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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "B4: Nuclear Energy".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 26927

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Special Issue Editor

Dr. Andrew Buchan

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Guest Editor

School of Engineering and Materials Science, Queen Mary University of London, London, UK
Interests: neutron transport; reactor physics; adaptive finite elements; sensitivity analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit your original research or review papers to this Special Issue of Energies on “Advances in Modeling for Nuclear Science and Engineering”.

Computer models have played a central role in assessing the functioning of nuclear power facilities for decades. They have ensured that nuclear operations are efficient, but also safe to both the public and the environment. The field of nuclear engineering is complex and multi-physics in nature, spanning the fields of neutron transport, thermal hydraulics, structural mechanics, heat transfer, and chemistry. Robust, accurate, and validated models are essential to the areas of rector design, operation and procedure analysis, fuel optimization, and lifetime extension, among others. Nuclear engineering research has been a significant contributor to the field of numerical analysis and modeling by advancing areas in predictive multi-physics modeling, sensitivity and uncertainty quantification, high-fidelity discretizations, reduced-order models, artificial intelligence, and HPC.

This Special Issue aims to bring together studies describing recent advances in modeling methods for all areas in nuclear engineering applications. We welcome contributions from academia and industry in the aforementioned fields.

Dr. Andrew Buchan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Energies is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

high-fidelity models
HPC
sensitivity analysis
uncertainty quantification
best estimate plus uncertainty
single and multi-physics modeling
reduced-order modeling
artificial intelligence.

Published Papers (12 papers)

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Research

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20 pages, 7802 KiB

Open AccessArticle

Modeling of Dynamic Operation Modes of IVG.1M Reactor

by Ruslan Irkimbekov, Alexander Vurim, Galina Vityuk, Olzhas Zhanbolatov, Zamanbek Kozhabayev and Artur Surayev

Energies 2023, 16(2), 932; https://doi.org/10.3390/en16020932 - 13 Jan 2023

Cited by 3 | Viewed by 1239

Abstract

This paper presents the results of a calculation code approach providing a solution to the point kinetics problem for the IVG.1M research reactor of the National Nuclear Center of the Republic of Kazakhstan and allowing the simulation of dynamic processes going on during reactor start-ups, including changes in the thermal state of all its elements, reactor regulator displacement, accumulation of absorbers in the fuel, and the beryllium reflector. A mathematical description of the IVG.1M point kinetics model is presented, which provides a calculation of the reactor neutron parameters, taking into account the dependence of reactivity effects on the temperature, changes in the isotopic composition of materials, and thermal expansion of core structural elements. An array of data values was formed of reactivity added by separate elements of the core when changing their thermal state and other reactor parameters, as well as an array of data with the parameters of heat exchange of coolant-based reactor structural elements. These are used in the process of solving the point kinetics problem to directly replace formal parameters, eliminating the need to calculate the values of these parameters at each calculation step. Preliminary calculations to form an array of values of reactivity effects was applied to the reactor by separate structural elements when their temperature changes were performed using the IVG.1M precision reactor calculation model. The model was validated by the reactor parameters in the critical state. Preliminary calculations to form an array of data with the parameters of heat exchange of coolant-based reactor structural elements were performed in ANSYS Fluent software using the calculation model that describes the IVG.1M reactor fuel element in detail. Validation of the developed calculation code based on the results of two start-ups of the IVG.1M reactor was performed and its applicability for the analysis of transient and emergency modes of reactor operation and evaluation of its safe operation limits was confirmed. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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22 pages, 5805 KiB

Open AccessArticle

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

by Konstantinos Prantikos, Lefteri H. Tsoukalas and Alexander Heifetz

Energies 2022, 15(20), 7697; https://doi.org/10.3390/en15207697 - 18 Oct 2022

Cited by 17 | Viewed by 2863

Abstract

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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15 pages, 1121 KiB

Open AccessArticle

Development of a Trajectory Period Folding Method for Burnup Calculations

by Przemysław Stanisz, Mikołaj Oettingen and Jerzy Cetnar

Energies 2022, 15(6), 2245; https://doi.org/10.3390/en15062245 - 18 Mar 2022

Cited by 16 | Viewed by 1749

Abstract

In this paper, we present a trajectory period folding method for numerical modelling of nuclear transformations. The method uses the linear chain method, commonly applied for modelling of isotopic changes in matter. The developed method folds two consecutive periods of time and forms linear chain representations. In the same way as in the linear chain method, the mass flow of straight nuclide-to-nuclide transitions following the formation of nuclide transmutation chains in every step is considered over the total period of interest. Therefore, all quantitative data about the isotopic transformations for the period beyond a particular calculation step are preserved. Moreover, it is possible to investigate the formation history of any isotope from the beginning of irradiation to the arbitrary time step, including cooling periods and multi-recycling for any designed nuclear fuel cycle. We present a case study for the transition from ²³⁸U to ²³⁹Pu and define the properties of the developed method and its possible applications in reactor physics calculations. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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38 pages, 1673 KiB

Open AccessEditor’s ChoiceArticle

On the Need to Determine Accurately the Impact of Higher-Order Sensitivities on Model Sensitivity Analysis, Uncertainty Quantification and Best-Estimate Predictions

by Dan Gabriel Cacuci

Energies 2021, 14(19), 6318; https://doi.org/10.3390/en14196318 - 3 Oct 2021

Cited by 6 | Viewed by 1365

Abstract

This work aims at underscoring the need for the accurate quantification of the sensitivities (i.e., functional derivatives) of the results (a.k.a. “responses”) produced by large-scale computational models with respect to the models’ parameters, which are seldom known perfectly in practice. The large impact that can arise from sensitivities of order higher than first has been highlighted by the results of a third-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark, which will be briefly reviewed in this work to underscore that neglecting the higher-order sensitivities causes substantial errors in predicting the expectation and variance of model responses. The importance of accurately computing the higher-order sensitivities is further highlighted in this work by presenting a text-book analytical example from the field of neutron transport, which impresses the need for the accurate quantification of higher-order response sensitivities by demonstrating that their neglect would lead to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis) of the model response’s distribution in the phase space of model parameters. The incorporation of response sensitivities in methodologies for uncertainty quantification, data adjustment and predictive modeling currently available for nuclear engineering systems is also reviewed. The fundamental conclusion highlighted by this work is that confidence intervals and tolerance limits on results predicted by models that only employ first-order sensitivities are likely to provide a false sense of confidence, unless such models also demonstrate quantitatively that the second- and higher-order sensitivities provide negligibly small contributions to the respective tolerance limits and confidence intervals. The high-order response sensitivities to parameters underlying large-scale models can be computed most accurately and most efficiently by employing the high-order comprehensive adjoint sensitivity analysis methodology, which overcomes the curse of dimensionality that hampers other methods when applied to large-scale models involving many parameters. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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19 pages, 2996 KiB

Open AccessArticle

Linear Chain Method for Numerical Modelling of Burnup Systems

by Jerzy Cetnar, Przemysław Stanisz and Mikołaj Oettingen

Energies 2021, 14(6), 1520; https://doi.org/10.3390/en14061520 - 10 Mar 2021

Cited by 28 | Viewed by 3598

Abstract

The theoretical aspects of the linear chain method for the numerical modelling of nuclear transmutation systems, and particularly regarding the transmutation trajectory analysis (TTA), are presented. The theoretical background of the TTA method, as an advanced version of the linear chain method, with the detailed description of the applied mathematical set-up and graphical visualisation of transformation chains, is shown. As the TTA method was initially developed at the AGH University of Science and Technology almost 25 years ago, several numerical implementations were introduced worldwide, yet the mathematical improvements or alternative forms of solutions and numerical algorithms were reported since then. The method was also implemented and tested by different research groups, also in confrontation with alternative approaches to the nuclear transformation problem known as the matrix method. The aim of the paper is to present the background of the developed method and its advantages, clarify misunderstandings in the method perception and suggest unexplored options in numerical algorithm implementation. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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13 pages, 4608 KiB

Open AccessArticle

Assessment of Realistic Departure from Nucleate Boiling Ratio (DNBR) Considering Uncertainty Quantification of Core Flow Asymmetry

by Il Suk Lee, Dong Hyeog Yoon, Young Seok Bang, Tae Hoon Kim and Yong Chan Kim

Energies 2021, 14(5), 1504; https://doi.org/10.3390/en14051504 - 9 Mar 2021

Cited by 3 | Viewed by 2055

Abstract

Concern over the asymmetric phenomena in the core region has increased considering safety issues that are highly possible to reduce the thermal margin significantly in nuclear power plants. Since the seized reactor coolant pump (RCP) accident of an advanced power reactor 1400 (APR1400) can be regarded as a representative core asymmetric event with respect to core inlet flow, the departure from nucleate boiling ratio (DNBR), which is a regulatory acceptance criterion in nuclear safety, should be evaluated with consideration of the uncertainty range of the core inlet flow reflecting the actual geometry. This study investigates the DNBR quantitatively in the entire fuel assemblies in the core using several codes for system behavior, computational flow dynamics, sub-channel analysis, and uncertainty evaluation. Based on the results from a system thermal-hydraulic analysis of a seized RCP accident of APR1400, this study presents the uncertainty range calculated by computational fluid dynamics on the asymmetry of the core inlet flow. Damaged fuel rods are quantitatively identified through a sub-channel analysis, which presents statistic relevance to obtain the DNBR at 95% reliability and 95% accuracy level. Additionally, an optimized evaluation methodology of a non-loss of coolant accident (non-LOCA) is realized by several nuclear codes. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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25 pages, 1943 KiB

Open AccessArticle

Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

by Toby R. F. Phillips, Claire E. Heaney, Brendan S. Tollit, Paul N. Smith and Christopher C. Pain

Energies 2021, 14(5), 1369; https://doi.org/10.3390/en14051369 - 3 Mar 2021

Cited by 8 | Viewed by 1835

Abstract

Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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27 pages, 2001 KiB

Open AccessArticle

Reduced-Order Modelling Applied to the Multigroup Neutron Diffusion Equation Using a Nonlinear Interpolation Method for Control-Rod Movement

by Claire E. Heaney, Andrew G. Buchan, Christopher C. Pain and Simon Jewer

Energies 2021, 14(5), 1350; https://doi.org/10.3390/en14051350 - 2 Mar 2021

Cited by 10 | Viewed by 1810

Abstract

Producing high-fidelity real-time simulations of neutron diffusion in a reactor is computationally extremely challenging, due, in part, to multiscale behaviour in energy and space. In many scientific fields, including nuclear modelling, the application of reduced-order modelling can lead to much faster computation times without much loss of accuracy, paving the way for real-time simulation as well as multi-query problems such as uncertainty quantification and data assimilation. This paper compares two reduced-order models that are applied to model the movement of control rods in a fuel assembly for a given temperature profile. The first is a standard approach using proper orthogonal decomposition (POD) to generate global basis functions, and the second, a new method, uses POD but produces global basis functions that are local in the parameter space (associated with the control-rod height). To approximate the eigenvalue problem in reduced space, a novel, nonlinear interpolation is proposed for modelling dependence on the control-rod height. This is seen to improve the accuracy in the predictions of both methods for unseen parameter values by two orders of magnitude for

k^{eff}

and by one order of magnitude for the scalar flux. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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14 pages, 993 KiB

Open AccessArticle

A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

by Alamir Elsayed, Mohamed El-Beltagy, Amnah Al-Juhani and Shorooq Al-Qahtani

Energies 2021, 14(4), 955; https://doi.org/10.3390/en14040955 - 11 Feb 2021

Cited by 2 | Viewed by 1445

Abstract

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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18 pages, 7020 KiB

Open AccessArticle

A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

by Dean Wang and Zuolong Zhu

Energies 2021, 14(2), 424; https://doi.org/10.3390/en14020424 - 14 Jan 2021

Cited by 6 | Viewed by 4462

Abstract

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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23 pages, 4091 KiB

Open AccessArticle

A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches

by Khashayar Sadeghi, Seyed Hadi Ghazaie, Ekaterina Sokolova, Ahmad Zolfaghari and Mohammad Reza Abbasi

Energies 2020, 13(20), 5424; https://doi.org/10.3390/en13205424 - 17 Oct 2020

Viewed by 1506

Abstract

The application of continuous and discontinuous approaches of the finite element method (FEM) to the neutron transport equation (NTE) has been investigated. A comparative algorithm for analyzing the capability of various types of numerical solutions to the NTE based on variational formulation and discontinuous finite element method (DFEM) has been developed. The developed module is coupled to the program discontinuous finite element method for neutron (DISFENT). Each variational principle (VP) is applied to an example with drastic changes in the distribution of neutron flux density, and the obtained results of the continuous and discontinuous finite element (DFE) have been compared. The comparison between the level of accuracy of each approach using new module of DISFENT program has been performed based on the fine mesh solutions of the multi-PN (MPN) approximation. The obtained results of conjoint principles (CPs) have been demonstrated to be very accurate in comparison to other VPs. The reduction in the number of required meshes for solving the problem is considered as the main advantage of this principle. Finally, the spatial additivity to the context of the spherical harmonics has been implemented to the CP, to avoid from computational error accumulation. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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Review

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44 pages, 4391 KiB

Open AccessReview

Overview of Arbitrarily High-Order Adjoint Sensitivity and Uncertainty Quantification Methodology for Large-Scale Systems

by Dan Gabriel Cacuci

Energies 2022, 15(18), 6590; https://doi.org/10.3390/en15186590 - 8 Sep 2022

Viewed by 1082

Abstract

This work reviews from a unified viewpoint the concepts underlying the “n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems” (n^th-CASAM-L) and the “n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n^th-CASAM-N) methodologies. The practical application of the n^th-CASAM-L methodology is illustrated for an OECD/NEA reactor physics benchmark, while the practical application of the n^th-CASAM-N methodology is illustrated for a nonlinear model of reactor dynamics that exhibits periodic and chaotic oscillations. As illustrated both by the general theory and by the examples reviewed in this work, both the n^th-CASAM-L and n^th-CASAM-N methodologies overcome the curse of dimensionality in sensitivity analysis. The availability of efficiently and exactly computed sensitivities of arbitrarily high order can lead to major advances in all areas that need such high-order sensitivities, including data assimilation, model calibration, uncertainty reduction, and predictive modeling. Full article

(This article belongs to the Special Issue Advances in Modelling for Nuclear Science and Engineering)

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