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Verification of the multi-group generation capability of FRENDY nuclear data processing code for recent nuclear data through comparison of one-group reaction rates

Yamamoto A., Tada K., Chiba G., Endo T.

Transactions of the American Nuclear Society 124 巻 ( 1 ) 頁： 544 - 547 2021年

Adaptive setting of background cross sections for generation of effective multi-group cross sections in FRENDY nuclear data processing code

Yamamoto A., Endo T., Tada K.

Journal of Nuclear Science and Technology 58 巻 ( 12 ) 頁： 1343 - 1350 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

An adaptive setting method of background cross sections is implemented to FRENDY/MG, which is a multi-group neutron cross section generation module, for accurate interpolation of self-shielding factors with a minimum number of background cross sections. Since the dependence of self-shielding factors on background cross section is significantly different among energy group, reaction type, and nuclide, appropriate setting of background cross sections usually requires considerable works. In the present adaptive setting method, the range of background cross section is initially divided into 10 equal intervals and unnecessary background cross section points are eliminated. Then interpolation accuracy at each interval is tested. If the interpolation accuracy in an interval is not sufficient, the interval is successively halved until sufficient interpolation accuracy is obtained. For accurate interpolation of self-shielding factor or reaction rates, the monotone cubic interpolation is used. Verification calculations are carried out for all isotopes in JENDL-4.0. Calculation results indicate that the present method provides an appropriate set of background cross sections while satisfying input error tolerance for self-shielding factors or reaction rates. Typical numbers of background cross sections are from 10 to 25 when the monotone cubic interpolation and error tolerance of 0.01 for self-shielding factors are used.

DOI： 10.1080/00223131.2021.1944930

Proposal and applicability of estimated criticality lower-limit multiplication factor using the bootstrap method

Hayashi T., Endo T., Yamamoto A.

Journal of Nuclear Science and Technology 58 巻 ( 9 ) 頁： 1008 - 1017 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

To judge whether an application system is a subcritical state or not based on numerical results of the effective neutron multiplication factor (Formula presented.), an evaluation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method is newly proposed. By utilizing numerical results of (Formula presented.) for critical benchmark-problems that are selected depending on neutronic similarity to the application system, the ECLLMF should be carefully and conservatively estimated based on uncertainties of (Formula presented.) due to a criticality safety analysis code, experimental uncertainty, and covariance matrix of the nuclear data library. Furthermore, the frequency distribution of (Formula presented.) for these problems does not necessarily obey an ideal normal distribution. Using a resampling technique called ‘bootstrap method,’ the proposed method can reasonably estimate the ECLLMF considering the uncertainties and nuclear data-induced correlation between each critical benchmark-problem without the assumption of normality. To investigate the applicability of the proposed method, the approach-to-criticality experiment was carried out at the Kyoto University Critical Assembly (KUCA). Comparison of numerical results of (Formula presented.) and the ECLLMF using the bootstrap method indicated that the proposed method was able to judge an actual subcritical core as subcritical state.

DOI： 10.1080/00223131.2021.1902416

Multi-group neutron cross section generation capability for FRENDY nuclear data processing code

Yamamoto A., Tada K., Chiba G., Endo T.

Journal of Nuclear Science and Technology 58 巻 ( 11 ) 頁： 1165 - 1183 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

The multi-group cross-section generation capability for neutrons is implemented in the FRENDY nuclear data processing code. ACE-formatted files are used as the source of nuclear data instead of ENDF-formatted files since FRENDY already has the capability to generate pointwise cross sections in the ACE format. The several distinguished features are implemented for the multi-group generation capability, e.g. explicit consideration of resonance interference effect among nuclides, enhanced resonance treatment for various nuclear reactions, and accurate numerical integration of thermal cross sections. Verification calculations of the newly implemented capability are carried out through the comparison with the NJOY nuclear data processing code. Cross-section generations for all nuclides in JENDL-4.0, -4.0u, - (Formula presented.), ENDF/B-VII.1, -VIII.0, JEFF-3.3, and TENDL-2019 are carried out without unexpected processing issues, except for Pu-238 of TENDL-2019 that includes inconsistent data. The verification results indicate that the multi-group cross sections generated by FRENDY are consistent with those generated by NJOY. Now FRENDY can generate not only the pointwise cross sections for continuous energy Monte-Carlo codes but also the multi-group cross sections for deterministic neutronics analysis codes.

DOI： 10.1080/00223131.2021.1921631

Application of continuous Markov-chain Monte-Carlo method to multi-unit risk evaluations considering interdependence of accident progression among multiple units

Sawada K., Yamamoto A., Endo T., Sato C., Maeda K., Jang S.

Journal of Nuclear Science and Technology 58 巻 ( 12 ) 頁： 1308 - 1317 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Journal of Nuclear Science and Technology

The accident in Fukushima Dai-ichi nuclear power plants reconfirms the necessity of the safety assessment considering multiple nuclear reactor units. However, consideration of the interdependency among safety systems or events in multiple units as well as the time dependency of accident progressions is difficult in the conventional event tree method, which is widely used in probabilistic risk assessments. Recently, the continuous Markov-chain Monte-Carlo (CMMC) method coupled with a plant safety analysis or a severe accident analysis code has been paid attention to address these issues. In the present study, the CMMC coupling method is applied to the risk assessment of multiple units to clarify the benefits and issues to be resolved of this method. Since the CMMC coupling method requires many executions of an accident analysis code, a meta-model that simplifies systems and physical phenomena in accidents is used in this study to reduce computational cost. Furthermore, the inverse transform sampling method is newly adapted. Numerical analyses of BWR accident under station blackout with loss of cooling capability are carried out considering the correlation among the availabilities of mitigation systems. The results suggested that the CMMC coupling method can quantitatively treat the interdependency and time dependency among events in multiple units.

DOI： 10.1080/00223131.2021.1940341

Application of Regionwise Even-Parity Discontinuity Factor to the Multigroup Analog Monte-Carlo Method

Oshima Y., Endo T., Yamamoto A., Aizawa N.

Transactions of the American Nuclear Society 125 巻 ( 1 ) 頁： 904 - 907 2021年

Verification of Medium-Wise Multi-Group Cross Section Calculation Capability of FRENDY/MG

Chiba G., Yamamoto A.

Transactions of the American Nuclear Society 125 巻 ( 1 ) 頁： 934 - 937 2021年

Dimension-reduced Nuclear Data Adjustment Method based on the Bayesian Monte-Carlo Method

Fukui Y., Endo T., Yamamoto A.

Transactions of the American Nuclear Society 125 巻 ( 1 ) 頁： 900 - 903 2021年

THEORETICAL DERIVATION OF UNIQUE COMBINATION-NUMBER FOR HIGHER ORDER NEUTRON CORRELATION FACTORS BASED ON PÁL-BELL EQUATION

Endo T., Yamamoto A.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1568 - 1576 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

The Pál-Bell equation is a master equation to describe the probability generating function (PGF) of neutron counts in the neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. Thereby, the unique combination numbers for the higher-order neutron-correlation factors for a near-critical state can be theoretically clarified. This knowledge is useful to judge whether a target system is a near-critical state or not using only a histogram (or factorial moments) of neutron counts.

DOI： 10.13182/M&C21-33627

DEVELOPMENT OF ESTIMATION METHOD FOR PROMPT NEUTRON DECAY CONSTANT USING DYNAMIC MODE DECOMPOSITION

Nishioka F., Fukui Y., Endo T., Yamamoto A., Yamanaka M., Pyeon C.H.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1719 - 1728 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

To estimate the prompt neutron decay constant α corresponding to the fundamental mode in a subcritical system, we try applying the Dynamic Mode Decomposition (DMD) to time-series data of neutron counts obtained by the pulsed-neutron source (PNS) method. In this study, we newly develop an estimation method of α with the statistical uncertainty by the DMD and the random sampling method. The applicability of the proposed method is demonstrated by analyzing a PNS experiment carried out at the Kyoto University Critical Assembly (KUCA).

DOI： 10.13182/M&C21-33631

FRENDY/MG: A MULTI-GROUP CROSS SECTION GENERATION MODULE USING ACE POINTWISE CROSS SECTIONS

Yamamoto A., Endo T., Foad B., Chiba G., Tada K.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 710 - 720 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

A generation capability of neutron multi-group cross sections is being implemented to the FRENDY nuclear data processing code, as FRENDY/MG. FRENDY/MG generates neutron multi-group cross sections for deterministic core analysis codes considering an arbitrary energy group structure. Distinguished features of FRENDY/MG are 1) use of ACE pointwise cross sections as the source of nuclear data (no evaluated nuclear data file is directly used), 2) treatment of a compound material consisting of multiple nuclides to explicitly consider the resonance interference effect. Various verifications are being carried out through the comparison with the multi-group cross sections generated by NJOY.

DOI： 10.13182/M&C21-33679

FUEL ASSEMBLY ANALYSES WITH RESONANCE CALCULATION USING ENERGY SPECTRUM EXPANSION METHOD

Kondo R., Endo T., Yamamoto A., Takeda S., Koike H., Yamaji K., Sato D.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 2219 - 2230 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

Efficient numerical algorithms for a Resonance calculation using energy Spectrum Expansion (RSE) method were proposed for a large and complicated geometry such as a fuel assembly. The RSE method can treat complicated heterogeneous geometry considering resonance interference effect among different regions. Calculation procedure of the RSE method is composed of (1)generation of ultra-fine group spectra from ultra-fine group calculations in homogeneous geometry, (2)expansion of the spectra by orthogonal basis on energy based on singular value decomposition, (3)transport calculation for expansion coefficients and (4)reconstruction of ultra-fine group spectra in target heterogeneous regions by the expansion coefficients and the orthogonal basis. In this study, the efficient numerical algorithms for the RSE method were developed and applied. The algorithms are composed of (i)scattering source calculation by the combination of conventional slowing down and moment-to-moment transfer calculations, and (ii)matrix exponential generation in transport calculation of the RSE method with method of characteristics by diagonalization using eigenvalue decomposition. Through numerical verification, it was confirmed that effective multi-group cross sections by the RSE method with the new algorithms are well agreed with those by direct ultra-fine group calculation in the fuel assembly geometry. The RSE method with the new algorithms is applicable to the fuel assembly analysis.

DOI： 10.13182/M&C21-33621

IMPLEMENTATION OF A RESONANCE CALCULATION USING ENERGY SPECTRUM EXPANSION METHOD INTO HETEROGENEOUS TRANSPORT CALCULATION CODE GALAXY-Z

Yamaji K., Koike H., Ieyama K., Sato D., Yamamoto A., Takeda S.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1982 - 1991 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

A resonance calculation using the energy spectrum expansion (RSE) method has been developed in order to efficiently treat complicated heterogeneous geometry and resonance interference effect among both nuclides and regions. The three-dimensional (3D) heterogeneous transport calculation code GALAXY-Z developed by Mitsubishi Heavy Industries Ltd. uses the RSE method as resonance calculation method. In this study, resonane calculations of the GALAXY-Z code using the RSE method were performed and showed good agreements of nuclear characteristics with the ultra-fine-group method in wide range of moderator density for actual PWR fuel specifications. The GALAXY-Z code using the RSE method is applicable with high accuracy to generation of nuclear constants in normal operations and accident conditions including low moderator density conditions and can siginificantly reduce computational memory in comparison with the ultra-fine-group method.

DOI： 10.13182/M&C21-33788

S2 Consistent Analytic CMFD Acceleration for Method of Characteristics

Oshima Y., Yamamoto A., Endo T.

Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 頁： 1840 - 1849 2021年

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

A coarse mesh finite-difference (CMFD) acceleration consistent with the S2 discrete ordinate method using the step-characteristics is proposed. The analytically derived finite-difference formulation for diffusion theory (ACMFD), which is theoretically consistent with the discrete ordinate method in one-dimensional slab geometry with the S2 Gauss-Legendre quadrature, is used for the acceleration of a transport calculation. Our numerical calculations in simple geometry revealed that the consistent treatment of scattering source distribution in the ACMFD acceleration has a significant impact on the convergence property. Further, the linearized Fourier analysis of ACMFD acceleration shows the same convergence property as numerical calculations. These numerical and theoretical analyses show that the S2- consistent ACMFD acceleration is unconditionally stable without any correction to the diffusion coefficient.

DOI： 10.13182/M&C21-33737

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant

Endo T., Yamamoto A.

Nuclear Science and Engineering 194 巻 ( 11 ) 頁： 1089 - 1104 2020年11月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The prompt neutron decay constant (Formula presented.) in a steady-state subcritical system can be directly measured using a reactor noise analysis method such as the Feynman- (Formula presented.) method. To reduce the nuclear data–induced uncertainty of (Formula presented.) for a target system, this study investigates the applicability of data assimilation techniques, i.e., the bias factor method and the cross-section adjustment method, based on a subcritical measurement of (Formula presented.) conducted at Kyoto University Critical Assembly (KUCA). The sensitivity coefficients of (Formula presented.) and (Formula presented.) with respect to the nuclear data were efficiently estimated using a deterministic SN transport code with first-order perturbation theory. As a result, the a priori relative uncertainty of (Formula presented.) due to the 56-group SCALE covariance data can be reduced if there is strong correlation between the measured (Formula presented.) and the target (Formula presented.). The experimental value of (Formula presented.) contributes to improving the nuclear data of total fission spectrum (Formula presented.) and total fission neutron number (Formula presented.) via strong correlations between (Formula presented.) and prompt (Formula presented.) and between (Formula presented.) and prompt (Formula presented.), by utilizing the sensitivity coefficients of (Formula presented.) with respect to prompt (Formula presented.) and (Formula presented.).

DOI： 10.1080/00295639.2020.1720499

Implementation of the unscented transformation with low rank approximation in uncertainty analysis during large-break loss of coolant accident 国際共著

Foad B., Yamamoto A., Endo T.

Annals of Nuclear Energy 146 巻 2020年10月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

The Low Rank Approximation (LRA) and Unscented Transform (UT) are integrated to produce a new algorithm having the capability to decrease the time required for the uncertainty quantification during Loss of coolant accident (LOCA) in Pressurized Water Reactors (PWR). The LRA is an efficient technique used in reducing computational cost due to its ability to perform dimensionality reduction by revealing the active or important degrees of freedom and calculate the basis of the so-called active subspace basing on the Singular Value Decomposition (SVD). For further reduction in the computational time; the UT algorithm is also implemented to generate a set of sigma points, these sigma points are the representatives of the whole probability distribution (the UT is restricted to Gaussian distribution). The main safety parameter is the maximum cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The reactivity coefficients and the covariance matrix are calculated using the SCALE 6.2 code. The present calculation model has 14-dimensions, therefore the number of sigma points needed for the SVD/UT technique is 29, and can be minimized to 5 sigma points only if the LRA/UT is used where two singular values are sufficient to reproduce/span the space thanks to the strong correlations between the reactivity coefficients.

DOI： 10.1016/j.anucene.2020.107614

Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation 国際共著

Foad B., Yamamoto A., Endo T.

Annals of Nuclear Energy 143 巻 2020年8月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

The present studies focus on the quantification of uncertainty during the main steam line break accident scenario (MSLB) in PWR, assuming that there is a failure on the feed-water regulating valve of the broken steam generator. The scenario is characterized by the associated positive Doppler and coolant density reactivities which bring the core back to critical (return-to-power). Accordingly, the input uncertainty parameters are the Doppler and coolant density reactivities taking into account the correlation matrix among the input parameters, which is calculated by SCALE 6.2 code. The main safety parameters are the maximum cladding surface temperatures and average core power during the accident which are computed by ATHLET thermal-hydraulic code. The sampling-based uncertainty technique is considered to be the most dependable technique which can be applicable to any code, however it is computationally expensive. Therefore, it is important to develop efficient techniques which are capable of reducing the calculation time. The first approach is the SVD-UT where the Unscented Transform (UT) algorithm and singular value decomposition (SVD) are combined to generate a minimal sample points. In addition, due to the strong correlation between the input reactivities, the computational time can be further reduced by implementing the Low Rank Approximation (LRA) and revealing the active subspace.

DOI： 10.1016/j.anucene.2020.107493

Applicability of a reduced order model for a safety analysis code to statistical safety analysis 査読有り

Matsushita Masaki, Endo Tomohiro, Yamamoto Akio

JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY 頁： 1-12 2020年7月

Efficient uncertainty quantification for PWR during LOCA using unscented transform with singular value decomposition 国際共著

Foad B., Yamamoto A., Endo T.

Annals of Nuclear Energy 141 巻 2020年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Annals of Nuclear Energy

This paper discusses one of the most important issues facing the regulatory body while performing the uncertainty analysis of the nuclear reactor parameter during accident conditions. This problem is the long computational time required by the statistical sampling methods to compute the uncertainty. We overcome this problem by introducing the Unscented Transform (UT) algorithm and singular value decomposition (SVD). Where both algorithms are combined (SVD/UT) to generate a set of sigma points, these sigma points are the representatives of whole probability distribution. The uncertainty quantification is performed during Loss of coolant accident in Pressurized Water Reactor (PWR), where the input variable of uncertainty is the coolant density reactivity. The SCALE 6.2 code is used for calculating the reactivity coefficients and the covariance matrix. The response variables are the peak cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The results obviously confirm the efficiency of the SVD/UT sampling in predicting the new mean values, and assure its ability to reduce the sampling size leading to a dramatic reduction of computational cost.

DOI： 10.1016/j.anucene.2020.107341

Impact of Various Parameters on Convergence Performance of CMFD Acceleration for MOC in Multigroup Heterogeneous Geometry

Oshima Y., Endo T., Yamamoto A., Kodama Y., Ohoka Y., Nagano H.

Nuclear Science and Engineering 194 巻 ( 6 ) 頁： 477 - 491 2020年6月

記述言語：英語掲載種別：研究論文（学術雑誌）出版者・発行元：Nuclear Science and Engineering

The impact of various parameters in the coarse mesh finite difference (CMFD) acceleration method on overall convergence behavior is investigated through numerical calculations using the method of characteristics (MOC). Four parameters appearing in the CMFD acceleration with MOC, i.e., scalar flux distribution in flat flux regions (FFRFlux), the scalar flux distribution in CMFD meshes (CMFDFlux), homogenized cross sections (HXSs) in CMFD meshes, and current correction factors (CCFs), are considered. Parts of these four parameters are fixed to the converged values throughout iterations in order to estimate their impact on convergence. Numerical calculations are carried out for Korea Advanced Institute of Science and Technology’s (KAIST’s) benchmark problem KAIST-2A, which is a heterogeneous and multigroup problem, and the number of outer iterations to reach convergence is evaluated. The impact of geometric heterogeneity and cross-section homogenization in the CMFD acceleration has not been considered in linearized Fourier analysis so far. The calculation results indicate that (1) convergence of HXS has little impact on the overall convergence, (2) convergence of FFRFlux is dominant followed by CCF when a CMFD mesh is optically thin, and (3) convergence of FFRFlux is dominant when a CMFD mesh is optically thick and contains many flat flux regions.

DOI： 10.1080/00295639.2020.1722512

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