Nuclear Energy Systems

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Energies energies	3.0	6.2	2008	16.8 Days	CHF 2600
Journal of Nuclear Engineering jne	-	-	2020	38.3 Days	CHF 1000
Entropy entropy	2.1	4.9	1999	22.3 Days	CHF 2600
Symmetry symmetry	2.2	5.4	2009	17.3 Days	CHF 2400
Sci sci	-	4.5	2019	37.1 Days	CHF 1200

26 pages, 14905 KiB

Open AccessArticle

3D Analysis of Hydrogen Distribution and Its Mitigation Using Passive Autocatalytic Recombiners (PARs) Inside VVER-1000 Containment

by Muhammet Enis Kanik, Omid Noori-kalkhoran, Kevin Fernández-Cosials and Massimiliano Gei

Energies 2023, 16(18), 6612; https://doi.org/10.3390/en16186612 - 14 Sep 2023

Cited by 1 | Viewed by 1568

Abstract

Hydrogen is a flammable gas that can generate thermal and mechanical loads which could jeopardise the containment integrity upon combustion inside nuclear power plants containment. Hydrogen can be generated from various sources and disperses into the containment atmosphere, mixing with steam and air [...] Read more.

Hydrogen is a flammable gas that can generate thermal and mechanical loads which could jeopardise the containment integrity upon combustion inside nuclear power plants containment. Hydrogen can be generated from various sources and disperses into the containment atmosphere, mixing with steam and air following a loss of coolant accident and its progression. Therefore, the volumetric hydrogen concentration should be examined within the containment to determine whether a flammable mixture is formed or not. Codes with 3D capabilities could serve this examination by providing detailed contours/maps of the hydrogen distribution inside containment in view of the local stratification phenomenon. In this study, a 3D VVER-1000 as-built containment model was sketched in AutoCAD and then processed into GOTHIC nuclear containment analysis code for hydrogen evaluation. The model was modified to a great extent by installing 80 passive autocatalytic recombiners and locating hydrogen sources to evaluate the performance of the hydrogen removal system inside the containment on maintaining the hydrogen concentration below the flammability limit during a large break loss of coolant accident. 2D profiles and 3D contours of volumetric hydrogen concentration with and without PARs are presented as the simulation outcome of this study. The results were validated against the results of the Final Safety Analysis Report, which also demonstrates the effectiveness of the hydrogen removal system as an engineered safety feature to keep the containment within a safe margin. Detailed 3D contours of hydrogen distribution inside containment can be employed to evaluate the local hot spots of hydrogen, rearranging and optimising the number and location of PARs to avoid the hydrogen explosion inside containment. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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17 pages, 1617 KiB

Open AccessArticle

Classical Thermodynamic Analysis of D-Based Nuclear Fusion Reactions: The Role of Entropy

by Silvano Tosti

Energies 2023, 16(10), 3996; https://doi.org/10.3390/en16103996 - 9 May 2023

Cited by 1 | Viewed by 2534

Abstract

In this work, the feasibility of nuclear processes is studied via classical thermodynamics by assessing the change in entropy, a parameter that has so far been neglected in the analysis of these reactions. The contribution of the entropy to the reaction spontaneity plays [...] Read more.

In this work, the feasibility of nuclear processes is studied via classical thermodynamics by assessing the change in entropy, a parameter that has so far been neglected in the analysis of these reactions. The contribution of the entropy to the reaction spontaneity plays a different role in the fission and fusion reactions. In particular, in fusion reactions the temperature acts as a very powerful amplifier of the entropic term (−T ΔS) that, at the temperature of tokamaks (millions Kelvin), may significantly reduce the thermodynamic spontaneity of these processes. A new approach is followed for assessing the feasibility of the D-based reactions of interest for the magnetically confined nuclear fusion through the investigation of the effect of the temperature on both kinetics and thermodynamics. The results confirm that the deuterium–tritium reaction is the most promising fusion reaction to be realized in tokamak devices. At the temperature of 1.5 × 10⁸ K (≈13 keV), the DT reaction exhibits a large thermodynamic spontaneity (ΔG = −16.0 MeV) and its reactivity is of the order of 10⁻²² m³/s, a value capable of guaranteeing the tritium burning rate needed to operate the nuclear plants under tritium self-sufficiency conditions and with a net energy production. The other results show that at the tokamaks’ temperature the two branches of the DD reaction exhibit a modest spontaneity (ΔG around −2 MeV) coupled to very low reactivity values (10⁻²⁴ m³/s). The temperature rise that could be aimed to increase the reactivity is however ineffective to improve the reaction feasibility since it would augment the entropic term as well, thus shifting the ΔG towards positive values. The D³He reaction is soundly spontaneous at the tokamaks’ temperature (ΔG values of −17.2 MeV) while its kinetics is close to that of the DD reactions, which are at least two orders of magnitude lower than that of the DT reaction. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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16 pages, 7627 KiB

Open AccessArticle

Hybrid Surrogate Model-Based Multi-Objective Lightweight Optimization of Spherical Fuel Element Canister

by Yuchen Hao, Jinhua Wang, Musen Lin, Menghang Gong, Wei Zhang, Bin Wu, Tao Ma, Haitao Wang, Bing Liu and Yue Li

Energies 2023, 16(8), 3587; https://doi.org/10.3390/en16083587 - 21 Apr 2023

Viewed by 1838

Abstract

A number of canisters need to be lightweight designed to store the spherical fuel elements (SFE) used in high-temperature gas-cooled reactors (HTGR). The main challenge for engineering is pursuing high-accuracy and high-efficiency optimization simultaneously. Accordingly, a hybrid surrogate model-based multi-objective optimization method with [...] Read more.

A number of canisters need to be lightweight designed to store the spherical fuel elements (SFE) used in high-temperature gas-cooled reactors (HTGR). The main challenge for engineering is pursuing high-accuracy and high-efficiency optimization simultaneously. Accordingly, a hybrid surrogate model-based multi-objective optimization method with the numerical method for the lightweight and safe design of the SFE canister is proposed. To be specific, the drop analysis model of the SFE canister is firstly established where the finite element method—discrete element method (FEM–DEM) coupled method is integrated to simulate the interaction force between the SFE and canister. Through simulation, the design variables, optimization objectives, and constraints are identified. Then the hybrid radial basis function—response surface method (RBF–RSM) surrogate method is carried out to approximate and simplify the accurate numerical model. A non-dominated sorting genetic algorithm (NSGA-II) is used for resolving this multi-objective model. Optimal design is validated using comprehensive comparison, and the reduction of weight and maximum strain can be up to 2.46% and 44.65%, respectively. High-accuracy simulation with high-efficiency optimization is successfully demonstrated to perform the lightweight design on nuclear facilities. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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25 pages, 6672 KiB

Open AccessArticle

Repowering a Coal Power Plant Steam Cycle Using Modular Light-Water Reactor Technology

by Henryk Łukowicz, Łukasz Bartela, Paweł Gładysz and Staffan Qvist

Energies 2023, 16(7), 3083; https://doi.org/10.3390/en16073083 - 28 Mar 2023

Cited by 15 | Viewed by 3978

Abstract

This article presents the results of a techno-economic analysis of repowering a coal-fired power plant’s steam turbine system to instead accept heat produced by a pressurized water reactor-type small modular nuclear system (PWR SMR). This type of repowering presents a challenge due to [...] Read more.

This article presents the results of a techno-economic analysis of repowering a coal-fired power plant’s steam turbine system to instead accept heat produced by a pressurized water reactor-type small modular nuclear system (PWR SMR). This type of repowering presents a challenge due to the significantly lower steam pressure and temperature produced by the nuclear system. A 460 MW supercritical power unit with steam parameters of 28 MPa/560 °C/580 °C, operated in the Łagisza Power Plant in Poland, was selected for the analysis. After repowering, the turbine system would be fed with saturated steam from the steam generators of the SMRs at a pressure of 7 MPa and a temperature of 285 °C. In total, four options for repowering were analyzed. In all cases, the existing high-pressure section of the turbine was disconnected, and the existing low-pressure stages of the turbine, as well as all auxiliary and outward components (feedwater heaters, pumps, generator, condenser, condenser cooling, etc.), are re-used in their existing configurations, except for a feedwater-heater pump that needs to be replaced. In three cases, the existing intermediate pressure turbine section acts as the high-pressure stage of the repowered system. These cases include repowering without an additional reheater (case A), with an added single-stage reheater (B) and with an added two-stage reheater (C). In the fourth case (D), the existing intermediate pressure section was replaced by a new high-pressure turbine stage suited to the SMR live steam conditions. While all four repowering options are technically possible and may represent an economic advantage compared to a complete greenfield SMR installation, option D with a new high-pressure stage is clearly the best option available, with significant cost savings, leading to a lower levelized cost of electricity (LCOE) and a higher net present value (NPV) and net present value ratio (NPVR) than the greenfield case and all other repowering. For relatively new coal power plants with equipment in good condition, this type of repowering may present a cost optimal near-term pathway. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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27 pages, 3465 KiB

Open AccessArticle

Optimization of Natural Circulation District Heating Reactor Primary Heat Exchangers

by Jussi Saari, Heikki Suikkanen, Clara Mendoza-Martinez and Juhani Hyvärinen

Energies 2023, 16(6), 2739; https://doi.org/10.3390/en16062739 - 15 Mar 2023

Cited by 3 | Viewed by 2295

Abstract

Small modular reactors (SMRs) are gaining interest as a potential solution for cost-effective, carbon-neutral district heat (DH) production. The low pressures and temperatures permit much lighter and cheaper designs than in power plants, and efficiency is high as all heat generated can be [...] Read more.

Small modular reactors (SMRs) are gaining interest as a potential solution for cost-effective, carbon-neutral district heat (DH) production. The low pressures and temperatures permit much lighter and cheaper designs than in power plants, and efficiency is high as all heat generated can be sold to customers. In this work, the optimization of the primary heat exchangers in a natural-circulation 50-MW heating reactor concept was carried out to obtain an initial feasibility estimate for the concept for both baseload and load-following operation, as well as to obtain information on the characteristics of an optimized design. Studies on small natural circulation heat-only SMRs and the impact of heat exchanger design on the overall dimensions and economics have not been published before. Although a detailed heat exchanger cost model was used, the results should be considered tentative initial estimates, as much of the cost impact from the heat exchanger design comes from the effect the design has on the pressure vessel dimensions. While more detailed pressure vessel designs and cost functions are needed for final optimization, the feasibility of the concept is shown. Optimization for different load profiles produced near-identical designs, with the downcomer divided approximately in half between the heat exchanger at the top and an empty space at the bottom to maximize the pressure difference available for natural circulation. Although conservative, even pessimistic estimates were used in the absence of detailed cost functions, cost prices of 30–55 EUR/MWh_DH at a 10% interest rate were obtained, or only 20–40 EUR/MWh_DH at a 5% interest rate. This indicates potentially good competitiveness for the considered DH SMR concept. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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20 pages, 1824 KiB

Open AccessArticle

Radiation Workers and Risk Perceptions: Low Dose Radiation, Nuclear Power Production, and Small Modular Nuclear Reactors

by Margot Hurlbert, Larissa Shasko, Jose Condor and Dazawray Landrie-Parker

J. Nucl. Eng. 2023, 4(1), 258-277; https://doi.org/10.3390/jne4010020 - 8 Mar 2023

Cited by 1 | Viewed by 3694

Abstract

People’s affective response in relation to radiation is important in their risk perceptions of low-dose radiation (LDR), medical interventions involving LDR, and acceptance of nuclear power production. Risk perception studies generally relate to the health field of LDR or nuclear power. This study [...] Read more.

People’s affective response in relation to radiation is important in their risk perceptions of low-dose radiation (LDR), medical interventions involving LDR, and acceptance of nuclear power production. Risk perception studies generally relate to the health field of LDR or nuclear power. This study combines risk perceptions and acceptance of both. While acceptance by those with an understanding of radiation is demonstrated in focus groups, survey results disproved this correlation. Emotional response to the word radiation together with greater perceptions of risk to X-rays, were predictors of acceptance of nuclear power production. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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16 pages, 280 KiB

Open AccessArticle

A Zero-Carbon Nuclear Energy Future? Lessons Learned from Perceptions of Climate Change and Nuclear Waste

by Grace Dehner, Mark K. McBeth, Rae Moss and Irene van Woerden

Energies 2023, 16(4), 2025; https://doi.org/10.3390/en16042025 - 18 Feb 2023

Cited by 16 | Viewed by 7918

Abstract

Nuclear energy is proposed as part of the solution to a net-zero carbon future. However, environmental issues with nuclear energy remain. In this study, a total of 1616 participants from across the U.S. stated their position on the following statements: “Nuclear energy is [...] Read more.

Nuclear energy is proposed as part of the solution to a net-zero carbon future. However, environmental issues with nuclear energy remain. In this study, a total of 1616 participants from across the U.S. stated their position on the following statements: “Nuclear energy is a clean energy source”, “Nuclear energy may be part of the solution to climate change”, “I am willing to accept the building of new nuclear power stations if it is environmentally friendly and had a zero-carbon footprint”, and “Nuclear power may lead to more pollution and environmental contamination”. Participants were also asked “Do you think nuclear energy is a zero-carbon energy?” Logistic regression was used to determine how concern around climate change and nuclear waste predicted participant responses. Latent class analysis (LCA) was used to determine segments of respondents based on their perceptions of nuclear energy and the environment. Nuclear energy was perceived as being zero-carbon (74% agree), but not necessarily clean (50% agree). Nuclear energy was perceived as part of the solution to climate change (51% agree), but concern around more pollution and environmental contamination remained (42% agree). Concern around climate change was associated with greater odds of acceptance of nuclear energy, while concern around nuclear waste was associated with the opposite. The LCA suggested a “favorable”, “neutral”, and “negative” class, for which approximately 40%, 52%, and 8% of participants, respectively, belonged. This study suggests conditional (or reluctant) support for nuclear energy is occurring. Full article

(This article belongs to the Topic Nuclear Energy Systems)

14 pages, 4434 KiB

Open AccessArticle

Symmetric Heat Transfer Pattern of Fuel Assembly Subchannels in a Sodium-Cooled Fast Reactor

by Chao Huang, Jianquan Liu, Lihan Hai, Zenghao Dong and Xinyi Niu

Symmetry 2022, 14(11), 2423; https://doi.org/10.3390/sym14112423 - 16 Nov 2022

Cited by 2 | Viewed by 1719

Abstract

The method outlined in this paper is convenient and effective for studying the thermal performance of fuel assemblies cooled with sodium fast reactors using the subchannel procedure. To initially study an optimization model for a symmetric single fuel assembly heat transfer pattern analysis [...] Read more.

The method outlined in this paper is convenient and effective for studying the thermal performance of fuel assemblies cooled with sodium fast reactors using the subchannel procedure. To initially study an optimization model for a symmetric single fuel assembly heat transfer pattern analysis in a fast sodium-cooled reactor based on subchannel calculations, this paper innovatively proposes a subchannel heat transfer analysis method with the entransy dissipation theory, which can solve the limitations and inaccuracies of the traditional entropy method such as poor applicability for heat transfer processes without functional conversion and the paradox of entropy production of heat exchangers. The symmetric distributions of the thermal-hydraulic parameters such as coolant flow rate, coolant temperature, cladding temperature, and fuel pellet temperature were calculated, and the entransy dissipation calculation method corresponding to the fuel assembly subchannels was derived based on the entransy theory. The effect of subchannel differences on the thermal-hydraulic parameters and the symmetric distribution pattern of entransy dissipation during the cooling process of the fuel assembly was analyzed and compared from the symmetrical arrangement of subchannels in the axial and radial directions. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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17 pages, 3176 KiB

Open AccessArticle

Investigation of the Effect of Rod Worth Uncertainty on the Reactivity Measurements of CEFR Start-Up Tests via McCARD Monte Carlo Calculations

by Min Jae Lee, Jong-Hyuck Won, Jiwon Choe and Jae-Yong Lim

Energies 2022, 15(21), 8259; https://doi.org/10.3390/en15218259 - 4 Nov 2022

Cited by 1 | Viewed by 1671

Abstract

In the reactivity measurements of the China Experimental Fast Reactor (CEFR) start-up tests, five independent control rods were moved to compensate for the reactivity insertion. Since the recorded control rod positions were converted to reactivity via S-curves (rod worth curves), any uncertainty in [...] Read more.

In the reactivity measurements of the China Experimental Fast Reactor (CEFR) start-up tests, five independent control rods were moved to compensate for the reactivity insertion. Since the recorded control rod positions were converted to reactivity via S-curves (rod worth curves), any uncertainty in the S-curves can propagate to all reactivity measurements. In this work, we rigorously derived the uncertainty of the reactivity in terms of the statistical uncertainty of the S-curves with Monte Carlo (MC) simulations. Additionally, the average error of the control rod worth from the MC calculation was estimated from experiments and embedded into the uncertainty formulation. The formulation shows that the error of the reactivity is highly correlated to the changes in the control rod position during the reactivity measurements. McCARD MC simulations were then conducted for the CEFR start-up tests, and the calculated reactivity and uncertainty were compared with the measurements. The main error factor of each reactivity calculation was figured out by quantifying the uncertainty components. With the uncertainty formulation, the calculation results showed a better agreement compared with the measurements, as the relative errors were observed mostly within

2 σ

of the uncertainty. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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11 pages, 956 KiB

Open AccessArticle

The Modeling of Bubble Lift-Off Diameter in Vertical Subcooled Boiling Flow

by Jingyu Du, Chenru Zhao, Hanliang Bo and Xin Ren

Energies 2022, 15(18), 6857; https://doi.org/10.3390/en15186857 - 19 Sep 2022

Cited by 4 | Viewed by 2172

Abstract

Bubble lift-off diameter is characterized as the size of a bubble rising from a wall, which is vital in the boundary condition of heat transfer model and interfacial area transport equation. In this paper, mechanistic force analysis was conducted to explore a predictive [...] Read more.

Bubble lift-off diameter is characterized as the size of a bubble rising from a wall, which is vital in the boundary condition of heat transfer model and interfacial area transport equation. In this paper, mechanistic force analysis was conducted to explore a predictive model for bubble lift-off diameter in a vertical channel of subcooled boiling flow. Specifically, the component of growth force normal to the wall and the shear lift force lead to the lift-off of a bubble on the vertical surface. Through force analysis, we found that bubble lift-off diameter is arranged to be related to wall superheat, latent heat, liquid velocity, fluid properties, bulk liquid subcooling, etc. To account for the contribution of the influencing factors, the dimensionless bubble lift-off diameter was correlated with dimensionless parameters, including the Prandtl number, the Reynolds number, the Jacob number, and dimensionless subcooling. The proposed correlation was assessed according to experimental data and the predictions showed good agreement with the data. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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11 pages, 1962 KiB

Open AccessFeature PaperArticle

Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations

by Andrew G. Buchan, Dan G. Cacuci, Steven Dargaville and Christopher C. Pain

Energies 2022, 15(14), 5102; https://doi.org/10.3390/en15145102 - 13 Jul 2022

Viewed by 1908

Abstract

This article presents a new approach for the efficient calculation of sensitivities in radiation dose estimates, subject to imprecisely known nuclear material cross-section data. The method is a combined application of adjoint-based models to perform, simultaneously, both the sensitivity calculation together with optimal [...] Read more.

This article presents a new approach for the efficient calculation of sensitivities in radiation dose estimates, subject to imprecisely known nuclear material cross-section data. The method is a combined application of adjoint-based models to perform, simultaneously, both the sensitivity calculation together with optimal adaptive mesh refinement. Adjoint-based sensitivity methods are known for their efficiency since they enable sensitivities of all parameters to be formed through only two solutions to the problem. However, the efficient solutions can also be obtained by their computation on optimal meshes, here guided by goal-based adjoint approaches. It is shown that both mesh adaptivity and sensitivity can be computed by the same adjoint solution, meaning both can be performed without additional costs. A simple demonstration is presented based on the Maynard fixed-source problem where uncertainties, with respect to material cross-sections, of doses received in local regions are examined. It is shown that the method is able to calculate sensitivities with reduced computational costs in terms of memory and potentially computational time through reduced mesh size when using adaptive resolution in comparison to uniform resolution. In particular, it is the local spatial contributions to the sensitivity that are resolved more effectively due to the adaptive meshes concentrating resolution in those areas contributing the most to its value. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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11 pages, 3870 KiB

Open AccessArticle

First Prototype of a Cesium Oven Design for Negative-Ion-Source-Based Neutral Beam Injector at ASIPP

by Wei Liu, Bo Liu, Yuanzhe Zhao, Qinglong Cui, Chundong Hu and Lizhen Liang

Energies 2022, 15(12), 4409; https://doi.org/10.3390/en15124409 - 16 Jun 2022

Cited by 5 | Viewed by 2300

Abstract

The RF-driven negative ion source has a steady state characteristic and will be a promising ion source for neutral beam injection (NBI) in the future. Cesium (Cs) injection is an efficient method to enhance the yield of negative ions during plasma discharge. In [...] Read more.

The RF-driven negative ion source has a steady state characteristic and will be a promising ion source for neutral beam injection (NBI) in the future. Cesium (Cs) injection is an efficient method to enhance the yield of negative ions during plasma discharge. In order to support the engineering and physical research in this field, the Cs oven prototype has been developed for negative ion source based neutral beam injector at ASIPP. This article presents the design details of a Cs oven system, including the constant temperature control system, the mechanical structure of Cs oven, and the surface ionization detector (SID). SID is a measurement method for the cesium flux in the nozzle. The experiment results of constant temperature control system show that the control accuracy and function meet the requirements of device operation. Meanwhile, the simulation analysis of Cs vapor concentration has been carried out in this paper. According to the simulation results, the graph of total Cs flux is given in the article, which presents the reference for the subsequent device testing. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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18 pages, 5343 KiB

Open AccessArticle

Bayesian Inference of Cavitation Model Coefficients and Uncertainty Quantification of a Venturi Flow Simulation

by Jae-Hyeon Bae, Kyoungsik Chang, Gong-Hee Lee and Byeong-Cheon Kim

Energies 2022, 15(12), 4204; https://doi.org/10.3390/en15124204 - 7 Jun 2022

Cited by 6 | Viewed by 1993

Abstract

In the present work, uncertainty quantification of a venturi tube simulation with the cavitating flow is conducted based on Bayesian inference and point-collocation nonintrusive polynomial chaos (PC-NIPC). A Zwart–Gerber–Belamri (ZGB) cavitation model and RNG k-ε turbulence model are adopted to simulate the cavitating [...] Read more.

In the present work, uncertainty quantification of a venturi tube simulation with the cavitating flow is conducted based on Bayesian inference and point-collocation nonintrusive polynomial chaos (PC-NIPC). A Zwart–Gerber–Belamri (ZGB) cavitation model and RNG k-ε turbulence model are adopted to simulate the cavitating flow in the venturi tube using ANSYS Fluent, and the simulation results, with void fractions and velocity profiles, are validated with experimental data. A grid convergence index (GCI) based on the SLS-GCI method is investigated for the cavitation area, and the uncertainty error (U_G) is estimated as 1.12 × 10⁻⁵. First, for uncertainty quantification of the venturi flow simulation, the ZGB cavitation model coefficients are calibrated with an experimental void fraction as observation data, and posterior distributions of the four model coefficients are obtained using MCMC. Second, based on the calibrated model coefficients, the forward problem with two random inputs, an inlet velocity, and wall roughness, is conducted using PC-NIPC for the surrogate model. The quantities of interest are set to the cavitation area and the profile of the velocity and void fraction. It is confirmed that the wall roughness with a Sobol index of 0.72 has a more significant effect on the uncertainty of the cavitating flow simulation than the inlet velocity of 0.52. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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12 pages, 3695 KiB

Open AccessArticle

Optimal Radial Build and Transmutation Properties of a Fusion-Based Transmutation Reactor with Molten Salt Coolants

by Bong-Guen Hong

Energies 2022, 15(10), 3667; https://doi.org/10.3390/en15103667 - 17 May 2022

Viewed by 1802

Abstract

The optimal shape of a fusion-based transmutation reactor with a molten salt coolant was determined by plasma physics, technology, and neutronic requirements. System parameters such as neutron multiplication, power density, shielding, and tritium breeding, were calculated in a self-consistent manner by coupling neutron [...] Read more.

The optimal shape of a fusion-based transmutation reactor with a molten salt coolant was determined by plasma physics, technology, and neutronic requirements. System parameters such as neutron multiplication, power density, shielding, and tritium breeding, were calculated in a self-consistent manner by coupling neutron transport analysis with conventional tokamak systems analysis. The plasma physics and engineering levels were similar to those used in the International Thermonuclear Experimental Reactor. The influence of aspect ratio of the tokamak and fusion power on the radial build, and the transmutation properties associated with two molten salt options, FLiBe and FliNaBe, were investigated. Being compared with a transmutation reactor with a small aspect ratio, a transmutation reactor with large aspect ratio was smaller in size and had a larger maximum fusion power. This type of reactor also revealed increased tritium-breeding capability and a smaller initial transuranic (TRU) inventory with a slightly lower burn-up rate. The burn-up rate for molten salt using either FLiBe or FLiNaBe was similar, but the initial TRU inventory and the tritium-breeding capability were smaller with FLiNaBe compared with FLiBe. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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22 pages, 7025 KiB

Open AccessArticle

A Comparative Assessment on Different Aspects of the Non-Linear Instability Dynamics of Supercritical Fluid in Parallel Channel Systems

by Munendra Pal Singh, Abdallah Sofiane Berrouk and Suneet Singh

Energies 2022, 15(10), 3652; https://doi.org/10.3390/en15103652 - 16 May 2022

Cited by 3 | Viewed by 2599

Abstract

The thermal-hydraulic behavior of supercritical water reactors with a parallel channel configuration was examined through a non-linear instability analysis. This analysis was performed under wide-ranging conditions and aspects, including different working supercritical fluids, varied heat-flux and flow-rate conditions, and channel inclinations. The supercritical [...] Read more.

The thermal-hydraulic behavior of supercritical water reactors with a parallel channel configuration was examined through a non-linear instability analysis. This analysis was performed under wide-ranging conditions and aspects, including different working supercritical fluids, varied heat-flux and flow-rate conditions, and channel inclinations. The supercritical fluid (SCFs) dynamics were captured using the density, enthalpy, and velocity analytical approximation functions. The major findings show that both SCFs (water and carbon dioxide) experienced density wave oscillations at a low pseudo-subcooling number. Static instability characteristics were observed for supercritical water, at a relatively high subcooling number. Further, it was found that at different heat flux, the hotter channel makes the overall system more unstable, whereas, at equal heat flux, parallel channels perform similar to a single-channel system. However, the effect of the inclination angle was found to be negligible owing to supercritical pressure conditions. Moreover, stable and unstable limit cycles along with out-of-phase oscillation characteristics were observed in dynamic stability regions. The present model was also compared with experimental and numerical data. Moreover, co-dimension and numerical simulations were performed to confirm the observed non-linear characteristics. This study helps to enhance the heat transfer characteristics during safe operation of heated channel systems, such as nuclear reactors and solar thermal systems. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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20 pages, 12819 KiB

Open AccessArticle

Comparison of Blind and Open Calculation Results for Top-Slot Break LOCA in Fourth ATLAS Domestic Standard Problem

by Jongrok Kim, Byoung-Uhn Bae, Yusun Park, Jae Bong Lee, Nam-Hyun Choi, Seok Cho and Kyoung-Ho Kang

Energies 2022, 15(9), 3189; https://doi.org/10.3390/en15093189 - 27 Apr 2022

Cited by 1 | Viewed by 1932

Abstract

The advanced thermal-hydraulic test loop for accident simulation (ATLAS) was developed and operated at The Korea Atomic Energy Research Institute. The ATLAS is operated to simulate accidents in pressurized water reactors (PWRs). A domestic standard problem (DSP) using the ATLAS was proposed for [...] Read more.

The advanced thermal-hydraulic test loop for accident simulation (ATLAS) was developed and operated at The Korea Atomic Energy Research Institute. The ATLAS is operated to simulate accidents in pressurized water reactors (PWRs). A domestic standard problem (DSP) using the ATLAS was proposed for transferring the database of the integral effect test to Korean nuclear researchers and developing the safety analysis methodology of PWRs. The fourth DSP (DSP-04) exercise was performed during 2015–2017 with 15 participants (13 organizations), that are universities, government, and nuclear industries. In DSP-04, a top-slot break at the cold leg was chosen as the target scenario to resolve an issue about the effect of loop seal clearing and the reformation on the peak cladding temperature during the cold leg top-slot break LOCA for APR1400. The participants performed a code calculation for the experimental simulation and sensitivity studies for the enhancement of the code. This paper includes brief information about the experimental and major code assessment results. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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31 pages, 4237 KiB

Open AccessReview

A Review of Environmental and Economic Implications of Closing the Nuclear Fuel Cycle—Part Two: Economic Impacts

by Robin Taylor, William Bodel and Gregg Butler

Energies 2022, 15(7), 2472; https://doi.org/10.3390/en15072472 - 28 Mar 2022

Cited by 17 | Viewed by 4745

Abstract

Globally, around half a million tonnes of spent nuclear fuel (SNF) will be in dry or wet storage by around 2050. Continued storage is not sustainable and this SNF must eventually either be disposed (the open nuclear fuel cycle) or recycled (the closed [...] Read more.

Globally, around half a million tonnes of spent nuclear fuel (SNF) will be in dry or wet storage by around 2050. Continued storage is not sustainable and this SNF must eventually either be disposed (the open nuclear fuel cycle) or recycled (the closed fuel cycle). Many international studies have addressed the advantages and disadvantages of these options which can be considered now in the framework of sustainable development and the three pillars of: economic, environmental and societal impacts. To inform this debate, a detailed survey of the available literature related to economic assessments of closed and open cycles has been undertaken—this complements an earlier review on environmental impacts. Results of economic assessments showing how the management of spent fuels in the open and closed cycles impacts the costs of the nuclear fuel cycle, are usually presented in terms of the levelised cost of electricity (LCOE). It is clear that the costs of the back end of the fuel cycle are a relatively minor component of the LCOE and that there is significant overlap between calculations on open and closed fuel cycles. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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35 pages, 4558 KiB

Open AccessEditor’s ChoiceReview

A Review of Environmental and Economic Implications of Closing the Nuclear Fuel Cycle—Part One: Wastes and Environmental Impacts

by Robin Taylor, William Bodel, Laurence Stamford and Gregg Butler

Energies 2022, 15(4), 1433; https://doi.org/10.3390/en15041433 - 16 Feb 2022

Cited by 36 | Viewed by 10679

Abstract

Globally, around half a million tonnes of spent nuclear fuel (SNF) will be in dry or wet storage by around 2050. Continued storage is not sustainable, and this SNF must eventually either be disposed (the open nuclear fuel cycle) or recycled (the closed [...] Read more.

Globally, around half a million tonnes of spent nuclear fuel (SNF) will be in dry or wet storage by around 2050. Continued storage is not sustainable, and this SNF must eventually either be disposed (the open nuclear fuel cycle) or recycled (the closed fuel cycle). Many international studies have addressed the advantages and disadvantages of these options. To inform this debate, a detailed survey of the available literature related to environmental assessments of closed and open cycles has been undertaken. Environmental impacts are one of the three pillars that, alongside economic and societal impacts, must be considered for sustainable development. The aims are to provide a critical review of the open literature in order to determine what generic conclusions can be drawn from the broad base of international studies. This review covers the results of life cycle assessments and studies on waste arisings, showing how the management of spent fuels in the open and closed cycles impact the environment, including the use of natural resources, radioactive waste characteristics (heat loading, radiotoxicity and volume) and the size of the geological repository. In the framework of sustainable development, the next part of this review will consider economic impacts. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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18 pages, 7971 KiB

Open AccessArticle

Neutronic Analysis of Start-Up Tests at China Experimental Fast Reactor

by Jiwon Choe, Chirayu Batra, Vladimir Kriventsev and Deokjung Lee

Energies 2022, 15(3), 1249; https://doi.org/10.3390/en15031249 - 8 Feb 2022

Cited by 3 | Viewed by 2976

Abstract

The China Experimental Fast Reactor (CEFR) is a small, sodium-cooled fast reactor with 20 MW(e) of power. Start-up tests of the CEFR were performed from 2010 to 2011. The China Institute of Atomic Energy made some of the neutronics start-up-test data available to [...] Read more.

The China Experimental Fast Reactor (CEFR) is a small, sodium-cooled fast reactor with 20 MW(e) of power. Start-up tests of the CEFR were performed from 2010 to 2011. The China Institute of Atomic Energy made some of the neutronics start-up-test data available to the International Atomic Energy Agency (IAEA) as part of an international neutronics benchmarking exercise by distributing the experimental data to interested organizations from the member states of the IAEA. This benchmarking aims to validate and verify the physical models and neutronics simulation codes with the help of the recorded experimental data. The six start-up tests include evaluating criticality, control-rod worth, reactivity effects, and neutron spectral characteristics. As part of this coordinated research, the IAEA performed neutronics calculations using the Monte Carlo codes Serpent 2 and OpenMC, which can minimize modeling assumptions and produce reference solutions for code verification. Both codes model a three-dimensional heterogeneous core with an ENDF/B-VII.1 cross-section library. This study presents the calculation results with a well-estimated criticality and a reasonably good estimation of reactivities. The description and analysis of the core modeling assumptions, challenges in modeling a dense SFR core, results of the first phase of this project, and comparative analysis with measurements are presented. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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16 pages, 933 KiB

Open AccessArticle

Fourth-Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Response Uncertainties

by Ruixian Fang and Dan Gabriel Cacuci

J. Nucl. Eng. 2022, 3(1), 1-16; https://doi.org/10.3390/jne3010001 - 21 Jan 2022

Cited by 4 | Viewed by 2635

Abstract

This work quantifies the impact of the most important 4th-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) reactor physics benchmark with respect to the benchmark’s 180 group-averaged microscopic total cross sections, on the expected value, variance and skewness of the [...] Read more.

This work quantifies the impact of the most important 4th-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) reactor physics benchmark with respect to the benchmark’s 180 group-averaged microscopic total cross sections, on the expected value, variance and skewness of the benchmark’s leakage response. This work shows that, as the standard deviations of the cross sections increase, the contributions of the 4th-order sensitivities to the response’s expected value and variance become significantly larger than the corresponding contributions stemming from the 1st-, 2nd- and 3rd-order sensitivities. Considering a uniform 5% relative standard deviation for all microscopic total cross sections, the contributions from the 4th-order sensitivities to the expected value and variance of the PERP leakage response amount to 56% and 52%, respectively. Considering 10% uniform relative standard deviations for the microscopic total cross sections, the contributions from the 4th-order sensitivities to the expected value increase to nearly 90%. Consequently, if the computed value L(a) were considered to represent the actual expected value of the leakage response and the 4th-order sensitivities were neglected, the computed value would represent the actual expected value with an error of 3400%. Furthermore, uniform relative standard deviations of 5% and larger (10%) for the microscopic total cross sections cause the higher-order sensitivities to contribute increasingly higher amounts to the response standard deviation: the contributions stemming from the 4th-order sensitivities are larger than the contributions stemming from the 3rd-order sensitivities, which in turn are larger than those stemming from the 2nd-order sensitivities, which are themselves larger than the contributions stemming from the 1st-order sensitivities. This finding evidently underscores the need for computing sensitivities of order higher than first-order. The results obtained in this work also indicate that the 4th-order sensitivities produce a positive response skewness, causing the leakage response distribution to be skewed towards the positive direction from its expected value. Increasing the parameter standard deviations tends to decrease the value of the response skewness, causing the leakage response distribution to become more symmetrical about the mean value. The results presented in this work highlight the finding that the microscopic total cross section for hydrogen (H) in the lowest (“thermal”) energy group is the single most important parameter among the 180 microscopic total cross sections of the PERP benchmark, as it contributes most to the various response moments. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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14 pages, 8006 KiB

Open AccessArticle

Vacuum System Optimization for EAST Neutral Beam Injector

by Guodong Wang, Si Zhang, Changqi Chen, Ning Tang, Jiaqi Lang and Yuanlai Xie

Energies 2022, 15(1), 264; https://doi.org/10.3390/en15010264 - 31 Dec 2021

Cited by 8 | Viewed by 2601

Abstract

The neutral beam injector (NBI) generates a high-energy ion beam and neutralizes it, and then relies on drift transmission to inject the formed neutral beam into the fusion plasma to increase the plasma temperature and drive the plasma current. In order to better [...] Read more.

The neutral beam injector (NBI) generates a high-energy ion beam and neutralizes it, and then relies on drift transmission to inject the formed neutral beam into the fusion plasma to increase the plasma temperature and drive the plasma current. In order to better cooperate with the Experimental Advanced Superconductive Tokamak (EAST), part of the Chinese major national scientific and technological infrastructure, in carrying out long-pulse high-parameter physics experiments of 400 s and above, this paper considers the optimization of the current design and operation of the NBI beam line with a pulse width of 100 s. Based on an upgraded and optimized NBI vacuum chamber and the structure of the beam-line components, the gas-source characteristics under the layout design of the NBI system are analyzed and an NBI vacuum system that meets relevant needs is designed. Using Molflow software to simulate the transport process of gas molecules in the vacuum chamber, the pressure gradient in the vacuum chamber and the heat-load distribution of the low-temperature condensation surface are obtained. The results show that when the NBI system is dynamically balanced, the pressure of each vacuum chamber section is lower than the set value, thus meeting the performance requirements for the NBI vacuum system and providing a basis for subsequent implementation of the NBI vacuum system upgrade using engineering. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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49 pages, 474 KiB

Open AccessArticle

The n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (n^th-CASAM-L): II. Illustrative Application

by Dan Gabriel Cacuci

Energies 2021, 14(24), 8315; https://doi.org/10.3390/en14248315 - 10 Dec 2021

Cited by 2 | Viewed by 1913

Abstract

This work illustrates the application of the n^th-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “n^th-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as [...] Read more.

This work illustrates the application of the n^th-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “n^th-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as encountered in radiation protection and shielding. The first-, second-, and third-order sensitivities of responses that depend on both the forward and adjoint particle fluxes are obtained exactly, in closed-form, underscoring the principles and methodology underlying the n^th-CASAM-L. The results presented in this work underscore the fundamentally important role of the n^th-CASAM-L in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling. Full article

(This article belongs to the Topic Nuclear Energy Systems)

42 pages, 477 KiB

Open AccessArticle

The n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (n^th-CASAM-L): I. Mathematical Framework

by Dan Gabriel Cacuci

Energies 2021, 14(24), 8314; https://doi.org/10.3390/en14248314 - 10 Dec 2021

Cited by 13 | Viewed by 2131

Abstract

This work presents the mathematical framework of the n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “n^th-CASAM-L”), which is conceived for obtaining the exact expressions of arbitrarily-high-order (n^th-order) sensitivities of a generic [...] Read more.

This work presents the mathematical framework of the n^th-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “n^th-CASAM-L”), which is conceived for obtaining the exact expressions of arbitrarily-high-order (n^th-order) sensitivities of a generic system response with respect to all of the parameters (including boundary and initial conditions) underlying the respective forward/adjoint systems. Since many of the most important responses for linear systems involve the solutions of both the forward and the adjoint linear models that correspond to the respective physical system, the sensitivity analysis of such responses makes it necessary to treat linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator admits an adjoint operator). The n^th-CASAM-L determines the exact expression of arbitrarily-high order sensitivities of responses to the parameters underlying both the forward and adjoint models of a nonlinear system, thus enable the most efficient and accurate computation of such sensitivities. The mathematical framework underlying the n^th-CASAM is developed in linearly increasing higher-dimensional Hilbert spaces, as opposed to the exponentially increasing “parameter-dimensional” spaces in which response sensitivities are computed by other methods, thus providing the basis for overcoming the “curse of dimensionality” in sensitivity analysis and all other fields (uncertainty quantification, predictive modeling, etc.) which need such sensitivities. In particular, for a scalar-valued valued response associated with a nonlinear model comprising TP parameters, the 1^st-⁻CASAM-L requires 1 additional large-scale adjoint computation (as opposed to TP large-scale computations, as required by other methods) for computing exactly all of the 1^st-⁻order response sensitivities. All of the (mixed) 2^nd-order sensitivities are computed exactly by the 2^nd-CASAM-L in at most TP computations, as opposed to TP(TP + 1)/2 computations required by all other methods, and so on. For every lower-order sensitivity of interest, the n^th-CASAM-L computes the “TP next-higher-order” sensitivities in one adjoint computation performed in a linearly increasing higher-dimensional Hilbert space. Very importantly, the n^th-CASAM-L computes the higher-level adjoint functions using the same forward and adjoint solvers (i.e., computer codes) as used for solving the original forward and adjoint systems, thus requiring relatively minor additional software development for computing the various-order sensitivities. Full article

(This article belongs to the Topic Nuclear Energy Systems)

17 pages, 12321 KiB

Open AccessArticle

RANS CFD Analysis of Hump Formation Mechanism in Double-Suction Centrifugal Pump under Part Load Condition

by Yong Liu, Dezhong Wang, Hongjuan Ran, Rui Xu, Yu Song and Bo Gong

Energies 2021, 14(20), 6815; https://doi.org/10.3390/en14206815 - 18 Oct 2021

Cited by 7 | Viewed by 2310

Abstract

The RANS (Reynolds-averaged Navier–Stokes equations) with CFD (Computational Fluid Dynamics) simulation method is used to analyze the head hump formation mechanism in the double-suction centrifugal pump under a part load condition. The purpose is to establish a clear connection between the head hump [...] Read more.

The RANS (Reynolds-averaged Navier–Stokes equations) with CFD (Computational Fluid Dynamics) simulation method is used to analyze the head hump formation mechanism in the double-suction centrifugal pump under a part load condition. The purpose is to establish a clear connection between the head hump and the microcosmic flow field structure, and reveal the influence mechanism between them. It is found that the diffuser stall causes a change in the impeller capacity for work, and this is the most critical reason for hump formation. The change in the hydraulic loss of volute is also a reason for hump, and it is analyzed using the energy balance equation. The hump formation mechanism has not been fully revealed so far. This paper found the most critical flow structure inducing hump and revealed its inducing mechanism, and greatly promoted the understanding of hump formation. The impeller capacity for work is analyzed using torque and rotational speed directly, avoiding large error caused by the Euler head formula, greatly enhancing the accuracy of establishing the connection between the impeller capacity for work and the coherent structure in the flow field under a part load condition. When a pump is running in the hump area, a strong vibration and noise are prone to occur, endangering the pump safety and reliability, and even the pump start and the transition of different working conditions may be interrupted. Revealing the hump formation mechanism provides a key theoretical basis for suppressing hump. Hump problems are widespread in many kinds of pumps, causing a series of troubles and hazards. The analysis method in this paper also provides a reference for other pumps. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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17 pages, 11688 KiB

Open AccessArticle

Experimental Validation of Flow Uniformity Improvement by a Perforated Plate in the Heat Exchanger of SFR Steam Generator

by Myung-Ho Kim, Van Toan Nguyen, Sunghyuk Im, Yohan Jung, Sun-Rock Choi and Byoung-Jae Kim

Energies 2021, 14(18), 5846; https://doi.org/10.3390/en14185846 - 15 Sep 2021

Cited by 3 | Viewed by 2789

Abstract

The steam generator in a nuclear power plant is a type of heat exchanger in which heat transfer occurs from the hot fluid in multiple channels to the cold fluid. Therefore, a uniform flow over multiple channels is necessary to improve heat exchanger [...] Read more.

The steam generator in a nuclear power plant is a type of heat exchanger in which heat transfer occurs from the hot fluid in multiple channels to the cold fluid. Therefore, a uniform flow over multiple channels is necessary to improve heat exchanger efficiency. The study aims at experimentally investigating the improvement of flow uniformity by the perforated plate in the heat exchanger used for a sodium-cooled fast reactor stream generator. A 1/4-scale experimental model for one heat exchanger unit with 33 × 66 channels was manufactured. The working fluid was water. A perforated plate was systematically designed using numerical simulations to improve the flow uniformity over the 33 × 66 channels. As a result, the flow uniformity greatly improved at a slight cost of pressure drop. To validate the numerical results, planar particle image velocimetry measurements were performed on the selected planes in the inlet and outlet headers. The experimental velocity profiles near the exits of the channels were compared with numerical simulation data. The experimental profiles agreed with the numerical data well. Both the numerical simulation and the experimental results showed a slight increase in pressure drop, despite significant improvement in the flow uniformity. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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28 pages, 3146 KiB

Open AccessArticle

Fourth-Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: I. Computed Sensitivities

by Ruixian Fang and Dan Gabriel Cacuci

J. Nucl. Eng. 2021, 2(3), 281-308; https://doi.org/10.3390/jne2030024 - 24 Aug 2021

Cited by 11 | Viewed by 3117

Abstract

This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd-order to 4th-order for a polyethylene-reflected plutonium (PERP) OECD/NEA reactor physics benchmark. Specifically, by applying the 4th-order comprehensive adjoint sensitivity analysis methodology (4th-CASAM) to the PERP benchmark, this work presents the [...] Read more.

This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd-order to 4th-order for a polyethylene-reflected plutonium (PERP) OECD/NEA reactor physics benchmark. Specifically, by applying the 4th-order comprehensive adjoint sensitivity analysis methodology (4th-CASAM) to the PERP benchmark, this work presents the numerical results of the most important 4th-order sensitivities of the benchmark’s total leakage response with respect to the benchmark’s 180 microscopic total cross sections, which includes 180 4th-order unmixed sensitivities and 360 4th-order mixed sensitivities corresponding to the largest 3rd-order ones. The numerical results obtained in this work reveal that the number of 4th-order relative sensitivities that have large values (e.g., greater than 1.0) is far greater than the number of important 1st-, 2nd- and 3rd-order sensitivities. The majority of those large sensitivities involve isotopes ¹H and ²³⁹Pu contained in the PERP benchmark. Furthermore, it is found that for most groups of isotopes ¹H and ²³⁹Pu of the PERP benchmark, the values of the 4th-order relative sensitivities are significantly larger than the corresponding 1st-, 2nd- and 3rd-order sensitivities. The overall largest 4th-order relative sensitivity

S^{(4)} (σ_{t, 6}^{g = 30}, σ_{t, 6}^{g = 30}, σ_{t, 6}^{g = 30}, σ_{t, 6}^{g = 30}) = 2.720 \times 10^{6}

is around 291,000 times, 6350 times and 90 times larger than the corresponding largest 1st-order, 2nd-order and 3rd-order sensitivities, respectively, and the overall largest mixed 4th-order relative sensitivity

S^{(4)} (σ_{t, 6}^{30}, σ_{t, 6}^{30}, σ_{t, 6}^{30}, σ_{t, 5}^{30}) = 2.279 \times 10^{5}

is also much larger than the largest 2nd-order and 3rd-order mixed sensitivities. The results of the 4th-order sensitivities presented in this work have been independently verified with the results obtained using the well-known finite difference method, as well as with the values of the corresponding symmetric 4th-order sensitivities. The 4th-order sensitivity results obtained in this work will be subsequently used on the 4th-order uncertainty analysis to evaluate their impact on the uncertainties they induce in the PERP leakage response. Full article

(This article belongs to the Topic Nuclear Energy Systems)

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