Frequency Transform Method for Transient Analysis of Nuclear Reactors in Monte Carlo
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows
The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. In order to extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Verification of AZTRAN v1.2 code with a PWR-MOX benchmark problem
The AZTLAN platform project is an effort focused on developing a modeling Mexican platform to design and analyze nuclear reactors. It is a national initiative lead by the National Institute of Nuclear Research (ININ), in collaboration with the main Mexico's public universities: the National Polytechnic Institute (IPN), the National Autonomous University of Mexico (UNAM) and the Autonomous Metropolitan University (UAM). The AZTRAN code is a module of AZTLAN that solves the 3D neutron transport equation using the discrete ordinates (SN) method and the nodal scheme RTN-0 on steady state and Cartesian geometry. AZTRAN works with cross sections generated externally by other code. It provides a solution to the eigenvalue problem and determine the neutron distribution for a specific medium at desired conditions. On the other hand, it is important to mention that the Working Group 4 (users group) of AZTLAN platform is responsible of verify and validate the codes development, in order to give feedback to the group of developers: neutronics and thermal-hydraulics. In this work, the AZTRAN v1.2 performance was studied for a PWR-MOX lattice, using as example the Yamamoto's benchmark for LWR fuels, comparing AZTRAN v1.2 results again those obtained with the well-known neutronic code SERPENT-2 (v1.27), and some results from an article presented at PHYSOR-2002. Results from AZTRAN for a BWR fuel lattice is presented in a companion paper in this meeting.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
A Review of Molten Salt Reactor Kinetics Models
Interest in circulating fuel reactors (CFRs), particularly molten salt reactors (MSRs) of the fluid fuel type, has been growing in the last two decades. Starting with a resurgence of interest in Europe, there have been a growing number of methods proposed and codes developed to model the kinetics of CFRs, which is a capability essential to the design and evaluation of such reactors. This work first reviews the physical phenomena unique to CFRs in light of current research and how CFR kinetics are impacted by these considerations. In general, it is found that the movement of delayed neutron precursors (DNPs) through the primary loop has significant impacts on transients at low reactor powers or those with significant spatial components such as a change in the primary loop mass flow rate. Effects on the neutron flux are exceedingly minimal and entirely negligible. An extensive review of published models and methods for simulating CFR kinetics is presented, along with transient simulations in fast and thermal neutron flux systems using representative codes from each of the main modeling categories. Comparisons among methods are presented as are recommendations for their use or nonuse in various transient and work-flow scenarios. In general, it is recommended that time-resolved, multigroup neutron diffusion approaches be used to establish ranges of applicability for point reactor kinetics (PRK)–based approaches that themselves may not be applicable for all modeling situations. In such cases, it is suggested that quasi-static approaches be used where PRK-based approaches cannot be used. Finally, a review of common assumptions used in these models is presented, along with an evaluation of their impact on model performance. It is found that neglecting turbulent diffusion in open core–type CFRs is a poor assumption that leads to an underestimation of the reduction of the delayed neutron fraction. Furthermore, it is seen that exclusion of secondary heat transfer loops in models leads to underestimation of transient peaks and troughs.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Availability of Neutronics Benchmarks in the ICSBEP and IRPhEP Handbooks for Computational Tools Testing
In the past several decades, numerous experiments have been performed worldwide to support reactor operations, measurements, design, and nuclear safety. Those experiments represent an extensive international investment in infrastructure, expertise, and cost, representing significantly valuable resources of data supporting past, current, and future research activities. Those valuable assets represent the basis for recording, development, and validation of our nuclear methods and integral nuclear data [1]. The loss of these experimental data, which has occurred all too much in the recent years, is tragic. The high cost to repeat many of these measurements can be prohibitive, if not impossible, to surmount. Two international projects were developed, and are under the direction of the Organisation for Co-operation and Development Nuclear Energy Agency (OECD NEA) to address the challenges of not just data preservation, but evaluation of the data to determine its merit for modern and future use. The International Criticality Safety Benchmark Evaluation Project (ICSBEP) was established to identify and verify comprehensive critical benchmark data sets; evaluate the data, including quantification of biases and uncertainties; compile the data and calculations in a standardized format; and formally document the effort into a single source of verified benchmark data [2]. Similarly, the International Reactor Physics Experiment Evaluation Project (IRPhEP) was established to preserve integral reactor physics experimental data, including separate or special effects data for nuclear energy and technology applications [3]. Annually, contributors from around the world continue to collaborate in the evaluation and review of select benchmark experiments for preservation and dissemination. The extensively peer-reviewed integral benchmark data can then be utilized to support nuclear design and safety analysts to validate the analytical tools, methods, and data needed for next-generation reactor design, safety analysis requirements, and all other front- and back-end activities contributing to the overall nuclear fuel cycle where quality neutronics calculations are paramount.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Lattice physics calculations using the embedded self-shielding method in polaris, Part II: Benchmark assessment
Polaris is a 2D multigroup lattice physics capability in the SCALE code system used for the analysis of light water reactor fuel designs. In this work, verification and validation results of Polaris in SCALE 6.2 are presented. The SCALE/KENO continuous-energy Monte Carlo code is used as a reference to compare the results of more than 2,000 combinations of pressurized water reactor and boiling water reactor lattice designs and state points. Radiochemical assay measurements were also used to assess the accuracy of depletion calculations. Results show that Polaris, with ENDF/B-VII.1 cross section library, produces accurate lattice physics data for core simulators.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
SCALE inventory and reactivity analysis as part of the Hermes 2021 PSAR review
The readiness of SCALE for comprehensive studies of pebble-bed reactors has been demonstrated through detailed analysis of a fluoride salt–cooled, high-temperature pebble-bed reactor (PB-FHR). The methods developed for pebble-bed reactor modeling in SCALE, particularly for inventory generation, have proven effective in gaining insights into the reactor physics of this advanced reactor. Excellent agreement with another code package has been observed, further highlighting SCALE’s strong performance. The SCALE results supported the US Nuclear Regulatory Commission’s construction permit application review of the Hermes low-power PB-FHR demonstration reactor. A SCALE model of the Hermes reactor was developed at Oak Ridge National Laboratory using information from the Preliminary Safety Analysis Report (PSAR) and supplemented with publicly available data. SCALE reactivity coefficient simulations reproduced PSAR results within 1σ statistical uncertainties. Sensitivity studies emphasized the importance of graphite specifications for accurate keff predictions.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Development of Whole System Digital Twins for Advanced Reactors: Leveraging Graph Neural Networks and SAM Simulations
Here, in this work, we introduce a novel method to develop whole system digital twins (DTs) for advanced nuclear reactors. This method treats a complex reactor system as a heterogeneous graph: with the system components as different types of graph nodes and their physical interconnections as edges. Based on the heterogeneous graph, a graph neural network combining graph convolution and temporal node attention is developed as the DT, facilitating a comprehensive understanding of the system's dynamic behavior. By utilizing the System Analysis Module (SAM) code for simulating various operational transients, we develop a graph-based database that trains the DT. This DT is characterized by two primary functions: It can infer the entire system's status using sparse node information, and it can predict the progress of transients based on current and historical system information. Our approach is validated through case studies on the Experimental Breeder Reactor II (EBR-II) system and a generic Fluoride-salt-cooled High-temperature Reactor (gFHR), demonstrating the DT's accuracy in forecasting operational transients. The DT's rapid computation capabilities enhance its potential for supporting advanced reactor operations, offering benefits in intelligent simulation, autonomous control, and anomaly detection, paving the way for improved safety analysis and intelligent component health management for advanced reactor systems and reducing their operations and maintenance cost.
EBR-II↗
At-power subcritical multiplication in the Advanced Test Reactor during nuclear requalification testing
Power division information during nuclear requalification of the Advanced Test Reactor (ATR) is of considerable interest as an importance function for observed changes to core reactivity. 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. When ATR operates at power, 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. Here, this work shows that fuel element and lobe powers in ATR can be related with subcritical multiplication theory. Subcritical multiplication factors are computed with a physically validated analytical method based on actual at-power operation, quantifying for each lobe its dependence on other lobes as an external neutron source. 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. For any physical subdivision of any other critical reactor, it is likewise true that the subdivision undergoes only subcritical multiplication.
21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
Addressing Over-Solving in Multiphysics Codes with Nested Solvers
Examples of multiphysics problems in the field of nuclear engineering are numerous. For light water reactors the coupling of neutronics with thermal-hydraulics is the most predominant. Often this coupling is modeled by combining existing codes in a Picard Iteration scheme, that is, by solving one physics then using that answer to solve the other and iterating until both answers stabilize. However, simply solving to a high precision on every Picard (multiphysics) iteration is much less efficient than progressively solving to higher precisions. This unneeded work is known as over-solving. Over-solving in single-physics solvers has been studied previously for the Newton method and Chebyshev iteration. Both of these methods solve an inner linear problem that determines the next update step for the outer loop. If the inner problem is solved to a high precision in every outer iteration, the result will be substantially more computational expense (over-solving) and a higher probability of reaching the 'wrong' solution. Methods for reducing over-solving in partitioned multiphysics codes have only been developed recently. This work introduces further improvements, including an investigation of over-solving methods on both the multiphysics and single-physics levels.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Future Opportunities for LWR Irradiations in US Test Reactors
After several years of relatively low activity in the field of Light Water Reactor (LWR) fuel development, the Department of Energy again began to engage in developing new fuel technologies and irradiation performance data prompted by the Fukushima Daichi nuclear accidents. New competencies for irradiation testing in material test reactors in the United States began to be developed at this time using the Advanced Test Reactor (ATR), High Flux Isotope Reactor (HFIR), Massachusetts Institute of Technology Reactor (MITR), and the Transient Reactor Test Facility (TREAT). Capsules for testing fuel and cladding materials in ATR and HFIR were deployed, a Pressurized Water Reactor (PWR) condition loop for testing fuel rods was established in ATR, cladding corrosion studies were performed using a water loop in MITR, and TREAT pulse testing capabilities were commissioned for fuel rods in water capsules. The more recent and unexpected closure of the Halden Boiling Water Reactor (HBWR) also prompted further investments in Loss of Coolant Accident (LOCA) testing capabilities at TREAT. New configurations of these test devices show further potential in enhanced steam condition control and other investigations are building toward a flowing water loop for testing transient to dryout conditions. The closure of HBWR also prompted a major project currently underway to construct additional water loops in ATR where a novel approach is being pursued to enable Boiling Water Reactor (BWR) conditions. A meaningful collaborative project was awarded to MITR which, amidst an unexpected major overhaul of the reactor, has expanded cladding corrosion test capabilities at MITR. New explorations have led to methods for unique experiments at HFIR including channel box irradiations. New device developments are also bridging toward future potential for instrumented capsule irradiation tests in ATR and HFIR. Finally, a new project referred to as the System Physics Advanced Reactor Critical facility (SPARC) is gaining traction towards a large zero-power reactor able to produce physics validation data for LWR fuel bundle designs with increased enrichment and enhanced absorbers for 24-month operation cycles. This paper provides a brief summary of the status of these irradiation testbed capabilities with an emphasis on current efforts toward future capabilities to obtain new data and maximize the performance potential of LWR fuel technologies.
Woolstenhulme, Nicolas [Idaho National Laboratory ↗
Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation
A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Application of Polynomial Chaos Expansion in One-Dimensional Inverse Transport Problems
In the problem of inverse radiation transport, measurements of particle leakages from radioactive source/shield systems are used to infer unknown parameters within the systems. This reconstruction can be accomplished by finding the physical parameters of the unknown system that minimize the difference between calculated detector responses and measured detector responses. The inverse transport solver should also propagate uncertainties from the detector responses to the reconstructed parameter values. Recently, the Differential Evolution Adaptive Metropolis (DREAM) method was shown to be a robust method for uncertainty quantification in inverse problems. The DREAM method uses the differential evolution algorithm to choose efficient steps in a Markov chain Monte Carlo (MCMC) simulation. Although the DREAM method has been shown to be more efficient than traditional MCMC approaches, it still requires thousands of transport computations to accurately quantify uncertainty. For the simple ray-tracing model, it was possible to perform these calculations in a reasonable amount of time (under an hour). However, inverse transport problems that require computationally-intensive transport solvers will need prohibitively long run times when using the DREAM method. A way to overcome the computational burden of the DREAM method is to perform surrogate modeling using the polynomial chaos expansion (PCE) approach. It was recently shown that the PCE method provides both accurate and computationally inexpensive uncertainty quantification in forward radiation source/shield problems. PCE was also recently applied to an inverse problem in nonlinear point reactor kinetics within a standard MCMC approach. PCE was first used with the DREAM method where it was applied to inverse problems in groundwater modeling.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
The development of a high sensitivity neutron displacement damage sensor
Here, the capability to characterize the neutron energy spectrum and fluence received by a test object is crucial to under-standing the damage effects observed in electronic components. For nuclear research reactors and high energy density physics fa-cilities this can pose exceptional challenges, especially with low level neutron fluences. An ASTM test method for characterizing neutron environments utilizes the 2N2222A transistor as a 1-MeV equivalent neutron fluence sensor and is applicable for environ-ments with 1 x 10 12 - 1 x 10 14 1-MeV(Si)-Eqv.-n/cm 2 . In this work we seek to extend the range of this test method to lower fluence environments utilizing the 2N1486 transistor. Here, the 2N1486 is shown to be an effective neutron displacement damage sensor as low as 1 x 10 10 1-MeV(Si)-Eqv.-n/cm 2 .
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Advanced Reactors Campaign and NCERC [Slides]
Abstract not provided.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Particle transport in Markov stochastic mixtures with spatial gradients
Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
In silico evaluation of a targeted metaproteomics strategy for broad screening of cellulolytic enzyme capacities in anaerobic microbiome bioreactors
Microbial-driven solubilization of lignocellulosic material is a natural mechanism that is exploited in anaerobic digesters (ADs) to produce biogas and other valuable bioproducts. Glycoside hydrolases (GHs) are the main enzymes that bacterial and archaeal populations use to break down complex polysaccharides in these reactors. Methodologies for rapidly screening the physical presence and types of GHs can provide information about their functional activities as well as the taxonomical diversity within AD systems but are largely unavailable. Targeted proteomic methods could potentially be used to provide snapshots of the GHs expressed by microbial consortia in ADs, giving valuable insights into the functional lignocellulolytic degradation diversity of a community. Such observations would be essential to evaluate the hydrolytic performance of a reactor or potential issues with it.
09 BIOMASS FUELS↗
Verification of a fully implicit particle-in-cell method for the <!--${MathJax: TeX-AMS-MML_HTMLorMML}--> v ∥ -formalism of electromagnetic gyrokinetics in the XGC code
A fully implicit particle-in-cell method for handling the v ∥ -formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the v ∥ -formalism, here we avoid introducing the nonphysical skin terms in Ampère's law, which are responsible for the well-known “cancellation problem” in the p ∥ -formalism. The v ∥ -formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional δf scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other δf gyrokinetic codes/schemes, whose verification has already been archived in the literature.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗