Neutron Flux Distribution Research Articles

Neutron flux evaluation algorithm with a combination of Monte Carlo and removal-diffusion calculation methods for boron neutron capture therapy.

In Japan, the clinical treatment of boron neutron capture therapy (BNCT) has been applied to unresectable, locally advanced, and recurrent head and neck carcinomas using an accelerator-based neutron source since June of 2020. Considering the increase in the number of patients receiving BNCT, efficiency of the treatment planning procedure is becoming increasingly important. Therefore, novel and rapid dose calculation algorithms must be developed. We developed a novel algorithm for calculating neutron flux, which comprises of a combination of a Monte Carlo (MC) method and a method based on the removal-diffusion (RD) theory (RD calculation method) for the purpose of dose calculation of BNCT. We present the details of our novel algorithm and the verification results of the calculation accuracy based on the MC calculation result. In this study, the "MC-RD" calculation method was developed, wherein the RD calculation method was used to calculate the thermalization process of neutrons and the MC method was used to calculate the moderation process. The RD parameters were determined by MC calculations in advance. The MC-RD calculation accuracy was verified by comparing the results of the MC-RD and MC calculations with respect to the neutron flux distributions in each of the cubic and head phantoms filled with water. Comparing the MC-RD calculation results with those of MC calculations, it was found that the MC-RD calculation accurately reproduced the thermal neutron flux distribution inside the phantom, with the exception of the region near the surface of the phantom. The MC-RD calculation method is useful for the evaluation of the neutron flux distribution for the purpose of BNCT dose calculation, except for the region near the surface.

Effects of Neutron Flux Distribution and Control Rod Shadowing on Control Rod Calibrations in the Oregon State TRIGA® Reactor

Control rod calibration experiment results for the Oregon State TRIGA® Reactor (OSTR) immediately following LEU conversion in 2008, and MCNP® 5 predicted rod worths from the 2008 LEU Conversion Safety Analysis Report (CSAR) are discussed. The reactivity worth of the four OSTR control rods is measured using the rod-pull method. Reactor power and period measurements in this method rely on the fission chamber power detector on the north side of the reflector. It is proposed that the location of the fission chamber and the neutron flux distribution in the core may result in an inaccurate reactor period measurement due to the asymmetry of the neutron flux distribution in the OSTR core. The asymmetry of the flux is believed to be more pronounced during super-criticality, resulting in errors in the time-of-power-rise measurements. As a result, control rod calibration experiments may under-predict or over-predict the reactivity worth of certain control rods. A time-independent Monte–Carlo method for the quantification of these effects is presented. Thermal flux maps at the core axial mid-plane are obtained from the model to inform discrepancies between predicted and observed results.

On the effect of the core boundary power distribution on the radiation situation in reactor components

The assessment of the neutron flux distribution in nuclear power plant components, like reactor internals and the pressure vessel, is one of the most important parts of their residual lifetime evaluation process because the irradiation damage of these components is strongly dependent on it. The fast neutron fluences in power reactors are generally determined using calculations and verified by measurements. Discrepancies between them sometimes occur, which can be caused by be the inaccuracies in the power distribution used in neutron transport calculations. This paper quantifies the effect of uncertainty in power density on the neutron fluences behind the reactor pressure vessel (RPV). An increase in power density was experimentally simulated by implementing a higher uranium enrichment of certain selected pins. The experiment was also simulated using the MCNP code with the ENDF/B-VII.1 library. Both the experimental and calculational data show a significant local increase in neutron flux. Even behind the RPV, the increase is as high as 25%, while the local power increase in the perturbed pins is about 70–80%, which is approximately equal to the 2 σ power density uncertainties. A good agreement between measurement and calculation was found.

Discussing the possibility of using thorium-based fuels as an alternative fuel to uranium dioxide fuel for APR-1400 reactor

This work investigates the possibility of using thorium-based fuels as an alternative fuel for advanced power reactor APR-1400. MCNPX code version 2.7 with cross-section library ENDF.VII has been used to design an APR-1400 fuel assembly. This code has been used to study the neutronic performance of the proposed thorium-based Fuel types (0.944Th, U)O2, (0.955Th, 233U)O2, (0.934Th, rgPu)O2. The fuel burn-up parameters such as infinity multiplication factor (kinf), initial heavy metals concentrations, Minor actinides concentration and fission products concentration have been analyzed during 1500 effective full power days (FPDSs) for thorium-based Fuel types and compared with the common fuel. The analysis of the horizontal thermal power and neutron flux distribution provides valuable insights into the behavior and performance of the suggested Fuel types in the APR-1400 assembly. The analysis of the neutronic results ensures the viability of using the proposed thorium-based fuel types as an alternative fuel to UO2 because they achieved acceptable safety parameter values and provided a good power distribution through the fuel assembly compared to UO2.

Nodal expansion method based reduced-order model for control rod movement

Control rod movement is one of the main considerations for nuclear reactor safety analysis, whose accuracy simulation requires a significant amount of computing time. In this paper, combined with the proper orthogonal method (POD) and least square method (LSM), a novel reduced-order method based on the nodal expansion method (RO-NEM) is proposed to reduce the consumption of computational resources. Based on the snapshots obtained from NEM, the reduced-order model constructed by RO-NEM can predict the neutron flux distribution at the unknown state efficiently. Results from typical benchmark problem demonstrate that the proposed RO-NEM can accurately and efficiently obtain neutron distribution. Global POD (GPOD) and local POD (LPOD) methods for selecting snapshots to generate POD basis are compared in this work. Results show that LPOD has better calculation accuracy and efficiency than GPOD. This work provides new perspectives and directions for improving the efficiency of numerical calculations in nuclear reactor engineering.

Preliminary conceptual design with neutronics and thermal-hydraulics assessments of FuSTAR

The fluoride-salt-cooled high-temperature advanced reactor (FuSTAR) is an advanced small modular reactor, which aims to the electric supplement and clean heat production to western China. In order to have good economy and safety, FuSTAR needs to have the characteristics of small size, light weight, deep burnup, and inherent safety. A conceptual design of FuSTAR is proposed in this study with neutronics and thermal-hydraulics assessments. In this study, its concept is established with two-region fuel to flatten core power, and the neutron spectrum of the core is in the thermal spectrum to improve the utilization of thermal neutrons and reduce fuel inventory. Neutronics and thermal-hydraulics analyses are also carried out, and established the core layout and material ratio under the near-critical condition. Burnup depth of the fuel, power distribution, neutron flux distribution, flow and heat transfer in rod-bundles channel, and 1/6 core porous media analysis are also investigated. The parameters of the designed core are evaluated quantitatively from various aspects. The results show that the core design in this study has sufficient shutdown depth, the equilibrium cycle is 3.24 years, and the discharge burnup depth is 106 GWd/MtU. The helical cruciform fuel (HCF) adopted by this reactor has a better flow and heat transfer capacity than cylindrical-type fuel at the inner channel. The analysis of 1/6 core porous media shows that the peak fuel temperature under normal operating condition is 1009.3 K, which is far below the limit of 1573 K. Relevant design and analysis results can provide the reference for the subsequent small modular FHR design and construction.

FEMFFUSION and its verification using the C5G7 benchmark

FEMFFUSION is an open source code that solves the multigroup neutron transport equation using the diffusion and the SPN approximations. This code uses the continuous Galerkin finite element method to be able to deal with any type of geometry, structured or unstructured, and problem dimension. To verify the program, a research study of the two-dimensional C5G7 benchmark has been performed, including the static, time-dependent and neutron noise computations. Numerical results include the effective multiplication factor, keff, the spatial neutron fluxes, and neutron power distributions for the static computations. The total neutron power evolution of a given transient and the neutron flux distribution evolution for the different energy groups. In addition, neutron noise frequency domain calculation were completed for perturbations of some cross-section in the reactor core. All computation have been performed using different SPN approximations. FEMFFUSION results are verified against the official OECD/NEA benchmark results.

Research on Neutronics Safety Parameters of the AP1000 Nuclear Reactor under Different Conditions

Changes in temperature during reactor operation may cause changes in physical parameters, leading to core overheating and accidents. It is essential to analyze and assess the safety parameters of the core under different operating conditions. This paper investigates the effects of fuel temperature, moderator density, boron concentration, and control rod state on AP1000 safety parameters. The study uses RMC and NJOY to calculate the changes in reactivity factor, effective delayed neutron fraction, and neutron generation time of the AP1000 reactor under different operating conditions. The changes in reactivity coefficients, neutron fluxes, and relative power densities of AP1000 reactors are analyzed for normal and accidental operating conditions. The results indicated that the reactivity coefficient remained negative under accident conditions, which ensured the safe operation of the reactor. The delayed neutron fraction, neutron flux, and power density distributions are affected by fuel temperature, moderator density, and control rod position. The control rod worth was sufficient for the emergency shutdown of the reactor under accidental conditions. It is demonstrated that the operation of the AP1000 reactor under study conditions is safe and controllable.

Neutronic calculations for the VVER-1000 MOX core computational benchmark using the OpenMC code

The goal of this study is to perform neutronic calculations of the VVER-1000 MOX core computational benchmarks with an OpenMC code along with ENDF/B-VII.1 nuclear data library. The results of neutronic analysis using the OpenMC Monte Carlo code for the VVER-1000 MOX core, containing 30% mixed oxide fuel with low enriched uranium fuel, are presented in this study. As per the benchmark report, all six states are considered in the present study. The keff values, assembly average fission reaction rates, and pin-by-pin fission rates were calculated as per benchmark criteria. In addition, 2D thermal and fast neutron-flux distribution were also generated. The reactivity results and neutron flux distribution were compared with other results in which benchmark analysis was performed using the same core geometry and it showed great similarity with slight deviation. This shows that the modeling of the VVER-1000 MOX core was done successfully using OpenMC. Because OpenMC was successfully used for neutronics calculation of the VVER-1000 whole core, it may be mentioned here that OpenMC code can also be utilized for neutronics and other reactor core physics analyses of the VVER-1200 reactor which is to be commissioned in Bangladesh in the upcoming year.

Estimation of Continuous Distribution of Iterated Fission Probability Using an Artificial Neural Network with Monte Carlo-Based Training Data

The Monte Carlo neutron transport method is used to accurately estimate various quantities, such as k-eigenvalue and integral neutron flux. However, in the case of estimating a distribution of a desired quantity, the Monte Carlo method does not typically provide continuous distribution. Recently, the functional expansion tally (FET) and kernel density estimation (KDE) methods have been developed to provide a continuous distribution of a Monte Carlo tally. In this paper, we propose a method to estimate a continuous distribution of a quantity in all phase-space variables using a fully connected feedforward artificial neural network (ANN) model with Monte Carlo-based training data. As a proof of concept, a continuous distribution of iterated fission probability (IFP) was estimated by ANN models in two distinct fissile systems. The ANN models were trained on the training data created using the Monte Carlo IFP method. The estimated IFP distributions by the ANN models were compared with the Monte Carlo-based data that include the training data. Additionally, the IFP distributions by the ANN models were also compared with the adjoint angular neutron flux distributions obtained with the deterministic neutron transport code PARTISN. The comparisons showed varying degrees of agreement or discrepancy; however, it was observed that the ANN models learned the general trend of the IFP distributions from the Monte Carlo-based training data.

Optimization of IEA-R1 reactor core parameters using the particle swarm algorithm

This work aims on the development of a FORTRAN 90 code to solve the Loading Pattern Optimization Problem (LPOP) in the IEA-R1 research reactor at the Nuclear and Energy Research Institute (IPEN/CNEN-SP) in São Paulo, Brazil. The code integrates the Particle Swarm Optimization (PSO) method, with the current reactor calculation methodology. The objective function seeks to maximize the effective multiplication factor (keff), minimize the peak power factor (PPF), and achieve the most uniform neutron flux distribution possible. A comparison with the parameters of the reactor’s current configuration, and the code successfully finds solutions meeting the standard problem requirements. The new configuration enhances peak power (6.93%) and variance (9.62%), slightly increases neutron flux (0.48%), and marginally reduces in keff (0.45%). Additionally, it lowers the maximum fuel cladding temperature (0.7%), contributing to reactor safety.

Empowering nuclear reactor analysis: OpenNode for accurate 3D core simulation through nodal expansion neutron diffusion equations solving

OpenNode is a sophisticated reactor core simulation tool, meticulously designed for educational purposes. Its main function is to solve the complex partial differential equation governing multi-group neutron diffusion in a Cartesian geometry. OpenNode relies on the second- and fourth-order Nodal Expansion Method (NEM) to provide accurate solutions to three-dimensional steady-state problems, encompassing both the direct and adjoint modes. At the heart of this method, the neutron balance equation serves as the fundamental framework for calculating the nodal neutron flux and the effective multiplication factor, enabling the complex evaluation of neutron flux distributions within individual nodes.The NEM methodology, carefully programmed in Fortran-90 in OpenNode, meticulously decomposes the reactor core into nodes of reasonable size. This approach balances computational efficiency and accuracy, achieving outstanding precision even when using a reduced number of computational meshes. To further increase the number of equations while maintaining the balance between unknowns, OpenNode judiciously incorporates two essential approximations: the Weighted Residual Method (WRM) and the Quadratic Transverse Leakage (QTL) approximation.OpenNode transcends simple computational prowess by adopting an intuitive Graphical User Interface (GUI), meticulously developed by combining Python 3, Qt Designer, and Blender software. This Python-powered graphical interface offers users a seamless, user-friendly experience, facilitating tasks such as data entry, execution of complex simulations, calculation of results, data visualization, 3D design of nuclear core geometry, and in-depth analysis of results. One of OpenNode’s key features is its innate flexibility, enabling it to solve problems in both 2D and 3D Cartesian geometries. This adaptability makes it a versatile tool suitable for a wide range of research and power reactor applications, offering users the ability to model and design reactors with unrivaled ease.To substantiate OpenNode’s reliability, comprehensive criticality calculations are carried out in various scenarios, including single-cell verification, BIBLIS, KOEBERG cores in two dimensions (2D), and IAEA cores in three dimensions (3D). The results clearly demonstrate OpenNode’s robustness and reliability in multidimensional criticality analysis. In particular, OpenNode adheres to an open-source philosophy, making it readily available for download. This commitment to open access fosters collaboration and paves the way for wider adoption within the education and research communities, nurturing a thriving ecosystem of shared knowledge and exploration.

A novel approach for managing the excess reactivity at the beginning of the fuel cycle of VVER-1200

This work discusses various fuel pellet designs loaded with different types and concentrations of burnable absorbers to suppress the excess reactivity at the early stage of the fuel life in the VVER-1200 fuel assembly. MCNPX, V. 2.7 with the CINDER 90 fuel depletion code was utilized to analyze the neutronic characteristics of the proposed cases. Concentric shells (CS) of integral burnable absorbers are investigated in the fuel tube. Gadolinium and Erbium at different concentrations are investigated in the CS at different operation cycles to manage the excess reactivity. Gadolinium and boron as traditional burnable absorbers (BAs) are investigated in the standard fuel assembly to compare their results with the suggested cases. The infinity multiplication factor (kinf), the concentrations of the fuel composition, reactor-grade plutonium (rgPu), minor actinides (MAs) and some important fission products poisoned were studied with burnup. The radial power and thermal neutron flux distribution through one-six of the VVER-1200 assembly have been analyzed to distinguish the optimum BA and design for flattening the power profile. The neutronic analysis indicates that using Er2O3 in a concentric shell of a fuel pellet is an interesting method for reactivity management.

Analysis of Kobayashi benchmark with indigenous Monte Carlo neutron transport code PATMOC

The solution of the neutron transport equation is the basic input for the reactor physics design of a nuclear reactor system. Because of the complexities of geometry and cross-section data, the neutron transport equation is generally solved using numerical methods. One of the difficulties in the solution using these methods concerns the accuracy of distribution of neutron flux in the system containing void regions in a highly absorbing medium. The difficulty arises because of the issue in the continuity of flux at the void and material interface. There is a sudden and large change in the flux at this interface. Kobayashi benchmarks are widely used problems for testing the ability and accuracy of reactor physics codes to compute neutron flux distribution on such systems. An indigenous Monte Carlo neutron transport code, named PATMOC, has been designed and developed at Bhabha Atomic Research Centre (BARC) for reactor physics design applications. The Kobayashi benchmarks have been used to test the PATMOC code to verify its accuracy in flux computation for systems with voids in-between high absorbing materials. Our results show that the PATMOC estimated values of flux distribution in the system compare very well with the reference results provided with the benchmark. In this paper we present the detailed results and analyses of this benchmark with PATMOC code.

Evaluation of the CNESTEN's TRIGA Mark II research reactor physical parameters with TRIPOLI-4® and MCNP

This paper focuses on the development of a new computational model of the CNESTEN's TRIGA Mark II research reactor using the 3D continuous energy Monte-Carlo code TRIPOLI-4 (T4). This new model was developed to assess neutronic simulations and determine quantities of interest such as kinetic parameters of the reactor, control rods worth, power peaking factors and neutron flux distributions. This model is also a key tool used to accurately design new experiments in the TRIGA reactor, to analyze these experiments and to carry out sensitivity and uncertainty studies. The geometry and materials data, as part of the MCNP reference model, were used to build the T4 model. In this regard, the differences between the two models are mainly due to mathematical approaches of both codes. Indeed, the study presented in this article is divided into two parts: the first part deals with the development and the validation of the T4 model. The results obtained with the T4 model were compared to the existing MCNP reference model and to the experimental results from the Final Safety Analysis Report (FSAR). Different core configurations were investigated via simulations to test the computational model reliability in predicting the physical parameters of the reactor. As a fairly good agreement among the results was deduced, it seems reasonable to assume that the T4 model can accurately reproduce the MCNP calculated values. The second part of this study is devoted to the sensitivity and uncertainty (S/U) studies that were carried out to quantify the nuclear data uncertainty in the multiplication factor keff. For that purpose, the T4 model was used to calculate the sensitivity profiles of the keff to the nuclear data. The integrated-sensitivities were compared to the results obtained from the previous works that were carried out with MCNP and SCALE-6.2 simulation tools and differences of less than 5% were obtained for most of these quantities except for the C-graphite sensitivities. Moreover, the nuclear data uncertainties in the keff were derived using the COMAC-V2.1 covariance matrices library and the calculated sensitivities. The results have shown that the total nuclear data uncertainty in the keff is around 585 pcm using the COMAC-V2.1. This study also demonstrates that the contribution of zirconium isotopes to the nuclear data uncertainty in the keff is not negligible and should be taken into account when performing S/U analysis.

Validation and Neutronic Analysis of the CENM TRIGA MARK II SCALE Research Reactor Model: Computations Versus Experiment

This research analysis is mainly devoted to enhancing the safe and optimum use of the Center des Etudes Nucléaires de la Maâmora (CENM) TRIGA MARK II research reactor. To serve this purpose, various integral neutronic responses, such as the effective multiplication factor keff, the effective delayed neutron fraction βeff, the neutron flux distributions at the beam port entrances and the pneumatic transfer system bottom, the pin power peaking factors, the total excess reactivity, the control rod worth, the shutdown margin, and the worth of 11 fuel elements taken from different TRIGA core positions are calculated in order to evaluate the accuracy and the reliability of the developed TRIGA SCALE reactor model. The aim has been fulfilled by comparing the TRIGA SCALE results with those obtained by the MCNP TRIGA model, as well as with some recent experimental measurements from 2021. In general, all the obtained results reveal a good consistency between the SCALE and MCNP TRIGA models studied in this paper. The results analysis indicates also that the B-2 fuel element (Ring B) is the hottest rod among the 101 fuel rods existing in the TRIGA reactor core, which releases a maximum power of 31.67 kW. Furthermore, the total control rod worth, the total core excess reactivity, and the shutdown margin results are also closer to the experimental measurements.

Neutron and Gamma Flux Distributions of an Americium–Beryllium Facility: Modelling and Simulation

Neutron and Gamma Flux Distributions of an Americium–Beryllium Facility: Modelling and Simulation

Readout Electronics for Spatial Distribution Measurement of Neutron Beam Flux in BNCT

Boron neutron capture therapy (BNCT) is a promising cancer treatment that selectively destroys tumor cells using a neutron beam. However, accurately and fast measuring the spatial distribution of neutron flux is critical to ensuring effective treatment. To address this challenge, Micromegas detectors are applied for the first time to measure the spatial distribution of neutron beam flux in BNCT. Due to the high flux, large area, and multiple components of the BNCT beam, the design of readout electronics that can handle high counting rate, large channel numbers, high integration, and discrimination of multiple beam components is challenging. This paper proposes a targeted readout electronics system to overcome this challenge. A modular readout structure based on the PCI Express (PXIe) platform is designed for 384-channel readout. A fully parallel readout structure is developed and fast shaper parameters are optimized to achieve high counting rate for each readout channel. A multi-channel high-speed, large-capacity caching technique is developed to address the high-speed data storage problem. Digital shapers are implemented in field-programmable gate array (FPGA) to achieve high integration. Tests demonstrate that each readout channel can support a counting rate of 800 kHz and achieve an excellent position resolution of 1.4 mm. Furthermore, final tests on the BNCT beam confirm that our system can successfully measure the flux spatial distribution of different neutron components.

Results and lessons learned from the Generation IV SCWR-FQT comprehensive Monte Carlo computational benchmark

A joint European Canadian Chinese development of a supercritical water-cooled small modular reactor technology has been in progress since September 2020 in the framework of a Horizon 2020 project called ECC-SMART. A specific work package has been dedicated to studying the design- and safety-related neutronic parameters and reactor physics behavior of the SCW-SMR to support the pre-conceptual design process. Three Monte Carlo codes, viz., MCNP, OpenMC, and Serpent, were selected for pre-conceptual design applications and code-to-code comparison within the Gen-IV SCWR-FQT reactor physics computational benchmark. The effective multiplication factor, the axial power distribution within the fuel, the axial three-group neutron flux distribution, and the spatial distribution of the energy deposition due to neutron and photon interactions were determined. In this paper, results and lessons learned from this study are presented, and useful considerations are summarized to provide guidance in obtaining consistent results among the three Monte Carlo codes.

Three-Dimensional Surrogate Model Based on Back-Propagation Neural Network for Key Neutronics Parameters Prediction in Molten Salt Reactor

The simulation and analysis of neutronics parameters in Molten Salt Reactors (MSRs) is fundamental for the design of the reactor core. However, high-fidelity neutron transport calculations of the MSR are time-consuming and require significant computational resources. Artificial neural networks (ANNs) have been used in various industries, and in recent years are increasingly introduced in the nuclear industry. Back-Propagation neural network (BPNN) is one type of ANN. A surrogate model based on BP neural network is developed to quickly predict two key neutronics parameters in reactor core: the effective multiplication factor (keff) and the three-dimensional channel-by-channel neutron flux distribution. The dataset samples are generated by modeling and simulating different operation states of the Molten Salt Reactor Experiment (MSRE) using the Monte Carlo code. Hyper-parameters optimization is performed to obtain the optimal surrogate model. The numerical results on the test dataset show good agreement between the surrogate model and the Monte Carlo code. Additionally, the surrogate model significantly reduces computation time compared to the Monte Carlo code and greatly enhances efficiency. The feasibility and advantages of the proposed surrogate model is demonstrated, which has important significance for real-time prediction and design optimization of the reactor core.