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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

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↗
DOE OSTI2022

Multiphysics Simulation of the NASA SIRIUS-CAL Fuel Experiment in the Transient Test Reactor Using Griffin

After approximately 50 years, NASA is restarting efforts to develop nuclear thermal propulsion (NTP) for interplanetary missions. Building upon nuclear engine tests performed from the late 1950s to the early 1970s, the present research and testing focuses on advanced materials and fabrication methods. A number of transient tests have been performed to evaluate materials performance under high-temperature, high-flux conditions, with several more experiments in the pipeline for future testing. The measured data obtained from those tests are being used to validate the Griffin reactor multiphysics code for this particular type of application. Griffin was developed at Idaho National Laboratory (INL) using the MOOSE framework. This article describes the simulation results of the SIRIUS-CAL calibration experiment in the Transient Reactor Test Facility (TREAT). SIRIUS-CAL was the first transient test conducted on NASA fuels, and although the test was performed with a relatively low core peak power, the test specimen survived a temperature exceeding 900 K. Griffin simulations of the experiment successfully matched the reactor’s power transient after calibrating the initial control rod position to match the initial reactor period. The thermal-hydraulics model largely matches the time-dependent response of a thermocouple located within the experiment specimen to within the uncertainty estimate. However, the uncertainty range is significant and must be reduced in the future.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

An Initial Study of the Convergence Rate of Griffin’s Pebble Bed Reactors Algorithm

This paper presents an initial study of the convergence properties of an iterative algorithm for computing the burnup distribution in a pebble bed reactor (PBR) in its equilibrium core condition. The algorithm is implemented in the Griffin code. Griffin is a reactor multiphysics analysis application jointly developed by Idaho National Laboratory (INL) and Argonne National Laboratory (ANL). Griffin’s PBR algorithm is discussed and simulation data are presented. An alternative matrix formulation of the algorithm is presented that facilitates analysis of the iterative algorithm. The dependence of the spectral radius of the iterative algorithm on operational and discretization parameters is investigated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Griffin: A Moose-based Reactor Multiphysics Application For Radiation Transport And Depletion Simulations

Griffin is a MOOSE-based reactor multiphysics application that streamlines the analysis of a variety of nuclear multiphysics applications, including steady-state and transient radiation transport, core performance, fuel depletion, criticality and decay heat calculations, reprocessing and post-irradiation examination. This streamlining is accomplished via enhanced flexibility of the tools, uniform syntax in the MOOSE framework, dynamic linking of all relevant physics and a single point of execution. The design for flexible multi-physics, multi-radiation, multi-scheme tasks demands and ultimately makes Griffin a highly extendable code system. A software quality assurance (SQA) procedure is enforced during Griffin development.

DeHart, MarkD.↗
DOE OSTI2021

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↗
DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Integration of Online Cross-Section Generation Capability with Depletion and Transient Solvers in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE)-based reactor multiphysics analysis application jointly developed by Argonne and Idaho National Laboratories under the DOENE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In FY25, an online crosssection generation capability based on the Self-Shielding Application Programming Interface (SSAPI) was demonstrated for TRISO-fueled reactor problems under steady-state conditions. This fiscal year, that capability was extended to support depletion and transient multiphysics calculations, enabling high-fidelity analyses that generate self-shielded cross sections on the fly from the actual evolving composition and temperature states rather than from pre-tabulated libraries. For depletion, a two-way coupling was established in which SSAPI computes compact-averaged self-shielded cross sections that the depletion solver then uses to advance the Bateman equations, with the updated compositions returned to SSAPI at each step; the depletion module was refactored to support both library-based and SSAPI-based cross sections, and additional logic was added to track daughter isotopes and to exclude minor isotopes for efficiency. For transient analysis, the SSAPI multigroup library was extended with the kinetics data required for time-dependent calculations, the Improved Quasi-Static (IQS) scheme was coupled with SSAPI, and several supporting capabilities were implemented, including a self-shielding treatment that lets control rods and drums move within a self-shielded model, which had previously been impossible and had ruled out rod- and drum-movement transients with on-the-fly cross sections altogether, a new mixing scheme for delayed-neutron precursor decay constants, a checkpoint-based restart workflow, and performance improvements such as pointwise cross-section interpolation and the bypassing of unnecessary Dancoff factor calculations. The implemented capabilities were verified against Serpent Monte Carlo solutions. For depletion, a prismatic pin-cell problem based on a Next Generation Nuclear Plant (NGNP) Very High Temperature Reactor benchmark showed excellent agreement, with eigenvalue differences within 200 pcm over the entire burnup range (up to 140 MWD/kgU) and fission-product and actinide inventories agreeing to within 0.8% and 2.5%, respectively; a heat-pipe microreactor assembly problem with a much higher fuel loading confirmed the same behavior and quantified the bias introduced when the multigroup equivalence effect is neglected. For transient analysis, a pin-cell problem with a step reactivity insertion and temperature feedback reproduced the analytically expected asymptotic power and showed close agreement between the direct and IQS solutions, and a two-dimensional microreactor core problem with control-drum rotation exercised the new moving-drum self-shielding treatment and demonstrated successful coupling of the online crosssection generation with both the direct and IQS transient methods. The capability was further exercised on a full-core pebble-bed problem, in which Griffin was coupled with the System Analysis Module (SAM) to simulate load-following operation of the gPBR with the Doppler feedback resolved at the TRISO fuel kernel temperature. These developments in Griffin provide a convenient, high-fidelity approach to cross-section generation for advanced thermal reactors with geometrically complex and highly heterogeneous configurations, including TRISO-fueled prismatic and pebble-bed systems, and support steady-state, depletion, and transient multiphysics calculations. They also enable self-shielded cross sections to be evaluated directly at the actual coupled state of the system, thereby establishing a foundation for high-fidelity, fully coupled multiphysics analysis of advanced reactors

Park, H.↗
DOE OSTI2025

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↗
DOE OSTI2024

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin 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. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Implementation of Isotopic Removal Capability in Griffin for Multi-Region MSR Depletion Analysis

This work reports the first step in such an analysis, the verification of isotope removal capability for multi-region MSR depletion in Griffin. Verification studies are performed against SERPENT for chemical species removal from the core to an off-gas system for MSR analysis. A brief review of the Bateman equations including the isotopic removal term is provided along with a description of the example problem used in the verification studies performed in Griffin versus SERPENT. Next, the results of the verification study are presented for isotopic depletion, isotopic depletion with removal, and the specific analysis case of varying the solubility of Iodine in a salt system and how this can affect material buildup in the off-gas system. Lastly, the results are analyzed and future work detailing the fully coupled MSR depletion analysis that incorporates the true multiphysics of the system is discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Verification of the Serpent-Griffin Workflow using the SNAP 8 Experimental Reactor

The Systems for Nuclear Auxiliary Power (SNAP) program accumulated extensive experimental measurements over a span of 15 years. This work builds upon previous studies which validated Serpent against experimental data for various criticality configurations of the SNAP 8 Experimental Reactor (S8ER). A 2-stage sequence is applied here with Serpent used for the generation of few-group cross sections and Griffin as the transport eigenvalue solver. Sensitivity studies are performed to qualify the effect and uncertainty of various parameters, comparing against reference models for the S8ER. The results from this work will then be expanded to create a generalized methodology for the Serpent-Griffin 2-stage approach for microreactor applications.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

CNRS Molten Salt Reactor Benchmark Analysis Using Griffin-Pronghorn Coupled Multi-physics Code System

Molten salt reactors (MSRs) with flowing fuel have the unique feature of utilizing the fuel salt for heat generation and extraction at the same time, since the fuel salt is circulating through the whole primary loop. This movement of fuel salt results in a partial decay of the delayed neutron precursors (DNPs) outside the core and the corresponding redistribution of the DNPs in the active region of the core. To capture this effect, neutronics and thermal-hydraulics (T/H) codes need to be able to handle the movement of DNPs and their decay [1, 2]. Idaho National Laboratory (INL) is actively working on developing the neutronics and T/H codes to model the MSRs with flowing fuel. As one of the efforts, the neutronics code Griffin [3] and the T/H code Pronghorn [4] that are built upon the MOOSE framework [5] have been extended to handle the flowing fuel involving the drift of DNPs, and this capability is being tested and verified with MSR benchmark problems including the CNRS benchmark problem [6]. Additionally, a multi-physics analysis of the molten salt reactor experiment (MSRE) is being conducted to verify and validate the codes against available experimental data [7]. This work presents the analysis of the CNRS benchmark problem using the Griffin-Pronghorn coupled multi-physics code system of INL. Both steady-state and transient problems are analyzed, and the results are compared with those of other participants presented in [6]. The following section provides a description of the benchmark, along with input parameters and observables for each step. Then, the results for each step are presented in comparison with other participants’ results, followed by summary and conclusion.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Numerical Method Improvements in Griffin for Pebble Bed Reactors with a Focus on the Computation of Burnup

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient multiphysics modeling of advanced reactors, has been used recently to model both high-temperature gas-cooled and fluoride-salt-cooled pebble bed reactors (PBRs). Griffin uses deterministic methods for solving neutron transport and an Eulerian approach to model pebble movement. An Eulerian approach is also used to directly compute burnup instead of using a pass approach like other tools such as VSOP or PANGU. This work discusses verification efforts and numerical method improvements related specifically to the Eulerian modeling approach implemented for directly computing pebble burnup.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Using Griffin's Transmutation Solver to Calculate Radiation Damage

Displacement Radiation Damage originates from all nuclides, not just those that are naturally occurring. Currently only damage from naturally-occurring nuclides, or sometimes damage from one transmutation product is considered. It is proposed that the transmutation solvers implemented in many codes be used to calculate this radiation damage. This would explicitly treat damage from all sources without additionally burdening the user. A proof-of-concept implementation was created in Griffin. The implementation showed that only minor code modifications are necessary to add this feature. When compared against an analytical benchmark the results Griffin could calculate were very accurate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Implementation of hybrid finite element method based transport solver in GRIFFIN

A new transport solver option based on the hybrid FEM (HFEM) was implemented in GRIFFIN, the MOOSE-based reactor analysis code, as an effort to support routine core design calculations for advanced reactor applications. The HFEM formulation with P{sub N} (spherical harmonics expansion), akin to the variational nodal method, is effective for solving a spatially homogenized problem with strong transport effect. The residual and Jacobian evaluations of the HFEM weak form were derived and successfully implemented in GRIFFIN, having the diffusion and the PN options available in the new HFEM based transport solver. The performance was tested with the simplified ABTR benchmark problems. The results indicate that the HFEM-based transport solver is a feasible option for solving problems with spatially homogenized and strong streaming by providing superior accuracy with a proper p-refinement. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Investigation of the excited states of 114 Sn using the GRIFFIN spectrometer at TRIUMF

The semi-magic 110-122 Sn isotopes display signs of shape coexistence in their excited 0 + states, which, in contrast to the spherical 0+ ground states, are deformed. Here, this paper investigates the nuclear structure of 114 Sn using the competing β + decay and electron capture of a radioactive beam of 114 Sb produced at the TRIUMF-ISAC facility using the GRIFFIN spectrometer. This study will allow for an in-depth understanding of the excited 0 + states in 114 Sn, by focusing on their decay patterns. In the present experiment, transitions at 856.2-keV and 1405.0-keV, which were observed in an earlier β + decay study but not placed in the 114 Sn level scheme, have been Physics, assigned to the level scheme in connection to the 0$^+_3$ level at 2156.0-keV. Properly assigning these transitions refines the level scheme and enhances our understanding of the nuclear structure in 114 Sn.

GRIFFIN↗
DOE OSTI2025

A Refined BISON-Griffin Workflow For Designing Targeted TRISO Transient Experiments In The Transient Reactor Test Facility

U.S. industry is expected to deploy tristructural isotropic (TRISO) particle fuel technologies for commercial reactors within the next decade. In our previous work, we defined a preliminary transient design space for TRISO fuels, identified potential gaps in the available data, and began to develop multiphysics modeling tools that could be applied to design targeted Transient Reactor Test Facility (TREAT) experiments to fill these gaps. This work builds on that foundation by (1) updating BISON fuel performance and Griffin reactor physics models to reflect the current TREAT experiment tube and capsule designs,(2) coupling the codes to improve the accuracy and usability of the transient design analyses, and (3) demonstrating their use over an expanded design space that includes fuel burnup. The simulated mechanical responses of the TRISO particles were complex functions of fission product accumulation, fission gas release, and irradiation-induced dimensional change in the pyrolytic carbon layers. Predicted tangential stresses in particle silicon carbide layers were least compressive for preheated tests involving fresh fuels but remained compressive throughout the ranges of temperature, heat rate, and burnup considered in this work. Finally, comparisons between the potential TREAT transients and historical test reactor irradiations showed that the TREAT tests would produce significantly lower average energy deposition rates, yielding less severe transients with greater relevance to near-term commercial applications. Use of these predictive capabilities has the potential to increase the value of each test, improving the overall efficiency and cost effectiveness of transient testing for TRISO and other advanced fuels.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗