A Method of Calculation of Detailed Power Distribution in Fuel Assemblies

Abstract

A method has been developed that effectively estimates the detailed distribution of power generation in the fuel or blanket assemblies in nuclear reactors. A two-dimensional, one-group diffusion model is applied to a region of homogeneous composition enclosed in a contour devoid of concavity viewed from outside. The diffusion equation is reduced to the form of Helmholtz equation, and a non-homogeneous boundary condition of Dirichlet or Neumann type is given on the contour, using neutron fluxes previously obtained in coarse mesh diffusion criticality calculations covering the whole reactor. This boundary value problem in two-dimensional space is made to yield a solution in the form of a potential due to a single or double layer. The method is applied to a hexagonal cell of a fast reactor. The results of calculation are amply accurate in comparison with the corresponding values from the usual fine-mesh diffusion scheme and with much shorter computing time.     

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.     

Calculation Model for Predicting Power Distribution in Fast Reactors

An electrolyzer model for the analysis of a hydrogen production system using a solid oxide electrolysis cell has been developed, and the effects of principal parameters have been estimated via sensitivity studies based on the developed model. The main parameters considered were current density, area-specific resistance, temperature, pressure, molar fraction, and flow rates in the inlet and outlet. A simple model is also estimated for a high-temperature hydrogen production system that integrates the solid oxide electrolysis cell with a very high temperature reactor.     

快堆金属燃料的发展

国外早期快堆发展的燃料集中在金属燃料上,但金属燃料辐照肿胀严重,只能实现较低的燃耗深度,且较低的固相线温度和与包壳间的共晶温度又制约了金属燃料的实际应用。文章回顾国外金属燃料的发展和主要问题的解决方法,并总结金属燃料改进后可行的设计方案。随后整理早期、后期金属燃料的辐照经验,给出已验证的最大燃耗深度。     

快堆燃料组件内精细功率分布的计算

堆芯热通道因子是堆芯热工设计及安全分析的一项重要参数,确定热通道因子需用中子学计算给出较准确的燃料组件内元件棒功率分布。在三维六角形几何节块扩散理论基础上,使用多项式重构的方法计算节块内中子通量密度分布和功率密度分布。针对快堆六角形燃料组件的特点,用小六角形积分的方法计算组件内元件棒功率,得到组件内各元件棒功率分布。在NAS程序基础上,编制了元件棒功率分布计算模块NAS PIN。通过与蒙特卡罗程序的校验可发现,二者计算结果符合较好,计算精度可满足工程设计的需要。     

Application of Coarse Mesh Method to Neutron Diffusion Calculation for Fast Breeder Reactors

The improved coarse mesh method, which was originally derived by Askew and extended by Takeda, has been modified and applied to a 1,000-MWe and a 300-MWe homogeneous FBR core. In the present method, mesh average neutron flux and mesh center neutron flux are distinguished, and transverse neutron bucklings are taken into account. The results of numerical calculations showed that, with the present method, the power distribution and CR worths are appreciably improved for the 1,000-MWe FBR core with large-pitch fuel assemblies. When CRs are withdrawn, the use of the present method reduces the error of power distribution by half for both cores. However, it yields less satisfactory results, particularly with repect to CR worths, for the 300-MWe FBR core with small-pitch fuel assemblies.     

Analysis of Mixed Oxide Fuel Critical Experiments with Neutronics ANalysis Codes for Boiling Water Reactors

Critical experiments of UO₂ and full mixed oxide (MOX) fuel cores conducted at the Tank-type Critical Assembly (TCA) were aNalyzed using BWR design-purpose codes HINES and CERES with ENDF/B files and Monte Carlo fine analysis codes VMONT and MVP with the JENDL-3.2 library.

The averaged values of the multiplication factors calculated with HINES/CERES, VMONT and MVP agreed with those of experiments within 0.3%ΔAk. The values by the design-purpose codes showed a small difference of 0.1%Δk between UO₂ and MOX cores. Monte Carlo code results showed that the JENDL-3.2 library had a tendency to overestimate the multiplication factors of UO₂ cores by about 0.3%Δk compared with those values of MOX cores. The root mean square errors of calculated power distributions were less than 1% for HINES/CERES and VMONT.

These results showed that (1) the accuracy of these codes when applied to full MOX cores was almost the same as their accuracy for UO₂ cores, which confirmed the accuracy of present core design codes for full MOX cores; and (2) the accuracy of the 190-energy-group Monte Carlo calculation code VMONT was almost the same as that of the continuous-energy Monte Carlo calculation code MVP.     

Development of a Numerical Analysis Method for Cross-sectional Void Fraction Distribution in Subchannels of Nuclear Fuel Assemblies

Detailed information about the void fraction distribution in fuel assemblies is increasingly important with the development of high burn-up fuels. A numerical method has been developed for the steady cross-sectional void fraction profile in fuel assemblies using a marching method in the axial direction, considering cross-flows due to lift forces, void diffusion and momentum balance. Uniform pressure in a cross section was assumed under the dominant vertical flow and the secondary lateral flow condition in each subchannel. The merit of this simplified method is its high-performance computation using many BFC meshes for expression of complex void fraction and velocity distributions inside the subchannels. The calculated results were compared with the observed void distributions obtained with X-ray computed tomography in the NUPEC tests of full-scale advanced BWR fuels. The comparison showed the capability of this method for predictions of overall void fraction distributions inside the subchannels. This method will provide a good tool for void fraction profile prediction in high burn-up fuels, while future studies for reliable correlations of lift forces are required over a wide range of flow conditions.     

研究堆燃料的发展现状与前景

在过去33年中,国际降低研究和试验堆铀浓度计划已成功开发和应用了U₃Si₂-Al弥散型燃料。但由于U₃Si₂的抗辐照性能限制了它可能承受的运行温度与裂变密度,所以该燃料只适用于低功率密度的研究堆。U7Mo-Al弥散型燃料中的UMo颗粒与Al基体发生广泛的化学反应,将引起严重的肿胀与起泡问题。近年来,给U7Mo颗粒表面涂敷ZrN隔离层,获得防止反应的显著效果,使U7Mo-Al弥散型燃料有望应用于实践。U10Mo单片型燃料的芯体铀密度可达16g/cm³,辐照性能良好,但制造方法需进一步完善;应用中国核动力研究设计院改进的框架结构与轧制方法,能够控制UMo芯体与Al包壳具有相近的延伸率,从而可成功地轧制出合格的U10Mo合金单片型燃料板。     

Optimization of Fuel Assembly Allocation for Boiling Water Reactors

Abstract

A direct search algorithm is applied to the optimization of fuel assembly allocation of BWR with particular consideration given to the nuclear model and the treatment of operating constraints. A simple expression is derived for evaluating the stuck rod margin, based on regression analysis of data obtained by three-dimensional full core analysis, and the expression is applied to optimization procedure.

The practical applicability of the method is confirmed through trial computations for the second and equilibrium cycles of a medium-sized commercial BWR, with an examination based on various initial guesses and objective functions for radial power peaking.     

Analytical Method of Fuel Pin Deformations in LMFBR Assembly

A new analytical method is presented for analyzing, in three dimensions, the mechanical response of fuel pins with wire spacers, to their thermal and neutronic environment in a fuel assembly of a LMFBR. It analyzes the mechanical interactions between fuel pins in the assembly in each of three directions, which form an angle of π/3 radians with one another, based on the mathematical relationship between the displacements at the contact points and the associated contact forces with respect to all fuel pins forming a line in one of the three directions.

Based on this method, a new computational code, the Subchannel Deformation Analysis Code for Wire-Wrap Assemblies (SHADOW) has been developed, and is applied to a fuel assembly of a prototype fast breeder reactor in order to analyze the deformation of 169 fuel pins due to thermal bowing.

Conclusions drawn from the study confirm that the SHADOW code can be an effective tool for analyzing or evaluating thermal and structural designs of a LMFBR fuel assembly.     

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method

Abstract

Whole core calculations have been performed for a commercial size PWR and a prototype LMFBR by using vectorized Monte Carlo codes. Geometries of cores were precisely represented in a pin by pin model. The calculated parameters were k _eff, control rod worth, power distribution and so on. Both multigroup and continuous energy models were used and the accuracy of multigroup approximation was evaluated through the comparison of both results. One million neutron histories were tracked to considerably reduce variances. It was demonstrated that the high speed vectorized codes could calculate k _eff, assembly power and some reactivity worths within practical computation time. For pin power and small reactivity worth calculations, the order of 10 million histories would be necessary. It would be difficult for the conventional scalar code to solve such large scale problems while the present codes consumed computation time less than 30 min for a PWR and 1 hour for an LMFBR. Required number of histories to achieve target design accuracy were estimated for those neutronic parameters.     

Three-Dimensional First-Order Perturbation Calculation Method for Reactivity Changes Due to Core Deformations of Fast Breeder Reactors

A three-dimensional diffusion calculation method has been proposed to rapidly and accurately calculate reactivity changes of LMFBRs caused by assembly displacements in accidental events. The method requires shorter computation times and provides almost the same accuracy as a conventional direct eigenvalue calculation method. In this method, changes in macroscopic neutron cross-sections and diffusion coefficient are defined so that changes in both region volume and material composition can be treated in a mesh-centered finite-difference program under the same coarse mesh division as used for the normal, non-deformed core. Reactivity changes are calculated from the above-mentioned changes by the first-order perturbation method using normal and adjoint neutron fluxes calculated beforehand for the normal core.

The method was applied to deformations of a 1,000-MWe LMFBR core. Reactivity changes calculated by the method agreed within 0.4% with those by a conventional direct eigenvalue calculation method, while computation time was less than 1/35.     

Irradiation Performance of Fast Reactor MOX Fuel Assemblies Irradiated to High Burnups

Mixed oxide fuel assemblies (MFA-1 and MFA-2 assemblies) were irradiated in the fast flux test facility to evaluate the irradiation performance of fast reactor core fuels at high burnups and high fast neutron fluences. The MFA-1 and MFA-2 assemblies achieved respective peak pellet burnups of 147 and 162GWd/t, and resisted to respective peak fast neutron fluences (E > 0:1 MeV) of 21:4 _ 1026 and 23:8 _ 1026 n/m2, without any indication of fuel pin breaching. Structural components of these assemblies were made of modified type 316 stainless steel and 15Cr-20Ni base advanced austenitic stainless steel. Postirradiation examinations of these assemblies revealed dimensional changes of fuel pins and assembly ducts due to irradiation-induced void swelling and irradiation creep, and fuel cladding local oval distortions due to bundle-duct interaction (BDI). The swelling resistance of 15Cr-20Ni base advanced austenitic stainless steel fuel pin cladding was almost the same as that of the modified type 316 stainless steel cladding, while the assembly duct of the former material had a slightly higher swelling resistance than that of the latter material. Analyses of fuel pin bundle deformations indicated that these assemblies likely mitigate BDI mainly by fuel pin bowings and cladding oval distortions.     

Application of BWR Simulator to Neutronics Calculation Tool in Fast Reactors

Scaling considerations have been made for liquid line small break simulation tests of a BWR affected by the stored heat released from loop structures. Necessary scaling parameters were given from lumped energy and mass balances equations. It was possible to compensate for excess stored heat released in the reduced-scale facility by increasing the coolant discharge flow area A_D . Although this compensation accelerated the blowdown process, actual pressure and coolant mass changes of the reactor system could be obtained by altering the time scale of the test results by the ratio of A_D/V (V: vessel volume) between the test loop and the reactor system. A semi-experimental evaluation of the stored heat release rate in the Two Bundle Loop (TBL) during blowdown after the operation of Automatic Depressurization System (ADS) was also presented on the basis of comparison of experimental diathermic and analytical adiabatic blowdown pressure changes. The obtained results were used in the determination of simulated ADS nozzle diameter for small break tests at the TBL.     

Requisite Accuracy for Hot Spot Factors in Fast Reactors

In the thermal design of a fast reactor, it should be most effective to reduce hot spot factors to the lowest possible level compatible with safety considerations, in order to minimize the design margin for the temperature prevailing in the core. Hot spot factors account for probabilistic and statistic deviations from nominal value of fuel element temperatures, due to uncertainties in the data adopted for estimating various factors including the physical properties. Such temperature deviations necessitate the provision of correspondingly large design margins for temperatures in order to keep within permissible limits the probability of exceeding the allowable temperatures.

Evaluation of the desired accuracy for hot spot factors is performed by a method of optimization, which permits determination of the degree of accuracy that should minimize the design margins, to give realistic results with consideration given not only to sensitivity coefficients but also to the present-day uncertainty levels in the data adopted in the calculations. A concept of “degree of difficulty” is introduced for the purpose of determining the hot spot factors to be given higher priority for reduction.

Application of this method to the core of a prototype fast reactor leads to the conclusion that the hot spot factors to be given the highest priority are those relevant to the power distribution, the flow distribution, the fuel enrichment, the fuel-cladding gap conductance and the fuel thermal conductivity.     

Treatment of Radioactive Waste Regenerant of Ion Exchange Resin by Preferential Flotation Method

To answer the increasing demand for electric power in Japan, Very Large Fast Reactors of 10,000 MWe unit capacity are expected to make their appearance in due course. The paper describes the method and results of a design study on a 10,000 MWe Liquid Metal Fast Breeder Reactor. First, a reference design was obtained for this unit of unprecedented capacity by extrapolating the various characteristics of a 1,000 MWe LMFBR and the nuclear characteristics thereof were studied. It was found that reactivity increase could be reduced to about 6 ¢ when seven subassemblies were voided in the central part of the core, and that the increase of reactivity and the decrease of breeding ratio with time were rather large for the initial loading core.

Secondly, a design optimization procedure was developed based on complex method of nonlinear programming, and the method was applied to the Very Large Fast Reactor. The process resulted in a relatively large core height and fuel pin diameter, while the power cost was improved due to enhanced breeding gain. The fuel center temperature and the coolant velocity were found close to the upper boundaries of their prescribed ranges. These results concurred qualitatively with calculations using more straightforward optimization techniques.     

快堆燃料组件热工流体力学计算研究

对于钠冷快堆,在燃料和包壳最高温度等设计限值下,为获得较高的堆芯出口温度,需深入分析燃料组件内的热工流体力学问题,准确预测组件内的冷却剂温度分布。本文在CRT模型和F.C.Engel等人工作的基础上,提出了ICRT压降关系式,用以计算冷却剂在湍流区、过渡流区和层流区的棒束压降;引入CRT模型和WEST对流传热模型,改进了SUPERENERGY子通道分析程序,并将改进程序与原程序计算结果进行了对比,结果表明：最热子通道出口温度略有降低,液膜温压略有增加;并用计算流体力学软件CFX对中国实验快堆单盒燃料组件活性段进行了三维数值模拟,将计算结果用CRT模型、ICRT压降关系式及改进后的SUPERENERGY子通道分析程序进行了验证,相互符合较好。