly, we solve a neutron transport benchmark problem simulating fast critical assemblies composed of thin material plates with a discrete ordinates transport solver. The discrete ordinates transport solutions agree well with the Monte Carlo reference solutions; hence, we confirm the validity of the deterministic transport calculations for the sodium void reactivity worth of lattice-heterogeneous critical assemblies. Thereafter, the existing experimental data are calculated without whole-lattice homogenization. The result suggests that the lattice homogenization results in the overestimation of the leakage component of sodium void reactivity worth when the leakage component parallel to plate boundaries is dominant. Utilizing the numerical method without whole-lattice homogenization and the nuclear data JENDL-3.3, numerical solutions agree with the experimental data within 3σ of the experimental uncertainties.     

Analysis of Heavy-Water-Moderated,Cluster-Type Fuel Lattices by Cluster Physics Code ‘MESSIAH’

This paper presents a comprehensive analysis performed by a new cluster analysis code ‘MESSIAH’ on reactor physics constants measured in the critical facility for a pressure-tube-type, heavy-water-moderated reactor. The MESSIAH code system utilizes the method of the collision probability to solve the neutron transport equation. The effective space dependent cross sections are calculated in the thermal and resonance energy range before the eigenvalue calculation for the whole energy range. With use of these cross sections, the multi-group, space dependent transport equation is solved, and the flux distribution, spectrum and k _eff are obtained to the input bucking. In the above three steps the method of the collision probability is used consistently and extensively. The treatment of leakage neutrons from lattices in MESSIAH is also confirmed by an independent method using a Monte Carlo calculation. The calculated reactor physics constants, especially the micro-parameters and the activation traverse of Dy, agreed fairly well with the experiment. The diffusion calculation with use of the group constants calculated by MESSIAH predicts the reactivity of 0% void core excellently (<0.12%). However, for a 100% void core, the calculated reactivity was slightly lower than the experiment (~0.74%), which was attributed to over prediction of the diffusion constants.     

TOPAZ-Ⅱ反应堆~(135)Xe小反应性计算方法研究

TOPAZ-Ⅱ反应堆的中子通量密度很低,这使其在运行过程中引入的135Xe反应性很小,其数值难以采用现有的蒙特卡罗程序进行计算。本文考虑了中子价值对反应性的作用,采用MVP-BURN程序对TOPAZ-Ⅱ反应堆的135Xe小反应性进行了计算。该方法可为其他类似反应堆的小反应性计算提供参考。     

Investigation of the void reactivity effect in large-size Lead Fast Reactors

An aspect of great relevance in Lead Fast Reactors (LFRs) is the actual void reactivity evaluation. The purpose of this work is double: to inquire into the physical problem, and to evaluate the impact of different approaches and numerical methods on the calculation of the critical reactor parameters involved. Thus, results concerning void effect contributors have been evaluated through a cross-checked analysis performed by means of both a deterministic and a stochastic code. The field of investigation that has been assumed consists in the reference configuration of the 600 MW_e European Lead-cooled SYstem (ELSY), under development within the 6th and 7th EURATOM Framework Programmes. Calculations have been carried out on a 1500 MW_th MOX-fuelled core, composed by wrapper-less square Fuel Assemblies (FAs) with pins on a square lattice. The ERANOS (European Reactor Analysis Optimized System) deterministic code ver. 2.1 and the MCNP Monte Carlo code ver. 4c have been employed in conjunction with the JEFF-3.1 nuclear data library to assess the void reactivity variation and its breakdown into the most relevant nuclides, using both the neutron balance equation method and perturbation theory. Results have shown a very good agreement between ERANOS and MCNP outcomes: the huge reactivity worth determined by the core active region voiding (approximately 5000 pcm) is due to the predominant contributions of even isotopes – among which ²³⁸U plays a major role, being responsible for roughly 4300 pcm – as a consequence of their fission cross-section high sensitivity to spectral hardening (threshold reactions), despite their modest contribution to the total fissions.     

Adjoint Sensitivity and Uncertainty Analyses in Monte Carlo Forward Calculations

The adjoint-weighted perturbation (AWP) method, in which the required adjoint flux is estimated in the course of Monte Carlo (MC) forward calculations, has recently been proposed as an alternative to the conventional MC perturbation techniques, such as the correlated sampling and differential operator sampling (DOS) methods. The equivalence of the first-order AWP method and first-order DOS method with the fission source perturbation taken into account is proven. An algorithm for the AWP calculations is implemented in the Seoul National University MC code McCARD and applied to the sensitivity and uncertainty analyses of the Godiva and Bigten criticalities.     

在蒙特卡罗程序中统计共轭通量并计算中子动力学参数的方法

文章介绍了在蒙特卡罗程序中,使用反复裂变几率的统计结果作为共轭通量的估计,并作为权重函数计算动力学参数β_eff和Λ的方法,阐释了在连续能量蒙特卡罗程序MCNP和多群蒙特卡罗程序MCMG中实现这种方法的过程。数值校验结果表明：在几乎不带来附加计算量的同时,在MCMG中使用该方法统计得到的共轭通量与ANISN的共轭通量计算结果符合较好,在MCNP中使用该方法计算得到的中子动力学参数与基准测量结果符合较好。在蒙特卡罗程序中实现了高效率计算中子动力学参数的功能,为蒙特卡罗程序进一步用于反应堆动态行为的分析奠定了基础。     

基于JMCT的堆外核仪表系统刻度系数计算

以三维蒙特卡罗粒子输运程序JMCT为主要数值模拟工具,计算了某反应堆多个运行循环下的堆外核仪表系统（RPN）功率量程刻度系数。使用直接蒙特卡罗模拟方法、响应矩阵方法和伴随蒙特卡罗方法,得到了多组RPN刻度系数,通过这些系数计算出不同工况下的堆芯功率水平和轴向功率差,并与实测值进行了比对。结果表明,3种方法所得计算值与实测值的偏差均满足工程精度要求,其中伴随蒙特卡罗方法计算开销最小,验证了通过蒙特卡罗数值模拟得到RPN刻度系数的可行性。     

Monte Carlo simulation of core physics parameters of the Nigeria Research Reactor-1 (NIRR-1)

The Monte Carlo N-Particle (MCNP) code, version 4C (MCNP4C) and a set of neutron cross-section data were used to develop an accurate three-dimensional computational model of the Nigeria Research Reactor-1 (NIRR-1). The geometry of the reactor core was modeled as closely as possible including the details of all the fuel elements, reactivity regulators, the control rod, all irradiation channels, and Be reflectors. The following reactor core physics parameters were calculated for the present highly enriched uranium (HEU) core: clean cold core excess reactivity (ρ_ex), control rod (CR) and shim worth, shut down margin (SDM), neutron flux distributions in the irradiation channels, reactivity feedback coefficients and the kinetics parameters. The HEU input model was validated by experimental data from the final safety analyses report (SAR). The model predicted various key neutronics parameters fairly accurately and the calculated thermal neutron fluxes in the irradiation channels agree with the values obtained by foil activation method. Results indicate that the established Monte Carlo model is an accurate representation of the NIRR-1 HEU core and will be used to perform feasibility for conversion to low enriched uranium (LEU).     

Correlations among FBR core characteristics for various fuel compositions

In the design of a fast breeder reactor (FBR) core for the light water reactor (LWR) to FBR transition stage, it is indispensable to grasp the effect of a wide range of fuel composition variations on the core characteristics. This study finds good correlations between burnup reactivity and safety parameters, such as the sodium void reactivity and Doppler coefficient, for various fuel compositions and determines the mechanisms behind these correlations with the aid of sensitivity analyses. It is clarified that the Doppler coefficient is actually correlated with the other core characteristics by considering the constraint imposed by the requirement of sustaining criticality on the fuel composition variations. These correlations make it easy to specify the various properties ranges for core reactivity control and core safety, which are important for core design in determining the core specifications and performance. They provide significant information for FBR core design for the transition stage. Moreover, as an application of the above-mentioned correlations, a simplified burnup reactivity index is developed for rapid and rational estimation of the core characteristic variations. With the use of this index and these correlations, the core characteristic variations can be estimated for various fuel compositions without repeating the core calculations.     

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.     

反应堆时空动力学蒙特卡罗改进准静态方法研究

改进准静态方法可采用大时间步,减少反应堆时空动力学问题的计算耗时。本文提出了蒙特卡罗改进准静态方法,将两种方法的优势结合,用于新型反应堆的时空动力学问题。基于改进准静态方法的理论框架,研究设计了伴随通量统计、动态参数统计和形状函数计算等相应的蒙特卡罗算法。针对一维两群问题,实现了相应的算法。与确定论程序计算结果的比较表明,蒙特卡罗改进准静态方法是可行的。     

Monte Carlo Modelling of Increasing Void Fraction in 100% MOX ABWR: Lessons Drawn from the FUBILA Program

The French Atomic Energy Commission CEA and the Japanese Incorporated Administrative Agency JNES (Japan Nuclear Energy Safety Organisation) have undertaken first-of-a-kind full MOX core physics experiments, FUBILA, in the EOLE critical facility of the CEA Cadarache Centre. The experiments have been designed to obtain core physics data under high-burn-up 9 × 9 and 10 × 10 BWR MOX assemblies operating conditions. The experimental program, consisting of eight different core configurations, started in January 2005 and ended on September 1, 2006. The analysis of the void increase part of the experimental data between 0 and 70% void has been carried out using the French TRIPOLI-4.5 continuous-energy Monte Carlo calculation code with the newly released JEFF3.1.1 nuclear data library. The average C/E discrepancies obtained on critical masses, reactivity worth, and pin-by-pin power distributions enable us to estimate all the integral and local parameters with uncertainties largely within the target uncertainties, demonstrating the capability of the code to treat complex geometries with a high degree of accuracy. Additional k_eff calculations performed with the latest ENDF/B-VII evaluation exhibit a clear tendency to overestimate the k_eff by about 500 to 650 pcm and the void worth by more than 4%, showing that the JEFF3.1.1 library is more precise for MOX lattices.     

Application of forward and adjoint Monte Carlo coupling technique to detector system designs

Forward and adjoint Monte Carlo coupling technique has been developed for analyzing neutron streaming in a system with large geometry. Particles (neutron and adjoint particle) are scored by surface type estimators such as the next event surface crossing estimators and the boundary crossing estimators. The detector response is calculated by folding the calculated neutron and adjoint angular fluxes. The reliability and efficiency for this method were studied by solving a sample problem of neutron streaming through narrow sodium pipe embedded in an iron shield. This method turned out to give a figure of merit several times better than the conventional method. The applicability of the method to detector system design has been demonstrated by calculating the signal to noise ratio for the fuel failure detector with delayed neutron detection method, which is located behind the reactor shield of concrete. This method gives an advantage in clarifying the spatial channels for neutron streaming.     

Interpretation of Pulsed-Neutron-Source Experiments in a Multiregion Reactor

By expanding the static flux into kinetic fluxes containing the fundamental and higher modes, we derive a kind of inhour equation which can express kinetic distortion, and can relate the static reactivity to prompt decay constants and to kinetic and adjoint fluxes. The equation is developed using the time-dependent, multigroup diffusion approximation, and is applied to the interpretation of pulsed-neutron-source experiments in a multiregion reactor. It is shown from this application that the Simmons-King formula can express the dynamic reactivity only under conditions of constant generation time and no kinetic distortion, and that the conventional inhour equation derived by the perturbation method cannot distinguish between the static and dynamic reactivities differing from each other on account of kinetic distortion.     

基于MC方法的小型压水堆全堆计算分析

使用蒙卡计算程序MCNP,建立小型压水堆四分之一堆芯几何模型,计算小型压水堆首循环初始装料冷态(20℃)、常压(1.01 bar)下的堆芯反应性、径向功率和轴向功率分布,并与输运+扩散方法程序SCIENCE-V2程序包的计算结果进行对比。结果表明:MCNP程序适用于小型堆堆芯核设计计算,并可与SCIENCE-V2程序包互相验证。     

Comparison and sensitivity analysis of the core characteristics of a sodium-cooled fast breeder reactor with 750 MWe output evaluated by JENDL-4.0 and ADJ2000R

Core characteristics of a sodium-cooled fast breeder reactor (FBR) with 750 MWe output using highly decontaminated uranium and plutonium and highly minor-actinide-containing compositions were evaluated using the fast reactor cross-section set generated by the new Japanese nuclear data library JENDL-4.0. The core characteristics were compared with those obtained using the unified cross-section set ADJ2000R in order to investigate the differences between both the results. The effects on the core characteristics caused by the differences in the nuclear data of important reactions and nuclides in the cross-section sets were analyzed by a burnup sensitivity analysis. It was confirmed that adopting JENDL-4.0 to the FBR core design improves the breeding ratio, the burnup reactivity, and the reactivity control balance, because of the differences in the capture cross-sections of U-238 and Pu-239 of both the libraries. The difference in the sodium void reactivity evaluated with both the libraries was less than 1% because the increase caused by the differences in the elastic scattering cross-sections of sodium, the inelastic scattering cross-section, and the μ-average value of U-238 was practically cancelled out by the decrease caused by the differences in the capture cross-sections of Pu-239, the inelastic scattering cross-section of iron, and the capture cross-sections of Am-241.