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DOE OSTI2024

Initial Demonstration of New Griffin Technologies for Simulating the Running-In Phase of Pebble Bed Reactors

Griffin is a reactor multiphysics modeling application based on MOOSE (Multiphysics Object-Oriented Simulation Environment) and specifically targeting transient modeling of advanced reactors. Griffin has been used recently to model pebble-bed reactors for the Nuclear Regulatory Commission (NRC) Office of Nuclear Regulatory Research and the Advanced Reactor Technology program. This modeling work has focused thus far on the direct calculation of equilibrium cores. This report documents an initial demonstration of a new running-in simulation capability. The new running-in capability is verified using the existing direct equilibrium core calculation capability. A simplified pebble-bed reactor model is then used to demonstrate the running-in simulation capability. This demonstration shows that Griffin is able to simulate years of operation during the running-in phase efficiently with each depletion step taking only several seconds. Two new technologies are also presented in this report which have been developed in Griffin that will be essential for improved accuracy both of the direct equilibrium core computation and the new running-in simulation capability. The first technology is an online cross section generation capability specifically targeted for pebble-bed reactors. This will improve the accuracy of the depletion calculation as the cross sections are generated at the exact core status. This also avoids the difficult step of pre-generating a separate standalone multigroup cross section set. Secondly, a newly implemented discretization for discontinuous finite element method (DFEM) SN transport in cylindrical (RZ) coordinates, which can be solved efficiently using the existing SN sweep solver, is discussed and some results are shown demonstrating the usefulness of the additional accuracy transport provides over a diffusion approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Initial Demonstration of New Griffin Capability for Simulating the Running-In Phase of Pebble-Bed Reactors with Multiphysics

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient modelling of advanced reactors, has been used recently to model pebble-bed reactors (PBRs). The modelling effort has focused thus far on modelling the equilibrium core. A new capability to simulate the running-in phase of PBR operation has been added to Griffin. This work demonstrates the newcapability with a sample multiphysics running-in simulation. The basic features of the new running-in capability were documented previously; however, the sample simulation results presented there did not include multiphysics; the fuel temperatures were assumed to be constant. In this work, Griffin computes power densities in the core at each timestep of the running-in simulation and passes these to Pronghorn which models fluid flow and heat transfer to calculate temperatures that are passed back to Griffin and accounted for with temperature dependent cross-sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Equilibrium core modeling of a pebble bed reactor similar to the Xe-100 with SCALE

As the nuclear industry moves towards licensing and constructing advanced reactors, new attention has been focused on the advanced reactor designs that have past operational experience, such as pebble-bed high-temperature gas-cooled reactors (PB-HTGRs). Pebble-bed reactor designs have many advantages, such as their higher operating temperatures and online refueling capabilities. However, high-fidelity computational modeling of pebble-bed reactor designs, from reactor startup to operation at equilibrium, is more challenging compared to conventionally fueled reactors due to the continuous movement of the fuel pebbles through the reactor during operation. In previous work at Oak Ridge National Laboratory (ORNL), the SCALE Leap-In method for Cores at Equilibrium (SLICE) was developed around tools within the SCALE code system. This iterative method can effectively generate pebble-bed reactor zone-wise fuel inventories at equilibrium core operation within a reasonable computational time. The objective of this work was to further verify the ORNL SLICE method and to investigate the impact of considering temperature profiles during the application of the method. The SLICE method was applied to a modular high-temperature gas-cooled reactor design based upon publicly available design specifications of the Xe-100 pebble-bed reactor. Upon comparing the results from the SLICE method to published literature, the differences in the eigenvalue k effective were on the order of several hundred pcm (percent millirho). To investigate one possible cause of these differences, a study looking at the sensitivity of the full-core equilibrium k effective and discharge nuclide inventory to temperature was performed by developing equilibrium cores of two additional temperature profiles. From this temperature study, differences on the order of hundreds of pcm for the full-core equilibrium k effective , and up to 15% difference for the discharge inventories were found. In conclusion, these results indicated the strong dependence on temperature that needs to be considered for future work in equilibrium modeling of PB-HTGRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Gas-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

This report details a fully coupled neutronics thermal hydraulics reference plant model for a gas-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission's Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory high performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON MOOSE-based applications. Griffin provides the reactor physics capabilities including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient solutions. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions. BISON solves thermal conduction problems for the average pebble and TRISO in the pebble-bed core thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel and moderator temperatures. We present results for the coupled steady state equilibrium core and a protected loss of flow event. Although this model is to be considered prototypical with regard to the capabilities in BlueCRAB, its results are consistent with published work by the Institute of Nuclear and New Energy Technology (INET) in China and other research entities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Sensitivity analysis, surrogate modeling, and optimization of pebble-bed reactors considering normal and accident conditions

This research provides a valuable tool that streamlines the optimization process while significantly increasing its accuracy. This study creates a robust framework for reactor design optimization by incorporating comprehensive modeling using the Comprehensive Reactor Analysis Bundle, or BlueCRAB, within the Multiphysics Object-Oriented Simulation Environment (MOOSE). BlueCRAB is the United States Nuclear Regulatory Commission's code suite for non-light water reactor analysis and includes the Griffin, Pronghorn, and Bison applications. This not only improves the efficiency of the optimization process but also enhances the reliability of the results. Such a tool is essential for advancing the state-of-the-art in pebble-bed reactor technology and is critical for achieving the goals of Generation IV reactors, which aim for safe, sustainable, and economically viable nuclear energy solutions. This work presents and applies this workflow on pebble-bed reactors while considering both normal and off-normal conditions. A representative gas-cooled pebble-bed reactor at equilibrium core conditions serves as the nominal design specification for normal operation and is based on previous research. The depressurized loss-of-forced-cooling accident is deployed for off-normal conditions in this work. After defining design-related parameters and quantities of interest regarding reactor safety and performance, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of surrogate models. Subsequently, the dataset and surrogate models are employed in two optimization studies aimed at maximizing fuel utilization and economic profit while adhering to safety and operational constraints. Performing the optimization process with fuel utilization as the metric leads to an improvement of approximately 10%, compared to engineering-judgment-based nominal conditions. The optimization on economic profit leads to an estimated increase of ~300 million USD over the lifetime of the reactor.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Sensitivity Analysis, Reduced-order Modeling, and Optimization of a Gas-Cooled Pebble Bed Reactor using Equilibrium-Core and DLOFC Performance

This work presents and applies a workflow for performing design optimization on gas-cooled pebble-bed reactors. Based on previous research, a representative equilibrium core of a pebble-bed reactor and a depressurized loss-of-forced-cooling model are created. These applications are built using the Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically utilizing Griffin, Pronghorn, and Bison. After defining design-related parameters and quantities of interest regarding reactor safety and efficiency, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of reduced-order models. Subsequently, the dataset and reduced-order models are employed in an optimization study aimed at maximizing fuel utilization while adhering to safety and operational constraints. The optimization process leads to an improvement of fuel utilization by approximately 10\%, compared to engineering-judgment-based nominal conditions.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy

This report describes how to produce reference solutions for the equilibrium core search of pebble bed reactors using the pyrates Python library. The pyrates library uses the kugelpy methodology to perform running-in calculations to reach an equilibrium core. This approach relies on full-core Monte Carlo neutron transport calculations and the shifting of fuel pebble inventory through the reactor to simulate pebble movement in the core from one step to the next of a running-in scenario. In addition to the use of Serpent for the Monte Carlo neutron transport calculations, as part of this work, updates for the use of the Shift Monte Carlo code were integrated into the official pyrates GitHub repository. Comparisons of running-in simulations for a generic pebble bed reactor produced by using pyrates with Serpent and Shift are shown. Although consistent trends are shown between the use of the two Monte Carlo codes, the limiting factor in either calculation is the computation time due to the need to perform several hundred full-core neutron transport calculations before an equilibrium core is reached.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Demonstration of Monte Carlo Reference Equilibrium Core Solutions for Pebble Bed Reactors Using Shift in kugelpy

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 OSTI2025

Multiphysics Running-In Simulations for Pebble-Bed Reactors with Griffin

Griffin, a Multiphysics Object-Oriented Simulation Environment (MOOSE)–based application targeting transient modeling of advanced reactors, has been used recently to model pebble-bed reactors (PBRs). The modeling effort has focused thus far on equilibrium core calculations. A new capability to simulate the running-in phase of PBR operation has been added to Griffin. This work demonstrates the new capability with a coupled multiphysics running-in simulation. Griffin computes power densities in the core at each time step of the running-in simulation and passes these to Pronghorn, which models fluid flow and heat transfer to calculate pebble surface temperatures. These surface temperatures are used along with the power densities in a heat conduction model to compute average fuel and moderator temperatures, which are passed back to Griffin and accounted for with temperature-dependent cross sections. This work also describes a novel methodology for determining appropriate pebble feed rates and control rod positioning during the running-in simulation. Furthermore, the RZ-geometry model used in this work requires minimal computational resources and can be used for optimization and uncertainty studies in future works.

Griffin↗

DOE OSTI2025

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model Updates

This work presents the latest improvements to, and investigations performed with, the Fluoride-Cooled High-Temperature Pebble-Bed Reactor reference plant models for the United States Nuclear Regulatory Commission. These models, developed with the Comprehensive Reactor Analysis Bundle, or BlueCRAB, serve as the foundation for the future development of detailed design evaluation models based on license applications. BlueCRAB is the code suite proposed for non-light-water reactor systems safety analyses, and it incorporates various simulation tools developed by the Nuclear Energy Advance Modeling and Simulation program, including the Griffin code for reactor physics, the Pronghorn and SAM codes for core thermal fluids, the BISON code for solid conduction and fuel performance, and the SAM code for system analysis. The primary objective of this work is to assess the level of readiness of BlueCRAB for modeling fluoride-cooled high-temperature pebble-bed reactors. We first developed numerical models in BlueCRAB that include the key physics for this technology, ensuring an adequate level of fidelity for modeling the core performance during accident scenarios. This was followed by simulation of transient scenarios, two loss-of-forced-cooling events (one protected and one unprotected), and two control rod withdrawal events (one delayed and one prompt supercritical reactivity insertion). The analysis includes comparisons between the 2-D thermal fluid porous media models in Pronghorn and SAM, comparisons between coupled Pronghorn-Griffin and coupled SAM-Griffin models for two loss-of-forced cooling events and one control rod withdrawal event, and comparisons between SAM single-solve and domain-overlapping approaches for multi-scale thermal fluid coupling. In addition, we performed comparisons between 3-D, 2-D, and 0-D neutronic models for the two control rod withdrawal scenarios with Pronghorn-Griffin. The results show that the BlueCRAB models led to physically intuitive solutions for the scenarios examined. The changes in the various scalar and vector fields such as the neutron flux, power, temperatures, densities, pressures, and velocities are all within the expected ranges, and their distributions can be explained from the system response of the transients and the geometric and material variations. Several comparisons suggest that the porous media models in Pronghorn and SAM can lead to similar solutions, even though they are based on different methodologies. The simulations demonstrate that there are differences between the various levels of fidelity, and it is advisable to have flexible tools that can cover the breadth and depth of needs that may arise in future technical evaluations. We believe that BlueCRAB’s capabilities represent a significant asset for confirmatory analyses aimed at resolving important safety questions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Capturing the run-in of a pebble-bed reactor by using thermal feedback and high-fidelity neutronics simulations

Modeling the run-in of a pebble-bed reactor (PBR) can be challenging as a result of changes in the power, fuel type, and temperatures that occur throughout the run-in period. Previous work utilized high-fidelity neutronics simulations or lower-fidelity coupled neutronics/thermal-hydraulics models to capture the general characteristics of the run-in process. Here, the present work employs high-fidelity neutronics simulations (using Serpent) coupled with thermal-hydraulics simulations (using Griffin–Pronghorn) to capture the thermal feedback present during the run-in and approach to equilibrium for a PBR. Incorporating thermal feedback enables important distinctions to be made about conditions occurring inside the core, as the power distribution, discharge burnup, and isotopic compositions are all affected by the temperature distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

In this report we present work performed in Fiscal Year 2022 that demonstrates the modeling and simulation of a fully coupled neutronics thermal hydraulics reference plant model for a fluoride-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission’s Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory’s high-performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON Multiphysics Object-Oriented Simulation Environment based applications. Griffin provides reactor physics capabilities, including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient. The unique direct equilibrium core capability in Griffin is based on a streamline methodology to spatially deplete the pebbles into burnup groups. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions and incorporates a fluidic diode model to simulate the transition from forced to natural convection during accident scenarios. MOOSE modules solves thermal conduction problems for the pebbles and tristructural isotropic in the pebble-bed core, thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel, moderator, and reflector temperatures as as well as the FLiBe salt density. Here, we present results for the uncoupled equilibrium core and perform comparisons to equivalent Monte Carlo models. The power distributions and kinetic parameters obtained with Griffin are consistent with those computed with Griffin. We demonstrate a noticeable improvement with the use of discrete ordinates method (SN) transport. The coupled steady-state equilibrium core provides the initial condition for two time-dependent problems: a control rod withdrawal event and an unprotected loss of flow event. In both cases, the reactor design is self-stabilizing and the solutions are consistent with the expected physics. Although this model is prototypical regarding BlueCRAB’s capabilities, its results are consistent with published work by Kairos Power and other research entities. Significant improvements to the model are planned in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Introducing the SLICE Method for estimating pebble-bed reactor inventories at equilibrium operation with SCALE

This paper introduces the SCALE Leap-In method for Cores at Equilibrium (SLICE) for estimating pebble-bed reactor equilibrium core isotopic inventories using capabilities in the SCALE code system, requiring only a small computational cluster and a few days of computation. This method uses an iterative approach that relies on (1) a surrogate spectrum model that captures spatial and time-dependent spectral conditions, (2) a multi-pass model that captures the pebble’s evolving nuclide inventory as a function of location and time in the core, and (3) a full-core model that captures the core’s spatial neutron flux distribution. The SLICE approach is applied to a generic fluoride salt–cooled high-temperature reactor, demonstrating fuel inventory convergence through nuclide concentration inspection across iterations and comparisons for core realizations with varying discretizations. Results agree within ~5% with another state-of-the-art code, with differences attributed to input parameter or modeling assumption variations in the equilibrium generation methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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 OSTI2024

Improving the modeling of near-wall interphase heat transfer in porous media models of Pebble Bed Reactors

Here, this work aims to improve capabilities for modeling localized effects in porous media models of Pebble Bed Reactors. The wall-channeling effect is the primary local phenomenon of interest in a PBR, where the presence of the reflector wall disrupts the pebble packing, causing the pebbles near the wall to pack less efficiently and creating large void regions. Accurate modeling of the near-wall region is important as it will affect core bypass flow and temperature predictions. Porous media models are commonly used for design scoping and plant-level simulations of PBRs. Although these models have some capabilities to model the near-wall region, the correlations that are available in porous media codes are often inaccurate when a multi-region model is used to discretize the near-wall region. This work employs a high-to-low analysis to study the accuracy of available interphase heat transfer closures. NekRS, a spectral element computational fluid dynamics code, is used to perform Large Eddy Simulations. These LES simulation results are compared to porous media model results from the Pronghorn porous media code. The friction term of the KTA drag closure is first improved, reducing the error in the prediction of the near-wall velocity from over 50% to less than 5%. This is combined with improvements to the form term from previous works to produce a drag closure that is capable of accurately modeling the wall-channeling effect across a variety of flow conditions. The Nusselt number predictions of several heat transfer correlations are compared to the high-fidelity results where it is found that the KTA heat transfer correlation is capable of accurately predicting the local Nusselt numbers that were determined in the high-fidelity simulation. Comparison of the radial solid temperature profiles, however, reveal discrepancies between NekRS and Pronghorn. It is discovered that the implementation of the interphase heat transfer coefficient that exists in many current porous media codes is not valid when local porosities are modeled. Instead, it is suggested that the interphase heat transfer coefficient should be dependent on the local porosity, the Nusselt number, and the local solid surface-to-volume ratio. Implementation of this change produces improvement in the agreement between the results obtained by NekRS and Pronghorn while using the KTA heat transfer correlation.

interphase heat transfer↗

DOE OSTI2024

High-Temperature Gas-Cooled Pebble-Bed Reactors Running In And Transient Modeling Capabilities Demonstration

This study presents a comprehensive benchmarking and verification effort of several thermal-hydraulic and multiphysics capabilities for high-temperature gas-cooled reactor (HTGR) applications. The first part of this effort focuses on the running-in verification of Griffin's multiphysics capabilities, specifically for simulating the evolution of Pebble Bed reactor cores from startup to equilibrium. In the absence of validation data, code-to-code comparisons are conducted with Kugelpy, showing good agreement for key quantities like maximum power density and fresh core k-eigenvalue predictions. However, discrepancies in equilibrium core predictions suggest potential issues with cross sections, underscoring the need for further refinement and evaluation. The HTTF system analysis code benchmark involves RELAP5-3D, SAM, and GAMMA+ to assess their predictive capabilities for HTTF behavior under both normal operation and pressurized conduction cooldown (PCC) transient conditions. While there is good agreement in predicting major parameters such as coolant temperature, solid temperature, and flow distribution, discrepancies in transient behavior highlight differences in modeling approaches, nodalizations, and heat transfer models. The HTTF lower plenum CFD benchmark employs nekRS to simulate flow mixing phenomena, successfully capturing relevant flow physics and demonstrating mesh independence in complex geometries. Preliminary results suggest a relatively uniform temperature field but significant unsteadiness in the flow, requiring time-averaging analyses. The GPBR200 system analysis code benchmark uses SAM's core channel and porous media models, incorporating an RCCS loop for decay heat removal. During steady-state and transient conditions, including protected de-pressurized and pressurized loss of forced cooling (DLOFC and PLOFC), both models show good agreement in predicting temperature profiles and key parameters. Notably, while the core channel model underpredicts convective heat transfer effects, both models maintain temperatures well below the TRISO fuel safety limit. These benchmarking efforts collectively enhance the predictive capabilities of the tools used in HTGR design and safety analysis, guiding developments to improve their accuracy and applicability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Nuclear Material Control & Accounting for Pebble Bed Reactors (FY 2023 Summary Report)

This report discusses the work done under the US Department of Energy NE-5 Advanced Reactor Safeguards and Security Program during FY 2023. It provides a summary of material control and accounting (MC&A) for pebble bed reactors (PBRs) and addresses some of the main challenges with current PBR MC&A approaches that will inform safeguards and security by design efforts. The efforts to date have focused on tristructural isotropic (TRISO) pebble fuel material accounting and control including working with partners in industry, loss and production of nuclear material as part of reactor operations, burnup modeling and measurements, uncertainty quantifications for such modeling and measurements, statistical approaches needed, and measurement methods. The unique fuel management and utilization in a PBR, where the fuel in spherical form is introduced and circulates through the reactor, poses special challenges for MC&A. This contrasts with traditional water-cooled reactors in which the fuel is contained in large assemblies and can be easily identified and counted. Even online fueled reactors, such as the CANDU reactors (none of which operate in the United States), are significantly different because the fuel is still contained in relatively large assemblies, is uniquely identified, and the number of assemblies that pass through the core on an annual basis is much fewer than the hundreds of thousands that circulate in a PBR, none of which are uniquely identified. Additionally, the nature of the TRISO fuel results in very low heavy metal loading with each pebble containing less than 10 g of uranium and on the order of less than 1 g of fissile material. This low fuel density and the robustness of the TRISO particles are major features of the TRISO fuel from a safety basis as each TRISO particle and pebble acts as a containment for the nuclear material and fission products during normal and accident conditions. This also results in very low plutonium loading per pebble during normal operations, which is on the order of 0.1 g at full burnup. A major feature of PBRs is that they will allow for significantly higher burnup, on the order of 160 GWd/THM compared to the burnup of traditional LWRs, which is on the order of 45 GWd/THM. This is achieved by monitoring the pebbles as they circulate through the reactor and allowing them to be reintroduced into the core until the desired burnup is achieved and they are removed from the reactor and enter the spent fuel storage areas.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗