• Nuclear Engineering and Technology
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• 제55권7호
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• pp.2474-2482
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• 2023

The development of fast reactors with complex designs and operation status requires more accurate and effective simulation. The Monte-Carlo method can generate multi-group cross-sections in arbitrary geometry without approximation on resonances treatment and leads to good results in combination with diffusion codes. However, in previous studies, the coupling of Monte-Carlo generated multi-group cross-sections (MC-MGXS) and transport solvers has shown relatively large biases in fast reactor problems. In this paper, the main contribution to the biases is proved to be the neglect of the angle-dependence of the total cross-sections. The flux-moment homogenization technique (MHT) is proposed to take into account this dependence. In this method, the angular dependence is attributed to the transfer cross-sections, keeping an independent form for the total sections. For the MET-1000 benchmark, the multi-group transport simulation results with MC-MGXS generated with MHT are improved by 700 pcm and an additional 120 pcm with higher order scattering. The factors that cause the residual bias are discussed. The core power distribution bias is also significantly reduced when MHT is used. It proves that the MCMGXS with MHT can be applicable with transport solvers in fast reactor analysis.

• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2112-2124
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• 2023

With the rise of economic and safety standards for nuclear reactors, new concepts of Gen-IV reactors and modular reactors showed more complex designs that challenge current tools for reactor physics analysis. A Monte Carlo (MC) two-step method was proposed in this work. This calculation scheme uses the continuous-energy MC method to generate multi-group cross-sections from heterogeneous models. The multi-group MC method, which can adapt locally-heterogeneous models, is used in the core calculation step. This calculation scheme is verified using a Gen-IV modular lead-based fast reactor (LFR) benchmark case. The influence of homogenized patterns, scatter approximations, flux separable approximation, and local heterogeneity in core calculation on simulation results are investigated. Results showed that the cross-sections generated using the 3D assembly model with a locally heterogeneous representation of control rods lead to an accurate estimation with less than 270 pcm bias in core reactivity, 0.5% bias in control rod worth, and 1.5% bias on power distribution. The study verified the applicability of multi-group cross-sections generated with the MC method for LFR analysis. The study also proved the feasibility of multi-group MC in core calculation with local heterogeneity, which saves 85% time compared to the continuous-energy MC.

• Nuclear Engineering and Technology
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• 제54권11호
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• pp.4280-4295
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• 2022

In this paper, a new multi-group neutron-gamma transport calculation code system STRAUM-MATXST for complicated geometrical problems is introduced and its development status including numerical tests is presented. In this code system, the MATXST (MATXS-based Cross Section Processor for S_N Transport) code generates multi-group neutron and gamma cross sections by processing MATXS format libraries generated using NJOY and the STRAUM (S_N Transport for Radiation Analysis with Unstructured Meshes) code performs multi-group neutron-gamma coupled transport calculation using tetrahedral meshes. In particular, this work presents the recent implementation and its test results of the Krylov subspace methods (i.e., Bi-CGSTAB and GMRES(m)) with preconditioners using DSA (Diffusion Synthetic Acceleration) and TSA (Transport Synthetic Acceleration). In addition, the Krylov subspace methods for accelerating the energy-group coupling iteration through thermal up-scatterings are implemented with new multi-group block DSA and TSA preconditioners in STRAUM.

• Nuclear Engineering and Technology
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• 제51권8호
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• pp.1871-1885
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• 2019

The deterministic MOC code STREAM of the Computational Reactor Physics and Experiment (CORE) laboratory of Ulsan National Institute of Science and Technology (UNIST), was initially designed for the calculation of pressurized water reactor two- and three-dimensional assemblies and cores. Since fast reactors play an important role in the generation-IV concept, it was decided that the code should be upgraded for the analysis of fast neutron spectrum reactors. This paper presents a coupled code - TULIP/STREAM, developed for the fast reactor assembly and core calculations. The TULIP code produces self-shielded multi-group cross-sections using a one-dimensional cylindrical model. The generated cross-section library is used in the STREAM code which solves eigenvalue problems for a two-dimensional assembly and a multi-assembly whole reactor core. Multiplication factors and steady-state power distributions were compared with the reference solutions obtained by the continuous energy Monte-Carlo code MCS. With the developed code, a sensitivity study of the number of energy groups, the order of anisotropic P_N scattering, and the multi-group cross-section generation model was performed on the k_eff and power distribution. The 2D core simulation calculations show that the TULIP/STREAM code gives a k_eff error smaller than 200 pcm and the root mean square errors of the pin-wise power distributions within 2%.

• Nuclear Engineering and Technology
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• 제52권2호
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• pp.287-295
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• 2020

Group method of data handling (GMDH) is considered one of the earliest deep learning methods. Deep learning gained additional interest in today's applications due to its capability to handle complex and high dimensional problems. In this study, multi-layer GMDH networks are used to perform uncertainty quantification (UQ) and sensitivity analysis (SA) of nuclear reactor simulations. GMDH is utilized as a surrogate/metamodel to replace high fidelity computer models with cheap-to-evaluate surrogate models, which facilitate UQ and SA tasks (e.g. variance decomposition, uncertainty propagation, etc.). GMDH performance is validated through two UQ applications in reactor simulations: (1) low dimensional input space (two-phase flow in a reactor channel), and (2) high dimensional space (8-group homogenized cross-sections). In both applications, GMDH networks show very good performance with small mean absolute and squared errors as well as high accuracy in capturing the target variance. GMDH is utilized afterward to perform UQ tasks such as variance decomposition through Sobol indices, and GMDH-based uncertainty propagation with large number of samples. GMDH performance is also compared to other surrogates including Gaussian processes and polynomial chaos expansions. The comparison shows that GMDH has competitive performance with the other methods for the low dimensional problem, and reliable performance for the high dimensional problem.

• Nuclear Engineering and Technology
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• 제46권3호
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• pp.313-342
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• 2014

A Nuclear Energy Agency (NEA), Organization for Economic Co-operation and Development (OECD) benchmark for Uncertainty Analysis in Modeling (UAM) is defined in order to facilitate the development and validation of available uncertainty analysis and sensitivity analysis methods for best-estimate Light water Reactor (LWR) design and safety calculations. The benchmark has been named the OECD/NEA UAM-LWR benchmark, and has been divided into three phases each of which focuses on a different portion of the uncertainty propagation in LWR multi-physics and multi-scale analysis. Several different reactor cases are modeled at various phases of a reactor calculation. This paper discusses Phase I, known as the "Neutronics Phase", which is devoted mostly to the propagation of nuclear data (cross-section) uncertainty throughout steady-state stand-alone neutronics core calculations. Three reactor systems (for which design, operation and measured data are available) are rigorously studied in this benchmark: Peach Bottom Unit 2 BWR, Three Mile Island Unit 1 PWR, and VVER-1000 Kozloduy-6/Kalinin-3. Additional measured data is analyzed such as the KRITZ LEU criticality experiments and the SNEAK-7A and 7B experiments of the Karlsruhe Fast Critical Facility. Analyzed results include the top five neutron-nuclide reactions, which contribute the most to the prediction uncertainty in keff, as well as the uncertainty in key parameters of neutronics analysis such as microscopic and macroscopic cross-sections, six-group decay constants, assembly discontinuity factors, and axial and radial core power distributions. Conclusions are drawn regarding where further studies should be done to reduce uncertainties in key nuclide reaction uncertainties (i.e.: $^{238}U$ radiative capture and inelastic scattering (n, n') as well as the average number of neutrons released per fission event of $^{239}Pu$).

• Nuclear Engineering and Technology
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• 제46권2호
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• pp.263-272
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• 2014

Scattering source calculations using conventional spherical harmonic expansion may require lots of computation time to treat full-coupled three-dimensional photon-electron transport in a highly anisotropic scattering medium where their scattering cross sections should be expanded with very high order (e.g., $P_7$ or higher) Legendre expansions. In this paper, we introduce a modified scattering kernel approach to avoid the unnecessarily repeated calculations involved with the scattering source calculation, and used it with parallel computing to effectively reduce the computation time. Its computational efficiency was tested for three-dimensional full-coupled photon-electron transport problems using our computer program which solves the multi-group discrete ordinates transport equation by using the discontinuous finite element method with unstructured tetrahedral meshes for complicated geometrical problems. The numerical tests show that we can improve speed up to 17~42 times for the elapsed time per iteration using the modified scattering kernel, not only in the single CPU calculation but also in the parallel computing with several CPUs.

• Nuclear Engineering and Technology
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• 제54권2호
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• pp.523-531
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• 2022

In order to study the sensitivity and the uncertainty of the Moroccan research reactor TRIGA Mark II, a model of this reactor has been developed in our ERSN laboratory for use with the N-Particle MCNP Monte Carlo transport codes (version 6). In this article, the sensitivities of the effective multiplication factor of this reactor are evaluated using the ENDF/B-VII.0, ENDF/B-VII.1 and JENDL-4.0 libraries and in 44 energy groups, for the cross sections of the fuel (U-235 and U-238) and the moderator (H-1 and O-16). However, the quantification of the uncertainty of the nuclear data is performed using the nuclear code NJOY99 for the generation and processing of covariance matrices. On the one hand, the highest uncertainty deviations, calculated using the ENDFB-VII.1 and JENDL4.0 evaluations, are 2275, 386 and 330 pcm respectively for the reactions U₂₃₅(n, f), $ U_{235}(n\bar{\nu})$ and H₁(n, γ). On the other hand, these differences are very small for the neutron reactions of O-16 and U-238. Regarding the neutron spectra, in CT-mid plane, they are very close for the three evaluations (ENDF/B-VII.0, ENDF/B-VII.1 and JENDL-4.0). These spectra present two peaks (thermal and fission) around the energies 0.05 eV and 1 MeV.

• Steel and Composite Structures
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• 제24권5호
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• pp.549-559
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• 2017

As few multi-tower single-box multi-cell cable-stayed bridges with corrugated steel webs have been built, analysis is mostly achieved by combining single-girder model, beam grillage model and solid model in support of the design. However, such analysis methods usually suffer from major limitations in terms of the engineering applications: single-girder model fails to account for spatial effect such as shear lag effect of the box girder and the relevant effective girder width and eccentric load coefficient; owing to the approximation in the principle equivalence, the plane grillage model cannot accurately capture shear stress distribution and local stress state in both top and bottom flange of composite box girder; and solid model is difficult to be practically combined with the overall calculation. The usual effective width method fails to provide a uniform and accurate "effective length" (and the codes fail to provide a unified design approach at those circumstance) considering different shear lag effects resulting from dead load, prestress and cable tension in the construction. Therefore, a novel spatial grid model has been developed to account for shear lag effect. The theoretical principle of the proposed spatial grid model has been elaborated along with the relevant illustrations of modeling parameters of composite box girder with corrugated steel webs. Then typical transverse and longitudinal shear lag coefficient distribution pattern at the side-span and mid-span key cross sections have been analyzed and summarized to provide reference for similar bridges. The effectiveness and accuracy of spatial grid analysis methods has been finally validated through a practical cable-stayed bridge.

• 대한소아치과학회지
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• 제26권2호
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• pp.284-295
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• 1999

아말감의 단점인 건전 치질 삭제와 미세 누출을 줄이기 위한 접착 아말감(bonded amalgam)에 사용되는 치과용 접착제의 접착 강도를 측정하고 파절면을 관찰하여 콤포지트 레진과 비교 평가하였다. 발거한 우전치의 순면을 직경 8mm의 원형으로 천공하여 얻은 부분을 순면이 바깥쪽으로 향하도록 아크릴릭 레진 블록에 매몰하여 상아질과 법랑질군을 각각 55개씩 준비하였다. 1군:Superbond C&B, 2군:Panavia 21, 3군:All-Bond 2, 4군:Fuji I Glass Ionomer Luting Cement, 5군:Scotchbond Multi-Purpose(Restorative Z-100)의 5개 군으로 나누어 지름 6.3mm, 깊이 1.5mm의 구멍이 뚫린 충전용 틀(mold)을 위치시키고 표면을 접착제로 처리한 후 아말감 충전을 하였다. 5군은 레진 충전 후 40초간 광중합하였다. 각 시편은 아말감 충전 24시간 후 접착 강도 측정용 기구에 장착하고 만능 시험기에서 0.2mm/min의 cross-head 속도로 하중을 가하여 시편이 탈락할 때까지의 하중값(kg)을 측정하고, 파절면을 검사하여 다음과 같은 결론을 얻었다. 1. 상아질군에서 1, 2, 4군은 5군에 비하여 통계학적으로 유의성 있게 낮은 접착 강도를 보였다(P<0.05). 2. 법랑질군에서 4군은 5군에 비하여 통계학적으로 유의성 있게 낮은 접착 강도를 보였다(P<0.05). 3. 2군에서는 상아질군에서 법랑질군에 비하여 통계학적으로 유의성 있게 낮은 접착 강도를 보였으나(P<0.05), 다른 접착제에서는 상아질군과 법랑질군에서의 접착 강도가 유의성 있는 차이를 보이지 않았다(P>0.05). 4. Cohesive failure는 1E군과 5D군에서 관찰되었고, mixed failure는 1, 5군에서 관찰되었으며, 2, 3, 4군에서는 adhesive failure만 관찰되었다.