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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

CFD Simulations of Lower Plenum Mixing

Review of model development and validation performed in the Advanced Reactor Technologies (ART) program for thermal mixing at the outlet of High Temperature Gas Reactors (HTGRs). Understanding the mixing that occurs in the lower plenum in an HTGR is necessary to facilitate design improvements and to perform reactor safety analysis. Numerical models are one possible approach to gain a better understanding of mixing in the lower plenum. Given the complexity of the geometry and the intense mixing present, it is important to perform validation of numerical models. Three models have been developed during FY2025: a porous media with Pronghorn, a Reynolds Averaged Navier Stokes (RANS) with STAR-CCM+, and a Large Eddy Simulation (LES) with NekRS. The reference facility is a scaled-down version of the lower plenum of the High Temperature Gas-Cooled Reactor - Pebble-bed Module (HTR-PM) demonstration reactor. Preliminary results of the porous media and the RANS shows general good agreement against experimental benchmark data. Future work will leverage high-fidelity results obtained through LES to guide model selection and improvements to the lower-fidelity models, with particular attention to the Pronghorn porous media.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Modeling of a Generic Pebble Bed High-temperature Gas-cooled Reactor (PB-HTGR) with SAM

This report presents the modeling of the core of a generic pebble-bed reactor (PBR) at the system level using the System Analysis Module (SAM) code. This work is an extension of a previous work by the authors (Ooi et al. (2021)) that used the so-called 2-D ring model approach to model the PBMR-400. With the new approach, the pebble bed of the reactor is modeled with multiple PBCoreChannel components with spherical heat structures which allows the code to calculate thermal fluid parameters with built-in closure relations. The new core-channel approach is an improvement to the 2-D ring model approach as it does not introduce geometric distortions to the model and thus reduces the uncertainties of the predictions. In addition to thermal fluid simulations, point kinetics (PKE) are included to the model. Simulations are performed under a steady-state normal operation condition and a load-following transient scenario. This particular transient scenario is chosen as it tests both the thermal fluid and neutronics aspects of the model. The predicted results from both the steady-state and transient scenarios are compared with the results by Stew- art et al. (2021) who performed similar simulations with a Griffin-Pronghorn coupled tool. Despite the differences between the codes, with SAM being a system-analysis code and Pronghorn being a porous-medium code, both sets of results compare favorably. The over- all profiles and trends of the predicted temperatures and reactivities from the SAM and Griffin/Pronghorn simulations are similar, with some differences in their predicted values. The first part of the report covers the significance of a relatively fast-running approach that is capable of modeling the pebble bed reactor at the system-level while simultaneously capturing the radial thermal behavior of the core. Then, the modeling approach used in this work is discussed in details. Lastly, the results and comparisons with the Griffin/Pronghorn simulation are presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Pronghorn Porous Media Model Validation with Pressure Drop Measurements

The verification and validation (V&V) of Pronghorn is imperative to assert its accuracy when predicting the fluid velocity, temperature, and pressure in high temperature gas-cooled reactors. Pronghorn is a coarse-mesh, intermediate-fidelity, and multidimensional thermal-hydraulics (TH) code developed by the Idaho National Laboratory (INL). New pebble bed experiments are used to observe the details of the fluid motion and pressure drop in the porous bed under the reactor normal operation. This paper focuses on the validation of the Pronghorn compressible and incompressible Navier-Stokes equations using the pressure drop measurements performed at the engineering-scale pebble bed facility at the Texas A&M university (TAMU). Various pressure drop correlations and porosity functions are implemented in both Pronghorn and STAR-CCM+ to compare the pressure drop due to the combined viscous and inertial resistances in the porous bed. The correlations accounting for the near-wall effect are also utilized to observe if the pressure drop estimates can be improved. Pronghorn porous media models predict the pressure drop well relative to the STAR-CCM+ simulation results and 1D correlations, and both the finite element method (FEM) and finite volume method (FVM) perform accurately. Pronghorn models are also validated with the experimental measurements given the different Reynolds number ranges and specific aspect ratios. The likelihood of the statistical significance between the pressure drop measurements and specific correlations or simulations is low provided that the overlap of their confidence intervals is more than the half of a single arm. Several validation metrics are reasonable in regard to the similar studies from other literature. The precise average pebble bed porosity estimation has much impact on the pressure drop, and the Foumeny and Montillet (dense packing) models carry out the accurate pressure drop prediction by considering the near-wall effect.

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

Discrete element simulation of Pebble Bed Reactors on graphics processing units

Prediction of pebble positions in a Pebble Bed Reactor (PBR) is necessary for both reactor physics and thermal hydraulics simulations as the arrangement of pebbles has a significant impact on the resulting core power, coolant flow, and fuel temperature. Knowledge of pebble movement as the fuel is cycled through the core is also critical for predicting the fuel residence time and subsequently, the fuel burnup. Simulation with the Discrete Element Method (DEM) can provide knowledge of both the fuel packing and the fuel movement during cycling. Previous works that have performed 3D full-core DEM simulation of PBRs have used simplified models that neglect reflector wall features. This work employs a graphics processing unit (GPU)-enabled DEM code, Project Chrono, to analyze the differences in pebble packing and pebble velocities between a simplified smooth PBR reflector and a more realistic reflector that includes circular wall features. Additionally, a sensitivity study is performed on the depth of the wall features to ensure that crystallization is prevented. Project Chrono is also validated for PBR cycling applications using experimental data. It is found that wall features with a depth of at least 0.5 pebble diameters significantly reduce crystallization in the near-wall region, leading to discrepancies in both packing fraction and pebble velocity in this region compared to the simplified reflector models. These discrepancies are found to lead to roughly a 5–10% difference in the prediction of the near-wall porosity and a 10% difference in the prediction of the velocity of pebbles near the wall. As a result of these discrepancies, it is suggested that future DEM simulations of PBRs include wall features to reduce modeling errors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Cardinal: A Lower-Length-Scale Multiphysics Simulator for Pebble-Bed Reactors

This paper demonstrates a multiphysics solver for pebble-bed reactors, in particular, for Berkeley’s pebble-bed -fluoride-salt-cooled high-temperature reactor (PB-FHR) (Mark I design). The FHR is a class of advanced nuclear reactors that combines the robust coated particle fuel form from high-temperature gas-cooled reactors, the direct reactor auxiliary cooling system passive decay removal of liquid-metal fast reactors, and the transparent, high-volumetric heat capacitance liquid-fluoride salt working fluids (e.g., FLiBe) from molten salt reactors. This fuel and coolant combination enables FHRs to operate in a high-temperature, low-pressure design space that has beneficial safety and economic implications. The PB-FHR relies on a pebble-bed approach, and pebble-bed reactors are, in a sense, the poster child for multiscale analysis. Relying heavily on the MultiApp capability of the Multiphysics Object-Oriented Simulation Environment (MOOSE), we have developed Cardinal, a new platform for lower-length-scale simulation of pebble-bed cores. The lower-length-scale simulator comprises three physics: neutronics (OpenMC), thermal fluids (Nek5000/NekRS), and fuel performance (BISON). Cardinal tightly couples all three physics and leverages advances in MOOSE, such as the MultiApp system and the concept of MOOSE-wrapped applications. Moreover, Cardinal can utilize graphics processing units for accelerating solutions. In this paper, we discuss the development of Cardinal and the verification and validation and demonstration simulations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Coupling of Pronghorn and RELAP-7 for a Pebble Bed Reactor

High temperature gas cooled reactors (HTGR) are a candidate for timely Gen-IV reactor technology deployment because of high technology readiness and walk-away safety. Among HTGRs, pebble bed reactors (PBRs) have attractive features such as low excess reactivity and online refueling. Pebble bed reactors pose unique challenges to analysts and reactor designers such as continuous burnup distribution depending on pebble motion and recirculation, radiative heat transfer across a variety of gas-filled gaps, and long design basis transients such as pressurized and depressurized loss of forced circulation. Modeling and simulation is essential for both the PBR’s safety case and design process. In order to verify and validate the new generation codes the Nuclear Energy Agency (NEA) Data bank provide a set of benchmarks data together with solutions calculated by the participants using the state of the art codes of that time. An important milestone to test the new PBR simulation codes is the OECD NEA PBMR-400 benchmark which includes thermal hydraulic and neutron kinetic standalone exercises as well as coupled exercises and transients scenarios. In this work, the reactor multiphysics code MAMMOTH and the thermal hydraulics code Pronghorn, both developed by the Idaho National Laboratory (INL) within the multiphysics object-oriented simulation environment (MOOSE), have been used to solve Phase 1 exercises 1 and 2 of the PBMR-400 benchmark. The steady state results are in agreement with the other participants’ solutions demonstrating the adequacy of MAMMOTH and Pronghorn for simulating PBRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

NRC Multiphysics Analysis Capability Deployment (FY2021--Part 1)

This report details progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” The tasks completed for this report are as follows: First, Task 1d: The net radiation transfer method was implemented into MOOSE for modeling reactor cavity cooling system geometries. RCCS models for two experiments were created: (1) Natural Convection Shutdown Heat Removal Test Facility (NSTF) experiment R022, and (2) HTTR VCS mockup. For validation, computed temperature distributions were compared to measured temperatures. Next, Task 4c: An algorithm for computing the pebble bed reactor equilibrium core isotopic com-position was developed and an initial version is implemented into the reactor multi-physics code Griffin. Initial results for a simplified axisymmetric pebble bed reactor are presented. Finally, Task 7: generation of a reference plant model for molten salt cooled pebble bed reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Modeling of a 1/20th Scaled-down Gas Reactor Using MOOSE-based Application Pronghorn

University of Idaho (UI) designed and built a 1/20th scaled-down HTGR system to examine the mixing and venting of helium and reactor cavity air after a loss-of-coolant, also known as LOCA, due to a break in the reactor pressure vessel. Computational fluid dynamics (CFD) models of the system were developed, but their computational cost is high for modeling long transient accident scenarios. The objective of the project is to develop a simulation of the scaled-down system using the MOOSE-based application Pronghorn. A numerical approach is needed to have a better understanding of the physics phenomena that takes place following a LOCA event, and it can guide plant designers to design parameters for the development of mitigation techniques. This scenario is applicable to all HTR designs including the pebble bed reactor concept.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

SCALE 6.2.4 Validation: Reactor Physics

This report is the third volume in a report series documenting the validation of SCALE 6.2.4, which is used herein with ENDF/B-VII.1 libraries, for nuclear criticality safety, reactor physics, and radiation shielding applications. This report focuses on validating SCALE capabilities that affect reactor physics applications. The experimental data used as basis for validation consists of measurement data for nuclide inventory, decay heat, and full-core experiments and include the following: 1. radiochemical assay measurements of 40 nuclides of importance to burnup credit, decay heat, and radiation shielding in 169 light-water reactor (LWR) spent nuclear fuel samples that cover burnups up to 70 GWd/MTU and initial enrichments up to 4.9% 235 U; 2. full-assembly decay heat measurements for 236 LWR assemblies with: a. initial fuel enrichments up to 4% 235 U, b. assembly burnups of 5–51 GWd/MTU, and c. cooling times after discharge in the 2- to 27-year range (of importance to spent nuclear fuel storage, transportation, and disposal); and 3. pulse fission irradiations for fissionable materials at cooling times of interest to severe accident analyses (<10 5 s). Validation examples for full-core analysis are based on startup experiments for the Watts Bar Nuclear Unit 1 (WBN1) pressurized water reactor (PWR) and two high-temperature gas-cooled reactor (HTGR) benchmarks for the HTR-10 pebble bed and the prismatic HTTR reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
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 OSTI2023

Multiphysics Pebble-Bed Reactor Control Rod Withdrawal Study

This work studied the responses of both a generic gas- and a fluoride-cooled PBR concept---the gPBR-200 and gFHR, respectively---during reactivity insertion accidents. Both models rely on 2-D axisymmetric simulations to solve the neutron flux distribution, nuclide concentrations, and temperature across the core---in addition to numerous representative pebble and TRISO particle simulations for determining fuel and moderator temperatures. This not only allows for computing maximum temperatures in the core---thus enabling estimation of how near the fuel is to peak operational and safety limits---as prescribed by specified acceptable fuel design limits, which are determined in such a way that fuel is not damaged during operational or anticipated abnormal occurrences---but also predicting how much of the core exceeds a given temperature limit, as well as determining the local energy deposition rate. These models consider both control rod withdrawal and ejection events. The former introduces a great deal more reactivity, as all the control rods are withdrawn (as opposed to a single one in the latter case), though at a much slower pace. In addition, for the gPBR-200, two limiting cases were considered: one with the core starting under hot full-power conditions and one with it starting under cold zero-power conditions. While the amount of reactivity added in the latter case is much higher (due to the far lower temperatures and the lack of neutron poisons such as Xe-135), the margin to temperature limits is also much more significant. Overall, for the design considered, none of the accidents resulted in the maximum fuel temperature reaching values close to the TRISO limit. However, the methodology presented herein could be very relevant if some designs consider reduced margins (e.g., higher temperatures) to achieve enhanced economics. Further model improvement is needed to better capture control rod worth, both in terms of cusping effects (as the rods are slowly withdrawn) and differential worth, especially as the tips of the rods near the upper cavity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

SCALE capabilities for high temperature gas-cooled reactor analysis

The SCALE code system’s ability to address stochastic distributions of fuel particles within a graphite matrix has been revisited in both multigroup (MG) features and continuous-energy (CE) Monte Carlo methods. Furthermore, this paper describes current and emergent SCALE capabilities within the CSAS sequence to address double-heterogeneous systems and presents verification and validation studies of these methods and data. Good agreement was obtained for a high temperature gas-cooled reactor (HTGR) fuel pebble model between CSAS MG eigenvalue calculations and corresponding CE reference solutions. Code-to-code comparisons for this HTGR pebble model showed good agreement of CSAS-KENO and CSAS-Shift CE calculations and the Serpent and MCNP codes in terms of eigenvalues and reaction rate ratios. Validation studies based on two HTGR experiments resulted in good agreement between MG and CE results, as well as between experiment and calculation, although the level of agreement was significantly influenced by the applied ENDF/B nuclear data library.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

SAM Code Development for Transient Safety Analyses of Fluoride-salt-cooled High-temperature Reactors

The System Analysis Module (SAM) is under development at Argonne National Laboratory as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. It utilizes the object-oriented application framework MOOSE to leverage the modern software environment and advanced numerical methods. The capabilities of SAM are being extended to enable the transient modeling, analysis, and design of various advanced nuclear reactor systems. The molten-salt-cooled pebble-bed reactor, or pebble-bed FHR (PB-FHR) is a promising candidate among advanced nuclear reactor concepts with its improved passive safety characteristics and high thermal efficiency. To support the development and utilization of the SAM code for PB-FHR safety analysis, activities on SAM code enhancements, reference plant model developments, and code validations have been performed in the past a few years to support near-term industry and NRC needs. This report summarizes recent progress under DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program in SAM code development and demonstration for transient safety analysis of Fluoride-salt-cooled High-temperature Reactors. SAM capabilities has been significantly enhanced over the years to add FHR specific modeling features, including salt freezing and thawing, spherical core channel and pebble bed core modeling, solid-fluid thermal radiation, tritium transport and general species transport in fluids and solids, and the general code enhancements on solver schemes of point kinetics module and reactivity feedback models. A reference PB-FHR model is developed, based on publicly available information from Kairos Power’s generic FHR design and the University of California, Berkeley (UCB) Mk1 design. A reference reactor model is foundational to the methodologies employed by NRC to verify the adequacy of computer codes and evaluation models. The reference FHR model was utilized for a number of selected FHR design basis accidents, including station blackout, loss of heat sink, loss of flow, transient overpower, and overcooling events.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

High-fidelity simulations of the run-in process for a pebble-bed reactor

Pebble-bed reactors (PBRs) rely on a continual feed of fuel pebbles being cycled through the core. As a result, they require a “run-in” period in order to reach an equilibrium state. The run-in period for a PBR is a complex, time-dependent problem that requires the injection of new fuel, different types of fuel, and power increases. This complexity in the run-in makes it important to capture the physical processes in order to generate an accurate representation. The present work details the creation of a high-fidelity Monte Carlo methodology for analyzing the run-in and subsequent approach to equilibrium for PBRs. The methodology entails a Python module wrapped around Serpent so as to perform neutronics calculations, move pebbles, refuel the core, and discharge pebbles, thereby modeling the explicit behavior of the PBR run-in. Further, three run-in simulations (a constant temperature profile, a linear temperature profile, and a constant temperature profile using control rods) were examined in order to identify the key physical phenomena present in the run-in process. Utilizing kugelpy, we found the inclusion of a temperature profile to be important for accurately capturing a discharge burnup (around 141 MWd/kg), a consistent k-eff (around 1.005), and an average pebble power (around 2.5 kW/pebble) that all fall within acceptable limits.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗