Faculty Profiles - ENDO Tomohiro

MISC - ENDO Tomohiro

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Improvement of a Convergence Technique for MOC Calculation with Large Negative Self-Scattering Cross Section Reviewed International journal

M. Tabuchi, M. Tatsumi, A. Yamamoto, T. Endo

Proc. PHYSOR2014 Vol. CD-ROM page： 1105664 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

In the method of characteristics, convergence behavior of inner iteration would be degraded by the transport correction. A previous study revealed that large negative self-scattering cross section due to the transport correction worsens convergence of inner iteration. In order to resolve this issue, a technique to improve the convergence behavior based on the successive over relaxation (SOR) method was proposed in the previous study. However, considerable calculation time is necessary to estimate the optimum acceleration factor for the SOR method especially in large scale geometries. In order to address this drawback, a fast estimation scheme of the acceleration factors is proposed in this study. The present approach can provide acceleration factors which ensure convergence of iterative calculation. In the present approach, the equation to obtain the appropriate acceleration factor is derived by using Gerschgorin’s theorem. Based on the equation, the acceleration factors can be easily obtained in each energy group with negligible calculation time. Verification calculations are performed in various critical experiments, in which degradation of convergence by the transport correction is significant. When the transport correction is used without the SOR method, all iterative calculations diverged. On the other hand, when the SOR method with the acceleration factors based on the present approach is applied, convergent solutions are successfully obtained in all cases. From these results, validity of the present approach is confirmed.

DOI： 10.11484/jaea-conf-2014-003

A Multi-Level Parallel Computation of Reactor Cores using GPU for Loading Pattern Optimization Reviewed International journal

T. Okubo, T. Endo, A. Yamamoto

Proc. PHYSOR2014 Vol. CD-ROM page： 1101184 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

Efficient and rapid computation of multiple loading patterns using GPU is studied aiming application to loading pattern optimization of LWR. The loading pattern has significant impacts on safety and economy of a reactor. However, design of loading pattern is a combinatorial optimization problem, thus it is computationally intensive task. In order to address this issue, efficient and rapid computation method of loading patterns using massively parallel computing capability of GPU is studied in the present paper. Though GPU has higher computational performance than CPU, but different computational algorithm and coding approach are necessary to maximize the performance of GPU, due to different architecture of GPU. In the present study, a multi-level parallel computing approach is examined considering hardware architecture of GPU, i.e., parallel computing is carried out not only in spatial mesh-wise, but also in loading pattern-wise. In other words, multiple loading patterns are simultaneously computed and domain (mesh-wise) decomposition is applied to each loading pattern. With the present approach, computational efficiency using GPU is approximately four times higher than that of CPU. The present core analysis algorithm can be used for screening of poor loading patterns in optimization process.

DOI： 10.11484/jaea-conf-2014-003

Development of Legendre Expansion of Angular Flux Method for 3D-MOC Calculation Reviewed International journal

Y. Kato, T. Endo, A. Yamamoto

Proc. PHYSOR2014 Vol. CD-ROM page： 1106157 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

A three-dimensional transport calculation method, Legendre Expansion of Angular Flux Method (LEAF method) has been proposed for practical MOC calculations in three-dimensional geometry. In the LEAF method, transport calculation is carried out on "characteristics planes(CP)" rather than conventional ray traces, whose concept is similar to that of the ASMOC3D method. By utilizing the characteristics plane, required memory and computational load are significantly reduced. Each characteristics plane forms rectangular regions, thus efficient transport calculation scheme based on transmission probability can be adopted. Consequently, the LEAF method can practically perform MOC calculation in three-dimensional geometry. In the LEAF method, spatial distribution of incoming, outgoing and average angular fluxes in a CP are expressed as a series of the Legendre polynomials in order to accurately capture their spatial dependence. Calculation results in a test problem indicate the accuracy and effectiveness of the LEAF method.

DOI： 10.11484/jaea-conf-2014-003

Investigation on Subcriticality Measurement using Inherent Neutron Source in Nuclear Fuel Reviewed International journal

T. Shiozawa, T. Endo, A. Yamamoto, C.H. Pyeon, T. Yagi

Proc. PHYSOR2014 Vol. CD-ROM page： 1086633 2014.9

Authorship：Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

The subcriticality measurement techniques using inherent neutron source are investigated in this study. In facilities where nuclear fuel is treated, it is considered to install a real-time subcriticality monitoring system. However, it is often unfavorable or impractical to bring an external neutron source into a nuclear facility to carry out subcriticality measurement. Thus, we focus on the inherent neutron source in nuclear fuel such as spontaneous fission and (alpha, n) reaction. By utilizing the inherent neutron source, the subcriticality measurement technique, which does not introduce an external neutron source, can be realized. In this study, the Feynman-alpha method and the neutron source multiplication (NSM) method are chosen as techniques which can be carried out only with the inherent neutron source, and have affinities with a real-time monitoring system. In the Kyoto University Critical Assembly (KUCA), subcriticality measurement experiments of these two techniques were carried out. From the experimental result, it is confirmed that both techniques can be carried out only with the inherent neutron source. It is noted that, however, measured values of subcriticality by both methods show different trends. While the subcriticality measured by the Feynman-alpha method is fairly constant among detectors, the measured value does not agree with that obtained by the pulsed neutron source (PNS) method, in deep subcritical systems. On the other hand, the subcriticality measured by the NSM method show significant dependence on detectors. However, the measurement values by the NSM method using detectors at appropriate position agree with values by the PNS method even in deep subcritical systems.

DOI： 10.11484/jaea-conf-2014-003

Impact of Nearest Neighbor Distribution of Fuel Particle on Neutronics Characteristics in Statistical Geometry Model Reviewed International journal

T. Koide, T. Endo, A. Yamamoto, K. Kirimura, K. Yamaji

Proc. PHYSOR2014 Vol. CD-ROM page： 1101295 2014.9

Generation of Simplified Burnup Chain using Contribution Matrix of Nuclide Production Reviewed International journal

R. Katano, A. Yamamoto, T. Endo, Y. Kamiyama, K. Kirimura, S. Kosaka

Proc. PHYSOR2014 Vol. CD-ROM page： 1101303 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

A procedure to automatically generate a simplified burnup chain is proposed, which preserves prediction accuracy of target nuclides number density using calculation results of a detail burnup chain. In the present procedure, the contributions to production of the target nuclides are quantitatively evaluated at first using the off-diagonal elements of a burnup matrix and nuclides number density. Then, by considering the contributions to nuclide production, which is represented as a “contribution matrix”, the nuclides in detail burnup chain are selected according to the importance represented as the contribution matrix. Finally, a simplified burnup chain is generated with the target nuclides and the selected nuclides from the contribution matrix. Since the present method only utilizes the burnup matrix, which is usually used in the common lattice physics computation, its implementation to production codes is easy. In order to examine the effectiveness of the present method, burnup calculation in a PWR fuel pin-cell problem with some simplification on calculation conditions is carried out. The calculation results suggest that the present method will be a good candidate for an automated generation method for a simplified burnup chain.

DOI： 10.11484/jaea-conf-2014-003

Uncertainty Quantification of BWR Core Characteristics using Latin Hypercube Sampling Method Reviewed International journal

K. Kinoshita, A. Yamamoto, T. Endo, Y. Kodama, Y. Ohoka, T. Ushio, H. Nagano

Proc. PHYSOR2014 Vol. CD-ROM page： 1090063 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

Uncertainties of neutronics characteristics in a commercial BWR core due to cross section covariance are evaluated by the Latin Hypercube Sampling (LHS) method, which is a Monte-Carlo based efficient sampling algorithms. The Peach Bottom Unit 2, which is a BWR core, is a target for the uncertainty quantification in the present study. Thermal hydraulics feedback and burnup effects are fully and explicitly taken into account using a licensing-grade core simulator. Uncertainties for various core characteristics and correlations among them are evaluated by the statistical processing of core calculation results based on the LHS method. The calculation results indicate that uncertainty of critical eigenvalue (i.e., core reactivity) in the BWR core is comparable to that of typical PWR. On the other hand, uncertainties of assembly relative power distribution and maximum assembly burnup in the present BWR core are much smaller than those of typical PWR. The strong thermal hydraulics feedback effect of BWR would significantly contribute the difference of uncertainties in BWR and PWR.

DOI： 10.11484/jaea-conf-2014-003

Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method Reviewed International journal

K. Kinoshita, A. Yamamoto, T. Endo, Y. Kodama, Y. Ohoka, T. Ushio, H. Nagano

Proc. PHYSOR2014 Vol. CD-ROM page： 1101192 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

The Latin Hypercube Sampling (LHS) method is applied to the uncertainty quantification of neutronics characteristics based on the Monte-Carlo based sampling method. The Monte-Carlo based sampling method is one of the uncertainty quantification methods of neutronics characteristics (e.g. neutron multiplication factor) due to uncertainty cross section. The sampling method has the advantage that burnup and thermal-hydraulics feedback effects are easily considered in complicated light water reactor core analysis. Contrary, the sampling method has the disadvantage that statistical errors are involved in estimated uncertainties of neutronics characteristics since the sampling method is a probabilistic approach. Although the statistical errors can be reduced by increasing the number of samples (e.g. number of perturbed cross section libraries), computational cost also increases. Therefore development of an efficient uncertainty quantification method, which provides smaller statistical error of estimated uncertainty while reducing number of samples, is highly desirable. In the present study, adequacy and performance of the LHS method is investigated as an efficient Monte-Carlo based sampling method. Uncertainty quantification of multiplication factor for a BWR fuel assembly is carried out with the LHS method. The results indicate that uncertainty quantification using the LHS method is more efficient than that using the conventional sampling method, which utilizes simple random sampling of cross sections.

DOI： 10.11484/jaea-conf-2014-003

Theoretical Prediction on Underestimation of Statistical Uncertainty for Fission Rate Tally in Monte Carlo Calculation Reviewed International journal

T. Endo, A. Yamamoto, K. Sakata

Proc. PHYSOR2014 Vol. CD-ROM page： 1126624 2014.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

A theoretical model to predict underestimation of standard deviation for the mean of fission rate in each tally region is proposed on the basis of the behavior of higher order modes in fission source distribution and the autoregressive (AR) model. The predicted underestimation of standard deviation for the mean of fission rate is compared with that obtained by actual Monte Carlo calculations and they agree well each other. Dependency of underestimation of standard deviation on number of tally regions and spatial position is clarified by the proposed theoretical model. The present theoretical model can be used to quantitatively predict underestimation of standard deviation of local fission rate tally.

DOI： 10.11484/jaea-conf-2014-003

Applicability of the Cross Section Adjustment Method Based on Random Sampling Technique for Burnup Calculation Reviewed International journal

T. Watanabe, T. Endo, A. Yamamoto, Y. Kodama, Y. Ohoka, T. Ushio

Proc. PHYSOR2014 Vol. CD-ROM page： 1098930 2014.9

Language：English Publishing type：Research paper, summary (international conference) Publisher：Japan Atomic Energy Agency

Applicability of the cross section adjustment method based on random sampling (RS) technique to burnup calculations is investigated. The cross section adjustment method is a technique for reduction of prediction uncertainties in reactor core analysis and has been widely applied to fast reactors. As a practical method, the cross section adjustment method based on RS technique is newly developed for application to light water reactors (LWRs). In this method, covariance among cross sections and neutronics parameters are statistically estimated by the RS technique and cross sections are adjusted without calculation of sensitivity coefficients of neutronics parameters, which are necessary in the conventional cross section adjustment method. Since sensitivity coefficients are not used, the RS-based method is expected to be practically applied to LWR core analysis, in which considerable computational costs are required for estimation of sensitivity coefficients. Through a simple pin-cell burnup calculation, applicability of the present method to burnup calculations is investigated. The calculation results indicate that the present method can adequately adjust cross sections including burnup characteristics.

DOI： 10.11484/jaea-conf-2014-003

Prediction on Underestimation of Variance for Fission Rate Distribution in Monte-Carlo Calculation Reviewed International journal

A. Yamamoto, K. Sakata, T. Endo

Trans. Am. Nucl. Soc. Vol. 110 page： 515 - 518 2014.6

An Improved CMFD Acceleration for SP3 Advanced Nodal Method Reviewed International journal

T. Sakamoto, A. Yamamoto, T. Endo

Trans. Am. Nucl. Soc. Vol. 110 page： 535 - 537 2014.6

Evaluation of Higher Mode Components of Fission Source Distribution in Monte-Carlo Calculation Reviewed International journal

K. Sakata, T. Endo, A. Yamamoto

Proc. SNA-MC 2013 page： 03503 2014.6

Language：English Publishing type：Research paper, summary (international conference) Publisher：EDP Sciences

In order to accurately estimate uncertainty of fission source distribution in a Monte Carlo calculation, a theoretical model predicting behavior of higher order modes in fission source distribution at each cycle is proposed considering the inter-cycle correlation. In a Monte Carlo calculation, statistical noise stimulates higher order modes in fission source distribution at each cycle thus the fission source distribution may not be fully converged to a fundamental mode even if number of power iterations is sufficiently large. This is especially true for a large geometry with high dominance ratio and is one of the root cause of underestimation of statistical uncertainty. In the present model, a fission source distribution is expanded by a series of higher order modes and their behaviors are estimated by variation of expansion coefficients at each cycle. The expansion coefficients show fluctuation due to statistical noise during a Monte Carlo calculation. By observing decay ratio of higher order modes in PWR single assembly geometry, validity of the present theoretical model is confirmed. Furthermore, behaviors of higher order mode components in PWR single or multi fuel assemblies geometry are investigated.

DOI： 10.1051/snamc/201403503

Estimation of Self-Shielding Effect on Uncertainty of Neutronics Characteristics using Random Sampling Method and Continuous-Energy Slowing-Down Calculation Reviewed International journal

A. Yamamoto, S. Sato, T. Endo

Trans. Am. Nucl. Soc. Vol. 109 page： 1436 - 1438 2013.11

Subcriticality Measurement Technique using Inherent Neutron Source in Uranium Fuel Reviewed International journal

T. Shiozawa, T. Endo, A. Yamamoto, C.H. Pyeon, T. Yagi

Trans. Am. Nucl. Soc. Vol. 109 page： 826 - 829 2013.11

Behavior of Higher Order Fission Source Distribution in Monte-Carlo Calculations Reviewed International journal

A. Yamamoto, K. Sakata, T. Endo

Trans. Am. Nucl. Soc. Vol. 109 page： 1361 - 1364 2013.11

Uncertainty and Correlation Estimation of Reload Safety Parameters of PWR using Random Sampling Method Reviewed International journal

T. Watanabe, T. Endo, A. Yamamoto, Y. Kodama, Y. Ohoka, T. Ushio

Trans. Am. Nucl. Soc. Vol. 109 page： 1365 - 1368 2013.11

Few-Group Macroscopic Cross Section Adjustment for LWRs using Random Sampling Technique Reviewed International journal

A. Yamamoto, S. Kato, T. Endo

Trans. Am. Nucl. Soc. Vol. 108 page： 894 - 897 2013.6

Study on Discontinuity Factor for Angular Flux in Transport Equation Reviewed International journal

T. Sakamoto, T. Endo, A. Yamamoto

Trans. Am. Nucl. Soc. Vol. 108 page： 887 - 890 2013.6

Reduction of Discretization Error for Ray Tracing of MOC Through a Correction on Collision Probabilities Reviewed International journal

M. Tabuchi, M. Tatsumi, A. Yamamoto, T. Endo

Proc. M&C2013 page： 1853 - 1864 2013.5

Language：English Publishing type：Research paper, summary (international conference)

A new correction model for ray tracing of the method of characteristics is proposed in order to reduce discretization error. As the ray tracing parameters such as azimuthal angle division, polar angle division and ray separation are considered in this study. In the method of characteristics, region average scalar fluxes can be implicitly expressed by collision probabilities, although these collision probabilities are not directly treated in the ordinary calculation scheme. From this viewpoint, difference between a coarse ray tracing condition and a detailed one can be interpreted as the difference in the estimation of collision probabilities. In other words, the discretization error for ray tracing can be recognized as a consequence of inaccurate collision probabilities caused by coarse ray tracing. This discussion suggests that accurate region average scalar flux can be obtained through an appropriate correction on collision probabilities. In this paper, a correction model on collision probabilities is theoretically derived based on the neutron balance equation, and its validity is confirmed through typical single assembly calculations. The effectiveness of the present correction method is also discussed in this paper. It is confirmed that discretization error for ray tracing can be significantly reduced by the present correction method in a multi-assembly calculation, though the correction factor is estimated in single assembly geometry.

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