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Calculation of neutron flux spectra of the VVER-1000 mock-up shielding benchmark with Monte Carlo code MCS utilizing mesh-based weight window

The measurements of neutron spectra compiled inside the NEA-1517/82 package from the Shielding Integral Benchmark Archive and Database (SINBAD) are chosen as benchmark cases to validate the variance reduction technique based on weight window in Monte Carlo Code MCS. A full 3D model for fixed source mode calculation with hexagonal lattice source definition is developed to simulate total of 6 points of measurements at the vicinity of the reactor and the reactor pressure vessel region. A code/code comparison against MCNP6 code is first conducted as verification element for the mesh-based weight window capability in MCS. Finally, the validation results are presented against measurements. The verification against MCNP6 code gives good agreement in addition of the insight to the importance of user understanding to determine proper reference point and reference lower weight bound for scaling which is not required in MCS code due to its capability of automatic scaling. The comparison of neutron spectra between MCS and measurements shows good agreement within 3 standard deviations for all of six detector positions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A Verification of Flux Sensitivity Estimates Using the MCNP Tally Perturbation Tool

Nuclear data is commonly used in applications such as nuclear nonproliferation, safeguards, and criticality safety. More specifically, nuclear data is used in predictive simulation codes like the Monte-Carlo N-Particle (MCNP ® ) transport code, Serpent, and similar radiation transport codes. The improvement of nuclear data enables more precise and accurate simulations, which result in higher fidelity designs and reduced operational/procedural costs. Therefore, the improvement of nuclear data is of paramount importance across the nuclear community. Nuclear data is improved and validated through integral benchmark experiments. The design of benchmark experiments is an extensive process; therefore, these experiments are often optimized on multiple characteristics, including sensitivity to the nuclear data, during the design process. Sensitivity is a measure of how much a quantity changes due to changes in independent variables such as experimental configuration. An experimental design that has a larger sensitivity to the nuclear data of interest will have a larger impact on the accuracy and precision of the validated data. Past integral benchmark experiments have primarily used the effective multiplication factor ($k_{eff}$) as the predominant measured quantity; however, experiments designed with other quantities in mind would be able to optimize on validating different areas of the nuclear data. A primary goal of the EUCLID project is to design, constrain, and reduce compensating errors in experiments focused on quantities other than $k_{eff}$ to better validate nuclear data across the board. Currently, there is a capability in MCNP to easily calculate the sensitivity of $k_{eff}$ to specific nuclear data of numerous reactions types and isotopes (KSEN card); however, the sensitivity of other quantities must be estimated in more strenuous manners. For example, the perturbation feature (PERT card) of MCNP can be used to estimate first-order sensitivities of some response in fixed source simulations. A recent announcement revealed that the first- and second-order perturbation features in previous releases of MCNP contained a bug. It was identified that particles were being scored into the wrong energy bin. The bug is in the most recent public release (MCNP6.2); however, a patch has been added to the most up to date version (MCNP6.2.2) that has not been released publicly. A direct comparison of the PERT card results for an F4 (neutron flux averaged over a cell) tally before and after the patch are shown in figure 1. All simulations used in the sensitivity estimates in this report were performed with MCNP6.2.2. This work verifies the patched MCNP perturbation tool by comparing first order sensitivities made using the PERT card to estimates made using manual perturbation of the compact ENDF (ACE) files.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the polynomial order used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SCEPTRE 2.2 Angular Quadrature Sets

This document includes details of the angular quadrature sets available in SCEPTRE for performing numerical integrations in the angular phase space. The angular dependence of the boundary and fixed-source terms an d initial angular flux are specified by angular index rather than by direction. It is, therefore, necessary to know the mapping from a specific direction to a direction index. This document includes angular quadrature weights and direction cosines for most of the quadrature sets available in SCEPTRE.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Fission Product Yield Data Adjustment in a Prototype Version of TSURFER

The TSURFER (Tool for Sensitivity/Uncertainty analysis of Response Functionals using Experimental Results) module of Oak Ridge National Laboratory’s (ORNL’s) SCALE code system has been updated to perform nuclear data adjustments for fixed-source irradiation/depletion problems. TSURFER uses a generalized linear least squares (GLLS) approach to consolidate a prior set of measured responses and corresponding calculated values to create the most self-consistent set of nuclear data. Traditionally, TSURFER adjustments have been performed for multigroup nuclear data such as reaction cross sections. In this work, TSURFER is expanded to perform adjustments to independent fission product yields and branching ratios that need equality constraints. To preserve equality constraints after the data adjustment procedure, an updated GLLS formulation includes a new Lagrange multiplier that forces data adjustment to sum to 0 for a given fission yield/branching ratio parent. A test problem illustrates that the newly updated TSURFER module satisfies the required constraint that adjustments for fission yield data sum to 0.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Cross Section Generation Capability in Griffin

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

VERA User's Guide for Ex-core Applications

The Virtual Environment for Reactor Applications, or VERA, allows users to set up models to calculate time-dependent and fully coupled solutions for ex-core quantities of interest such as vessel and coupon fluence, and detector responses for multiple statepoints and cycles. MPACT and COBRA-TF together perform in-core transport calculations with temperature feedback while Shift performs the fluence and detector response calculations in the ex-core region. The in-core region is modeled using VERA’s native input format and the ex-core region is defined using Shift’s general geometry package, also known as Omnibus General Geometry. Fixed source ex-core calculations with Shift can be run in forward mode without advanced variance reduction (VR) methods, or with Consistent Adjoint Driven Importance Sampling (CADIS), which is an automated VR method. This document serves as a guide for setting up inputs, running ex-core calculations and post-processing the results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Griffin Software Development Plan

Griffin is a MOOSE-based reactor physics application for advanced reactor multiphysics modeling and simulation. The application is developed in a consistent multiphysics environment with strong software quality assurance. Griffin inherited most of the capabilities of MAMMOTH/Rattlesnake and is adopting the capabilities from PROTEUS that are needed in the code. The toolset includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, ad-joint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code contains the cross-section preparation capabilities applicable to fast and thermal reactors, including TRISO-fueled reactors. Core management capabilities include core performance, fuel depletion and shuffling, equilibrium core calculation, pebble-bed reactor run-in and equilibrium core, molten-salt reactor delayed neutron precursor drift, and control rod and drum movement with cusping correction. This software development plan presents the current and future capabilities and features in Griffin for the design and analysis of non-light-water reactor systems in steady-state and transient conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. As some additional changes have been made to the ARC software since this point all versions between release 3012 and 3266 can be considered verified as version 3253 was used for all updates in this revision. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the methodology used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative noting that DIF3D will properly notify the user when the peaking values it is providing are potentially incorrect.

97 MATHEMATICS AND COMPUTING↗

(U) SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , α , and Subcritical Multiplication Using PARTISN

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff , α, and subcritical multiplication using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, a nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every nuclide and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations and outer boundaries. It computes sensitivities to user specified reactions whose cross sections are available in a user-supplied NJOY output file. The tool can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. For most responses, the tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. The tool is thus limited to computing sensitivities only for GPT-allowable responses. For subcritical multiplication, the tool implements sensitivities derived by O’Brien and Clark. SENSMG has a similar role as the old SWANLAKE (Ref. 8), FORSS (Ref. 9), and SENSIT (Ref. 10) codes. It has capabilities similar to those of SUSD3D (Refs. 11 and 12), which also uses PARTISN. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI presents some sample problems and discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists most of the input files whose results are presented in Sec. VI. Appendix B provides some useful details on one of the cross-section libraries that SENSMG supports.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Verification of the DIF3D Software to Support Fast Reactor Analysis (Rev. 3)

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. As some additional changes have been made to the ARC software since this point all versions between release 3012 and 3266 can be considered verified as version 3253 was used for all updates in this revision. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the methodology used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative noting that DIF3D will properly notify the user when the peaking values it is providing are potentially incorrect.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Two MCNP Models for Computational Performance Benchmarking

The purpose of this report is to describe two non-trivial MCNP models and execution configurations that are suitable to characterizing computational performance. To that end, this report uses a constructive solid geometry (CSG) representation of the Oak Ridge National Laboratory (ORNL) Pool Critical Assembly (PCA) [1–3] to perform a k-eigenvalue calculation and an unstructured mesh (UM) representation of the International Commission on Radiological Protection (ICRP) publication 145 (ICRP145) male human phantom [4, 5] to perform a fixed-source calculation assuming that a 1 MeV photon source is distributed throughout the phantom’s liver.

97 MATHEMATICS AND COMPUTING↗

Improved Cross Section Generation Capability of Griffin in FY22

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 deterministic steady-state transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication as well as transient solvers for spatial dynamics with the improved quasi-static method. Griffin uses cross section data in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. In recent years, the MC 2 -3 modules have been added to Griffin for fast reactor cross section generation, and the self-shielding application programming interface (SSAPI) was implemented in the ISOXML module for thermal reactor cross section generation. The on-the-fly slowing down method and double-heterogeneity treatment have been implemented to SSAPI and verified against particulate fuel-bearing graphite-moderated thermal reactor problems with high accuracy. This year, work has been focused on improving the cross section generation capability of ISOXML and streamlining the cross section generation procedures. In addition, the form function data were added to ISOXML in order to support the pin power reconstruction capability that was newly implemented in Griffin in this fiscal year. To facilitate the cross section generation using MC 2 -3 and SSAPI in Griffin, the cross section generation workflows have been set up for both fast and thermal spectrum reactors. The MOOSE action system tool was devised for fast spectrum problems, and the MOOSE stochastic tool was adopted to the branch calculation procedure for thermal spectrum problems. Meanwhile, to ensure the accuracy of group-constants, the thermal up-scattering kernel calculator accounting for resonance scattering was implemented in ISOXML, demonstrating the accurate computation of a Doppler-broadened scattering kernel of any Legendre order within a reasonable timescale. Other aspects of ISOXML, such as deletion solver and data, documentation, ISOXML file management, and the interface for Mixture, were improved as well.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Godiva IV Simulated Radiation Field Characterization and Variance Reduction

Godiva IV is a system comprised of highly enriched uranium alloyed with molybdenum in the form of fuel plate rings. The reactor, along with its predecessors, was designed with the unique ability to satisfy interests in the super-prompt-critical reactor operation space. Originally, the reactor was part of the Los Alamos Critical Experiments Facility (LACEF) at Technical Area-18 (TA-18). The radiation field around Godiva at this facility was well characterized and understood. As a fast neutron system, the neutron spectrum in and around Godiva was close to a Watt Fission spectrum. The Kiva where Godiva IV was located at LACEF was made of thin, sheet metal walls which did not contribute significantly to the neutron spectrum. Following the transition of LACEF to the National Critical Experiments and Research Center (NCERC) in Nevada, Godiva-IV was moved from TA-18 to the Device Assembly Facility (DAF) at the Nevada National Security Site (NNSS). Part of this move brought renewed interest in radiation field characterization. The new facility introduced significant changes to the environment surrounding Godiva, and preliminary foil irradiation results suggested that the room contribution to the neutron spectrum was significant. Unlike at TA-18, a large thermal neutron signature was added to the fast spectrum from Godiva due to significant room return. A primary goal due to the additional complexity that the room return adds to the Godiva IV radiation emission spectrum was the development of an efficient Monte Carlo N-Particle (MCNP) calculation capable of characterizing the neutron spectrum anywhere in the room around Godiva. A campaign of activation foil irradiations and analysis were completed to support the validation of the MCNP model. The modeling of these foils in MCNP can be easily done with a standard volumetric neutron flux tally. However, given the multitude of locations and reaction rates to be modeled, further steps must be taken to increase the efficiency of these calculations in MCNP. During this study, a benchmark model currently under development for Godiva IV was used. A qualitative assessment of the thermal neutron contributors was performed using spatial neutron distribution plots. Additional detail was added to the model based on the qualitative results showing the thermal spectrum’s large sensitivity to hydrogenous material. Neutron energy spectra was evaluated at discrete locations in the room around Godiva to quantify the relative contribution of various components. It was discovered that the concrete walls are the largest contributor to the thermal signature, with minor contributions from plastic components surrounding Godiva. Following these results, two different variance reduction techniques were implemented to improve the problem efficiency in these calculations. In the first approach, an F5 point detector tally was implemented in the standard Godiva IV criticality problem. The second approach involved a weight-window generator implementation with an F5 point detector tally in a fixed source problem. The weight window implementation reduced the runtime from 42739.55 minutes to 1803.34 minutes (computer time), compared to the F5 KCODE implementation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Griffin Capability Improvements in Support of Ex-core Deep-Penetration Problems

Advanced reactor designs, especially portable reactors that are designed to be located closer to humans and operate autonomously, require the ability to accurately compute the ex-core neutron and gamma flux solutions in terms of shielding design optimization to reduce dose rates at the vessel boundary and detector signal prediction to drive the reactor control system. The Nuclear Energy Advanced Modeling and Simulation program has prioritized improvements to the Griffin discrete ordinates (SN) solver for deep-penetration problems in fiscal year 2025. Significant advancements have been made to the Griffin methodologies for solving ex-core deep-penetration problems for steady-state, fixed-source and transient calculations. This work presents the methodology improvements as well as a comprehensive demonstration with a Transient Test Reactor model and measurements.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Cross Section Generation Capability in Griffin

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.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗