Статті в журналах: "Homogenized cross sections"

1

Ishii, Kazuya. "Reconstruction method of homogenized cross sections." Journal of Nuclear Science and Technology 50, no. 10 (October 2013): 1011–19. http://dx.doi.org/10.1080/00223131.2013.828661.

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2

Tomatis, Daniele. "A multivariate representation of compressed pin-by-pin cross sections." EPJ Nuclear Sciences & Technologies 7 (2021): 8. http://dx.doi.org/10.1051/epjn/2021006.

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Since the 80’s, industrial core calculations employ the two-step scheme based on prior cross sections preparation with few energy groups and in homogenized reference geometries. Spatial homogenization in the fuel assembly quarters is the most frequent calculation option nowadays, relying on efficient nodal solvers using a coarse mesh. Pin-wise reaction rates are then reconstructed by dehomogenization techniques. The future trend of core calculations is moving however toward pin-by-pin explicit representations, where few-group cross sections are homogenized in the single pins at many physical conditions and many nuclides are selected for the simplified depletion chains. The resulting data model requires a considerable memory occupation on disk-files and the time needed to evaluate all data exceeds the limits for practical feasibility of multi-physics reactor calculations. In this work, we study the compression of pin-by-pin homogenized cross sections by the Hotelling transform in typical PWR fuel assemblies. The reconstruction of these quantities at different physical states of the assembly is then addressed by interpolation of only a few compressed coefficients, instead of interpolating separately each homogenized cross section. Savings in memory higher than 90% are observed, which result in important gains in runtime when interpolating the few-group data.

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3

Price, Dean, Thomas Folk, Matthew Duschenes, Krishna Garikipati, and Brendan Kochunas. "Methodology for Sensitivity Analysis of Homogenized Cross-Sections to Instantaneous and Historical Lattice Conditions with Application to AP1000® PWR Lattice." Energies 14, no. 12 (June 8, 2021): 3378. http://dx.doi.org/10.3390/en14123378.

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In the two-step method for nuclear reactor simulation, lattice physics calculations are performed to compute homogenized cross-sections for a variety of burnups and lattice configurations. A nodal code is then used to perform full-core analysis using the pre-calculated homogenized cross-sections. One source of uncertainty introduced in this method is that the lattice configuration or depletion conditions typically do not match a pre-calculated one from the lattice physics simulations. Therefore, some interpolation model must be used to estimate the homogenized cross-sections in the nodal code. This current study provides a methodology for sensitivity analysis to quantify the impact of state variables on the homogenized cross-sections. This methodology also allows for analyses of the historical effect that the state variables have on homogenized cross-sections. An application of this methodology on a lattice for the Westinghouse AP1000® reactor is presented where coolant density, fuel temperature, soluble boron concentration, and control rod insertion are the state variables of interest. The effects of considering the instantaneous values of the state variables, historical values of the state variables, and burnup-averaged values of the state variables are analyzed. Using these methods, it was found that a linear model that only considers the instantaneous and burnup-averaged values of state variables can fail to capture some variations in the homogenized cross-sections.

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4

Hua, Guowei, Yunzhao Li, and Sicheng Wang. "PWR pin-homogenized cross-sections analysis using big-data technology." Progress in Nuclear Energy 121 (March 2020): 103228. http://dx.doi.org/10.1016/j.pnucene.2019.103228.

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5

Truffinet, Olivier, Karim Ammar, Jean-Philippe Argaud, Nicolas Gérard Castaing, and Bertrand Bouriquet. "Multi-output gaussian processes for the reconstruction of homogenized cross-sections." EPJ Web of Conferences 302 (2024): 02006. http://dx.doi.org/10.1051/epjconf/202430202006.

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Deterministic nuclear reactor simulators employing the prevalent two-step scheme often generate a substantial amount of intermediate data at the interface of their two subcodes, which can impede the overall performance of the software. The bulk of this data comprises “few-groups homogenized cross-sections” or HXS, which are stored as tabulated multivariate functions and interpolated inside the core simulator. A number of mathematical tools have been studied for this interpolation purpose over the years, but few meet all the challenging requirements of neutronics computation chains: extreme accuracy, low memory footprint, fast predictions… We here present a new framework to tackle this task, based on multi-outputs gaussian processes (MOGP). This machine learning model enables us to interpolate HXS’s with improved accuracy compared to the current multilinear standard, using only a fraction of its training data – meaning that the amount of required precomputation is reduced by a factor of several dozens. It also necessitates an even smaller fraction of its storage requirements, preserves its reconstruction speed, and unlocks new functionalities such as adaptive sampling and facilitated uncertainty quantification. We demonstrate the efficiency of this approach on a rich test case reproducing the VERA benchmark, proving in particular its scalability to datasets of millions of HXS.

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6

Truffinet, Olivier, Karim Ammar, Jean-Philippe Argaud, Nicolas Gérard Castaing, and Bertrand Bouriquet. "Adaptive sampling of homogenized cross-sections with multi-output gaussian processes." EPJ Web of Conferences 302 (2024): 02010. http://dx.doi.org/10.1051/epjconf/202430202010.

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In another talk submitted to this conference, we presented an efficient new framework based on multi-outputs gaussian processes (MOGP) for the interpolation of few-groups homogenized cross-sections (HXS) inside deterministic core simulators. We indicated that this methodology authorized a principled selection of interpolation points through adaptive sampling. We here develop this idea by trying simple sampling schemes on our problem. In particular, we compare sample scoring functions with and without integration of leave-one-out errors, and obtained with single-output and multi-output gaussian process models. We test these methods on a realistic PWR assembly with gadolinium-added fuel rods, comparing them with non-adaptive supports. Results are promising, as the sampling algorithms allow to significantly reduce the size of interpolation supports with almost preserved accuracy. However, they exhibit phenomena of instability and stagnation, which calls for further investigation of the sampling dynamics and trying other scoring functions for the selection of samples.

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7

Nguyen, Dinh Quoc Dang, and Emiliano Masiello. "Representation of few-group homogenized cross section by multi-variate polynomial regression." EPJ Web of Conferences 302 (2024): 02002. http://dx.doi.org/10.1051/epjconf/202430202002.

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In this paper, a representation of few-group homogenized cross section by multi-variate polynomial regression is presented. The method is applied on the few-group assembly homogenized cross sections of the assembly 22UA from the benchmark X2VVER[1], generated by the lattice transport code APOLLO3®[2], and conducted over a Cartesian grid of parametric state-points. The regression model [3, 4] allow to input a significantly larger number of points for training compared to the number of monomials, thus yielding higher accuracy than polynomial interpolation without being affected by the choice of points in the training set. Additionally, it can reduce data preparation time because the size of the training set can be smaller than the number of points in the complete Cartesian grid, while still providing a good approximation. Furthermore, its evaluation algorithm can be adapted for GPU utilization, similar to polynomial interpolation with the Newton method [5].

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8

Szames, E., K. Ammar, D. Tomatis, and J. M. Martinez. "FEW-GROUP CROSS SECTIONS MODELING BY ARTIFICIAL NEURAL NETWORKS." EPJ Web of Conferences 247 (2021): 06029. http://dx.doi.org/10.1051/epjconf/202124706029.

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This work deals with the modeling of homogenized few-group cross sections by Artificial Neural Networks (ANN). A comprehensive sensitivity study on data normalization, network architectures and training hyper-parameters specifically for Deep and Shallow Feed Forward ANN is presented. The optimal models in terms of reduction in the library size and training time are compared to multi-linear interpolation on a Cartesian grid. The use case is provided by the OECD-NEA Burn-up Credit Criticality Benchmark [1]. The Pytorch [2] machine learning framework is used.

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9

Griso, Georges, Larysa Khilkova, Julia Orlik, and Olena Sivak. "Asymptotic Behavior of Stable Structures Made of Beams." Journal of Elasticity 143, no. 2 (February 5, 2021): 239–99. http://dx.doi.org/10.1007/s10659-021-09816-w.

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AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

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10

Wang, Qiudong, Ding She, Bing Xia, and Lei Shi. "Evaluation of pebble-bed homogenized cross sections in HTGR fuel cycle simulations." Progress in Nuclear Energy 117 (November 2019): 103041. http://dx.doi.org/10.1016/j.pnucene.2019.103041.

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11

Hernandez-Solis, Augusto, Yohannes Molla, Edoaurd Malambu, Alexey Stankovskiy, and Gert Van den Eynde. "VERIFICATION OF THE OpenMC HOMOGENIZED MYRRHA-1.6 CORE MODEL." EPJ Web of Conferences 247 (2021): 04002. http://dx.doi.org/10.1051/epjconf/202124704002.

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The OpenMC code is being employed both as a multi-group nodal macroscopic cross-section generator and a reference multi-group Monte Carlo (MGMC) solution. The aim is to do a neutronic benchmark verification study versus a deterministic model (based on the MYRRHA-1.6 core) performed by the PHISICS simulator. MYRRHA, a novel research accelerator driven system concept that is also foreseen to work as a critical configuration, offers a rich opportunity of testing state-of-the art methods for reactor physics analysis due to its strong heterogeneous configuration utilized for both thermal and fast spectra irradiation purposes. The original core configuration representing MYRRHA-1.6 and formed by 169 assemblies, was launched in OpenMC for producing a homogenous nodal model that, when executed in its multi-group Monte Carlo mode, it produced a keff that differs in almost 500 pcm from the original case. This means that in the future, such approximation should correct the nodal cross-sections to preserve the reaction rates in order to match those ones from the heterogeneous model. Nevertheless, such MGMC mode of operation offered by OpenMC could be exploited in order to verify deterministic core simulators. By inputting the same nodal multi-group cross-section model into the transport solver of the PHISICS toolkit, the neutronic benchmark showed a difference of 171 pcm in eigenvalue while comparing it to its OpenMC MGMC counterpart. Also, local multi-group and energy-integrated nodal profiles of the neutron flux showed a maximum relative difference between methodologies of 15% and 1%, respectively. This means that the MGMC capabilities offered by OpenMC can be employed to verify other deterministic methodologies.

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12

Szames, E., K. Ammar, D. Tomatis, and J. M. Martinez. "FEW-GROUP CROSS SECTIONS LIBRARY BY ACTIVE LEARNING WITH SPLINE KERNELS." EPJ Web of Conferences 247 (2021): 06012. http://dx.doi.org/10.1051/epjconf/202124706012.

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This work deals with the representation of homogenized few-groups cross sections libraries by machine learning. A Reproducing Kernel Hilbert Space (RKHS) is used for different Pool Active Learning strategies to obtain an optimal support. Specifically a spline kernel is used and results are compared to multi-linear interpolation as used in industry, discussing the reduction of the library size and of the overall performance. A standard PWR fuel assembly provides the use case (OECD-NEA Burn-up Credit Criticality Benchmark [1]).

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13

Guo, Hui, Yuyang Shen, Yiwei Wu, Qufei Song, and Hanyang Gu. "Generating multi-group cross-sections using continuous-energy Monte Carlo method for fast reactor analysis." EPJ Web of Conferences 302 (2024): 02003. http://dx.doi.org/10.1051/epjconf/202430202003.

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The deterministic two-step method, comprising multigroup cross-section generation and core calculation, is widely applied in fast reactor design and analysis. Monte Carlo (MC) methods with continuous energy and fine geometry provide high-precision cross-sections essential for advanced fast reactor neutronics analysis. This paper presents an analysis of integrating MC-generated homogenized cross-sections with various core solvers, demonstrating their effectiveness and potential improvements in fast reactor simulations. For diffusion core calculations, the superhomogénéisation (SPH) technique reduces control rod worth overestimation from 13.5% to 0.35% in the MET-1000 benchmark, improving power distribution predictions. In transport core calculations, the flux-moment homogenization technique (MHT) addresses reactivity overestimation by incorporating cross-section anisotropy, reducing error by 698 pcm. For Method of Characteristics (MOC) core calculations, transport-corrected multigroup cross-sections yield high precision in pin-by-pin power distribution for a 100 MWe lead-based fast reactor benchmark. While MC methods require significant computational resources, such as 62 CPU-hours for the MET-1000 core and 85.5 CPU-hours for the 100 MWe lead-based fast reactor core, they offer flexibility in geometry modeling. This work highlights MC multigroup cross-section generation methods applicable to diffusion, MOC, and transport core calculations for fast reactor analysis, suggesting further exploration into their performance in various reactor parameters and computational efficiency.

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14

Suk, Pavel. "ADVANCED HOMOGENIZATION METHODS FOR PRESSURIZED WATER REACTORS." Acta Polytechnica CTU Proceedings 19 (December 14, 2018): 14. http://dx.doi.org/10.14311/app.2018.19.0014.

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Macroscopic cross section generation is key part of core calculation. Commonly, the data are prepared independently without a knowledge of fuel loading pattern. The fuel assemblies are simulated in infinite lattice (with mirror boundary conditions). Rehomogenization method is based on combination of actual neutron flux in fuel assembly with macroscopic data from infinite lattice. Rehomogenization method was implemented into the macrocode Andrea and tested on a reference cases. Cases consist of fuel cases, cases with strong absorber, cases with absorption rods, or cases with reflector assemblies. Testing method is based on a comparisons of homogenized and rehomogenized macroscopic cross sections and later on a comparisons of relative power of each fuel assembly. Above that there is comparison of eigenvalue.

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15

Han, Tae-Young, Jin-Young Cho, Chang-Keun Jo, and Hyun-Chul Lee. "Extension of Pin-Based Point-Wise Energy Slowing-Down Method for VHTR Fuel with Double Heterogeneity." Energies 14, no. 8 (April 14, 2021): 2179. http://dx.doi.org/10.3390/en14082179.

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For the resonance treatment of a very high temperature reactors (VHTR) fuel with the double heterogeneity, an extension of the pin-based pointwise energy slowing-down method (PSM) was developed and implemented into DeCART. The proposed method, PSM-double heterogeneity (DH), has an improved spherical unit cell model with an explicit tri-structural isotropic (TRISO) model, a matrix layer, and a moderator for reflecting the moderation effect. The moderator volume was analytically derived using the relation of the Dancoff factor and the mean chord length. In the first step, the pointwise homogenized cross-sections for the compact was obtained after solving the slowing down equation for the spherical unit cell. Then, the shielded cross-section for the homogenized fuel compact was generated using the original PSM. The verification calculations were performed for the fuel pins with various packing fractions, compact sizes, TRISO sizes, and fuel temperatures. Additionally, two fuel block problems with very different sizes were examined and the depletion calculation was carried out for investigating the accuracy of the proposed method. They revealed that the PSM-DH has a good performance in the VHTR problems.

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16

Ardiansyah, H., V. Seker, T. Downar, S. Skutnik, and W. Wieselquist. "Evaluation of PBMR-400 Core Design Steady State Condition with Serpent and AGREE." Journal of Physics: Conference Series 2048, no. 1 (October 1, 2021): 012024. http://dx.doi.org/10.1088/1742-6596/2048/1/012024.

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Abstract The significant recent advances in computer speed and memory have made possible an increasing fidelity and accuracy in reactor core simulation with minimal increase in the computational burden. This has been important for modeling some of the smaller advanced reactor designs for which simplified approximations such as few groups homogenized diffusion theory are not as accurate as they were for large light water reactor cores. For narrow cylindrical cores with large surface to volume ratios such the Ped Bed Modular Reactor (PBMR), neutron leakage from the core can be significant, particularly with the harder neutron spectrum and longer mean free path than a light water reactor. In this paper the core from the OECD PBMR-400 benchmark was analyzed using multigroup Monte Carlo cross sections in the HTR reactor core simulation code AGREE. Homogenized cross sections were generated for each of the discrete regions of the AGREE model using a full core SERPENT Monte Carlo model. The cross sections were generated for a variety of group structures in AGREE to assess the importance of finer group discretization on the accuracy of the core eigenvalue and flux predictions compared to the SERPENT full core Monte Carlo solution. A significant increase in the accuracy was observed by increasing the number of energy groups, with as much as a 530 pcm improvement in the eigenvalue calculation when increasing the number of energy groups from 2 to 14. Significant improvements were also observed in the AGREE neutron flux distributions compared to the SERPENT full core calculation.

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17

Hwang, Dae Hee, and Ser Gi Hong. "SMALL MODULAR PWR DESIGN FOR TRU RECYCLING WITH McCARD-MASTER TWO-STEP PROCEDURE." EPJ Web of Conferences 247 (2021): 01003. http://dx.doi.org/10.1051/epjconf/202124701003.

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In our previous study, a small modular PWR core was designed for TRU (Transuranics) recycling with multi-recycling scheme with a typical two-step procedure using DeCART2D/MASTER code system in which the lattice analysis for producing homogenized group constant was performed by DeCART2D while whole core analysis was conducted by MASTER code. However, the neutron spectrum hardening of the LWR core loaded with TRU requires validating the multi-group cross section library and resonance self-shielding treatment method in lattice calculation. In this study, a new procedure using McCARD/MASTER was used to analyze the SMR core, in which the lattice calculation was performed by a Monte Carlo code called McCARD with a continuous energy library to generate homogenized two-group assembly cross sections. The SMR core analysis was performed to show neutronic characteristics and TRU mass flow in the SMR core with TRU multi-recycling. The result shows that the analyses on the neutronic characteristics and TRU mass flow using the McCARD/MASTER code system showed good agreement with the previous ones using the DeCART2D/MASTER code system. The neutronic characteristics of each cycle of the core satisfied the typical limit of a commercial PWR core and the SMR core consumes effectively TRU with net TRU consumption rates of 8.46~14.33 %.

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18

Stephan, Kugler, Fotiu Peter, and Murín Justín. "On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures." Strojnícky časopis - Journal of Mechanical Engineering 69, no. 2 (June 1, 2019): 27–56. http://dx.doi.org/10.2478/scjme-2019-0016.

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AbstractThe application of first order shear beam theory in the analysis of beam structures made of functionally graded materials requires the access to homogenized stiffness quantities. These quantities depend on the cross-sectional shape and on the spatial variation of constitutive parameters. Some of these stiffness quantities can be evaluated easily by simple integration, however, the access to transverse shear stiffnesses and to stiffness quantities regarding warping torsion is typically cumbersome. In this contribution a novel approach for their evaluation is proposed, which is based on a reference beam problem. Here, we restrict ourselves to double symmetric cross-sections, however, a generalization of the proposed method to the arbitrary case is obvious. Besides that, a novel approach to cover non-uniform warping torsion is included. The proposed method is efficient, since the discretization of the cross-section suffices, and accurate as can be shown in challenging bench mark problems.

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19

Henry, Romain, Yann Périn, Kiril Velkov, and Sergei Pavlovich Nikonov. "3-D COUPLED SIMULATION OF A VVER 1000 WITH PARCS/ATHLET." EPJ Web of Conferences 247 (2021): 06015. http://dx.doi.org/10.1051/epjconf/202124706015.

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A new OECD/NEA benchmark entitled “Reactivity compensation with diluted boron by stepwise insertion of control rod cluster” is starting. This benchmark, based on high quality measurements performed at the NPP Rostov Unit 2, aims to validate and assess high fidelity multi-physics simulation code capabilities. The Benchmark is divided in two phases: assembly wise and pin-by-pin resolution of steady-state and transient multi-physics problems. Multi-physics simulation requires the generation of parametrized few-group cross-sections. This task used to be done with deterministic (2-D) lattice codes, but in the past few years the Monte-Carlo code SERPENT has demonstrate its ability to generate accurate few-group homogenized cross-section without approximations, neither on the geometry nor in the nuclear data. Since the whole core SERPENT models for production of such cross-section libraries would be computationally costly (and the standard 2-D approach may introduce unnecessary large approximations), 3-D models of each assembly type in infinite radial lattice configurations have been created. These cross-sections are then used to evaluate effective multiplication factors for different core configurations with the diffusion code PARCS. The results are compared with the reference SERPENT calculations. In the next step, a thermal-hydraulic model with the system code ATHLET applying an assembly-wise description of the core (i.e. one channel per fuel assembly) has been developed for coupled PARCS/ATHLET transient test calculations. This paper describes in detail the models and techniques used for the generation of the few-group parameterized cross section libraries, the PARCS model and the ATHLET model. Additionally, a simple exercise with coupled code system PARCS/ATHLET is presented and analysed.

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20

Nguyen, Dinh Q. D., Emiliano Masiello, and Daniele Tomatis. "MPOGen: A Python package to prepare few-group homogenized cross sections for core calculations by APOLLO3®." Nuclear Engineering and Design 417 (February 2024): 112802. http://dx.doi.org/10.1016/j.nucengdes.2023.112802.

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21

Elvira-Recuenco, M., and J. W. L. van Vuurde. "Natural incidence of endophytic bacteria in pea cultivars under field conditions." Canadian Journal of Microbiology 46, no. 11 (November 1, 2000): 1036–41. http://dx.doi.org/10.1139/w00-098.

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Pea plants grown in the field were used to study the natural incidence of endophytic bacteria in the stem. Eleven pea cultivars at the flowering stage were screened for the presence of endophytic bacteria using a printing technique with surface disinfested stem cross-sections on 5% Trypticase Soy Agar (TSA). Five cultivars showed colonization. Cultivar Twiggy showed the highest and most consistent colonization and was further investigated. Stems of cv. Twiggy at the pod stage were analyzed for endophytic bacterial types and populations. Cross-sections of surface disinfested stems were printed on 5% TSA. Endophytic bacterial populations decreased from the lower to the upper part of the stem. One section from the third and the fourth internode was surface disinfested, homogenized, and spiral plated on the media 5% TSA, R2A, and SC (Davis et al. 1980). Over a series of 30 samples, 5% TSA gave significantly better recovery of bacterial endophytes compared with R2A and SC media. For most stems, populations ranged from 104 to 105 CFU/g except in one of the field blocks in which endophyte populations were uniformly higher. Comparison of colony counts by spiral plating and printing showed a positive correlation. The most frequently recovered bacterial types were Pantoea agglomerans and Pseudomonas fluorescens. Less frequently isolated were Pseudomonas viridiflava and Bacillus megaterium.Key words: endophytic bacteria, pea, stem colonization, cultivar screening, biodiversity.

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22

Galchenko, V. V., А. М. Abdulaev, and І. І. Shlapak. "USING SOFTWARE BASED ON THE MONTE CARLO METHOD FOR RECEIVING THE FEW-GROUP HOMOGENIZED MACROSCOPIC INTERACTION CROSS-SECTIONS." Odes’kyi Politechnichnyi Universytet Pratsi, no. 3(53) (2017): 37–42. http://dx.doi.org/10.15276/opu.3.53.2017.05.

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23

Cao, Liangzhi, Yong Liu, Wei Shen, and Qingming He. "Development of a hybrid method to improve the sensitivity and uncertainty analysis for homogenized few-group cross sections." Journal of Nuclear Science and Technology 54, no. 7 (April 24, 2017): 769–83. http://dx.doi.org/10.1080/00223131.2017.1315973.

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24

Honda, Yuki, Sadao Uchikawa, and Yoshiaki Oka. "Reconstruction of cell homogenized macroscopic cross sections for analyzing fast and thermal coupled cores using the SRAC system." Journal of Nuclear Science and Technology 51, no. 5 (February 14, 2014): 645–55. http://dx.doi.org/10.1080/00223131.2014.885856.

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25

Hernández-Solís, Augusto, Christophe Demazière, and Christian Ekberg. "Uncertainty Analyses Applied to the UAM/TMI-1 Lattice Calculations Using the DRAGON (Version 4.05) Code and Based on JENDL-4 and ENDF/B-VII.1 Covariance Data." Science and Technology of Nuclear Installations 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/437854.

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The OECD/NEA Uncertainty Analysis in Modeling (UAM) expert group organized and launched the UAM benchmark. Its main objective is to perform uncertainty analysis in light water reactor (LWR) predictions at all modeling stages. In this paper, multigroup microscopic cross-sectional uncertainties are propagated through the DRAGON (version 4.05) lattice code in order to perform uncertainty analysis on and 2-group homogenized macroscopic cross-sections. The chosen test case corresponds to the Three Mile Island-1 (TMI-1) lattice, which is a 15 15 pressurized water reactor (PWR) fuel assembly segment with poison and at full power conditions. A statistical methodology is employed for the uncertainty assessment, where cross-sections of certain isotopes of various elements belonging to the 172-group DRAGLIB library format are considered as normal random variables. Two libraries were created for such purposes, one based on JENDL-4 data and the other one based on the recently released ENDF/B-VII.1 data. Therefore, multigroup uncertainties based on both nuclear data libraries needed to be computed for the different isotopic reactions by means of ERRORJ. The uncertainty assessment performed on and macroscopic cross-sections, that is based on JENDL-4 data, was much higher than the assessment based on ENDF/B-VII.1 data. It was found that the computed Uranium 235 fission covariance matrix based on JENDL-4 is much larger at the thermal and resonant regions than, for instance, the covariance matrix based on ENDF/B-VII.1 data. This can be the main cause of significant discrepancies between different uncertainty assessments.

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Schulc, Martin, Michal Kostal, Roberto Capote, Evzen Novak, Nicola Burianova, and Jan Simon. "Ratio of spectral averaged cross sections measured in standard 252Cf(sf) and 235U(nth,f) neutron fields." EPJ Web of Conferences 239 (2020): 19004. http://dx.doi.org/10.1051/epjconf/202023919004.

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The results of systematic evaluations of spectrum averaged cross section (SACS) measurements in the fission neutron fields of 252Cf and 235U are presented. The data form a complete database of high-threshold experimental SACS measured in the same installation under the same conditions and using the same high purity germanium gamma spectrometer. This is crucial to reduce the uncertainty of the ratio and the data scattering and therefore, to minimize discrepancies compared to cross section measured under different conditions in different laboratories. This new dataset complements and extends earlier experimental evaluations. The total emission of the 252Cf neutron source during the experiments varied from 9.5E8 to 4.5E8 neutrons per second. The emission was derived in accordance to the data in the Certificate of Calibration involving absolute flux measurements in a manganese sulphate bath. Concerning 235U fission neutron field, the irradiations were carried out in a specifically designed core assembled in the zero power light water LR-0 reactor. This special core has a well described neutron field. After the irradiation, the low volume irradiated samples to be measured by gamma spectrometry were placed directly on the upper cap of a coaxial high purity germanium (HPGe) detector in a vertical configuration (ORTEC GEM35P4). High volume samples were homogenized and strewn into the Marinelli beaker. The HPGe detector is surrounded by the lead shielding box with a thin inner copper cladding and covered with rubber for suppression of background signal and bremsstrahlung. The experimental reaction rates were derived for irradiated samples from the Net Peak Areas (NPA) measured using the semiconductor HPGe detector. The measured reaction rates are used to derive the spectrum-averaged cross sections. Furthermore, measured reaction rates are also compared with MCNP6 calculations using various nuclear data libraries, in particular IRDFF evaluations.

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Erasmus, B., J. A. Hendriks, A. Hogenbirk, S. C. van der Marck, and N. L. Asquith. "INTRODUCTION OF OSCAR-4 AT THE HIGH FLUX REACTOR (PETTEN)." EPJ Web of Conferences 247 (2021): 10029. http://dx.doi.org/10.1051/epjconf/202124710029.

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Since 2005 the nodal diffusion based code system, OSCAR-3, was used for reactor support calculations of operational cycles of the High Flux Reactor in Petten, The Netherlands. OSCAR uses a two-step deterministic calculation, in which homogenized cross sections are generated in lattice environments using neutron transport simulations, and then passed to a nodal diffusion core simulator to model the full reactor. Limitations in OSCAR-3 led to the need for improved modelling capabilities and better physics models for components present in the reactor core. OSCAR-4 offers improvements over OSCAR-3 in its approach to homogenization, and the new version of the diffusion core simulator allows for better modelling of movable components such as control rods. Fuel inventories calculated using OSCAR-4 can also easily be exported to MCNP, which allows the calculation of individual plate powers and local reaction rates amongst others. For these reasons OSCAR-4 is currently being introduced as a core support tool at the High Flux Reactor. In this work the steps that were followed to validate the reactor models are presented, and include results of validation calculations from both OSCAR-4 and MCNP6 over multiple reactor cycles. In addition differences in cross section library evaluations and their impact on the results are presented for the MCNP model.

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Kim, Wonkyeong, Jinsu Park, Tomasz Kozlowski, Hyun Chul Lee, and Deokjung Lee. "Comparative Neutronics Analysis of DIMPLE S06 Criticality Benchmark with Contemporary Reactor Core Analysis Computer Code Systems." Science and Technology of Nuclear Installations 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/180979.

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A high-leakage core has been known to be a challenging problem not only for a two-step homogenization approach but also for a direct heterogeneous approach. In this paper the DIMPLE S06 core, which is a small high-leakage core, has been analyzed by a direct heterogeneous modeling approach and by a two-step homogenization modeling approach, using contemporary code systems developed for reactor core analysis. The focus of this work is a comprehensive comparative analysis of the conventional approaches and codes with a small core design, DIMPLE S06 critical experiment. The calculation procedure for the two approaches is explicitly presented in this paper. Comprehensive comparative analysis is performed by neutronics parameters: multiplication factor and assembly power distribution. Comparison of two-group homogenized cross sections from each lattice physics codes shows that the generated transport cross section has significant difference according to the transport approximation to treat anisotropic scattering effect. The necessity of the ADF to correct the discontinuity at the assembly interfaces is clearly presented by the flux distributions and the result of two-step approach. Finally, the two approaches show consistent results for all codes, while the comparison with the reference generated by MCNP shows significant error except for another Monte Carlo code, SERPENT2.

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Zhuang, Kun, Xiaobin Tang, and Liangzhi Cao. "Development and verification of a model for generation of MSFR few-group homogenized cross-sections based on a Monte Carlo code OpenMC." Annals of Nuclear Energy 124 (February 2019): 187–97. http://dx.doi.org/10.1016/j.anucene.2018.09.037.

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30

Li, Hui, Jian Wang, Yuanchun Huang, and Rong Fu. "A Modified Constitutive Model and Microstructure Characterization for 2195 Al-Li Alloy Hot Extrusion." Materials 16, no. 10 (May 18, 2023): 3826. http://dx.doi.org/10.3390/ma16103826.

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The quality of extruded profiles depends largely on accurate constitutive models and thermal processing maps. In this study, a modified Arrhenius constitutive model for homogenized 2195 Al-Li alloy with multi-parameter co-compensation was developed and further enhanced the prediction accuracy of flow stresses. Through the processing map and microstructure characterization, the 2195 Al-Li alloy could be deformed optimally at the temperature range of 710~783 K and strain rate of 0.001~0.12 s−1, preventing the occurrence of local plastic flow and abnormal growth of recrystallized grains. The accuracy of the constitutive model was verified through numerical simulation of 2195 Al-Li alloy extruded profiles with large shaped cross-sections. Dynamic recrystallization occurred at different regions during the practical extrusion process, resulting in slight variations in the microstructure. The differences in microstructure were due to the varying degrees of temperature and stress experienced by the material in different regions.

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31

Garimella, N., M. P. Brady, and Yong Ho Sohn. "Interdiffusion in (fcc) Ni-Cr-X (X = Al, Si, Ge or Pd) Alloys at 700°C." Defect and Diffusion Forum 266 (September 2007): 191–98. http://dx.doi.org/10.4028/www.scientific.net/ddf.266.191.

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Interdiffusion at 700°C for Ni-22at.%Cr (fcc γ phase) alloys with small additions of Al, Si, Ge, or Pd was examined using solid-to-solid diffusion couples. Rods of Ni-22at.%Cr, Ni- 21at.%Cr-6.2at.%Al, Ni-22at.%Cr-4.0at.%Si, Ni-22at.%Cr-1.6at.%Ge and Ni-22at.%Cr-1.6at.%Pd alloys were cast using arc-melt and homogenized at 900°C for 168 hours. The diffusion couples were assembled with alloy disks in Invar steel jig, encapsulated in Argon after several hydrogen flushes, and annealed at 700°C for 720 hours. Experimental concentration profiles were determined from polished cross-sections by using electron probe microanalysis with pure standards of Ni, Cr, Al, Si, Ge and Pd. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion fluxes were examined to determine average ternary interdiffusion coefficients. Effects of ternary alloying additions on the interdiffusional behavior of Ni-Cr-X alloys at 700°C are presented in the light of the diffusional interactions and the formation of protective Cr2O3 scale.

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32

Kahrıman, Fulya, and Muzaffer Zeren. "Mechanical and Fractographical Characterization of Extruded Al-Mg-Si-Zr Alloys." MATEC Web of Conferences 188 (2018): 02017. http://dx.doi.org/10.1051/matecconf/201818802017.

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In this study, the chemical composition of Al-0.8Mg-0.8Si alloys was modified with the addition of 0.1 and 0.2 wt.-% Zr. The billets were manufactured by direct chill casting method, homogenized at 560 °C for 6h and then extruded in order to obtain profiles having hollow and circular sections. Recrystallization layer (shell) became narrower due to the addition of Zr. This was attributed to the formation of very fine precipitates (Al3Zr) within the matrix. The mechanical properties showed that both yield and tensile strengths increased as a function of Zr content. Tensile fracture surfaces were examined by scanning electron microscope and the fractographs reflected the effect of grain structure on the fracture behavior of studied alloys. All fracture surfaces indicated typical dimple ruptures, however, the size of dimples were observed as finer structures as a function of Zr content. As seen in cross-sectional graphs, as the Zr content increased the grain structure was refined due to Al3Zr precipitates. These fine precipitates caused the formation of fine and shallow dimples under loading.

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33

Muñoz-Peña, Guillermo, Juan Galicia-Aragon, Roberto Lopez-Solis, Armando Gomez-Torres, and Edmundo del Valle-Gallegos. "Verification and Validation of the SPL Module of the Deterministic Code AZNHEX through the Neutronics Benchmark of the CEFR Start-Up Tests." Journal of Nuclear Engineering 4, no. 1 (December 27, 2022): 59–76. http://dx.doi.org/10.3390/jne4010005.

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A new module for the AZtlan Nodal HEXagonal (AZNHEX) code, which is part of the AZTLAN Platform, was recently developed based on the Simplified Spherical Harmonics (SPL) scheme to deal with the challenges presented in small fast reactor cores, such as the China Experimental Fast Reactor (CEFR), with high leakage and significant scattering effects. For the verification and validation process, we generated nodal homogenized macroscopic cross-sections (XS) through a full heterogeneous core model using the stochastic code SERPENT and subsequently, these XS were employed in AZNHEX. To verify the SPL implementation, several mesh sensitivity exercises were performed demonstrating that the SPL module was implemented successfully. Furthermore, to validate the code with this new implementation, we modeled some exercises contained in the CEFR benchmark with AZNHEX and compared the results with the experimental data available. The final results show a great improvement compared with the original diffusion solver reducing the deviations significantly from experimental data. In conclusion, it is shown and discussed the relevance of improved numerical models (transport approximations instead of diffusion) for the deterministic calculations of small fast reactors.

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34

Radaideh, Majdi I., Tomasz Kozlowski, William A. Wieselquist, and Matthew A. Jessee. "Data-Driven and Precursor-Group Uncertainty Propagation of Lattice Kinetic Parameters in UAM Benchmark." Science and Technology of Nuclear Installations 2019 (May 2, 2019): 1–21. http://dx.doi.org/10.1155/2019/3702014.

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A new data-driven sampling-based framework was developed for uncertainty quantification (UQ) of the homogenized kinetic parameters calculated by lattice physics codes such as TRITON and Polaris. In this study, extension of the database for the delayed neutron data (DND) is performed by exploring more delayed neutron experiments and adding additional isotopes/actinides to the data libraries. Afterwards, the framework is utilized to obtain a deeper knowledge of the kinetic parameters’ sensitivity and uncertainty. The kinetic parameters include precursor-group-wise delayed neutron fraction (DNF) and decay constant. Input uncertainties include nuclear data (i.e., cross-sections) and DND (i.e., precursor group parameters and fractional delayed neutron yield). It is found that kinetic parameters, especially DNFs, have large uncertainties. The DNF uncertainty is driven by the cross-section uncertainties for LWR designs, while decay constant uncertainty is dominated by the DND uncertainties. The usage of correlated U-235 thermal DND in the UQ process significantly reduces the DND uncertainty contribution on the kinetic parameters. Large void fraction and presence of neutron absorber (e.g., control rod) increase the DNF uncertainty due to the hardening of neutron spectrum. High correlation between the DNF groups (β1,..,β6) is observed, while the decay constant groups (λ1,..,λ6) show weak correlation to each other and also to DNF groups. The DNF uncertainties of the dominant precursor group 4 for PWR, BWR, and VVER are about 7.5%, 9.4%, and 7.6%, respectively. The DNF uncertainty grows to larger values after fuel burnup. Kinetic parameters’ values and uncertainties provided here can be efficiently used in subsequent core calculations, point reactor kinetics, and other applications.

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35

Nikitin, E., E. Fridman, K. Mikityuk, S. Radman, and C. Fiorina. "NEUTRONIC MODELLING OF THE FFTF CONTROL ROD WORTH MEASUREMENTS WITH DIFFUSION CODES." EPJ Web of Conferences 247 (2021): 10017. http://dx.doi.org/10.1051/epjconf/202124710017.

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This paper presents an assessment of three deterministic core simulators with the focus on the neutronic performance in steady-state calculations of small Sodium cooled Fast Reactor cores. The selected codes are DYN3D, PARCS and the novel multi-physics solver GeN-Foam. By using these codes, the multi-group diffusion solutions are obtained for the selected twenty control rod worth measurements performed during the isothermal physics tests of the Fast Flux Test Facility (FFTF). The identical set of homogenized few-group cross sections applied in the calculations is generated with the Serpent Monte Carlo code. The numerical results are compared with each other as well as with the measured values. The obtained numerical results, such as the multiplication factors and control rod worth values, are in good agreement as compared to the experimental data. Furthermore, a comparison of the radial power distributions is presented between DYN3D, PARCS and GeN-Foam. Ultimately, the power distributions are compared to the full core Serpent solution, demonstrating an adequate performance of the selected deterministic tools. In overall, this study presents a verification and validation of the neutronic solvers applied by DYN3D, PARCS and GeN-Foam to steady-state calculations of SFR cores.

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36

Garimella, N., M. P. Brady та Yong Ho Sohn. "Ternary and Quaternary Interdiffusion in γ (fcc) Fe-Ni-Cr-X (X = Si, Ge) Alloys at 900°C". Materials Science Forum 595-598 (вересень 2008): 1145–52. http://dx.doi.org/10.4028/www.scientific.net/msf.595-598.1145.

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Interdiffusion in Fe-Ni-Cr (fcc γ phase) alloys with small additions of Si and Ge at 900°C was studied using solid-to-solid diffusion couples. Alloy rods of Fe-24 at.%Ni, Fe-24 at.%Ni- 22at.%Cr, Fe-24 at.%Ni-22at.%Cr-4at.%Si and Fe-24 at.%Ni-22at.%Cr-1.7at.%Ge were cast using arc-melt, and homogenized at 900°C for 168 hours. Sectioned alloy disks from the rods were polished, and diffusion couples were assembled with in Invar steel jig, encapsulated in Argon after several hydrogen flushes, and annealed atz 900°C for 168 hours. Polished cross-sections of the diffusion couples were characterized to determine experimental concentration profiles using electron probe microanalysis with pure elemental standards. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion flux profiles were examined to determine the average ternary and quaternary interdiffusion coefficients. Effects of alloying additions on the interdiffusional behavior of Fe-Ni- Cr-X alloys at 900°C are presented with due consideration for the formation of protective Cr2O3 scale.

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37

Au, Robert, and Jacques C. Tardif. "Chemical pretreatment of Thuja occidentalis tree rings: implications for dendroisotopic studies." Canadian Journal of Forest Research 39, no. 9 (September 2009): 1777–84. http://dx.doi.org/10.1139/x09-091.

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Whether or not extractives, lignin, and (or) hemicelluloses, all of which have specific isotopic signatures, should be removed prior to dendroisotopic analysis is still debated. This study reports the range of modern tree-ring δ13C values of cellulose from Thuja occidentalis L., a species that has been under-utilized in dendroisotopic research despite its broad distribution and great longevity in North America. The main objective of the study was to recommend a wood component from T. occidentalis to isolate for future δ13C dendroisotopic analyses. Annually resolved tree-ring decadal segments common to eight T. occidentalis trees were excised from cross sections and homogenized. The tree-ring decadal segment from each tree was then chemically processed from untreated whole wood to extractive-free wood, to holocellulose, and to α-cellulose. Subsamples were analyzed for δ13C, percent carbon, and percent yield after each stage of chemical treatment. We recommend that holocellulose be extracted for T. occidentalis, as the α-cellulose yield may be too low when tree-ring samples are very small. The δ13C values for T. occidentalis tree rings were found to be enriched with respect to those for needle-leaved conifers but in close agreement with those reported in the literature for other scale-leaved evergreens.

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38

Park, Young-Hui, Ye Cheng, Rabab Elzohery, Paul P. H. Wilson, Jeremy A. Roberts, and Mark D. DeHart. "EVALUATION OF CRITICAL EXPERIMENTS IN THE UNIVERSITY OF WISCONSIN NUCLEAR REACTOR (UWNR) WITH UNCERTAINTY QUANTIFICATION." EPJ Web of Conferences 247 (2021): 10032. http://dx.doi.org/10.1051/epjconf/202124710032.

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An improved computational model of the University of Wisconsin Nuclear Reactor (UWNR) was developed to support the benchmark evaluation of recent data acquired during an experimental campaign conducted at UWNR. Previous efforts led to a scripted UWNR model for automated generation of MCNP6 and Serpent inputs. This capability was extended to SCALE/KENO. All three tools were used to evaluate a variety of zero-power, fresh-critical configurations, and the results agreed well. The MCNP6 model was extended to support shuffling the core configuration, which allows the modeling of burnup for evaluation of depleted critical configurations. The MCNP6 model successfully predicts core reactivity over time, after accounting for the initial reactivity bias. The inclusion of SCALE/KENO input generation enables sensitivity and uncertainty analyses using the TSUNAMI and Sampler modules of SCALE. A preliminary uncertainty analysis was performed with TSUNAMI for nuclear data uncertainties while direct perturbation calculations were performed using MCNP6 for geometry and material uncertainties, which helped to identify model parameters with the largest effect on the eigenvalue. A transient UWNR transport Model in Mammoth/Rattlesnake is under development to simulate the transient experiments. The existing MCNP6 and Serpent models are used to provide the CAD file for meshing and homogenized cross-sections. In conclusion, the evaluation of UWNR benchmark data provides increased confidence in various states of the UWNR computational model and will provide a unique model for use by other analysts.

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Moslehifard, Elnaz, Mahmood Robati Anaraki, and Saeed Shirkavand. "Effect of adding TiO2 nanoparticles on the SEM morphology and mechanical properties of conventional heat-cured acrylic resin." Journal of Dental Research, Dental Clinics, Dental Prospects 13, no. 3 (December 5, 2019): 234–40. http://dx.doi.org/10.15171/joddd.2019.036.

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Background. The current study evaluated the compressive, flexural and impact strengths of heat-cured acrylic resins reinforced by TiO2 nanoparticles (NPs). Methods. TiO2 NPs were provided and characterized using scanning electron microscopy (SEM) to determine their morphology and crystalline structure. For three mechanical tests, 12 acrylic resin groups (n=9), totaling 108 specimens, were prepared using a special mold for each test, with TiO2 nanoparticle contents of 0, 0.5, 1 or 2 wt% in different groups. After curing, the compressive, flexural and impact strengths of the specimens were examined according to ISO 1567. Results. In the SEM and XRD study of TiO2 NPs, anatase was identified as the major crystalline phase followed by rutile (average particle size: 20.4 nm). SEM images showed that the nanocomposite with 1 wt% NPs had a more homogenized blend. 1 wt% TiO2 nanocomposite exhibited a higher, but non-significant, impact strength compared to the controls. ANOVA showed significant differences in the impact and flexural strengths between nanocomposites with various contents of TiO2 NPs. Conclusion. The nanocomposite with 1 wt% TiO2 NPs exhibited fewer micro-pores and micro-cracks in the SEM cross-sections. A non-significant increase was also observed in the impact strength with TiO2 NPs at 1 wt%. Further increase in TiO2 NPs decreased both the impact and flexural strengths. The compressive strength of the heat-cured acrylic resin was not affected by the incorporation of NPs.

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40

Mallouli, Marwa, and Mnaouar Chouchane. "Piezoelectric energy harvesting using macro fiber composite patches." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 21 (April 26, 2020): 4331–49. http://dx.doi.org/10.1177/0954406220920321.

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Over the last decade, vibration energy harvesting has received substantial attention of many researchers. Piezoelectric materials are able to capture energy from ambient vibration and convert it into electricity which can be stored in batteries or utilized to power small electronic devices. In order to benefit from the 33-mode of the piezoelectric effect, interdigitated electrodes have been utilized in the design of macro fiber composites which are made of piezoelectric fibers of square cross sections embedded into an epoxy matrix material. This paper presents an analytical model of a macro fiber composite bimorph energy harvester using the 33-mode. The mixing rule is applied to determine the equivalent and homogenized properties of the macro fiber composite structures. The electromechanical properties of a representative volume element composed of piezoelectric fibers and an epoxy matrix between two successive interdigitated electrodes are coupled with the overall electro-elastodynamics of the harvester utilizing the Euler–Bernoulli theory. Macro fiber composite bimorph cantilevers with diverse widths are simulated for power generation when a resistive shunt loading is applied. Stress components in the Kapton layers, which are typically a part of any macro fiber composite patch, and in the bonding layers have been included in the model contrary to previously published studies. Variable tip mass, attached at the free end of the beam, is utilized in this paper to tune the resonance frequency of the harvester. The generated power at the fundamental short circuit and open circuit resonance frequencies of harvesters having three different widths is analyzed. It has been observed that higher electrical outputs are produced by the wider macro fiber composite bimorph using (M8528-P1 patches).

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41

Jang, Seongdong, and Yonghee Kim. "A STUDY OF LEAKAGE-CORRECTED TWO-STEP METHOD BASED ON THE NODAL EQUIVALENCE THEORY FOR FAST REACTOR ANALYSIS." EPJ Web of Conferences 247 (2021): 02026. http://dx.doi.org/10.1051/epjconf/202124702026.

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The conventional two-step method based on the generalized equivalence theory (GET) cannot be directly applied to the fast reactor analysis since the assumption of the space-energy separability is not very valid due to a relatively long neutron mean free path. This study aims to develop a leakage-corrected two-step method for the fast reactor analysis with the aid of the albedo-corrected parameterized equivalence constants (APEC) method. The critical idea of the APEC method is to correct the homogenized group constants (HGCs) including discontinuity factors (DFs) during the nodal calculation through predetermined APEC functions. The APEC functions are functionalized in terms of the normalized leakage parameters such as a current-to-flux (CFR) ratio so that they can correct the cross-sections (XSs) and discontinuity factors by reflecting the in-situ neutron leakage information of the nodal analysis. The feasibility of the APEC-corrected two-step method was investigated by solving 5-group diffusion equations for a two-dimensional sodium-cooled fast reactor with a 6-triangle finite difference method. The 5-group HGCs for fuel assemblies were determined by using a continuous-energy Monte Carl code, and the conventional assembly discontinuity factors are also introduced for each hexagonal fuel assembly. First of all, it was demonstrated that the simple FDM scheme could reproduce the reference nodal quantities with the GET. And the APEC functions are formulated using the reference solutions to evaluate the feasibility of simple APEC functional for both XSs and DFs. Then, a smaller color-set problem was defined to determine practical APEC functions for the original benchmark, and various numerical evaluations are performed in terms of the k-eff value and nodal power distribution.

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Vojtasík, Karel, Eva Hrubešová, Marek Mohyla, and Jana Staňková. "Dependency of Elastic Modulus and Stress Redistribution Coefficients on a Layout of Steel Reinforcement in Steel-Concrete Cross Section." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series 11, no. 1 (January 1, 2011): 1–5. http://dx.doi.org/10.2478/v10160-011-0015-x.

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Dependency of Elastic Modulus and Stress Redistribution Coefficients on a Layout of Steel Reinforcement in Steel-Concrete Cross Section The paper presents the outputs of a computational parametric study investigating the influence of both reinforcement ratio and scheme of a cross-section reinforcement on a design value of the elastic module for the homogenized cross-section and the values of the stress redistribution coefficients. The design value of the elastic module represents the steel-concrete cross section in the calculations. The stress redistribution coefficients converts the state stress in the homogenized cross-section for the state stress in steel and concrete individually. The design value of the homogenized cross-section elastic module and the stress redistribution coefficients are determined from the theory of the cooperating rings and computed by program HOMO. The result of a study is a set of the stress redistribution coefficients and a dependency of stress redistribution coefficients on the reinforcement ratio of a steel-concrete section.

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43

Mascarenhas, M. L., and L. Trabucho. "Homogenized behaviour of a beam with a multicellular cross section." Applicable Analysis 38, no. 1-2 (January 1990): 97–119. http://dx.doi.org/10.1080/00036819008839956.

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44

Han, Tae Young, Hyun Chul Lee, Chang Keun Jo, and Jae Man Noh. "Homogenized cross section generation considering axial heterogeneity for VHTR fuel block." Nuclear Engineering and Design 271 (May 2014): 332–36. http://dx.doi.org/10.1016/j.nucengdes.2013.11.057.

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45

Melicher, Valdemar, and Peter Sergeant. "Nondestructive Testing of Metallic Cables Based on a Homogenized Model and Global Measurements." Mathematical Problems in Engineering 2010 (2010): 1–21. http://dx.doi.org/10.1155/2010/163420.

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We propose a simple, quick, and cost-effective method for nondestructive eddy-current testing of metallic cables. Inclusions in the cross section of the cable are detected on the basis of certain global data: hysteresis loop measurements for different frequencies. We detect air-gap inclusions inside the cross section using a homogenized model. The problem, which can be understood as an inverse spectral problem, is posed in two dimensions. We consider its reduction to one dimension. The identifiability is studied. We obtain a uniqueness result for a single inclusion in 1D by two measurements for sufficiently low frequency. We study the sensibility of the inverse problem numerically. A study case with real data is performed to confirm the usefulness.

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46

Kazansky, Yury A., and Gleb V. Karpovich. "Heterogeneous effects in simulating a fast nuclear reactor on the BFS test facility." Nuclear Energy and Technology 5, no. 4 (December 10, 2019): 345–51. http://dx.doi.org/10.3897/nucet.5.48426.

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Simulating fast neutron reactor cores for comparing experimental and calculated data on the reactor neutronics characteristics is performed using zero power test stands. The BFS test facilities in operation in Russia (Obninsk) are discussed in the present paper. The geometrical arrangement of materials in the cores of the simulated reactors (fuel pins, fuel assemblies, coolant geometry) differs from the simulation assembly on the BFS. This can cause differences between the experimental results obtained at the BFS and theoretical calculations even in the case when homogenized concentrations of all materials of the reactor are thoroughly observed. The resulting differences in neutronics parameters due to the geometry of arrangement of materials with the same homogeneous concentrations are referred to as the heterogeneous effect. Heterogeneous effects tend to increase with increasing reactor power and its size, mainly due to changes in the neutron spectra. Calculations of a number of functional values were carried out for assessing the heterogeneous effects for different spatial arrangements of the reactor materials. The calculations were performed for the following cases: a) heterogeneous distribution of materials in accordance with the design of a fast reactor; b) heterogeneous arrangement of materials in accordance with the capabilities and design features of the BFS test facility; c) homogeneous representation of materials in the reactor core and breeding blankets. The configuration of materials in accordance with the design data for fast reactors of the BN-1200 type was accepted as the basic calculation option, relative to which the effect called the heterogeneous shift of the functional value (HSF) was calculated. The effect of neutron leakage on the HSF obtained as the result of calculations using different boundary conditions was estimated. All calculations were carried out for the same homogeneous concentrations of all materials for all the above three configurations. Calculations were carried out as well for the case when plutonium metal fuel was used in the BFS. The values of the following functionals were calculated for different cases of arrangement of materials: the effective multiplication factor (reactivity), the sodium void reactivity effect, the average energy of fission-inducing neutrons, and the ratios of radioactive capture cross-sections to fission cross-sections for 239Pu. The calculations were performed using the Serpent 2.1.30 (VTT, Finland) Monte Carlo software package for neutronics simulations and ENDF/B-VII.0 and JEFF-3.1.1 evaluated nuclear data libraries. The effects of various options of material arrangement on the values of keff were found to be the greatest (about 1.6%) for the case when fissile material in the form of dioxide is replaced with metal fissile material. Homogenization of the composition reduces the keff value by about 0.4%. The average energy of fission-inducing neutrons depends to a significant extent on the leakage of neutrons and the presence of sodium (the average energy of neutrons increases and reaches in the presence of sodium about 100 keV, that is, it increases by about 11–13%). Replacing fissile material metal with its dioxide in the BFS test facility (while maintaining homogeneous concentrations, including that of oxygen) allows reducing the average energy of fission-inducing neutrons by about 60 keV. The highest values of HSF, reaching 65%, are observed when calculation of sodium void reactivity effect is performed with materials distributed homogeneously; however, HSF is equal to 1.5% when calculation of the reactor mock-up assembled on the BFS is performed. In the absence of neutron leakage (infinitely extended medium), the sodium void reactivity effect becomes positive and the HSF is equal to 4–7%. The heterogeneous effect of α for 239Pu noticeably (6–8%) depends only on the replacement of metallic plutonium with its dioxide (maintaining, of course, the homogeneous concentrations).

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47

Galvez, Glecelyn M., Karl Andrie M. Olivar, Francis Rey G. Tolentino, Louis Angelo M. Danao, and Binoe E. Abuan. "Finite Element Analysis of Different Infill Patterns for 3D Printed Tidal Turbine Blade." Sustainability 15, no. 1 (December 30, 2022): 713. http://dx.doi.org/10.3390/su15010713.

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The fabrication route for tidal turbine blades has been compounded with the appearance of additive manufacturing; with the use of infill patterns, improvement of mechanical strength and material reduction for 3D printed parts can be obtained. Through finite element analysis and three-point bend tests, the optimal infill lattice pattern, and the viability of the shell–infill turbine blade model as an alternative to the conventional shell-spar model was determined. Out of a selection of infills, the best infill pattern was determined as the hexagonal infill pattern oriented in-plane. A representative volume element was modeled in ANSYS Material Designer, resulting in the homogenized properties of the in-plane hexagonal lattice. After validation, the homogenized properties were applied to the tidal turbine blade. The shell–infill model was based on the volume of the final shell-spar model which had a blade deflection of 9.720% of the blade length. The difference in the deflection between the homogenized infill and the spar cross-section was 0.00125% with a maximum stress of 170.3 MPa which was within the tensile strength and flexure strength of the carbon fiber with onyx base material. Conclusively, the homogenized infill was determined as a suitable alternative to the spar cross-section. The best orientation of the infill relative to the horizontal orientation of the blade was 0 degrees; however, the lack of trend made it inconclusive whether 0 degrees was the absolute optimal infill orientation.

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Zemčík, H., T. Kroupa, R. Zemčík, and L. Bureš. "Influence of fiber spatial distribution in unidirectional composite cross-section on homogenized elastic parameters." Composite Structures 203 (November 2018): 927–33. http://dx.doi.org/10.1016/j.compstruct.2018.06.083.

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49

Truffinet, Olivier, Karim Ammar, Nicolas Gérard Castaing, Jean-Philippe Argaud, and Bertrand Bouriquet. "An EIM-based compression-extrapolation tool for efficient treatment of homogenized cross-section data." Annals of Nuclear Energy 185 (June 2023): 109705. http://dx.doi.org/10.1016/j.anucene.2023.109705.

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50

Artioli, E., G. Elefante, A. Sommariva, and M. Vianello. "Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach." Mathematics in Engineering 6, no. 4 (2024): 510–35. http://dx.doi.org/10.3934/mine.2024021.

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<p>The paper presents an augmented curvilinear virtual element method to determine homogenized in-plane shear material moduli of long-fibre reinforced composites in the framework of asymptotic homogenization method. The new virtual element combine an exact representation of the curvilinear computational geometry for complex fibre cross section shapes through an innovative two-dimensional cubature suite for NURBS-like polygonal domains. A selection of representative numerical tests supports the accuracy and efficiency of the proposed approach for both doubly periodic and random fibre arrangement with matrix domain.</p>

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