Three-Dimensional Analysis Method for Sloshing Behavior of Fast Breeder Reactor and Its Application to Uni- and Multi-Vessel Type FBRs

A three-dimensional analysis method for sloshing behavior of fast breeder reactor (FBRs) is developed. The method treats the coolant in a reactor vessel as a potential flow with moving liquid surfaces. The Laplace equation of a velocity potential is solved by a boundary element method with its boundary condition described by a Bernoulli equation.

The vibration test results of a rectangular water pool are calculated by the method. Then, the method is applied to analysis of sloshing behavior of uni- and multi-vessel type FBRs. The latter consists of vessels for the core, heat exchangers and pumps. These vessels are connected by piping. In the case of the uni-vessel type FBR, heat exchangers and pumps are placed in the reactor vessel. The characteristics of sloshing behavior of both the reactors are presented.     

Application of X-Ray Computer Tomography for Observing the Deflection and Displacement of Fuel Pins in an Assembly Irradiated in FBR

A nondestructive method making use of X-ray computer tomography (X-ray CT) has been applied to post irradiation examination of fast breeder reactor (FBR) fuel assemblies. In the study, an examination is made of the deflection and displacement of fuel pin in a fuel assembly irradiated to 74.2GWd/t peak burnup in the fast reactor “JOYO.”

In the examination, X-ray CT images of transverse cross sections of fuel pin were obtained at different heights of fuel pin along its axis. Analysis of the resulting images indicated that:

1. The hexagonal wrapper tube had its lateral wall faces slightly bulged outward;

2. The fuel pins loaded in the outermost array were markedly displaced in the direction of wrapper tube, particularly in portions of fuel pin intermediate between positions constrained by wrapping wire.

The latter behavior of fuel pins was substantiated by the contours of fuel pin along its axis, which were derived from cross section images obtained at different levels along axis.

Such fuel pin displacement is surmised to have been caused by thermal stressing of the affected fuel assembly cladding.     

Application of Galerkin Finite Element Method to Subchannel Analysis

Most of the computer codes based upon subchannel analysis, which are important for thermal hydraulic analysis of the reactor core, use the finite difference method to solve the set of equations. In the present study, however, the Galerkin finite element method was tried, with the result that more accurate solutions and more efficient calculations were obtained than those by the finite difference method. The results of error evaluation obtained herein are useful for application of this method to actual subchannel analysis codes and to other general thermal hydraulic analysis codes. As an example, steady-state single-phase subchannel analysis was performed.     

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.     

Application of Galerkin Method to Hydraulic Analysis for Turbulent Fluid Flow around LMFBR Fuel Rod

Wide range of parameter surveys are made on the DT fusion tokamak experimental reactor next to JT-60. Various physics and engineering requirements are taken into account, e.g. self-ignition, available maximum toroidal β value, α-particle confinement, total fusion power, neutron wall loading, heat flux to divertor plate, structural restriction on major radius, device size, maximum toroidal magnetic field, poloidal field power supply and so on. Theoretical scaling law for the available maximum toroidal β value determined by ballooning mode instability is used. The toroidal magnetic field on plasma axis can be expressed by the aspect ratio A for a given maximum field at the toroidal field coil conductor. Empirical scaling law for the electron energy confinement and neoclassical heat conductivity for the ion are employed. These confinement times can be expressed by the plasma minor radius a and A through the maximum available β value and the toroidal field on axis. In the similar way, most of the physics and engineering requirements can be mapped on the a-A diagram. This diagram enables us to make systematic and wide range of parameter surveys of the device. In particular, this offers a clear perspective on the device parameters, which can mitigate the engineering difficulties and can also realize the required plasma performances.     

Development of the Hierarchical Domain Decomposition Boundary Element Method for Solving the Three-Dimensional Multiregion Neutron Diffusion Equations

A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the “lower level” calculations. At the “higher level” calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time.     

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.     

Application of Hexagonal Element Scheme in Finite Element Method to Three-Dimensional Diffusion Problem of Fast Reactors

The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes.

The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes.     

节块展开法求解对流扩散方程的稳定性和数值耗散特性分析

本文研究了节块展开法求解对流扩散方程的稳定性和数值耗散特性。通过离散方程精确解和数值实验方法分析不同阶节块展开法的稳定性和数值耗散特性,并将其与有限体积法中的中心差分和一阶迎风格式进行对比。结果表明:偶数阶节块展开法的稳定是有条件的,即Peclet数(Pe)小于限值,且Pe限值会随展开阶数的增大而增大,其稳定性范围和精度均优于中心差分格式;奇数阶节块展开法是无条件稳定的,但随Pe的增大,数值耗散增大、计算误差增大,且当Pe大于一定值后,产生的数值耗散大于一阶迎风格式。     

Classification of Criticality Calculations with Correlation Coefficient Method and Its Application to OECD/NEA Burnup Credit Benchmarks Phase III-A and II-A

A method for classifying benchmark results of criticality calculations according to similarity was proposed in this paper. After formulation of the method utilizing correlation coefficients, it was applied to burnup credit criticality benchmarks Phase III-A and II-A, which were conducted by the Expert Group on Burnup Credit Criticality Safety under auspices of the Nuclear Energy Agency of the Organisation for Economic Cooperation and Development (OECD/NEA). Phase III-A benchmark was a series of criticality calculations for irradiated Boiling Water Reactor (BWR) fuel assemblies, whereas Phase II-A benchmark was a suite of criticality calculations for irradiated Pressurized Water Reactor (PWR) fuel pins. These benchmark problems and their results were summarized. The correlation coefficients were calculated and sets of benchmark calculation results were classified according to the criterion that the values of the correlation coefficients were no less than 0.15 for Phase III-A and 0.10 for Phase II-A benchmarks. When a couple of benchmark calculation results belonged to the same group, one calculation result was found predictable from the other. An example was shown for each of the Benchmarks. While the evaluated nuclear data seemed the main factor for the classification, further investigations were required for finding other factors.     

核电站主蒸汽隔离阀气流诱发振动与噪声的数值分析

核电站主蒸汽隔离阀技术要求严、安全系数高,是核电装备国产化进程中的重点攻关项目之一。某些核电站在运行过程中其主蒸汽隔离阀出现过气流诱发振动与噪声,最终导致阀门部件磨损的现象。本文通过数值方法对主蒸汽隔离阀内三维湍流流场进行模拟分析,研究找出产生振动与噪声的流场诱因。本工作的数值分析结果与现场的测量结果相符。