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Special Issue "Mathematics and Computational Methods in Nuclear Energy Technology"

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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 2023) | Viewed by 12394

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Special Issue Editors

Dr. Jingang Liang

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Guest Editor

Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100871, China
Interests: nuclear reactor safety; advanced nuclear systems; Monte Carlo; radiation transport; radiation protection

Dr. Shichang Liu

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Guest Editor

School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, China
Interests: advanced nuclear systems; Monte Carlo; particle transport; fusion neutronics; radiation protection; multi-physical coupling
Special Issues, Collections and Topics in MDPI journals

Dr. Zhaoyuan Liu

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Guest Editor

Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China
Interests: Monte Carlo; nuclear reactor physics; high performance computing, machine learning; applied mathematics

Special Issue Information

Dear Colleagues,

Mathematics and computation play an important role in nuclear energy technologies, since they enable us to predict the behaviors of nuclear systems through mathematical and computational models. Nuclear analysis software empowered with precise computational models has been supporting the entire process of nuclear power plant design, safety analysis, construction, operating, and decommission.

With the increasing requirements for nuclear reactor safety and economics as well as the rapid development of advanced nuclear systems, new generations of mathematics and computational methods and tools with improved accuracy and resolution, robustness, reliability, efficiency, etc., are highly anticipated in the field of nuclear energy. Advanced mathematics and computational methods will provide irreplaceable guidance for the design and optimization of current and next-generation reactors with newer and better models, including the ability to incorporate more underlying physical factors, to use models with higher fidelity, and to comprise different scales, etc.

This Special Issue aims to present the most recent research and developments in mathematics and computational methodologies (including theories, methods, models, frameworks, tools, etc.) applied to the nuclear energy technologies. Themes of interest include but are not limited to:

Multi-scale/multi-physics simulation for existing and advanced nuclear energy systems
Artificial intelligence applications in nuclear energy
Deterministic, Monte Carlo, and hybrid methods in reactor physics analyses
Thermal-hydraulics and safety analysis
Computational fluid dynamics and applications
Computer code development, verification, and validation
Uncertainty quantification, sensitivity analysis, and optimization
High-performance computing, visualization for fluid flow and radiation transport problems
Other applications related to advanced mathematics and computational methods in nuclear energy

We welcome submissions on novel concepts and innovations of original research articles as well as communications and review articles from different disciplines that are relevant to the abovementioned topics.

Dr. Jingang Liang
Dr. Shichang Liu
Dr. Zhaoyuan Liu
Guest Editors

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

mathematics and computational methods
nuclear energy system
modeling and simulation
artificial intelligence
nuclear reactor physics
thermal hydraulics
multiphysics analysis
deterministic methods
Monte Carlo
code development
verification and validation
sensitivity analysis and uncertainty quantification

Published Papers (12 papers)

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Research

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27 pages, 11007 KiB

Open AccessArticle

Transient Simulation and Parameter Sensitivity Analysis of Godiva Experiment Based on MOOSE Platform

and

Energies 2023, 16(18), 6575; https://doi.org/10.3390/en16186575 - 12 Sep 2023

Viewed by 504

Abstract

The fast-neutron burst reactor is a chain reactor that can operate in a prompt critical state. In order to ensure the operational safety of the fast-neutron-pulse reactor and prevent the supercritical pulse from causing physical damage to the material, it is necessary to simulate and analyze the pulse operating conditions of the fast-neutron-pulse reactor. Godiva-I is a spherical assembly of highly enriched uranium metal made during the 1950s. A prompt-critical transient in such a nuclear system impels a quick power excursion, which will cause a temperature rise and a subsequent reactivity reduction because of the metal sphere’s expansion. The overall transient lasts for a few fractions of a millisecond. Based on the point kinetics and Monte Carlo method, the temporal and spatial characteristics of transient input power were calculated, the difference of the average reactivity temperature coefficient between uniform density and non-uniform density was compared, and the transient power distribution condition was loaded into the thermal–mechanics calculation of the MOOSE platform; thus, the pulse process of Godiva-I with different initial reactivity periods was simulated. The JFNK (Jacobian–Free–Newton–Krylov) direct method and multi-app indirect method were used to analyze the transient response of the pulse dynamic process using the heat conduction module and tenor mechanics module, respectively. After considering the influence of the inertia effect and wall-reflected neutrons, the simulation results were much closer to the experimental values. Based on the stochastic tools module, the uncertainty propagation and sensitivity analysis of the Godiva-I model were carried out, the uncertainty of external surface displacement of Godiva under input disturbance of material properties and heat source amplitude factor was obtained, and the sensitivity of different input parameters to output parameters was quantified. The research results can lay a technical foundation for the thermal–mechanics coupling analysis and uncertainty quantification of the metal fast reactor. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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8 pages, 1213 KiB

Open AccessCommunication

Demonstrative Application to an OECD/NEA Reactor Physics Benchmark of the 2nd-BERRU-PM Method—II: Nominal Computations Apparently Inconsistent with Measurements

Ruixian Fang

and

Dan G. Cacuci

Energies 2023, 16(15), 5614; https://doi.org/10.3390/en16155614 - 26 Jul 2023

Cited by 1 | Viewed by 342

Abstract

This work presents illustrative applications of the 2nd-BERRU-PM (second-order best-estimate results with reduced uncertainties predictive modeling) methodology to the leakage response of a polyethylene-reflected plutonium OECD/NEA reactor physics benchmark, which is modeled using the neutron transport Boltzmann equation. The 2nd-BERRU-PM methodology simultaneously calibrates responses and parameters while simultaneously reducing the predicted standard deviation values of these quantities. The situations analyzed in this work pertain to the values of measured responses that appear to be inconsistent with the computed response values, in that the standard deviation values of the measured responses do not initially overlap with the standard deviation values of the computed responses. It is shown that the inconsistency diminishes as higher-order sensitivities are progressively included, thus illustrating their significant impact. In all cases, the 2nd-BERRU-PM methodology yields predicted best-estimate standard deviation values that are smaller than both the computed and the experimentally measured values of the standard deviation for the model response under consideration. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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18 pages, 2357 KiB

Open AccessFeature PaperArticle

Demonstrative Application to an OECD/NEA Reactor Physics Benchmark of the 2nd-BERRU-PM Method—I: Nominal Computations Consistent with Measurements

Dan G. Cacuci

and

Ruixian Fang

Energies 2023, 16(14), 5552; https://doi.org/10.3390/en16145552 - 22 Jul 2023

Cited by 1 | Viewed by 368

Abstract

This work illustrates the applications of the 2nd-BERRU-PM methodology to polyethylene-reflected plutonium (PERP) OECD/NEA reactor physics benchmark. Using concepts from information theory and thermodynamics, the 2nd-BERRU-PM (2nd-order best-estimate results with reduced uncertainties predictive modeling) methodology is constructed in the most inclusive “joint-phase-space of parameters, computed and measured responses”. Consequently, the 2nd-BERRU-PM methodology simultaneously calibrates responses and parameters, while simultaneously reducing the predicted standard deviations in these quantities. This uncertainty reduction is illustrated for the PERP benchmark, which is modeled using the neutron transport Boltzmann equation, the solution of which is representative of “large-scale computations”. The situations analyzed in this work pertain to values of the measured responses which are consistent with the computed response values, in that the standard deviations of the measured responses overlap with the standard deviations of the computed responses. The situations that can arise when the measured values appear to be inconsistent with the computed values will be analyzed in the accompanying Part II. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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26 pages, 9061 KiB

Open AccessArticle

A Multimodel Framework for Quantifying Flow and Advective Transport Controlled by Earthquake-Induced Canister Failures in a Reference Case for Radioactive Waste Geological Disposal

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Energies 2023, 16(13), 5081; https://doi.org/10.3390/en16135081 - 30 Jun 2023

Viewed by 474

Abstract

Characterizing flow and transport for earthquake-induced shear canister failure is critical for the performance and safety assessment of radioactive waste geological disposal. The study presents a modeling framework that integrates multiple models to account for fractures produced by shear displacements, evaluate canister failures, and simulate flow and advective transport in a conceptual repository site based on a selected reference case in an offshore island in western Taiwan. The typical KBS-3 disposal concept associated with 500 realizations of the shear-induced fracture properties is employed to quantify the uncertainty of flow and advective transport in the geological disposal site. The radionuclides in canisters are assumed to migrate through the shear-induced fractures surrounding the deposition holes. The results from 500 realizations show that two types of fractures produce a high potential to destroy canisters induced by the shear displacements. The earliest canister failure time influenced by possible shear movements is 0.23 million years for the reference case. The modeling framework identifies five canisters and the associated shear-induced fractures for flow and advective transport simulations. Based on the results of the density-dependent flow fields, the particle tracking algorithm enables the calculations of flow and transport parameters, including equivalent initial flux, equivalent flow rate, path length, travel time, and flow-related transport resistance for the identified five canisters. These parameters are critical for the performance and safety assessments of buffer erosion and canister corrosion near the disposal repository and the far field of the radioactive waste disposal site. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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13 pages, 2738 KiB

Open AccessArticle

Analysis of the Influence of Energy Group Structure on Iron Shielding Calculation

Jun Wu

Bin Zhang

and

Yixue Chen

Energies 2023, 16(8), 3538; https://doi.org/10.3390/en16083538 - 19 Apr 2023

Viewed by 575

Abstract

The energy group structure of a multi-group cross section library matched with a deterministic method has a significant influence on shielding calculation. The complex resonance cross section of Fe-56 has a significant influence on accuracy with different energy group structures when processing multi-group cross section data. In this study, in order to more accurately test the influence of the iron resonance phenomenon on shielding calculations, this group structure is modified by the 199-group with 69 points interpolated into its group boundaries at an energy range from 1.1 keV to 3.1164 MeV. The new 269-group library is then tested with selected SINBAD iron sphere benchmarks and compared with the results of 199-group, 299-group, and 172-group libraries and measurements. Upon analysis, it is shown that the resonance of Fe-56 has a great influence on the accuracy of the calculated leakage. Further, it is noted that the finer the energy group division, the greater the calculated leakage fluctuation, and the deeper the neutron passes through the iron sphere, the larger the calculated leakage fluctuation. This study and its leakage results may provide a good reference for the development of new multi-group structures for present and future shielding design. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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18 pages, 66689 KiB

Open AccessArticle

Verification and Analysis of the Problem-Dependent Multigroup Macroscopic Cross-Sections for Shielding Calculations

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Energies 2023, 16(8), 3366; https://doi.org/10.3390/en16083366 - 11 Apr 2023

Viewed by 800

Abstract

Multigroup constants are the foundation of neutron and photon transport problems, and the accuracy of multigroup cross-sections has a significant impact on shielding calculation. Challenges have arisen in generating accurate multigroup macroscopic cross-sections for some problems using the widely used cross-section processing code TRANSX 2.15. We developed the multigroup neutron-photon macroscopic cross-section processing module in the shielding transport code ARES. The module is capable of handling the neutron-photon coupled master libraries in MATXS format and providing the problem-dependent multigroup macroscopic cross-sections tailored to each specific shielding physics problem. The self-designed problems with a single nuclide, as well as the iron and OKTAVIAN experiments, are used to verify and analyze the accuracy of neutron and photon macroscopic cross-sections. Results indicate that the macroscopic cross-sections, neutron flux and neutron-photon leakage spectrum obtained by the MGMXS module are consistent with corresponding reference values. As for the JANUS Phase I fixed source shielding benchmark, the relative differences in the reaction rate between the calculation results and experimental data are within 20%. The module provides better problem-dependent multigroup macroscopic cross-sections for neutron and photon shielding calculations that satisfy the accuracy requirements of engineering applications. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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12 pages, 19200 KiB

Open AccessCommunication

Parallel Communication Optimization Based on Graph Partition for Hexagonal Neutron Transport Simulation Using MOC Method

and

Energies 2023, 16(6), 2823; https://doi.org/10.3390/en16062823 - 18 Mar 2023

Cited by 1 | Viewed by 852

Abstract

OpenMOC-HEX, a neutron transport calculation code with hexagonal modular ray tracing, has the capability of domain decomposition parallelism based on an MPI parallel programming model. In this paper, the optimization of inter-node communication was studied. Starting from the specific geometric arrangement of hexagonal reactors and the communication features of the Method of Characteristics, the computation and communication of all the hexagonal assemblies are mapped to a graph structure. Then, the METIS library is used for graph partitioning to minimize the inter-node communication under the premise of load balance on each node. Numerical results of an example hexagonal core with 1968 energy groups and 1027 assemblies demonstrate that the communication time is reduced by about 90%, and the MPI parallel efficiency is increased from 82.0% to 91.5%. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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19 pages, 4461 KiB

Open AccessArticle

Inventories of Short-Lived Fission Gas Nuclides in Nuclear Reactors

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Energies 2023, 16(6), 2530; https://doi.org/10.3390/en16062530 - 07 Mar 2023

Viewed by 1040

Abstract

Taking inventories in reactor cores is critical for understanding their radioactive source terms and establishing the relationship between the activity concentration in the primary loop and the status of the reactor core’s fuel. However, there is a niche in which a simple but accurate relationship between reactor conditions and nuclide inventories can reliably predict the fission gas nuclide activities of the reactor core in the primary loop. In this study, a simple and efficient model called “Inventories of a Point Reactor for Fission Gas Nuclides” (IPRFGN) was proposed to calculate and interpret such inventories, in which a 10 MW high-temperature gas-cooled experimental reactor (HTR-10) was used as the test case. The present study findings were consistent with those of a general point–depletion burnup code such as the KORIGEN code. Here, the relative error was <1%. Based on the application of the IPRFGN model in HTR-10, the results indicate that the proposed IPRFGN model has provided the relationship between the inventories of fission gas nuclides in the core and the reactor conditions in all types of nuclear fission reactors. In the future, the IPRFGN model will be used for calculating fission gas nuclide inventories in various reactors. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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16 pages, 2447 KiB

Open AccessArticle

Nuclear Data Sensitivity and Uncertainty Study for the Pressurized Water Reactor (PWR) Benchmark Using RMC and SCALE

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Energies 2022, 15(24), 9511; https://doi.org/10.3390/en15249511 - 15 Dec 2022

Viewed by 900

Abstract

In order to improve the safety and economy of nuclear reactors, it is necessary to analyze the sensitivity and uncertainty (S/U) of the nuclear data. The capabilities of S/U analysis has been developed in the Reactor Monte Carlo code RMC, using the iterated fission probability (IFP) method and the superhistory method. In this paper, the S/U capabilities of RMC are applied to a typical PWR benchmark B&W’s Core XI, and compared with the multigroup and continuous-energy S/U capabilities in the SCALE code system. The S/U results of the RMC-IFP method and the RMC-superhistory method are compared with TSUNAMI-CE/MG in SCALE. The sensitivity results and the uncertainty results of major nuclides that contribute a lot to the uncertainties in k_eff are in good agreement in both RMC and SCALE. The RMC-superhistory method has the same precision as the IFP method, but it reduces the memory footprint by more than 95% and only doubles the running time. The superhistory method has obvious advantages when there are many nuclides and reaction types to be analyzed. In addition, the total uncertainties in the k_eff of the first-order uncertainty quantification method are compared with the stochastic sampling method, and the maximum relative deviation of total uncertainties in the k_eff is 8.53%. Verification shows that the capabilities of S/U analysis developed in the RMC code has good accuracy. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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12 pages, 3266 KiB

Open AccessArticle

Uncertainty Propagation of Fission Product Yields from Uranium and Plutonium in Pebble-Bed HTGR Burnup Calculation

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Energies 2022, 15(22), 8369; https://doi.org/10.3390/en15228369 - 09 Nov 2022

Cited by 1 | Viewed by 727

Abstract

Quantifying fission product yield uncertainty contribution to reactor burnup calculation is an important aspect of pebble-bed High Temperature Gas-cooled Reactor (pebble-bed HTGR) uncertainty analysis. In this work, uncertainty propagation of fission product yield to pebble-bed HTGR burnup calculation is conducted. Uncertainty of fission product yields from four fissile isotopes, namely ²³³U, ²³⁵U, ²³⁹Pu and ²⁴¹Pu, are considered. The stochastic sampling-based uncertainty analysis method is adopted and fission product yield covariance matrices are estimated from ENDF/B-VII.1. The covariance matrix for each fissile actinide is estimated based on the Bayesian method and fission product yields are assigned with log-normal distribution in the sampling process with the Latin Hypercube Sampling (LHS) method. Since the fission fraction from ²³⁹Pu plays an important role in fissions of fuels with high burnup value in pebble-bed HTGR, the fission product yield uncertainty contribution from ²³⁹Pu is highlighted in this work. The result shows that, in the burnup equilibrium state of pebble-bed HTGR, fission product yield uncertainty contributions from ²³⁵U and ²³⁹Pu to relative uncertainty of k_eff are 0.027% and 0.026%, respectively. The overall uncertainty contribution from four fissile isotopes (²³³U, ²³⁵U, ²³⁹Pu and ²⁴¹Pu) to relative uncertainty of equilibrium core k_eff is 0.038%. Furthermore, fission product yield uncertainty has an important contribution to the nuclide density uncertainty of fission products. The most relative uncertainty, 10.82%, is observed in ¹⁰⁹Ag contributed from the fission product yield uncertainty of ²³⁹Pu at the burnup equilibrium state. This indicates the uncertainty contribution from the fission product yield of ²³⁹Pu cannot be neglected in pebble-bed HTGR burnup uncertainty analysis. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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13 pages, 29492 KiB

Open AccessArticle

Verification of the Discrete Ordinates Goal-Oriented Multi-Collision Source Algorithm with Neutron Streaming Problems

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Energies 2022, 15(22), 8335; https://doi.org/10.3390/en15228335 - 08 Nov 2022

Viewed by 811

Abstract

The shielding calculation of neutron streaming problems with ducts is characterized by the strong anisotropy of angular flux, which poses a challenge for the analysis of nuclear installations. The discrete ordinate method is one of the most commonly deterministic techniques to solve the neutron transport equation, in which the accuracy and efficiency neutron are crucial to ensure the reliability of the streaming shielding simulation. We implemented the goal-oriented multi-collision source algorithm in the 3D transport code ARES. This algorithm can determine the importance factor based on the adjoint transport calculation, obtain the response function to enable problem-dependent, goal-oriented spatial decomposition, and provide the error estimation as a driving force behind the dynamic quadrature to optimize the source iteration. This study focuses on verifying the goal-oriented multi-collision source algorithm under the neutron streaming problems, and the capabilities of the algorithm have been tested on IRI-TUB benchmark of SINBAD database. The numerical results show that the algorithm can effectively control the angular discretization error for the neutron streaming problems, which is more economical than the traditional discrete ordinate calculation. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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Review

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27 pages, 4708 KiB

Open AccessReview

Fault Diagnosis Techniques for Nuclear Power Plants: A Review from the Artificial Intelligence Perspective

Ben Qi

Jingang Liang

and

Jiejuan Tong

Energies 2023, 16(4), 1850; https://doi.org/10.3390/en16041850 - 13 Feb 2023

Cited by 3 | Viewed by 2370

Abstract

Fault diagnosis plays an important role in complex and safety-critical systems such as nuclear power plants (NPPs). With the development of artificial intelligence (AI), extensive research has been carried out for fast and efficient fault diagnosis based on intelligent methods. This paper presents a review of various AI-based system-level fault diagnosis methods for NPPs. We first discuss the development history of AI. Based on this exposition, AI-based fault diagnosis techniques are classified into knowledge-driven and data-driven approaches. For knowledge-driven methods, we discuss both the early if–then-based fault diagnosis techniques and the current new theory-based ones. The principles, application, and comparative analysis of the representative methods are systematically described. For data-driven strategies, we discuss single-algorithm-based techniques such as ANN, SVM, PCA, DT, and clustering, as well as hybrid techniques that combine algorithms together. The advantages and disadvantages of both knowledge-driven and data-driven methods are compared, illustrating the tendency to combine the two approaches. Finally, we provide some possible future research directions and suggestions. Full article

(This article belongs to the Special Issue Mathematics and Computational Methods in Nuclear Energy Technology)

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