MCNP tallied weight functions to improve multigroup simulations
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Critical volume of cylindrical reactors calculated using n-group diffusion theory
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Presentation discussing the research and development of deep neural network models for modeling microscopic neutron cross-section data in the Griffin reactor physics application for pebble-bed reactors. This work details advancements made between the last review meeting in July 2024 until July 2025.
This presentation provides an overview of the efforts to implement neural networks to model neutron cross section data.
The Department of Energy (DOE)’s NEAMS focuses its efforts on the development of advanced modeling and simulation (M&S) tools for light-water reactors (LWRs) and non–LWRs (i.e., molten salt reactors, high-temperature gas reactors, microreactors, and fast reactors). In the previous fiscal year, the Multiphysics Applications Driver Technical Area funded molten salt reactor (MSR) M&S at Oak Ridge National Laboratory (ORNL) to generate multigroup macroscopic cross sections with Shift for a MSRE 2D lattice model in Griffin. In addition, Shift’s capability to calculate gamma dose rates from activated components in the primary exchangers in a molten salt breeder reactor was also demonstrated. In fiscal year 2023, ORNL generated multigroup macroscopic cross sections using Shift for a 3D MSRE core model. MSRE depletion calculations using Griffin were also demonstrated in this fiscal year. For the depletion calculation, one-group microscopic cross sections for the 3D MSRE core were generated using Shift, and the decay transmutation library from ORIGEN was converted to an ISOXML file, which is required as input in Griffin. Several Monte Carlo codes, such as OpenMC and Serpent, were also used to benchmark and supplement multigroup cross sections generated by Shift. Multigroup libraries were generated with 8 and 20 group structures, and the study found the 8-group structure to be more accurate when comparing Griffin results to continuous energy (CE) Monte Carlo results. The average flux from CE Shift calculations is up to ~6% higher than the CE Serpent calculations because of different values applied for the energy released per fission (κ values). The average flux in the fuel salt calculated by Griffin using cross sections generated with Shift agrees well with the reference CE Shift solution; the same is valid for the corresponding Serpent results. The maximum relative error is ~6% and ~2% compared to the CE Shift and Serpent reference solutions, respectively. Meanwhile, the average flux calculated by Griffin in the graphite moderator shows a higher difference in the thermal range when compared to both reference Monte Carlo solutions; this result suggests a need for improvement in cross section generation for the graphite moderator in the thermal range in both Monte Carlo codes. Griffin depletion calculations using cross sections from Shift and Serpent were performed and compared against ORIGEN calculations, and the nuclide densities calculated by Griffin were found to be generally in agreement with those of ORIGEN. Because a different approach was taken to calculate the energy released per fission ( κ values) in Shift and Serpent, a difference in nuclide densities from differences in the average flux was observed between Griffin using Serpent and Shift cross sections. Griffin calculations with Shift cross sections produced higher average flux in the salt than with Serpent cross sections, leading to higher consumption of 235 U and higher production of 135 Xe. For time-dependent depletion calculations, cross sections were generated with Serpent, and Griffin’s results using these cross sections were compared to CE Serpent depletion results, demonstrating good agreement. The average difference in keff between Serpent and Griffin as a function of burnup is about 155 pcm. Similarly, good agreement with small differences up to ~0.5% was also noticed in the nuclide density of 235 U and 135 Xe. More details regarding the methodologies invoked to generate the cross section to make code-to-code comparisons are discussed further in this report. User feedback on Griffin and Shift capabilities that will enhance these calculations is provided in this report for future consideration. The work performed this fiscal year can be extended further for multiphysics coupling of Griffin-Pronghorn/SAM with Mole to study precursor flow and salt chemistry.
This research develops the initial coupling of the Shift Monte Carlo (MC) code and the Griffin reactor physics code for reactor analysis of non–light-water reactor systems. The novelty of this work is twofold. It is the first application of Shift to produce the multigroup cross sections needed for Griffin as applied to a non–light-water reactor system; and, the first investigation and analysis of characteristics of the Empire microreactor benchmark that should be considered for steady state and transient reactor physics calculations. This application uses the previously developed two-step neutronics analysis workflow to demonstrate this initial coupling. Here, we outline the two-step neutronics analysis workflow in which the Shift MC code is used to generate the multigroup cross sections and fluxes needed by the Griffin deterministic solver. Details on how these multigroup cross sections are generated using MC tallies are given, as well as the practicalities and limitations of the two-step neutronics workflow. The Empire microreactor benchmark was used to investigate and validate this coupling. Results using this benchmark show good agreement between Griffin calculations using Serpent-generated cross sections and Shift-generated cross sections. Analysis of the characteristics of this Empire benchmark show larger eigenvalue differences between heterogeneous and pin–homogenized solutions compared to those of traditional light-water reactor (LWR) designs, thus requiring super homogenization factor corrections for accurate eigenvalue and power distribution predictions.
The PERT card is used for first- and second-order perturbations of material densities, isotope densities, and isotope cross sections in the MCNP6.2 Monte Carlo code. Using the PERT card for firstand second-order sensitivities is straightforward. Reference 2 only looked at density perturbations with no energy dependence. This report looks at the sensitivity of a response to scattering cross sections as a function of energy and finds that there is a bug in the PERT capability. The SENSMG multigroup neutron sensitivity code was recently given the capability of computing sensitivities to user-specified reactions whose cross sections are available in a user-supplied NJOY output file. SENSMG uses the PARTISN multigroup discrete ordinates code for the transport. The NJOY-reaction capability is similar to that of SUSD3D, which also uses PARTISN for the multigroup transport. The PERT bug was identified by comparing MCNP6.2 outputs with SENSMG outputs. The next section of this report describes the test problem. Section III presents the MCNP6.2 PERT bug and proposes a solution. Section IV is a summary and conclusions. The SENSMG and MCNP input files are listed in the appendix.
Nuclear data is the linchpin underwriting several fundamental capabilities and mission needs at LANL. New techniques such as machine learning can be brought to bear to solve old problems such as multigroup cross-section accuracy. In neutron transport, generating multigroup cross sections is a complex and arcane task, but a crucial one, as accurate solutions require appropriate cross sections. There are two key challenges when generating multigroup cross sections: (1) choosing an accurate weight function, and (2) choosing appropriate energy boundaries. Often, energy boundaries are chosen using “expert judgment” that is not documented and is difficult to replicate. The long-standing Los Alamos 30-group structure has been in use since at least 1969 and is still in use today. Simplistic attempts over the years since to improve on the 30-group structure have been met with limited success. Machine learning algorithms would enable the selection of appropriate, problem-dependent group boundaries without an inordinate investment of scientist time. We will develop workflows and tools to enable these improved group boundary choices, which will reduce uncertainty and increase predictive capability of neutron-transport applications at LANL.
The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the equivalent Dancoff factor cell method performing slowing down calculations on the fly for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for pin-cell, unit-cell, and fuel assembly problems with various resonance self-shielding conditions based on very high temperature reactor, high temperature test reactor, and Empire benchmark cores, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also showed that the methodology worked well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.
Griffin, a MOOSE-based reactor multiphysics code jointly developed by Idaho National Laboratory and Argonne National Laboratory under the DOE Office of Nuclear Energy’s NEAMS program, has pursued the development of an online multigroup cross section generation capability for a few years to enable high-fidelity, problem-dependent neutronics analyses of advanced thermal reactors. Recent advancements in Griffin’s online multigroup cross section generation capability have significantly improved the accuracy, robustness, and efficiency of self-shielding calculations for both prismatic and pebble-bed TRISO-fueled reactor applications. Key developments include a unified fuel self-shielding method applicable to both TRISO and annular compact/spherical shell fuel zone geometries; an advanced Dancoff Category-based Equivalence Theory using a bell function for non-fuel resonance treatment, achieving more than an order-of-magnitude speedup compared to the Tone method; an on-the-fly multigroup equivalence approach to mitigate group condensation errors; and a streaming correction method for pebble-bed homogenization. A proof-of-concept demonstration of on-the-fly group condensation with consistent P0 transport correction was also achieved. The method reproduced direct fine-group solutions with excellent accuracy (eigenvalue errors within 10 pcm and pin-power differences within 0.5%), but due to performance limitations of the current fixed-source solver, improvements to solver efficiency will be addressed in future work. Verification tests were performed on graphite-moderated TRISO-fueled two-dimensional core benchmark problems representing gas-cooled microreactors, heat pipe-cooled microreactors, gas-cooled pebble-bed reactors, and fluoride salt-cooled high-temperature reactors. Across all cases, Griffin showed excellent agreement with Serpent2 continuous energy Monte Carlo solutions: eigenvalue errors within 200 pcm, pin-power root-mean-square errors within 2%, and control rod and drum worth errors less than 2%. It should be noted that, for the benchmark problem, cross section generation contributed less than 3% of the total simulation times. These results demonstrate that Griffin’s online cross section generation capability delivers accurate and efficient reactor physics solutions across a wide spectrum of TRISO-fueled advanced reactor designs. With further improvements to the fine-group fixed-source solver and planned extensions to depletion, transients, and coupled neutron–gamma transport, Griffin will be well-positioned to become a powerful and comprehensive tool for advanced reactor analysis.
The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the on-the-fly slowing down method for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Among various on-the-fly slowing down methods, the equivalent Dancoff factor cell method was employed. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for the very high temperature reactor (VHTR), high temperature test reactor (HTTR), and Empire benchmark problems with various resonance self-shielding conditions, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also show that the methodology works well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.
A nuclear data library is used as a starting input for all subsequent neutronics calculations. NJOY has been used worldwide as a nuclear data processing code to create cross section libraries for a long time. For the verification of NJOY method and for providing an alternative nuclear data processing tool, JAEA has been developed the new nuclear library processing code FRENDY. In this paper, nuclear calculations were performed using the ACE files and the multigroup libraries created by both FRENDY and NJOY, and the impacts on the neutronics characteristics due to nuclear data processing were investigated using those libraries. MCNP was used to compare the ACE files by calculating many benchmark problems including ICSBEP and it was confirmed that the k-eff values generally agree with each other within the range of statistical errors. The multigroup cross sections are verified by the BWR design codes LANCR/AETNA through calculation of a commercial BWR5 equilibrium core loaded with 9*9 fuels. It was confirmed that fuel assembly and core characteristics are consistent with each other. From the above investigations, it was confirmed that FRENDY can provide comparable continuous/multi-group neutron cross sections with NJOY. (authors)