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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Effect of the Flux Separability Approximation on Multigroup Neutron Transport

The angular dependence of flux-weighted multigroup cross sections is commonly neglected when generating multigroup libraries. The error of this flux separability approximation is typically not isolated from other error sources due to a lack of availability of library generation and corresponding solvers that cannot relax this approximation. These errors can now be isolated and quantified with the availability of a multigroup Monte Carlo transport and multigroup library-generation capability in the OpenMC Monte Carlo transport code. This work will discuss relevant details of the OpenMC implementation, provide an example case useful for detailing the type of errors one can expect from making the flux separability approximation, and end with more realistic problems which show the impact of the approximation and highlight how it can strongly arise from an energy-dependent resonance absorption effect. Since the angle-dependence is intrinsically linked to the energy group structure, these examples also show that relaxing the flux separability approximation with angle-dependent cross sections could be used to reduce either the fine-tuning required to set a multigroup energy structure for a specific reactor type or the number of energy groups required to obtain a desired level of accuracy for a given problem. This trade-off could increase the costs of generating multigroup cross sections, and has the potential to require more memory for storing the multigroup library during the transport calculations, but it can significantly reduce the computational time required since the runtime of a discrete ordinates or method of characteristics neutron transport solver scales roughly linearly with the number of groups.

42 ENGINEERING↗
DOE OSTI2020

Multigroup Constant Calculation with Static α-Eigenvalue Monte Carlo for Time-Dependent Neutron Transport Simulations

Herein, multigroup constants for deterministic methods that preserve the time-dependent physics of the neutron transport equations are derived. Alternative multigroup constant weighting spectra are discussed: (1) the fundamental k-eigenfunction, (2) the fundamental α-eigenfunction, and (3) a composite of several α-modes. To generate the fundamental α-eigenfunction for calculating the multigroup constants, a static fundamental α-eigenvalue method is implemented into the open source Monte Carlo code OpenMC. Several static and kinetic problems are devised to verify the implementations and to investigate the relative performance of the alternative multigroup constant weighting spectra. Results emphasize that as a multigroup constant weighting spectrum, the fundamental α-eigenfunction offers physical characteristics that make it advantageous (in producing accurate solutions) over the typically used fundamental k-eigenfunction.

42 ENGINEERING↗
DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Multigroup Cross-section Generation in MCNP6.3 [Slides]

This presentation states that in comparison to the NJOY-produced multigroup cross sections, the MCNP-produced multigroup cross sections are generally consistent. Statistical uncertainties, however, are challenging and the unresolved resonance region may be looked at in the future. It also discusses how the SPM and LCS options were compared to each other for internal consistency. Additionally, some reactor pin-cell-like problems were used to compare to multigroup capabilities in other Monte Carlo codes (e.g., Serpent, OpenMC).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint, and the sensitivity of $k$ ∞ to perturbations in the multigroup nuclear data of a single species isotropic elastic scattering material. In the appendix, we present the multigroup nuclear data for U-235 and U-238 along with the corresponding k-eigenvalue, flux, adjoint, and sensitivity profiles, which include the sensitivity of $k$ ∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Analytic Sensitivity Coefficients for General Multigroup Infinite Medium k-Eigenvalue Problems

This work presents a general set of equations that can be used to rapidly generate new benchmarks to verify nuclear data sensitivity calculations. The general multigroup infinite medium k-eigenvalue neutron transport equation is used to derive analytic expressions for the infinite medium k-eigenvalue, the scalar neutron flux and adjoint flux, and the sensitivity of k∞ to perturbations in the multigroup nuclear data of a single species, isotropic and elastic scattering, material. The multigroup nuclear data for U-235 and U-238 is presented along with their corresponding k-eigenvalues, forward flux, adjoint flux, and sensitivity profiles, which include the sensitivity of k∞ to the total, fission, capture, and scattering macroscopic cross sections as well as to the group-to-group scattering cross section matrix, group-wise fission neutron production, and the unconstrained and constrained fission neutron energy distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Extension of the discrete generalized multigroup method using SPH factors

The discrete generalized multigroup (DGM) method provides a way to treat the energy dependence of neutron transport similarly to the standard multigroup approximation. However, DGM uses an orthogonal basis to retain the energy dependence in higher-order terms. Using correction factors similar to traditional Superhomogénéisation (SPH) factors, the DGM method may be extended to produce cross sections that are homogenized over both space and energy. Additionally, since some fine-group energy dependence is retained, the resulting homogenized cross sections are more problem-independent than cross sections homogenized by SPH factors alone. In particular, a 44-group set of cross sections is collapsed to approximately a 1% error in the pincell fission densities for a test problem using three DOF per coarse energy group.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Multigroup Neutron Transport Using a Collision-Based Hybrid Method

A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the isotropic multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and approximates the fission and scattering sources on the coarser grids. The coupling of a collided transport equation, discretized on the coarse grid, with an uncollided transport equation, discretized on the fine grid, yields an algorithm that, in most cases, is more efficient than the traditional multigroup approach. In conclusion, the improvement over existing techniques is demonstrated for time-dependent problems with different materials, geometries, and energy groups.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Multigroup Thermal Radiation Transport with Tensor Trains

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than 100× and speedups exceeding 2×. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as 7. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Multigroup cross section generation capability in GRIFFIN

GRIFFIN is an advanced reactor multiphysics application built on the object-oriented simulation environment (MOOSE) and is jointly developed by Idaho National Laboratory and Argonne National Laboratory. The cross section application programming interface, originally developed for the PROTEUS code, has been integrated into GRIFFIN to prepare cross sections for thermal reactor applications with heterogeneous geometries. Additional improvements have been made by implementing an on-the-fly slowing down method, a double heterogeneity treatment capability, and updating the procedure to generate the fine multigroup library. The cross section preparation capability in GRIFFIN was verified for graphite-moderated TRISO fuel-based reactor benchmark problems: unit-cell problems of VHTR and EMPIRE micro reactor and HTTR assembly problems. Eigenvalues and multigroup cross sections of GRIFFIN agreed very well with those of the continuous-energy Monte Carlo code Serpent2 within 200 pcm in eigenvalue and 2% in cross sections. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Reduced-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Abstract – Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗
DOE OSTI2020

Space-energy separated representations for multigroup neutron diffusion using proper generalized decompositions

Proper generalized decomposition (PGD) can be described as a numerical extension of separation of variables and thus be employed as a solution technique for multi-dimensional problems, where dimensions should be understood in the phase-space context of the governing law at hand. This paper presents a PGD approach on efficiently solving problems involving multigroup neutron diffusion. Two PGD approaches are described: space-only and space-energy decompositions. Numerical results include 2-D and 3-D examples with two-, seven-, and 145-group structures. The PGD solutions are compared against traditional multi-dimensional finite element discretization. For few-group problems, both PGD approaches prove effective for mildly heterogeneous geometries, but showed reduced performance with increasing heterogeneity. The space-energy representation was found to be slower than the space-only approach for two-group problems, but proved more effective for seven-group problems. For even larger numbers of groups, the space-energy PGD decomposition was very effective at reducing the computational time.

42 ENGINEERING↗
DOE OSTI2024

Efficient continuous Energy-Multigroup hybrid depletion scheme using the Shift Monte Carlo code. Part I: Energy condensation sensitivity analysis

Monte Carlo (MC) codes coupled to depletion solvers are increasingly used to provide high fidelity fuel cycle modeling capabilities. Here, these coupled depletion-MC tools produce accurate results in general but can experience nonphysical spatial oscillations when time steps are large or when a system’s dominance ratio approaches unity. Two substepping techniques have been developed previously to remedy and dampen these spatial oscillations without needing to reduce step sizes. The first approach relied on higher-order techniques to account for spectral changes within steps (extrapolation and interpolation techniques). The second approach used the first order perturbation (FOP) theory to account for the change in the one-group spatial flux distribution within steps. This paper develops a hybrid depletion methodology which, in a way, combines how the flux is handled in both substepping techniques. Specifically, the multigroup (MG) MC Shift code is used to update the flux distribution within steps rather than a one-group FOP solver. A fully reflected pincell is investigated, which is not spatially dependent in the MG representation. Thus, the analysis in this paper is an initial demonstration of hybrid depletion. An upcoming companion paper will focus on how the hybrid depletion dampens spatial oscillations. The hybrid depletion approach is verified to be consistent with previous constant extrapolation depletion (CED) methods. This paper finds that the hybrid CED exhibits some error in the eigenvalue and one group constants within macro steps. To address this discrepancy, a simple interpolation scheme (CELI) is investigated. This work found that CELI sufficiently addresses the discrepancy in spectrum for macro steps up to 100 days. Overall, this work demonstrates that the hybrid depletion method can significantly reduce the number of high fidelity MC executions in a MC-coupled depletion with an acceptable eigenvalue error.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Multigroup Examination of Nickel-Reflected HEU System

Critical configurations of HEU-MET-FAST-003 (HMF-003) from the International Criticality Safety Benchmark Evaluation Project Handbook were modeled for addition into the Verified, Archived Library of Inputs and Data maintained at Oak Ridge National Laboratory. HMF-003 contains models of a highly enriched uranium sphere with a spherical metal reflector of natural uranium, tungsten carbide, or nickel. For these simple models, good agreement is expected between the k eff calculated with continuous-energy (CE) and multigroup (MG) transport. However, using the CSAS5 sequence of the SCALE 6.2.4 package, the 8 in. thick nickel reflector model resulted in a difference of around 1.2 % Δ k . Results presented a clear indication of poor performance for the SCALE 252-group based on ENDF/B-VII.1 cross section library for this model. The bias was investigated over a range of nickel thickness and then compared with other MG libraries available in SCALE 6.2.4. As the nickel thickness increases, the MG k eff deviates from the CE result, confirming a performance issue with the MG calculation. Additionally, the reactions were compared between the two libraries to help determine the cause of k eff bias. Finally, additional MG libraries within SCALE 6.3 and based on ENDF/B-VII.1 and ENDF/B-VIII were reviewed. The 302-group and 1597-group result in significant improvements compared with the 252-group library. Nickel cross sections were modified from ENDF/B-VII.1 to ENDF/B-VIII. For the ENDF/B-VIII library, the deviation between the CE libraries and MG libraries is less pronounced than for ENDF/VII.1, except for the 1597-group. This examination clearly indicates the importance of validating calculations with applicable benchmark experiments and caution when using MG libraries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

TRT Compton Scattering Data: Comparisons between LLNL and LANL: Multigroup

This memo is one of a pair of reports comparing Compton scattering data in the context of thermal radiation transport (TRT). This document focuses on Multigroup (MG) data while the other report focuses on Pointwise (PW) data. These complementary analyses, via PW comparisons, show if the same physics are used and if fundamental bugs are present, and, via MG comparisons, quantify macroscopic Compton effects such as mean amplification factors. No averaging of Compton data over photon energy is done for the PW comparisons, while lab-dependent numerical resolution choices become relevant for the MG comparisons. For this MG-comparison report, we make and document the numerical assumptions we use to convert LLNL PW data into MG data. This document plots and quantifies differences in Compton scattering data between MG LANL and LLNL for four disparate temperatures on a logarithmically-spaced photon-energy grid. In addition to LANL and LLNL data, we add a third and fourth independent vote from data generated by Brooks Kinch (LANL postdoc). For the purposes of these comparisons, we neglect induced scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Multigroup Scattering in Monte Carlo Radiation Transport Codes [Slides]

Legendre truncations to multigroup scattering distributions are not amenable to Monte Carlo sampling due to negative values. We have implemented two moment-preserving methods in MGMC that capture the shape of the truncation, are non-negative over [-1, 1], and can be efficiently sampled on CPUs and GPUs. MGMC can now simulate neutrons with anisotropic scattering mechanics and MGMC shows good agreement with LANL production codes PARTISN.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

The Influence of Demographic Variables on the Pooled Rideshare Acceptance Model Multigroup Analyses (PRAMMA)

Building on our prior research with a national survey sample of 5385 US participants, the Pooled Rideshare Acceptance Model (PRAM) was built upon two factor analyses. This exploratory study extends the PRAM framework using the Pooled Rideshare Acceptance Model Multigroup Analyses (PRAMMA) to examine how 16 demographic variables influence and interact with the acceptance of Pooled Rideshare (PR), filling a gap in understanding user segmentation and personalization. Using a national sample of 5385 US participants, this methodological approach allowed for the evaluation of how PRAM variables such as safety, privacy, service experience, and environmental impact vary across diverse groups, including gender, generation, driver’s license, rideshare experience, education level, employment status, household size, number of children, income, vehicle ownership, and typical commuting practices. Factors such as convenience, comfort, and passenger safety did not show significant differences across the moderators, suggesting their universal importance across all demographics. Furthermore, geographical differences did not significantly impact the relationships within the model, suggesting consistent relationships across different regions. The findings highlight the need to move beyond a “one size fits all” approach, demonstrating that tailored strategies may be crucial for enhancing the adoption and satisfaction of PR services among various demographic groups. The analyses provide valuable insight for policymakers and rideshare companies looking to optimize their services and increase user engagement in PR.

moderator↗