Faculty Profiles - ENDO Tomohiro

Papers - ENDO Tomohiro

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A unified approach for numerical calculation of space-dependent kinetic equation Reviewed International journal

Yuichiro Ban, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 49 ( 5 ) page： 496 - 515 2012.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A unified numerical method based on the factorization approach is developed to solve the spacedependent neutron kinetic equation. Various numerical methods for solving the space-dependent kinetic equation have been developed so far. These methods can be classified into two categories, i.e., the direct and the factorization methods. The factorization method is known as an effective numerical method. In the present study, a new factorization method named the multigrid amplitude function (MAF) method is developed. Unlike the improved quasi-static (IQS) method, an independent amplitude function is assigned for each spatial region and energy group in the MAF method. The MAF method is a generalization of conventional methods, e.g., the frequency transform, IQS, and Theta methods. To evaluate the amplitude function in the MAF method, the time-dependent coarse-mesh finite difference (TCMFD) method is developed. The MAF method is implemented into a space-dependent kinetic code on the basis of the analytical polynomial nodal method. In order to verify the effectiveness of the MAF method, the TWIGL, Langenbuch, Maurer, and Werner (LMW), and Laboratorium fü r Reaktorregelung and Anlagensicherung (LRA) benchmark problems are analyzed. The calculation results show the effectiveness of the present method.

DOI： 10.1080/00223131.2012.677126

Scopus

Application of quick subchannel analysis method for three-dimensional pin-by-pin BWR core calculations Reviewed International journal

Kenichi Tada, Tatsuya Fujita, Tomohiro Endo, Akio Yamamoto, Shinya Kosaka, Go Hirano, Kenichiro Nozaki

Journal of Nuclear Science and Technology Vol. 48 ( 12 ) page： 1437 - 1452 2011.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Three-dimensional pin-by-pin core analysis is considered to be a candidate for the next-generation BWR core calculation method. In our previous study, the applicability of the transport and burnup calculations for a three-dimensional pin-by-pin BWR core analysis was investigated. However, the thermal-hydraulics calculation has not yet been studied in this framework. In the conventional core analysis code, the bundlewise thermal-hydraulics calculation is adopted. In the actual core analysis, the power distribution inside a fuel assembly is tilted at the region adjacent to a control blade or the core peripheral region. In these regions, the consideration of the subchannel-wise void distribution has an impact on the fission rate distribution. Therefore, an evaluation of the detailed void distribution inside an assembly, i.e., the incorporation of the subchannel wise void distribution, is desirable for the pin-by-pin BWR core analysis. Although several subchannel analysis codes have been developed, these subchannel analysis codes generally require a large computational effort to estimate the subchannel-wise void distribution in a whole BWR core. Therefore, to analyze a whole BWR core within a reasonable computation time, it was necessary to apply a fast subchannel analysis code. In this paper, a quick subchannel analysis code dedicated to pin-by-pin BWR core analysis is newly developed, and the void distribution of the present subchannel analysis code is compared with the prevailing subchannel analysis code NASCA using three-dimensional single-assembly geometries. Since the present subchannel analysis code is used for a coupled neutronics/thermal-hydraulics analysis, the results of the coupling calculation are also compared with those of NASCA. The calculation result indicates that the void distribution difference between NASCA and the present subchannel analysis code is slightly less than 10%. This result indicates that the prediction accuracy of the present subchannel analysis code will be reasonably appropriate for a pin-by-pin BWR core analysis. Furthermore, the results show that the calculation time of the present subchannel analysis code is only 10 min for a hypothetical three-dimensional ABWR quarter-core geometry using a single CPU. This calculation time is sufficient for a pin-by-pin BWR core analysis.

DOI： 10.1080/18811248.2011.9711837

Scopus

Application of the robust design concept for fuel loading pattern Reviewed International journal

Tomohiro Endo, Kazuma Ohori, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 48 ( 7 ) page： 1077 - 1086 2011.7

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Application of the robust design concept for fuel loading pattern design is proposed as a new approach to improve the prediction accuracy of core characteristics. The robust design is a design concept that establishes a resistant (robust) system for perturbations or noises, by properly setting design variables. In order to apply the concept of robust design to fuel loading pattern design, we focus on a theoretical approach based on the higher order perturbation method. This approach indicates that the eigenvalue separation is one of the effective indices to measure the robustness of a designed fuel loading pattern. In order to verify the effectiveness of the eigenvalue separation as an index of robustness, numerical analysis is carried out for typical 3-loop PWR cores, and we evaluated the correlation between the eigenvalue separation and the variation of relative assembly power due to the perturbation of the cross section. The numerical results show that the variation of relative power decreases as the eigenvalue separation increases
thus, it is confirmed that the eigenvalue separation is an effective index of robustness. Based on the eigenvalue separation of a fuel loading pattern, we discuss design guidelines of a fuel loading pattern to improve the robustness. For example, if each fuel assembly has independent uncertainty on its cross section, the robustness of the core can be enhanced by increasing the relative power at the center of the core. The proposed guidelines will be useful to design a loading pattern that has robustness for uncertainties due to cross section, calculation method, and so on.

DOI： 10.1080/18811248.2011.9711792

Scopus

Improved derivation of multigroup effective cross section for heterogeneous system by equivalence theory Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Hiroki Koike

Nuclear Science and Engineering Vol. 168 ( 2 ) page： 75 - 92 2011.6

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The validity of effective cross section obtained by the conventional equivalence theory is discussed from the viewpoint of reaction rate preservation in a heterogeneous system. It is shown that the reaction rate is not preserved when the escape probability is expressed by a multiterm rational approximation, which is commonly used in light water reactor (LWR) analyses. A new derivation method for obtaining a multigroup effective cross section, which accurately reproduces the result of reference ultrafine group calculation, is proposed. The validity of the proposed method is confirmed through test calculations in various heterogeneous geometries, which represent typical LWR configurations. Because the implementation of the proposed method is very simple, it is useful for existing lattice physics codes that utilize the equivalence theory on the basis of two-term (or multiterm) rational approximation.

DOI： 10.13182/NSE10-50

Scopus

Resonance calculation for large and complicated geometry using Tone's method by incorporating the method of characteristics Reviewed International journal

Hao Yu, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 48 ( 3 ) page： 330 - 336 2011.3

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A new efficient approach for evaluating the background cross section, which is based on Tone's method, is presented. Though the collision probability method is used in the conventional Tone's method, the method of characteristics (MOC) is used in the present method. Since the computation time of MOC is shorter than that of the collision probability method in a large and complicated geometry, the present method will be useful not only for lattice physics calculation, but also for analyses of advanced reactors with complicated geometry. Verification calculations are carried out in two configurations, i.e., a PWR fuel assembly geometry and a multiassembly geometry adjacent to the baffle-reflector region. The validity of the present method has been confirmed through the results of verification calculations.

DOI： 10.1080/18811248.2011.9711707

Scopus

Overview of Core Simulation Methodologies for Light Water Reactor Analysis Reviewed International journal

A. Yamamoto, T. Endo

International Electronic Journal of Nuclear Safety and Simulation Vol. 2 ( 1 ) page： 12 - 21 2011.3

Language：English Publishing type：Research paper (scientific journal)

The current in-core fuel management calculation methods provide a very efficient route to predict neutronics behavior of light water reactor (LWR) cores and their prediction accuracy for current generation LWRs is generally sufficient. However, since neutronics calculations for LWRs are based on various assumptions and simplifications, we should also recognize many implicit limitations that are "embedded" in current neutronics calculation methodologies. Continuous effort for improvement of core simulation methodologies is also discussed.

Explicit Time Integration Scheme Using Krylov Subspace Method for Reactor Kinetics Equation Reviewed International journal

Yuichiro Ban, Tomohiro Endo, Akio Yamamoto, Yoshihiro Yamane

Journal of Nuclear Science and Technology Vol. 48 ( 2 ) page： 243 - 255 2011.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The spatial discretization form of the space-dependent reactor kinetics equation is a first-order simultaneous ordinary differential equation in time. Conventional numerical methods of the space-dependent kinetics equation, i.e., the generalized Runge-Kutta method, the implicit method (backward Euler method), and the Theta method, are based on the time difference approximation. However, the present study adopts the analytical solution of the space-dependent kinetics equation expressed by the matrix exponential and no time difference approximation is used. In this context, our present approach is classified as an explicit method in which no iteration calculation on space and energy is necessary. The Krylov subspace method is used to evaluate the matrix exponential observed in the solution of the spatially discretized space-dependent kinetics equation. The Krylov subspace method is implemented into a space-dependent kinetics solver. In order to examine the effectiveness of the Krylov subspace method, the TWIGL benchmark problem is analyzed as a verification calculation. The calculation results show the effectiveness of the present method especially in the step reactivity perturbation.

DOI： 10.1080/18811248.2011.9711698

Scopus

Improvement of Tone's method with two-term rational approximation Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Go Chiba

Journal of Nuclear Science and Technology Vol. 48 ( 2 ) page： 263 - 271 2011.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method.

DOI： 10.1080/18811248.2011.9711700

Scopus

AEGIS: An Advanced Lattice Physics Code for Light Water Reactor Analyses Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Masato Tabuchi, Naoki Sugimura, Tadashi Ushio, Masaaki Mori, Masahiro Tatsumi, Yasunori Ohoka

Nuclear Engineering and Technology Vol. 42 ( 5 ) page： 500 - 519 2010.10

Language：English Publishing type：Research paper (scientific journal) Publisher：Korean Nuclear Society

AEGIS is a lattice physics code incorporating the latest advances in lattice physics computation, innovative calculation models and efficient numerical algorithms and is mainly used for light water reactor analyses. Though the primary objective of the AEGIS code is the preparation of a cross section set for SCOPE2 that is a three-dimensional pin-by-pin core analysis code, the AEGIS code can handle not only a fuel assembly but also multi-assemblies and a whole core geometry in two-dimensional geometry. The present paper summarizes the major calculation models and part of the verification/validation efforts related to the AEGIS code.

DOI： 10.5516/NET.2010.42.5.500

Web of Science

Other Link： https://doi.org/10.5516/NET.2010.42.5.500

Development of deterministic code based on the discrete ordinates method for the third-order neutron correlation technique Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Yoshihiro Yamane

Annals of Nuclear Energy Vol. 35 ( 5 ) page： 927 - 936 2008.5

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

The third-order neutron correlation technique is one of the subcriticality measurement techniques. The significant feature of this technique is that an absolute value of subcriticality can be evaluated from the measured neutron correlation factors, namely Y-infinity and X-infinity In order to extend the applicability of the third-order neutron correlation technique to actual complicated subcritical systems, we previously derived the spatial and neutron energy dependent theoretical formulas of Y-infinity and X-infinity by using the first-, second-, and third-order importance functions. These theoretical formulas depend on the locations of both an external neutron source and a neutron detector. The numerical solutions of these formulas are very useful to design the arrangements of the external neutron source and the neutron detector and to investigate the contamination of the spatial effect in the measured neutron correlation factors, Y-infinity and X-infinity Therefore, we developed a novel deterministic code that can calculate both Y-infinity and X-infinity based on the SN method. In this paper, we focus on the description of the numerical procedure of this code and its verification by comparing it with the results of Monte Carlo simulations.

DOI： 10.1016/j.anucene.2007.09.014

Web of Science

Neutron Transport Models of AEGIS: An Advanced Next-Generation Neutronics Design System Reviewed International journal

Naoki Sugimura, Akio Yamamoto, Tadashi Ushio, Masaaki Mori, Masato Tabuchi, Tomohiro Endo

Nuclear Science and Engineering Vol. 155 ( 2 ) page： 276 - 289 2007.2

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

A very rigorous and advanced next-generation neutronics design system, AEGIS (Anisotropic, Extended Geometry, Integrated Neutronics Solver), which is based on the deterministic method, is being developed using advanced computer science technology. The method of characteristics, which has the merit of treating heterogeneous geometry explicitly, is utilized in AEGIS as a neutron transport solver. So, the AEGIS code can explicitly model many types of fuel lattices in both commercial light water reactors (LWRs) and advanced reactors such as Generation IV reactors. The AEGIS code can also treat higher-order anisotropic scattering accurately based on spherical harmonics expansion. To compute a large-scale problem, a nonuniform ray-tracing method is implemented in AEGIS. It utilizes the Gauss-Legendre quadrature weight and the macroband method to decide position and width of ray traces to reduce spatial discretization error efficiently. The transport solution of AEGIS has been verified through various benchmark problems. It was found that the AEGIS code can explicitly treat complicated geometry and can efficiently solve a large-scale problem. These results show that flexibility in handling geometry and the very rigorous neutronics calculation models of AEGIS will contribute to predicting neutronics characteristics accurately, not only for commercial LWRs but also for advanced reactors.

DOI： 10.13182/NSE155-276

Web of Science

Effect of error propagation of nuclide number densities on Monte Carlo burn-up calculations Reviewed International journal

Masayuki Tohjoh, Tomohiro Endo, Masato Watanabe, Akio Yamamoto

Annals of Nuclear Energy Vol. 33 ( 17-18 ) page： 1424 - 1436 2006.11

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

As a result of improvements in computer technology, the continuous energy Monte Carlo burn-up calculation has received attention as a good candidate for an assembly calculation method. However, the results of Monte Carlo calculations contain the statistical errors. The results of Monte Carlo burn-up calculations, in particular, include propagated statistical errors through the variance of the nuclide number densities. Therefore, if statistical error alone is evaluated, the errors in Monte Carlo burn-up calculations may be underestimated. To make clear this effect of error propagation on Monte Carlo burn-up calculations, we here proposed an equation that can predict the variance of nuclide number densities after burn-up calculations, and we verified this equation using enormous numbers of the Monte Carlo burn-up calculations by changing only the initial random numbers. We also verified the effect of the number of burn-up calculation points on Monte Carlo burn-up calculations. From these verifications, we estimated the errors in Monte Carlo burn-up calculations including both statistical and propagated errors. Finally, we made clear the effects of error propagation on Monte Carlo burn-up calculations by comparing statistical errors alone versus both statistical and propagated errors. The results revealed that the effects of error propagation on the Monte Carlo burn-up calculations of 8 x 8 BWR fuel assembly are low up to 60 GWd/t.

DOI： 10.1016/j.anucene.2006.09.010

Web of Science

Derivation of theoretical formula for the third order neutron correlation technique by using importance function Reviewed International journal

Tomohiro Endo, Yoshihiro Yamane, Akio Yamamoto

Annals of Nuclear Energy Vol. 33 ( 10 ) page： 857 - 868 2006.7

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

The third order neutron correlation technique is one of the subcriticality measurement techniques. This technique was originally proposed by Furuhashi and utilizes the second and third order neutron correlation factors Y(T) and X(T), which are evaluated from the variance and third order central moment of neutron counts detected during a counting gate width T, respectively. We can obtain the absolute value of subcriticality from the Y infinity and X infinity, which are saturation values of Y(T) and X(T) when T goes to infinity. In the previous paper, we derived the generalized theoretical formulas of Y infinity and X infinity that took account of both the spatial and neutron energy effects. Its derivation was based on a heuristic method in which we consider the branching process of neutron family, and we utilized the alpha-eigenfunction expansion technique. Then, the previous formulas are expressed by multiple sums involving both the alpha-eigenfunctions and their adjoint functions. In this paper, we derive the new compact expressions of Y infinity and X infinity by using the importance functions related to the neutron detection process. Present derivation is based on the stochastic equation of neutron transport. New expressions have two advantages. We can clarify the physical meanings of Y infinity and X infinity. And, without alpha-eigenfunction expansion, we can calculate Y infinity and X infinity directly by calculating the importance functions which satisfy the adjoint neutron transport equations. Moreover, we prove that new expressions of Y infinity and X infinity are identical with the previous ones, so that we can conclude that our previous derivation based on a heuristic method is correct.

DOI： 10.1016/j.anucene.2006.05.005

Web of Science

Space and energy dependent theoretical formula for the third order neutron correlation technique Reviewed International journal

Tomohiro Endo, Yoshihiro Yamane, Akio Yamamoto

Annals of Nuclear Energy Vol. 33 ( 6 ) page： 521 - 537 2006.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

We have studied measurement techniques of subcriticality by using the neutron correlation techniques. Among various techniques, we have paid attention to the third order neutron correlation technique, which was proposed by Furuhashi originally and utilizes the third order fluctuations of neutron counts. By using this technique, we can obtain the absolute value of subcriticality with the aid of factorial moments of fission neutron v and external source neutron q, without prior knowledge of the prompt neutron decay constant at a reference state. However, in order to apply the third order neutron correlation technique to actual experiments, we must consider the spatial and neutron energy effects in this technique. For this purpose, we derived more generalized theoretical formulas of the third order neutron correlation technique that took account of the spatial and neutron energy effects by virtue of the alpha-eigenfunction expansion. Making use of the newly derived formulas, we propose the practical formulas and the experimental procedures based on the fundamental mode approximation.

DOI： 10.1016/j.anucene.2006.02.002

Web of Science

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Papers - ENDO Tomohiro