Faculty Profiles - ENDO Tomohiro

Papers - ENDO Tomohiro

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Efficient reduced order model based on the proper orthogonal decomposition for time-dependent MOC calculations Reviewed International journal Open Access

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 60 ( 3 ) page： 343 - 357 2023.3

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

An efficient reduced order model (ROM) for time-dependent transport calculations using the method of characteristics (MOC) is proposed. In the present ROM, the flux distributions and the net neutron currents between the adjacent unstructured mesh regions are taken from the MOC solution. Then, the coefficient matrices for the MOC-equivalent diffusion equation are reconstructed from them. The proper orthogonal decomposition (POD) is applied for the MOC-equivalent diffusion equation to reduce the degree of freedoms (DOFs) using the orthogonal bases obtained by the singular value decomposition (SVD) for the sampled MOC solution. The accuracy and computation time of the present ROM are verified in the C5G7-TD 2D benchmark problem. The calculation results show that the present ROM enables us approximately 5000–6000 times faster computation than the full order model (FOM) for kinetic calculations itself in the present calculation condition. The present method can be substituted as real-time simulations without the spatial homogenization when typical flux distributions and the net neutron currents of a target problem can be precalculated.

DOI： 10.1080/00223131.2022.2097963

Nuclear data adjustment using a deterministic sampling method with unscented transformation Reviewed International journal

Yuhei Fukui, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 60 ( 3 ) page： 238 - 250 2023.3

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

A nuclear data adjustment method using a deterministic sampling method based on an unscented transform was developed, and its validity was confirmed through a twin experiment using a critical benchmark problem. Conventional nuclear data adjustment methods require sensitivity analysis using generalized perturbation theory or many forward calculations using stochastically sampled nuclear data. To address this issue, this study focused on unscented transform-based sampling (UTS), which is used in uncertainty quantification. Based on the UTS, perturbed nuclear data can be deterministically sampled to reproduce the population covariance matrix with minimum sample size. Therefore, UTS can significantly reduce the computational cost compared to conventional nuclear data adjustment using random sampling (RS). Furthermore, the UTS was improved to prevent the sampling of negative nuclear data while accurately reproducing the population covariance matrix. The proposed method was applied to the numerical experiment of Godiva, and the adjusted nuclear data were compared with those obtained using conventional methods. Consequently, it was demonstrated that UTS can adjust nuclear data at a lower computational cost than RS.

DOI： 10.1080/00223131.2022.2095051

Implementation of Resonance Upscattering Treatment in FRENDY Nuclear Data Processing System Reviewed International journal

Akio Yamamoto, Tomohiro Endo, Go Chiba, Kenichi Tada

Nuclear Science and Engineering Vol. 196 ( 11 ) page： 1267 - 1279 2022.11

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

The resonance upscattering effect (the thermal agitation effect) is implemented in the generation capability of multigroup neutron cross sections of the FRENDY nuclear data processing system. The resonance upscattering effect is considered by (1) the variation of self-shielding factors (effective cross sections) due to the change in the ultra-fine group spectrum and (2) the variation of group-to-group elastic scattering cross sections. Since the upscattering effect is considered in the ultra-fine group spectrum calculation, an iteration calculation is necessary to consider the upscattering. The impacts of the iteration strategy (Jacobi or Gauss-Seidel), as well as the number of iterations, are discussed. In the verification calculations, impacts on the ultra-fine group spectrum, effective cross sections, and neutronics characteristics (the Doppler effect) are confirmed. The effect of energy group structure and the impact of resonance upscattering treatments on the Doppler effect through the variation of effective cross sections and the elastic scattering matrix are investigated. The results indicate that FRENDY can provide appropriate multigroup cross sections considering the resonance upscattering effect.

DOI： 10.1080/00295639.2022.2087833

Sensitivity Coefficient Evaluation of an Accelerator-Driven System Using ROM-Lasso Method Invited Reviewed International journal

Ryota Katano, Akio Yamamoto, Tomohiro Endo

Nuclear Science and Engineering Vol. 196 ( 10 ) page： 1194 - 1208 2022.10

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

We propose the use of reduced-order modeling to improve the sensitivity coefficient evaluation method based on Lasso-type penalized linear regression. In this method, cross sections of interest are uniformly randomly sampled, and corresponding perturbed core analyses are performed. The sensitivity coefficients of the higher-dimensional model are expanded by the active subspace (AS) attained by the lower-dimensional model, and the expansion coefficients are estimated by the Lasso regression. In addition, AS bases can be flexibly chosen according to neutronics parameters of interest. We conducted a verification calculation for an accelerator-driven system and clarified that the proposed method successfully reduces the calculation cost by a couple of orders of magnitude compared with the direct method. The proposed method can be used to practically evaluate the sensitivity coefficients of various parameters.

DOI： 10.1080/00295639.2022.2067447

Improvements in Computational Efficiency for Resonance Calculation Using Energy Spectrum Expansion Method Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Koji Asano

Nuclear Science and Engineering Vol. 196 ( 7 ) page： 769 - 791 2022.7

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

Improvements in computational efficiency for the Resonance calculation using energy Spectrum Expansion (RSE) method are proposed in order to increase the applicability of the method for core nuclear analyses. First, efficient treatment of the neutron source for the RSE method has been newly developed. This is a balanced approach from the viewpoints of computation time and memory size, in comparison with the other approaches mentioned in a previous study [R. KONDO et al., “A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model,” Nucl. Sci. Eng., 195, 694 (2021)]. Second, low-rank approximation has been applied to the RSE method considering the deficit ratio of the singular value for the orthogonal basis. Computation time was reduced by ~68% while maintaining sufficient accuracy of effective cross sections. Third, the impacts of the discretization parameters in the method of characteristics on the RSE method have been investigated, and coarser conditions of the parameters were found to be appropriate from the viewpoints of computation time and accuracy of effective cross sections. Finally, RSE calculations with these improvements have been performed for the fuel assembly geometry of a light water reactor. The computation time was reduced by ~70%, and the data size of the scattering cross-section moments was approximately 3900 times smaller in comparison with the RSE calculation without the improvements.

DOI： 10.1080/00295639.2021.2025297

Impact of Angular and Spatial Source Distribution Approximations on Convergence Performance of Nonlinear Acceleration Methods for MOC in Slab Geometry Reviewed International journal

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 196 ( 4 ) page： 379 - 394 2022.4

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

The convergence performance of nonlinear acceleration methods for the method of characteristics (MOC) with flat source (FS) approximation (FS MOC) or linear source (LS) approximation (LS MOC) is numerically investigated by focusing on the spatial and angular approximations in the acceleration calculations. The convergence of nonlinear acceleration depends on the consistency of the calculation models between the higher-order and lower-order (acceleration) methods. The convergence of four acceleration methods is evaluated to clarify the relationship between model consistency and convergence performance. These methods consist of FS or LS for the spatial source distribution and P1 or discrete angle for the angular distribution, i.e., (1) FS analytic coarse mesh finite difference (ACMFD) acceleration (FS ACMFD), (2) LS ACMFD, (3) FS angular-dependent discontinuity factor MOC (ADMOC) acceleration (FS ADMOC), and (4) LS ADMOC. The ACMFD and ADMOC accelerations are based on P1 and discrete angle approximations, respectively. The FS MOC and LS MOC are considered higher-order methods. The FS MOC and LS MOC with five acceleration methods, i.e., the aforementioned four acceleration methods and the conventional coarse mesh finite difference acceleration method, are used to perform fixed-source calculations in one-group one-dimensional homogeneous slab geometry, and the spectral radii are numerically evaluated. The numerical results indicate that (1) the nonlinear acceleration methods that are unconditionally stable for FS MOC also show similar convergence properties for LS MOC in one-dimensional slab geometry; (2) better convergence is observed when the consistency of higher- and lower-order models is high; and (3) when a coarse mesh is optically thick, the spatial homogenization degrades the convergence performance, even if spatial and angular approximations are consistent between the higher- and lower-order models.

DOI： 10.1080/00295639.2021.1982549

Applicability of Dynamic Mode Decomposition to Estimate Fundamental Mode Component of Prompt Neutron Decay Constant from Experimental Data Reviewed International journal Open Access

Fuga Nishioka, Tomohiro Endo, Akio Yamamoto, Masao Yamanaka, Cheol Ho Pyeon

Nuclear Science and Engineering Vol. 196 ( 2 ) page： 133 - 143 2022.2

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

To robustly estimate the fundamental mode component of prompt neutron decay constant α in a subcritical system, dynamic mode decomposition (DMD) is applied to time-series data obtained by the pulsed-neutron source (PNS) and Rossi-α methods. For the statistical uncertainty quantification of α by DMD, randomly sampled virtual data are used for the DMD procedure. The applicability of DMD is demonstrated by analyzing the experimental results by the PNS and Rossi-α methods, which are performed at the Kyoto University Critical Assembly (KUCA). When applying the DMD to the PNS and Rossi-α experimental data, a constant signal was added to the experimental data to remove the background constant component. The application results indicate that DMD enables one to robustly estimate the fundamental mode component of α in the PNS and Rossi-α methods.

DOI： 10.1080/00295639.2021.1968225

Open Access

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

Akio Yamamoto, Tomohiro Endo, Kenichi Tada

Journal of Nuclear Science and Technology Vol. 58 ( 12 ) page： 1343 - 1350 2021.12

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

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

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

Kento Sawada, Akio Yamamoto, Tomohiro Endo, Chikahiro Sato, Keisuke Maeda, Sunghyon Jang

Journal of Nuclear Science and Technology Vol. 58 ( 12 ) page： 1308 - 1317 2021.12

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

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

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

Akio Yamamoto, Kenichi Tada, Go Chiba, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. 58 ( 11 ) page： 1165 - 1183 2021.11

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

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, -5α4, 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

Web of Science

Proposal and applicability of estimated criticality lower-limit multiplication factor using the bootstrap method Reviewed International journal Open Access

Takuto Hayashi, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 58 ( 9 ) page： 1008 - 1017 2021.9

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

To judge whether an application system is a subcritical state or not based on numerical results of the effective neutron multiplication factor keff, an evaluation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method is newly proposed. By utilizing numerical results of keff 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 keff due to a criticality safety analysis code, experimental uncertainty, and covariance matrix of the nuclear data library. Furthermore, the frequency distribution of keff 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 keff 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

Open Access

A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model Reviewed International journal Open Access

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto, Satoshi Takeda, Hiroki Koike, Kazuya Yamaji, Daisuke Sato

Nuclear Science and Engineering Vol. 195 ( 7 ) page： 694 - 716 2021.7

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

A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry.

DOI： 10.1080/00295639.2020.1863066

Open Access

Web of Science

Fast reproduction of time-dependent diffusion calculations using the reduced order model based on the proper orthogonal and singular value decompositions Reviewed International journal

Kosuke Tsujita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 58 ( 2 ) page： 173 - 183 2021.2

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

An efficient reduced order model (ROM) for time-dependent diffusion calculations using the proper orthogonal decomposition (POD) is proposed. Employing the singular value decomposition (SVD) and low-rank approximation (LRA) for the flux distributions sampled from the detail full order model (FOM) solutions, the orthogonal basis suitable for a target problem is numerically obtained. In the present ROM, flux distribution is expanded with an orthogonal basis on space. Then, the dimensionality reduction is performed for the neutron diffusion equation using the orthogonal basis, and the equation for the expansion coefficients is obtained. Since any flux distributions can be used to construct the orthogonal bases, different orthogonal bases calculated from different flux distribution sets are tested. The accuracy and computation time of the present ROM are verified in the TWIGL benchmark problem. The calculation results show that the present ROM is approximately 100 times faster than the FOM for kinetic calculations in the present conditions. The present method can be substituted as real-time FOM simulations when typical flux distributions of a target problem can be precalculated to represent the solution space with less degree of freedom (DOF).

DOI： 10.1080/00223131.2020.1814891

Web of Science

Compression of Cross-Section Data Size for High-Resolution Core Analysis Using Dimensionality Reduction Technique Reviewed International journal

Masato Yamamoto, Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 195 ( 1 ) page： 33 - 49 2021.1

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

Compression of cross-section data used for high-resolution core analysis is performed using a dimensionality reduction technique based on the singular value decomposition (SVD) and low-rank approximation. The size of cross-section data can be a significant issue in high-resolution core analysis using detailed energy and spatial resolutions. This study addresses this issue focusing on the similarity of multigroup cross sections among different spatial regions. A data compression method using the SVD and low-rank approximation is applied for the multigroup microscopic cross sections of heterogeneous material regions obtained by a lattice physics calculation with burnup and branch calculations. Weighting by nuclide number densities and neutron spectra is considered to improve the efficiency of compression for cross sections. Single-assembly transport calculations with the method of characteristics are carried out using the original cross sections and the reconstructed cross sections after data compression. The accuracy of data compression for cross sections is evaluated by comparing the multiplication factor and multigroup scalar fluxes. The results indicate that the present data compression for microscopic cross sections can reduce approximately 99.7% of the original cross-section data size under the present calculation condition.

DOI： 10.1080/00295639.2020.1781482

Web of Science

Neutron Generation Time in Highly-Enriched Uranium Core at Kyoto University Critical Assembly Reviewed International journal Open Access

Cheol Ho Pyeon, Masao Yamanaka, Tomohiro Endo, Go Chiba, Willem F. G Van Rooijen, Kenichi Watanabe

Nuclear Science and Engineering Vol. 194 ( 12 ) page： 1116 - 1127 2020.12

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

At the Kyoto University Critical Assembly experiments on kinetics parameters are carried out at near-critical configurations, supercritical and subcritical states, in the thermal neutron spectrum made with a highly enriched uranium fuel. The main calculated kinetics parameters, the effective delayed neutron fraction (βeff) and the neutron generation time (Ʌ), are used effectively for the estimation of experimental parameters, and the accuracy of experiments on prompt neutron decay constant (α) and subcriticality (ρ_dollar) in dollar units is attained by the numerical results of βeff and Ʌ. Furthermore, the value of βeff/Ʌ is experimentally deduced with the use of the experimental results of α and ρ_dollar, ranging between 250 and −80 pcm. Thus, the experimentally deduced values of βeff/Ʌ that reveal good accuracy through a comparison with those by the MCNP6.1 calculations with JENDL-4.0 are then taken as an index of Ʌ by introducing an acceptable assumption of βeff at near-critical configurations. From the results of experimental and numerical analyses, the experimental value of βeff/Ʌ is important for the validation of Ʌ since kinetics parameters are successfully obtained from the clean cores of near-critical configurations in the thermal neutron spectrum.

DOI： 10.1080/00295639.2020.1774230

Web of Science

Applicability of a reduced order model for a safety analysis code to statistical safety analysis Reviewed International journal

Masaki Matsushita, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 57 ( 12 ) page： 1307 - 1318 2020.12

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

A reduced order model (ROM) for a safety analysis code (RELAP/SCDAPSIM) is developed and is applied to the statistical safety analysis in order to reduce computational load. The ROM that reproduces output of the safety analysis code (e.g., the peak cladding temperature) is constructed using the singular value decomposition and the low-rank approximation for time-series data of a safety analysis code. A sampling method that incorporates dissimilarity among input data is tested to generate training data for the ROM. A loss of coolant accident with multiple failures of safety functions in a BWR is considered as an accident scenario. Statistical results such as the average, the standard deviation, and the 95% cumulative probability value of safety parameters obtained by the ROM and those obtained by the safety analysis code are compared. The reference results obtained by the direct random sampling method with the safety analysis code are within the 95% confidence interval of the results obtained by ROM. Thus the applicability and effectiveness of the ROM to the statistical safety analysis are confirmed through numerical analysis.

DOI： 10.1080/00223131.2020.1783382

Web of Science

Implementation of the unscented transformation with low rank approximation in uncertainty analysis during large-break loss of coolant accident Reviewed International journal

Basma Foad, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 146 page： 107614 2020.10

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

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

Web of Science

Uncertainty and regression analysis of the MSLB accident in PWR based on unscented transformation and low rank approximation Reviewed International journal

Basma Foad, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 143 page： 107493 2020.8

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

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

Web of Science

Efficient uncertainty quantification for PWR during LOCA using unscented transform with singular value decomposition Reviewed International journal

Basma Foad, Akio Yamamoto, Tomohiro Endo

Annals of Nuclear Energy Vol. 141 page： 107341 2020.6

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

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

Web of Science

Scopus

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

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto, Yasuhiro Kodama, Yasunori Ohoka, Hiroaki Nagano

Nuclear Science and Engineering Vol. 194 ( 6 ) page： 477 - 491 2020.6

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

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

Web of Science

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Papers - ENDO Tomohiro