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The KIR computer code intended for calculations of nuclear reactor kinetics using the Monte Carlo method is described. The algorithm implemented in the code is described in detail. Some results of test calculations are given.
The dilute-acid thermochemical hydrolysis step used in the production of liquid fuels from lignocellulosic biomass requires precise residence-time control to achieve high monomeric sugar yields. Difficulty has been encountered reproducing residence times and yields when small batch reaction conditions are scaled up to larger pilot-scale horizontal auger-tube type continuous reactors. A commonly used naive model estimated residence times of 6.2-16.7 min, but measured mean times were actually 1.4-2.2 the estimates. Here, this study investigated how reactor residence-time distribution (RTD) is affected by reactor characteristics and operational conditions, and developed a method to accurately predict the RTD based on key parameters. Screw speed, reactor physical dimensions, throughput rate, and process material density were identified as major factors affecting both the mean and standard deviation of RTDs. The general shape of RTDs was consistent with a constant value determined for skewness. The Peclet number quantified reactor plug-flow performance, which ranged between 20 and 357.
A recent article [D. A. Brown, G. P. A. Nobre, and M. W. Herman, Phys. Rev. C 98, 024616 (2018)] proposed a modification of the cross section formula used in practical calculations of compound nucleus reactions. In this work, we discuss the main concepts and approximations of statistical reaction theory and conclude that the standard practical implementations of the cross section formula remain the preferred choice.
A nuclear weapon test would be a prolific source of neutrinos in a relatively short time window (<1 s). These neutrinos could be easily detected at distances of 10s of meters or more by detector technology that has been developed for studying neutrino interactions from nuclear reactors. Such a concept was already proposed at LANL in the 50’s but was finally reject for a more controlled experiment at a nuclear reactor – this latter method went on to win the 1995 Nobel prize in physics for the detection of the neutrino. However, times have changed and revisiting this concept could have new unappreciated applications.
Multiphysics reactor analysis has become one of the leading activities of most nuclear engineering research groups. Coupled neutronics and thermal/hydraulics (T/H) simulations have traditionally been performed by adopting deterministic transport tools and reactor system T/H codes. The main reason for avoiding higher fidelity numerical methods like continuous-energy Monte Carlo analysis has been the high computational cost of coupled, full-scale simulations. Nowadays, high fidelity multiphysics simulations represent a hot research topic, with several applications involving advanced nuclear systems. Liquid fuel Molten Salt Reactors (MSRs) feature peculiar physical phenomena that are not present in solid fuel reactors. Some of these phenomena are not correctly resolved by legacy reactor physics tools, and require specific treatments. This work focuses in particular on the analysis of the effect of the delayed neutron precursors drift and the impact of liquid fluid thermal expansion and compressibility in postulated criticality excursion transients in fast-spectrum MSRs. A new modeling tool based on a Monte Carlo approach for neutronics (Serpent code) coupled to a Computational Fluid Dynamic (CFD) analysis (OpenFOAM) was developed to obtain accurate modeling and simulation of these phenomena. The development of the Serpent Monte Carlo code [1] at VTT in the past few years has made this code particularly attractive for performing multiphysics studies. The availability of a flexible multiphysics interface, on-the-fly Doppler broadening and density-based collision rejection, and Delta-tracking, proved of paramount importance for the computationally efficient performance of coupled Monte Carlo/CFD calculations [2]. OpenFOAM is a C++ multiphysics toolkit featured by automatic matrix construction and solution capabilities for scalar and vector partial differential equations (PDEs), adopting several possible differencing and interpolation schemes, based on the Finite-Volume method. The ease of implementing the constitutive equations of different physical phenomena makes OpenFOAM particularly suitable for the modeling of complex coupled phenomena. In the past, several research activities proposed the adoption of both Serpent and OpenFOAM for the modeling and simulation of MSRs and the associated fuel cycles. In this work, these tools have been internally coupled for the steady-state and transient analysis of fast-spectrum systems, accounting for the effect of delayed neutron precursors transport and the salt thermal expansion and compressibility.
Nuclear data, along with numerical methods and the associated calculation schemes, continue to play a key role in reactor design, reactor core operating parameters calculations, fuel cycle management and criticality safety calculations. Due to the intensive use of Monte-Carlo calculations reducing numerical biases, the final accuracy of neutronic calculations increasingly depends on the quality of nuclear data used. This paper gives a broad picture of all ingredients treated by nuclear data evaluators during their analyses. After giving an introduction to nuclear data evaluation, we present implications of using the Bayesian inference to obtain evaluated cross sections and related uncertainties. In particular, a focus is made on systematic uncertainties appearing in the analysis of differential measurements as well as advantages and drawbacks one may encounter by analyzing integral experiments. The evaluation work is in general done independently in the resonance and in the continuum energy ranges giving rise to inconsistencies in evaluated files. For future evaluations on the whole energy range, we call attention to two innovative methods used to analyze several nuclear reaction models and impose constraints. Finally, we discuss suggestions for possible improvements in the evaluation process to master the quantification of uncertainties. These are associated with experiments (microscopic and integral), nuclear reaction theories and the Bayesian inference.
Parallelization is applied to the neutron calculations performed by the heterogeneous method on a graphics processing unit. The parallel algorithm of the modified TREC code is described. The efficiency of the parallel algorithm is evaluated.
The physical phenomena associated with the modes of heat transfer within a packed pebble bed can be modelled by explicitly solving the associated partial differential equations using a finite volume method approach. Convection from the spheres to coolant, conduction inside and between spheres as well as radiation between various components of a packed bed reactor are the main modes of heat transfer, with several lesser, albeit contributing, phenomena also present. Advances both in software and computing power allow for a larger portion of a packed bed to be modeled with greater accuracy by integrating all applicable physics models in one simulation. A representative unstructured packed bed of uniform spheres was generated with a discrete element method (DEM) and the flow domain modelled using the CFD software package Star-CCM+, taking into account all primary modes of heat transfer as well as a user-specified approach to take secondary effects into account. Effects in the bulk, near-wall and wall-contact regions were investigated. By using such a fully integrated explicit model, a deeper understanding can be can be gained into the role of the underlying phenomena and their respective contributions to the overall heat transfer process. Fuel spheres were modeled explicitly with the conduction between spheres, bed and reflectors being prescribed by contact heat transfer theory as a function of temperature and compressive forces within the bed. The effective thermal conductivity (k{sub eff}), flow pressure drop, as well as temperature distributions in the spheres and coolant were calculated and compared with experimental results from published literature. Good agreement was found with experimental results and the significant contribution of radiation as well as inter-pebble conduction to the effective thermal conductivity could be observed from the results. (authors)
In the advanced reactor domain, a flexible and scalable software/hardware infrastructure is crucial for integrating and validating various control technologies. This study used the Microreactor Automated Control System (MACS) hardware platform as a testbed. MACS was originally designed to mirror Idaho National Laboratory (INL)'s Microreactor Applications Research Validation and Evaluation (MARVEL), a 85-kW thermal fission microreactor. It features control drums for simulated reactivity control; lights that function as a surrogate reactor core, with the brightness being proportional to the reactor power; and light sensors that emulate neutron detectors. To transform MACS into a physical twin of MARVEL for evaluating control methods, the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND) software was employed. This software integrated the hardware with two models of the MARVEL core, based on Reactor Excursion and Leak Analysis Program (RELAP5-3D) and Monte Carlo N-Particle (MCNP) models. The study aimed to demonstrate the gap between control theory and actual practice—a gap that often necessitates empirical adjustments such as control gain retuning, filters, time discretization, and integrator anti-windup measures. Controllers were developed based on increasingly complex simulations without hardware, starting from the base MARVEL model and then introducing actuator saturation constraints and sensor noise. The final control strategy was then tested using MACS, and a comparative performance analysis was conducted.
A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)
A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.
These are lecture notes for a Monte Carlo class given at the University of New Mexico. The following topics are covered: course information; nuclear eng. review & MC; random numbers and sampling; computational geometry; collision physics; tallies and statistics; eigenvalue calculations I; eigenvalue calculations II; eigenvalue calculations III; variance reduction; parallel Monte Carlo; parameter studies; fission matrix and higher eigenmodes; doppler broadening; Monte Carlo depletion; HTGR modeling; coupled MC and T/H calculations; fission energy deposition. Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. These lectures provide a balanced approach to the theory and practice of Monte Carlo simulation codes. The first lectures provide an overview of Monte Carlo simulation methods, covering the transport equation, random sampling, computational geometry, collision physics, and statistics. The next lectures focus on the state-of-the-art in Monte Carlo criticality simulations, covering the theory of eigenvalue calculations, convergence analysis, dominance ratio calculations, bias in Keff and tallies, bias in uncertainties, a case study of a realistic calculation, and Wielandt acceleration techniques. The remaining lectures cover advanced topics, including HTGR modeling and stochastic geometry, temperature dependence, fission energy deposition, depletion calculations, parallel calculations, and parameter studies. This portion of the class focuses on using MCNP to perform criticality calculations for reactor physics and criticality safety applications. It is an intermediate level class, intended for those with at least some familiarity with MCNP. Class examples provide hands-on experience at running the code, plotting both geometry and results, and understanding the code output. The class includes lectures & hands-on computer use for a variety of Monte Carlo calculations. Beginning MCNP users are encouraged to review LA-UR-09-00380, "Criticality Calculations with MCNP: A Primer (3nd Edition)" (available at http:// mcnp.lanl.gov under "Reference Collection") prior to the class. No Monte Carlo class can be complete without having students write their own simple Monte Carlo routines for basic random sampling, use of the random number generator, and simplified particle transport simulation.
The purpose of this paper is to inform advanced reactor developers of the conditions and requirements needed to manage the water used to reject heat from advanced reactor demonstrations at the INL. While there are many advanced reactor concepts, all of them require heat rejection, and some plan to use water for hear rejection. Cooling water for heat rejection is frequently the largest fresh-water load for a nuclear reactor, and therefore the focus of water management. The type of reactor and its purpose, the physical conditions at the INL, and the regulatory structure of the demonstration also influence the optimal method of heat rejection. Choosing the best method of rejecting heat will significantly influence the cost and probability of success for any advanced reactor demonstration. One of the important considerations in the deployment of demonstration plants at the INL site is water use and its implications. Advanced reactor developers need to consider the limitations of the water consumption based on the state and federal regulations. The water consumption may become a limitation when the demonstration reactor capacities reach to conventional nuclear power plants.
Nuclear nonproliferation serves as a key goal, being undertaken by the International Atomic Energy Agency (IAEA). To recognize proliferation there are two pathways that states, who intend to use nuclear material for malicious purposes can take, diversion can misuse. Diversion is when fissile nuclear material is declared to the IAEA for non-weapon purposes, but then covertly removed. If the source of nuclear material, that is not declared and not fissionable, is placed inside the reactor core to create fissile material used to create weapons then the state is using the second pathway of proliferation, misuse. With the emerging development in areas of simulation and machine learning the creation of virtual models of reactor systems, digital twins, serve as a potential method to identify proliferation through detecting anomalous behavior in the reactor. A digital twin for a physical nuclear reactor has never been developed, as digital twins serve as an emerging technology. To investigate the process for development and use of a digital twin for a nuclear reactor Idaho State University’s AGN-201m serves as the nuclear reactor used for development of this digital twin. A data acquisition system has been installed to the reactor system allowing for the transfer of collected data from a reactor operation to Idaho National Laboratory’s Deeplynx data warehouse. When utilizing data to train reactor physics and machine learning models, a significant challenge encountered is the initial state of the data. Nuclear proliferation will have the capacity to be detected when the reactor immediately starts up, nor will it occur after the reactor shuts down. Generally, it will be detected when the reactor is operating at some desired power over a sufficient period for that specific reactor design. For the AGN-201m this will be when the reactor is critical (generally 1 mW or above) for a timespan that is within or less than the range of a regular business day. Datasets sent to Deeplynx have had to be manually cut to when the reactor is critical based on plots of power levels. This method is inefficient and laborious, especially when using multiple datasets at once to train a model. To provide a more streamlined approach an automated critical data extrapolator is developed, with capabilities of recognizing when the reactor operation first reaches criticality, and when the reactor undergoes a SCRAM and is shutdown.
Tristructural-isotropic (TRISO) fuel particles have been developed as a high-performance fuel for use in high-temperature gas-cooled reactor (HTGR) systems due to their high efficiency and stability under both normal and off-normal conditions. Broader deployment of this technology in advanced nuclear applications may benefit from quantitative quality assurance and quality control (QA/QC) methods that directly link TRISO properties to downstream performance. A key TRISO property is the SiC layer microstructure, which influences fission product retention during irradiation. However, existing QA/QC for the TRISO-SiC microstructure comprises only a qualitative visual inspection; therefore, there is a clear opportunity for the development of quantitative methods for TRISO QA/QC. Here, to this end, previous work has demonstrated an image processing approach to grain boundary (GB) identification and subsequent extraction of microstructural metrics; however, extensive twinning within the SiC layer complicates such analyses because twin GBs significantly influence microstructural metrics but are not expected to contribute to fission product transport. This study presents the initial development, training, and testing of an ML-based image segmentation algorithm designed to identify and remove twin GBs from standard backscattered electron micrographs, providing an industrially applicable, quantitative, and physically meaningful QA/QC approach for the TRISO-SiC microstructure. Although pixel-wise performance metrics for the twin predictions are low, the change in grain area and the number of GB pixels after twin removal predicted by the ML workflow are within 1% of the true values calculated using crystallographic data. This suggests that the model is well capable of predicting overall twin boundary structures and grain morphology, and continued advancement of this approach could enable automated, scalable, and physics-informed QA/QC for TRISO-SiC microstructures, supporting the reliable qualification of coated particle fuels for next-generation reactor systems.
This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)
Many new reactor designs, such as advanced reactors and micro reactors, have materials that lack nuclear data validation. This is also true for many other applications in criticality safety and global security. Both differential and integral experiments are needed to validate cross-section data. Without this, a user cannot have confidence in the predicted results of a radiation-transport code. This work describes an approach called ARCHIMEDES (Application Relevant Critical/Subcritical HEU/Pu-based Integral Measurements for Enhancing Data and Evaluating Sensitivities) to design new criticality experiments that have similar k eff cross-section sensitivities to an application of interest. This process involves simulations to generate cross-section sensitivities to a parameter of interest (such as k eff ), a gap analysis to determine which existing benchmarks are most similar to the application, and an experiment optimization. Recently, there has been a great deal of interest in the reactor physics community on advanced reactors, micro reactors, and accelerator driven systems (ADS). This work will apply the described method to specific examples in this area. The focus of this work will be on the sensitivity study and gap analysis, while future work will include experiment design.
A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.