Critical Reactor Research Articles

Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: regularity and error analysis

Abstract Stochastic partial differential equation (PDE) eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic crystal structures. In this paper we present a multilevel quasi-Monte Carlo (MLQMC) method for approximating the expectation of the minimal eigenvalue of an elliptic eigenvalue problem with coefficients that are given as a series expansion of countably-many stochastic parameters. The MLQMC algorithm is based on a hierarchy of discretizations of the spatial domain and truncations of the dimension of the stochastic parameter domain. To approximate the expectations, randomly shifted lattice rules are employed. This paper is primarily dedicated to giving a rigorous analysis of the error of this algorithm. A key step in the error analysis requires bounds on the mixed derivatives of the eigenfunction with respect to both the stochastic and spatial variables simultaneously. Under stronger smoothness assumptions on the parametric dependence, our analysis also extends to multilevel higher-order quasi-Monte Carlo rules. An accompanying paper (Gilbert, A. D. & Scheichl, R. (2023) Multilevel quasi-Monte Carlo methods for random elliptic eigenvalue problems II: efficient algorithms and numerical results. IMA J. Numer. Anal.) focusses on practical extensions of the MLQMC algorithm to improve efficiency and presents numerical results.

Low-cost photoreactors for highly photon/energy-efficient solar-driven synthesis

Low-cost photoreactors for highly photon/energy-efficient solar-driven synthesis

Propagation of Uncertainties due to Nuclear Data for the LCT086 Reactor System

An Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) benchmark has been established over recent years to satisfy an increasing demand from the nuclear community for best-estimate predictions accompanied by uncertainty and sensitivity analyses. The main objectives of the OECD/NEA benchmark activity are to determine uncertainties in modeling for reactor systems using best-estimate methods under steady-state and transient conditions and to quantify the impact of these uncertainties for each type of calculation in multiphysics analyses. In terms of light water reactor analyses, an international uncertainty analysis, “Benchmarks for Uncertainty Analysis in Modelling (UAM) for the Design, Operation and Safety Analysis of LWRs” is currently in progress, being coordinated by the OECD/NEA. In the neutronic phases of the benchmark, the uncertainty due to nuclear data is being studied for various LWR types. The LCT086 benchmark, which is a VVER-type reactor criticality benchmark experiment, has been identified to form part of the validation matrix for the uncertainty methodology development. Resulting from this, the main focus of the present work is to propagate the uncertainty due to the nuclear data for two cases (LCT086/Case1 and LCT086/Case3) presented in the LCT086 benchmark. Both fuel assembly and core models were used for the analysis. The code package used to perform the calculations was SCALE 6.2.1. In particular, the function modules KENO-VI, SAMPLER, and TSUNAMI-3D of SCALE 6.2.1 were used. MCNP 6.1 was also used for continuous-energy criticality calculations. In addition to propagating the uncertainty due to the nuclear data, the uncertainty due to selected input parameters as bounded by the manufacturing tolerances were also propagated so that the modeling methods employed could be verified against those reported in the LCT086 benchmark. The results obtained for the nuclear data uncertainty were further compared with nuclear data uncertainty propagation results for the OECD/NEA UAM Kozloduy-6 reactor system. The uncertainty in the multiplication factor k eff is reported in pcm together with the main contributors to the uncertainty from the nuclear data reported in %Δk / k .

Analisis Kekritisan dan Rasio Konversi Reaktor Cepat Berpendingin Gas dengan Variasi Fraksi Bahan Bakar UN-PuN Menggunakan Skema Burn-up Modified CANDLE Arah Radial

Analysis of the criticality and conversion ratio of a gas-cooled fast reactor (GFR) with various UN-PuN fuel fractions using modified CANDLE scheme burn-up in radial direction has been conducted. The fuel fraction varies from 40% - 60% with 5% intervals, the cladding fraction is 10% and the coolant fraction varies from 30% -50%. Data calculations were performed using SRAC 2006 programming with JENDL 4.0 library data. The reactor is divided into 10 regions with equal volume in the radial direction. Each region is filled with natural uranium fuel without enrichment with different burn-up levels. Regions are arranged in such a way that the reactor can reach critical conditions throughout the burn-up period. The results showed that variations in the 40% fuel fraction had not been able to reach critical conditions at the beginning of life, while 45%-60% fuel fraction variations had reached reactor criticality. The conversion ratio for all fuel fractions is greater than 1, which indicates that a breeding process appears in the GFR reactor core. The conversion ratio for all variations in fuel fractions has almost the same pattern for all regions. The first region has the largest conversion ratio value because it has natural uranium as fuel input which has the highest density compared to other regions.

Estimate of Neutron Fluence Using Isotope Ratio Method for ZR-2.5NB Materials Irradiated in the National Research Universal Reactor

Abstract The isotope ratio method (IRM) is a technique used for estimating the energy production in a fission reactor by measuring isotope ratios in nonfuel reactor components. This method has been successfully demonstrated on the estimation of cumulative energy production as well as plutonium production in graphite-moderated and light-water-moderated reactors for nonproliferation purposes. In this paper, IRM was used to estimate neutron fluence in Zr-2.5Nb materials irradiated in fast neutron (FN) irradiation facilities in the National Research Universal (NRU) reactor. Neutron fluence has been shown to be an important parameter for studying irradiation effects on the performance and properties of critical reactor components. Selected isotope ratios of hafnium and iron were used as indicators of the neutron fluence in Zr-2.5Nb sample materials. Correlations between neutron fluence and the indicator element isotope ratios were generated using the reactor physics simulation codes Winfrith improved multigroup scheme (WIMS)-AECL and SCALE/Oak Ridge Isotope GENeration code (ORIGEN). Inductively coupled plasma-mass spectrometry (ICP-MS) was used to obtain accurate measurements of the isotope ratios. Neutron fluence values estimated using IRM, were in good agreement with the values based on measured irradiation power histories of the NRU reactor. This study proposes a potential application of IRM to the estimation of neutron fluence for critical reactor components in heavy-water-moderated reactors such as pressure and calandria tubes in CANDU® reactors.

Multi-group analysis of Minor Actinides transmutation in a Fusion Hybrid Reactor

New nuclear technologies are currently being study to face High Level Waste treatment and disposal issues. Generally, GEN-IV fission Fast Reactors (FR) are considered the waste-burners of the future. In fact, a fast flux turns out to be the best choice for actinides irradiation in critical reactors because of favorable cross section conditions. Differently, Fusion Fission Hybrid Reactors (FFHR) are futuristic devices based on the combination of fusion and fission systems and could represent an alternative to FRs. In such systems, the choice spectrum of the neutron flux that irradiates HLW may be non-obvious due to some operational constraints which have to be considered. To design and optimize these systems as waste-burners, one should fully understand the transmutation dynamics occurring into the fission region. A multi-energy-group analysis by FISPACT-II code has been set to analyze the conversion processes in scenarios characterized by different neutron energy spectra and fluences. The results of this study show that, despite fast fluxes are characterized by better behaviors in terms of radiotoxicity treatment, the difficulties of reaching high reaction yields may require solutions involving moderators or broadened neutron fluxes to increase the reactions probabilities and, consequently, actinides mass conversion yield.

Reactor physics calculation and measurement during first approach to criticality of Apsara-U research reactor

Apsara-U is 2 MW swimming pool type research reactor with low enriched uranium fuelled core. On 10th September 2018, Apsara-U was made critical at 18:41 hrs. After the First Approach to Criticality (FAC) of Apsara-U, low power physics experiments were carried out. The experiments included reactivity worth measurement of all reactivity devices and measurement of the isothermal temperature coefficient of reactivity. Inflated reactivity worth of Shut off Rods as calculated from the power from some of the neutronic channels were obtained on account of shadowing effect of neutron reaching the detector locations. Further the isothermal coefficient of reactivity was observed positive. In this paper, we discuss the mentioned Reactor Physics measurement and related theoretical calculation during FAC that includes solving the benchmark problem for validating the calculation tools, and steady state thermal hydraulic analysis, Reactivity initiated transients for the FAC core configuration for ascertaining the safety of the reactor.

At-power subcritical multiplication in the advanced test reactor

The degree to which a given physical subdivision of a critical reactor acts as a neutron source for other lobes is not analytically characterized for general application. ATR and ATRC both operate at power, and individual power-producing lobes rely on each other as neutron sources in order to maintain constant power, which in general requires either exactly critical multiplication within a reactor or an external neutron source. This work shows that lobe powers in ATR or ATRC can be related with subcritical multiplication theory, demonstrating that the lobes are not individually critical. This explanation is significant for ATR due to the desire to irradiate a large variety of experiments simultaneously, each having its impact on the core neutron population. This work also establishes the lack of relationship between experiment reactivity worth and cross-sections calculated from fundamental nuclear data. For any physical subdivision of any other critical reactor, it is likewise true that the subdivision undergoes only subcritical multiplication.

Neutronic analysis on molten salt reactor FUJI-12 using 235U as fissile material in LiF-BeF2-UF4 fuel

Neutronic analysis on the Molten Salt Reactor FUJI-12 using the fissile material 235U in LiF-BeF2-UF4 has been carried out. The problem faced in the use of thorium-based fuel is that the amount of 233U is small and not available in nature. 233U was produced through the 232Th breeding at a cost of $46 million/kg. That is a very high price when compared to 235U enrichment, which is only $100/kg. The MSR FUJI-12 used in this study is a generation IV reactor with a mixture of liquid salt fuel LiF-BeF2-ThF4-UF4 and thorium-based fuel (232Th+233U). In this study, neutronic analysis was carried out by replacing thorium-based fuel with uranium-based fuel (235U+238U). Neutronic analysis was performed using the OpenMC 0.13.0 code, which is a Monte Carlo simulation-based neutron analysis code. The nuclear data library used for neutronic calculations is ENDF B-VII/1. The fuel is used in a LiF-BeF2-UF4 molten salt mixture with three eutectic compositions: fuel 1, fuel 2, and fuel 3. Each fuel composition is optimized by enriching 235U in UF4 by 3 % to 8 %. The optimization results show the stability of the reactor criticality value, which is the main parameter so that the reactor can operate for the specified time. The optimization results show that fuel 1 cannot reach its optimal state in each variation of 235U enrichment. Fuel 2 and fuel 3 can reach optimal conditions at a minimum enrichment of 8 % and 7 % 235U. The results of the analysis of the distribution of the neutron flux in the reactor core show the distribution of nuclear reactions that occur in the core. The distribution of flux values in fuel 1 shows that the fission chain reaction is not running perfectly. Fuel 2 and fuel 3 are more stable by maintaining maximum flux at the center of the reactor core.

A Criticality and depletion analysis of the European Lead-Cooled Training Reactor (ELECTRA)

In this article, a criticality and depletion analysis of the European Lead-Cooled Training Reactor (ELECTRA), a low-power, compact, fast lead-cooled reactor, was performed. The active core model and simulations were made by using the MCNPX code. First, the model is compared with the reference and the influence of the reflector radius on the system is analyzed. Secondly, it was simulated the fuel combustion after 30 years of continuous operation of the ELECTRA, managing to evaluate the transmutation of a reprocessed fuel in a compact lead-cooled reactor.

Parametric Study of Thorium Fuel Utilization on Small Modular Pressurized Water Reactors (PWR)

Small Modular Pressurized Water Reactor (PWR) can be used to overcome the problem of electricity shortages in remote areas with fewer populations. These reactors usually use uranium-based fuel. Currently, the use of thorium-based fuels for this type of reactor has received constant attention, leading to several investigations of fuel performance. This study aims to determine the performance of thorium-based fuel in the PWR core at a power level of 300 MWt. The analysis was carried out by varying the percentage of U-233 as fissile material in Thorium (Th-233U)O2 fuel by 3%-8% and Pa-231 variation as burnable poison 0.2%-5%. In addition, analysis of changes in the volume fraction of fuel ranging from 40%-60%, with the type of cladding used in the form of Zirlo. The calculation system uses the SRAC computer code with PIJ and CITATION modules for cell and core calculations, using JENDL-4.0 nuclide data. Parameters analyzed from the fuel cell calculation results are reactor criticality, excess reactivity, and power density profile. The analysis results show that the best fuel performance is found in fuel volume fraction of 60%, U-233 configuration on the fuel of 4-5-6%, and the addition of 2.5% Pa-231. This fuel configuration can achieve cycles of up to 19 years with excess reactivity at BOL of 2.57% dk/k and excess reactivity at EOL of 0.87% dk/k.

Capturing the Temperature Dependence of Cleavage Fracture Toughness in the Ductile-to-Brittle Transition Regime in Ferritic Steels Using an Improved Engineering Local Approach

Abstract Ferritic steels, which are typically used for critical reactor components, including reactor pressure vessels (RPV), exhibit a temperature-dependent probability of cleavage fracture, termed ductile-to-brittle transition. The fracture process has been linked to the interaction between matrix plasticity and second-phase particles. Under high-enough loads, a competition exists between cleavage and ductile fracture, which results from particles rupturing to form microcracks or particles decohering to form microvoids, respectively. Currently, there is no sufficiently adequate model that can predict accurately the reduced probability of cleavage with increasing temperature and the associated increase of plastic deformation. In this work, failure probability has been estimated using a local approach to cleavage fracture incorporating the statistics of microcracks. It is shown that changes in the deformation material properties are not enough to capture the significant changes in fracture toughness. Instead, a correction to the fraction of particles converted to eligible for cleavage microcracks, with an exponential dependence on the plastic strains, is proposed. The proposed method is compared with previous corrections that incorporate the plastic strains, and its advantages are demonstrated. The method is developed for the RPV steel 22NiMoCr37 and using experimental data for a standard compact tension C(T) specimen. The proposed approach offers more accurate calculations of cleavage fracture toughness in the ductile-to-brittle transition regime using only a decoupled model, which is attractive for engineering practice.

Flow-Induced Vibration of Solitary Wire-Wrapped Cylinders in Axial Flow

Vibration of nuclear power plant components can cause fretting wear and fatigue that can eventually lead to component failure. Flexible, high-aspect-ratio components under flow, such as the wire-wrapped cylindrical fuel elements in a liquid metal-cooled fast reactor core, are particularly susceptible to vibration due to their low natural frequencies. The flow-induced vibrations experienced by such components tend to be random and of low amplitude and frequency; however, at critical flow velocities these components can experience self-excited, fluid-elastic instabilities that can lead to immediate failure. Such failures of critical reactor components, particularly those that act as fission product barriers, can lead to prolonged shutdowns of nuclear power plants and even to their permanent closure. Thus, a better understanding of the vibration response of wire-wrapped cylinders in axial flow is needed. This study details the development of a theoretical model that incorporates the effects of a helical wire wrap along a cylinder to understand its impact on the dynamic response of the cylinder under flow. This theoretical model is compared against experimental vibration data of varying geometries of solitary wire-wrapped cylinders in confined axial flow. The results of this study provide an improved knowledge of how a helical wire wrap can affect the dynamic response of a cylinder under flow.

The Hypatia Experiment: Yttrium Hydride and Highly Enriched Uranium Critical Experiment

The Hypatia measurement campaign with YHx moderators and highly enriched uranium (HEU) was completed in January 2021 at the U.S. Department of Energy’s National Criticality Experiments Research Center at the Nevada National Security Site. This measurement campaign provided unique integral measurements based on two experimental configurations and investigated the temperature effects of yttrium hydride (YHX = 1.8 and 1.9) in a critical reactor system, which is of potential interest for microreactor designs. The Hypatia experiment consisted of a fuel column composed of HEU, 93 wt% 235 U discs, encapsulated YHX, aluminum oxide heater plates, and other moderator and reflector materials (beryllium, depleted uranium, and graphite) inserted into a thick beryllium reflector. During the Hypatia experiment, baseline measurements were taken at room temperature. The aluminum oxide heater plates were specially designed and used for this project to increase the central core temperature to a range of temperatures, after which additional reactivity measurements were taken. Thermal and neutronic calculations predicted that YHX is a unique material that can exhibit a positive temperature coefficient of reactivity (i.e., reactivity can increase as the temperature in the YHX increases). Reactors using YHX should account for this unique feature during design, and the results of the Hypatia experiment significantly aid that process. For configuration 1, six different temperature reactivity measurements were taken with four YHX cans in the fuel column. For configuration 2, six different temperature reactivity measurements were taken with two YHX cans in the fuel column. The use of these two configurations provide a comparison of neutronic effects from the YHX cans versus other components. Preliminary conclusions show the positive temperature coefficient is similar but slightly less than predicted by simulations. These two sets of data will be used to separate the reactivity coefficients of the fuel and other materials in the fuel column.

Evaluation of the aging management system for the Triga research nuclear reactor in Brazil / Avaliação do sistema de gerenciamento do envelhecimento do reator nuclear de pesquisa Triga no Brasil

As most research reactors have over 40 years of operational experience, maintenance, modernization and renovation are increasingly important for safety and operational life extension. This is due to the monitoring and development of techniques to control and mitigate the negative effects of operating conditions on structures, systems and components. Aging management is a strategy of engineering, operation, maintenance and other actions to control, within acceptable limits, the aging degradation of the facility. The first criticality of the IPR-R1 Triga research reactor (Training, Research, Isotopes, Atomics) occurred in 1960 with a maximum thermal power of 30 kW. Therefore, this reactor has been operating for more than 60 years. One of the issues that comes from the long time of the operation is the management of aging. This includes functions and issues related to operation, inspections, design changes, testing, and others. The IPR-R1 reactor is a North American project. So, the requirements of United State Nuclear Regulatory Commission (U.S.NRC) are applicable. This article discusses the International Atomic Energy Agency (IAEA), and U.S.NRC requirements to implement an aging management system for the CDTN IPR-R1 Triga Reactor.

Are tungsten-based nuclear fusion components truly invisible to x-ray inspection?

The ability to detect undesired volumetric defects in reactor components could affect the safety and reliability of a fusion power plant and change the expected lifetime and performance of the reactor. This is even more true for critical reactor parts like plasma-facing components (PFCs) which have to withstand challenging in-vessel conditions due to a combination of plasma bombardment, radiation, and nuclear heating. The structural integrity of these components prior to their installation in a nuclear fusion reactor needs to be assessed non-destructively. Until now, industrial x-ray radiography and tomography have not been used to non-destructively inspect fusion components due to their lack of penetration power into dense material such as tungsten which is often used to manufacture PFCs. However, aiming to revert this consolidated belief, we have demonstrated for the first time the feasibility of assessing volumetric defects non-destructively on DEMO divertor mock-up by means of MeV energy range x-ray tomography. The authors believe that the application of this technology could be easily extended for inspecting large fusion components and positively impact procedures to be followed in the qualification of fusion components for current and future nuclear reactors.

ANALYSIS OF FUEL TEMPERATURE REACTIVITY COEFFICIENT OF THE PWR USING WIMS CODE

The Fuel Temperature Reactivity Coefficient (FTRC) is an important parameter in design, control, and safety, particularly in PWR reactor. It is then very important to validate any new library for an accurate prediction of this parameter. The objective of this work is to determine the value of the FTRC parameter using the new WIMDS library based on ENDF/BVIII.0 nuclear data files. For this purpose, it is used a set of light water moderated lattice experiments as the PWR-1175 MWe experiment critical reactors, the reactor using UO2 fuel pellet. The analysis is used with WIMSD-5B lattice code with original cross-section libraries and WIMSD-5B with ENDF/B-VIII.0 new cross-section libraries. The results showed that the fuel temperatures reactivity coefficients for the PWR reactor using original libraries is – 3.10 pcm/K with enrichment of 3.1% but for ENDF/B-VlII.0 libraries is – 3.00 pcm/K. Compared to the experimental data of the reactor core, the difference is in the range of 6.9 % for ENDF/B-VIII.0 libraries. It can be concluded that for the reactor, it is better to use ENDF/B-VIII.0 libraries because the original library is not accurate anymore.

Time dependent reliability analysis for a critical reactor safety system based on fault tree approach

Loss of coolant in the operation of any nuclear power plant will eventually become the primary source of hazard in the sequence of events leading to reactor core uncovery. Subsequent failure in removing the nuclear decay heat and preventing the core uncovery will further lead to loss of coolant accident (LOCA). In conjunction to this safety concern, it is crucial that the reliability of the plant emergency core cooling system is systematically and critically analysed. This article presents a case study on the time dependent reliability analysis for a safety injection system (SIS) of an advanced pressurized water reactor, based on the failure mode and effect analysis (FMEA) and fault tree (FT) analysis approach. The identified generic data for component reliability are carefully reviewed and used in this study. Based on the base case model, sensitivity and importance measure analysis for basic events are performed and the outcomes gained are presented and discussed. From the analysis, it is shown that the safety injection pumps of the SIS contribute significantly to the reliability of the system. In the short (at 0.5 hour) and long (7.0 hours and 72.0 hours) run, safety injection pumps are critical and influence the reliability of the SIS the most. The SIS’s FT logic model that has been developed and calculated shows the usability of the FMEA and FT approach that are implemented in analysing SIS time dependent reliability.

Reactor Physics Calculation and Measurement During First Approach to Criticality of Apsara-U Research Reactor

Reactor Physics Calculation and Measurement During First Approach to Criticality of Apsara-U Research Reactor

О ТРАНСМУТАЦИИ МИНОРНЫХ АКТИНОИДОВ В ЖИДКОСОЛЕВОМ РЕАКТОРЕ-СЖИГАТЕЛЕ

Reduction in the amount of accumulated minor actinides (Np, Am, and Cm isotopes), as well as, the long-lived fission products, to the extent possible, is a top-priority task for the nuclear power engineering. Transmutation of this waste in a special-purpose molten-salt burner reactor has been currently proposed as a possible solution for this problem. The objective of the present paper is to investigate basic regularities of Np, Am, and Cm transmutation in the molten salt burner reactor and to determine optimal operational conditions of the reactor. In the optimal equilibrium mode just fluorides of these elements are added into the fuel composition but the fission products are extracted from it. This mode are reached by maintaining a specified actinide concentration. In order to provide the reactor criticality with a lower than optimum actinide concentration, it is required to add plutonium in the feed fuel instead of a certain amount of minor actinides, thus impairing the transmutation efficiency. To keep the critical state in the equilibrium mode, in situations where the actinide concentration is higher than the optimum one, it is essential to extract a portion of fuel with high content of 238Pu. It has been shown that the reactor configuration is the primary factor responsible for optimum actinide concentration value and that this value varies little with the feed fuel composition, the type of salt dissolving agent, and the fuel reprocessing mode. Optimal concentration for the molten-salt burner reactor with the core volume ranging from 2 to 30 m3 is within 17…10 mole %.