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Parallel Algorithms and Software for Nuclear, Energy, and Environmental Applications. Part II: Multiphysics Software

This paper is the second part of a two part sequence on multiphysics algorithms and software. The first [1] focused on the algorithms; this part treats the multiphysics software framework and applications based on it. Tight coupling is typically designed into the analysis application at inception, as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously. The application must also take care to minimize both time and space error between the physics, particularly if more than one mesh representation is needed in the solution process. This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis. The Multiphysics Object Oriented Simulation Environment (MOOSE) is based on the Jacobian-free Newton-Krylov (JFNK) method combined with physics-based preconditioning to provide the underlying mathematical structure for applications. The report concludes with the presentation of a host of nuclear, energy, and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.

97 MATHEMATICS AND COMPUTING↗

A MULTIDIMENSIONAL AND MULTIPHYSICS APPROACH TO NUCLEAR FUEL BEHAVIOR SIMULATION

Important aspects of fuel rod behavior, for example pellet-clad mechanical interaction (PCMI), fuel fracture, oxide formation, non-axisymmetric cooling, and response to fuel manufacturing defects, are inherently multidimensional in addition to being complicated multiphysics problems. Many current modeling tools are strictly 2D axisymmetric or even 1.5D. This paper outlines the capabilities of a new fuel modeling tool able to analyze either 2D axisymmetric or fully 3D models. These capabilities include temperature-dependent thermal conductivity of fuel; swelling and densification; fuel creep; pellet fracture; fission gas release; cladding creep; irradiation growth; and gap mechanics (contact and gap heat transfer). The need for multiphysics, multidimensional modeling is then demonstrated through a discussion of results for a set of example problems. The first, a 10-pellet rodlet, demonstrates the viability of the solution method employed. This example highlights the effect of our smeared cracking model and also shows the multidimensional nature of discrete fuel pellet modeling. The second example relies on our the multidimensional, multiphysics approach to analyze a missing pellet surface problem. As a final example, we show a lower-length-scale simulation coupled to a continuum-scale simulation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

High-fidelity multiphysics load following and accidental transient modeling of microreactors using NEAMS tools: Application of NEAMS codes to perform multiphysics modeling analyses of micro-reactor concepts

The feasibility of modeling microreactors using high-fidelity models with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) tools is investigated in this report. Three overarching questions guided this research: can NEAMS tools readily be applied for high-fidelity multiphysics modeling of different types of transients in microreactor designs; how accurate are the results obtained; and are improvements needed in accuracy or user experience of NEAMS tools, especially considering newly developed capabilities? This work builds upon FY-2022 work, and two microreactor concepts considering heat pipe (HP-MR) and gas-cooled (GC-MR) technologies were further analyzed using high-fidelity multiphysics simulations. The NEAMS tools considered and coupled within the MultiApp environment are Griffin for neutronics, BISON for thermo-mechanics, Sockeye for heat pipe modeling (in HP-MR), SAM for 1D Fluid – 3D solid modeling of coolant channels and system modeling of balance of plant components (in GC-MR), and the SWIFT code for hydrogen redistribution in hydride moderator. The Heat Pipe MicroReactor (HP-MR) concept was further analyzed in FY-2023 to demonstrate the stochastic TRISO failure modeling capability in BISON to check operational limits of the TRISO fuel. A new full-core Gas-Cooled MicroReactor (GC-MR) model was developed based on the initial assembly-model used in Y-2022 and used for steady-state and accidental depressurization transient simulations. Accuracy of the simulations performed was assessed through 1) verification analyses completed on the different physics with code-to-code comparison, and 2) validation of the multiphysics simulations based on modeling of the Kilopower Reactor Using Stirling Technology (KRUSTY) experiment. In FY-2023, the mesh and model of KRUSTY was updated to closely match publicly available data, and the neutronic model was verified and validated against experimental control rod worth measurements. The multiphysics model of KRUSTY was developed and used for steady-state analysis and for modeling reactivity insertion transient. The calculated power increase and stabilization agrees well with experimental data following adjustment in fuel thermal expansion coefficient. As an important component of this project, the ANL team gathered experience with a wide range of NEAMS tools: the MOOSE Mesh System, Griffin, BISON, SWIFT, Sockeye, SAM, Workbench, and the MOOSE MultiApp System, and provided assessment of new capabilities. Noteworthy are the user assessment of the “vapor-only” flow model in Sockeye and development of a multiphysics startup transient in HP-MR unit cell for use as tutorial in Sockeye. The full-core GC-MR model was used for assessment of SAM for balance of plant modeling and for demonstrating the SWIFT code capability for hydrogen redistribution modeling in multiphysics transient analyses. In this process, several bugs/issues were identified and reported to developers. Finally, the assembly GC-MR model developed in FY-2022 coupling Griffin, BISON and SAM through flow blockage and rod ejection transients was published to the National Reactor Innovation Center (NRIC) Virtual Test Bed (VTB). The Heat Pipe MicroReactor (HP-MR) concept high-fidelity multiphysics coupling of Griffin/BISON/Sockeye in load-following and heat pipe failure transients was also published on the VTB. Those submissions are enabling thorough review of these models as well as wide distribution to industry, regulator, and university users. In this analysis, several new research questions were uncovered, and follow-up analyses are recommended to further improve some models, consider additional transients, and continue development of VTB models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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.↗

Enhancements to the SHARP Build System and NEK5000 Coupling

The SHARP project for the Department of Energy's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program provides a multiphysics framework for coupled simulations of advanced nuclear reactor designs. It provides an overall coupling environment that utilizes custom interfaces to couple existing physics codes through a common spatial decomposition and unique solution transfer component. As of this writing, SHARP couples neutronics, thermal hydraulics, and structural mechanics using PROTEUS, Nek5000, and Diablo respectively. This report details two primary SHARP improvements regarding the Nek5000 and Diablo individual physics codes: (1) an improved Nek5000 coupling interface that lets SHARP achieve a vast increase in overall solution accuracy by manipulating the structure of the internal Nek5000 spatial mesh, and (2) the capability to seamlessly couple structural mechanics calculations into the framework through improvements to the SHARP build system. The Nek5000 coupling interface now uses a barycentric Lagrange interpolation method that takes the vertex-based power and density computed from the PROTEUS neutronics solver and maps it to the user-specified, general-order Nek5000 spectral element mesh. Before this work, SHARP handled this vertex-based solution transfer in an averaging-based manner. SHARP users can now achieve higher levels of accuracy by specifying any arbitrary Nek5000 spectral mesh order. This improvement takes the average percentage error between the PROTEUS power solution and the Nek5000 interpolated result down drastically from over 23 % to just above 2 %, and maintains the correct power profile. We have integrated Diablo into the SHARP build system to facilitate the future coupling of structural mechanics calculations into SHARP. Previously, simulations involving Diablo were done in an iterative manner, requiring a large amount manual work, and left only as a task for advanced users. This report will detail a new Diablo build system that was implemented using GNU Autotools, mirroring much of the current SHARP build system, and easing the use of structural mechanics calculations for end-users of the SHARP multiphysics framework. It lets users easily build and use Diablo as a stand-alone simulation, as well as fully couple with the other SHARP physics modules. The top-level SHARP build system was modified to allow Diablo to hook in directly. New dependency handlers were implemented to let SHARP users easily build the framework with these new simulation capabilities. The remainder of this report will describe this work in full, with a detailed discussion of the overall design philosophy of SHARP, the new solution interpolation method introduced, and the Diablo integration work. We will conclude with a discussion of possible future SHARP improvements that will serve to increase solution accuracy and framework capability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Coupling Microstructural Evolution Simulations to Material Property Degradation Predictions for Plasma-Facing Materials

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500 C to 1500 C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 D/m^2-s. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

The Virtual Test Bed (VTB) Repository: A Library of Multiphysics Reference Reactor Models using NEAMS Tools

With the next generation of nuclear reactors under development, modeling and simulation (M&S) tools are being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in order to support their design, licensing, and future operation. Mirroring the physical test beds currently under construction (i.e., EBR-II and ZPPR), the Virtual Test Bed (VTB) was launched by the National Reactor Innovation Center (NRIC) in collaboration with NEAMS to support the advanced reactor community. This collaborative effort, which involves multiple teams at both Idaho National Laboratory and Argonne National Laboratory aims to use NEAMS tools to model a wide range of reactor designs. Those models are automatically tested to ensure their continued functionality as the tools are further developed. Examples are extensively documented, each acting as a tutorial for applying the relevant NEAMS tools to that reactor design. Currently, five advanced reactor types (with a total of eight specific design variants) are simulated by a variety of different models. These models range from steady-state, core multiphysics simulations to integrated plant analysis during loss-of-flow transients.

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↗

Development of Preliminary VERA-CS Crud Induced Localized Corrosion Modeling Capability

The Consortium for Advanced Simulation of Light Water Reactors (CASL) is developing multiphysics core-simulator software for light water reactors (LWRs) known as VERA-CS in order to improve the state of the art in modeling and simulation of challenge problems that are limiting to the nuclear industry. One of these challenge problems includes fuel rod crud deposition, which can lead to crud-induced power shift (CIPS) and crud-induced localized corrosion (CILC). This paper documents work that was performed to develop a preliminary CILC-modeling capability in VERA-CS in support of the crud challenge problem. The CILC capabilities were developed by coupling VERA-CS to the CASL-developed Cicada code, which provides 1D and 3D clad conduction and oxide growth modeling tools, as well as coupling to the CASL-developed MAMBA code, which is used for modeling clad crud deposition. An approach called rod thermal-hydraulic reconstruction (ROTHCON) was developed and integrated into VERA-CS. This allows the modeler to capture spacer-grid turbulence and heat transfer effects in the CTF subchannel code so that the spatial resolution of crud and oxide rod surface growth could be better resolved. After implementing these capabilities, several assessments were performed to ensure that the capabilities function as expected, and a pin-resolved quarter-core simulation was run as a demonstration.

Salko Jr, Robert↗

Coupling coarse-mesh CFD with fine-mesh CFD for modeling molten-salt reactors in the Virtual Test Bed (VTB)

The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims at developing a simulation tool kit to accelerate the development and deployment of nuclear power technologies. NEAMS multiphysics tools have been designed to provide numerical simulation support for the design and licensing of GEN IV reactors. Pronghorn is NEAMS's coarse-mesh computational fluid dynamics (CFD) tool, which is designed to run 3D core transients in GEN IV reactors at a reduced computational cost. To increase their accuracy, coarse-mesh CFD simulations require calibrated closure coefficients. One way of computing these coefficients is via the Nek5000, NEAMS's high-fidelity CFD tool. This article discusses our current research lines in informing Pronghorn closure coefficients via Nek5000 to enable multiphysics simulations of the core cavity of the molten-salt fast reactor. We present an application in which Pronghorn mixing length turbulent viscosity has been calibrated from Nek5000 simulations. The resulting Pronghorn thermal-hydraulics model is then coupled to Griffin, the NEAMS neutron transport solver, to solve for the steady-state configuration of the molten-salt fast reactor. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Coupling coarse mesh CFD with fine mesh CFD for modeling for Molten Salt Reactors in the Virtual Test Bed VTB

The Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims at developing a simulation tool kit to accelerate the development and deployment of nuclear power technologies. NEAMS multiphysics tools have been designed to provide numerical simulation support for the design and licensing of GEN IV reactors. Pronghorn is NEAMS’s coarse-mesh computational fluid dynamics (CFD) tool, which is designed to run 3D core transients in GEN IV reactors at a reduced computational cost. To increase their accuracy, coarse-mesh CFD simulations require calibrated closure coefficients. One way of computing these coefficients is via the Nek5000, NEAMS’s high-fidelity CFD tool. This article discusses our current research lines in informing Pronghorn closure coefficients via Nek5000 to enable multiphysics simulations of the core cavity of the molten-salt fast reactor. We present an application in which Pronghorn mixing length turbulent viscosity has been calibrated from Nek5000 simulations. The resulting Pronghorn thermal-hydraulics model is then coupled to Griffin, the NEAMS neutron transport solver, to solve for the steady-state configuration of the molten-salt fast reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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↗

Assessment of a Hybrid Continuous/Discontinuous Galerkin Finite Element Code for Geothermal Reservoir Simulations

FALCON (“Fracturing And Liquid CONvection”) is a hybrid continuous / discontinuous Galerkin finite element geothermal reservoir simulation code based on the MOOSE (“Multiphysics Object-Oriented Simulation Environment”) framework being developed and used for multiphysics applications. In the present work, a suite of verification and validation (“V&V”) test problems for FALCON was defined to meet the design requirements, and solved to the interests of enhanced geothermal system (“EGS”) design. Furthermore, the intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the FALCON solution methods. The simulation problems vary in complexity from singly mechanical or thermo process, to coupled thermo-hydro-mechanical processes in geological porous media. Numerical results obtained by FALCON agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these capabilities in FALCON. Some form of solution verification has been attempted to identify sensitivities in the solution methods, where possible, and suggest best practices when using the FALCON code.

15 GEOTHERMAL ENERGY↗

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↗

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↗

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↗

DireWolf

DireWolf is an integrated micro-reactor capability being developed using an advanced multiphysics modeling and simulation capability for heat pipe-cooled micro-reactor concepts. The DireWolf application is built on INL’s Multiphysics Object-Oriented Simulation Environment (MOOSE) development and runtime framework and is composed of the following MOOSE- based applications as submodules, coupled together using the MOOSE MultiApps and Transfers capability and executed as a single application: Griffin (reactor physics and radiation transport), BISON (nuclear fuel performance), Grizzly (structural mechanics), Sockeye (heat pipe technology), and RELAP-7 (open-air and super-critical CO2 Brayton cycle).

Permann, Cody↗

Implementation of Creep-Damage Model for Concrete Fracture in MOOSE

Numerical implementation of an isotropic creep-damage model for concrete in multiphysics object-oriented simulation environment (MOOSE) finite element framework is presented in this paper. The constitutive model considers the combined effect of instantaneous and delayed strains on damage propagation. The implementation considers creep using generalized Maxwell or Kelvin-Voigt models. Using strain splitting assumptions, the total mechanical strains are split into elastic and creep components. Damage is considered to evolve as a function of the elastic and creep strains. This work considers damage as a function of fracture energy using the characteristic length of each finite element. This approach preserves the energy release rate of each element and avoids vanishing energy dissipation as the mesh is refined. Further, a creep-damage parameter is used to quantify the effect of creep strain on damage. The model is tested against published results on notched three-point bending specimens involving non-linear creep and predicts that about a third of the creep strain contributes towards damage for the experiments simulated. Results show that the proposed framework has predictive capabilities, and the model can be extended for more complex systems.

36 MATERIALS SCIENCE↗