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Validation of NEAMS Tools Using MSRE Data

This report documents the benchmarks developed and performed for the tools and codes developed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program utilizing the MSRE experiment data. There are three focus areas explored in this work: fuel evolution, CFD, and system transient analyses. Fuel depletion is important for MSR reactor physics and fuel cycle analysis. Fuel depletion capability is currently being developed in the Griffin reactor physics code. To support this, a benchmark problem is developed using the MSRE data and an existing depletion code with flowing fuel analysis functionality (ADDER) to validate this new capability in Griffin. The ADDER calculation is compared with the TRITON-MSR results as well as the MSRE experimental data. This benchmark can be directly used to verify and validate the Griffin fuel depletion capability in future years. For CFD simulation, the MSRE CAD model is obtained from the Copenhagen Atomics and a mesh is generated for the MSRE inlet plenum. The Nek5000 code will be employed to find the flow distribution in the MSRE inlet plenum based on the mesh generated. For system analysis, a simple benchmark problem for three types of MSR system transients is developed. The SAM and SPECTRA codes are used to solve the simple problem, and the results from the two codes agree well. The SAM code is also employed to obtain the frequency response of the MSRE system at the 5 and 8 MWt power levels. The results agree well with the experiment measurements. These verification and validation efforts gives SAM users more confidence in MSR system transient simulations using SAM. Lastly, the SAM-Griffin Multiphysics coupling work is initiated. A simple one-way coupling of evaluating the precursor drift effect on the MSRE k-eff is demonstrated. This preliminary coupling work serves as the basis for future more complex Multiphysics simulation and modelling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Solar fuel generator including a catalytic mesh

This disclosure provides systems, methods, and apparatus related to a solar fuel generator. In one aspect, a device includes a photovoltaic cell, the photovoltaic cell having a first surface and a second surface, a mesh disposed on the first surface of the photovoltaic cell, and a polymer disposed on the mesh and on the first surface of the photovoltaic cell. The mesh has a catalyst disposed thereon. The polymer covers the first surface of the photovoltaic cell, with at least a portion of the mesh not being covered with the polymer.

Walczak, Karl A.↗

Impact of LWR assembly structural features on cladding burst behavior under LOCA conditions

This provides an initial scoping study on clad balloon and burst behavior for burnup extension of reactor fuel. The associated issues with burnup extension are fuel fragmentation, relocation, and dispersal in the event of cladding failure. The general finding of this work is that the structural features, spacer grids and mixing vanes, locally suppress cladding deformation but have little impact on the overall clad performance during loss-of-coolant accidents. The work detailed in a previous report by Capps et al. focused on core optimization via neutronics, thermal hydraulics and thermomechanical analysis for burnups beyond 62 GWD/tU and enrichments above 5%. Uncertainty of fuel fragmentation relocation and dispersal in high-burnup rods during accident conditions was also investigated. The dispersal aspect of fuel fragmentation depends on cladding rupture. Thus, assessing uncertainties in the rupture behavior is helpful in estimating the dispersal of high-burnup fuel. This study builds on the previous work by assessing the impact of assembly structural features on cladding balloon and burst behavior in a full-length fuel rod. In this work, the BISON fuel performance code was used to generate 2D radial and height meshes containing structural features commonly used in nuclear fuel assemblies. First, meshes were generated with spacer grids. Results were then compared to the cladding burst temperature and balloon strain results from the previous work. A mesh sensitivity study was performed to ensure that mixing vanes and spacer grid effects were appropriately considered, resulting in a more refined mesh than the previous study. The balloon deformation and burst times of the cladding were compared to the original case. Consideration was also given to the effect of rod initial pressure. In conclusion, 3D quarter rod simulations were also performed and found good agreement with the 2D simulations in clad deformation and reasonable agreement in burst times.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Cubit v.16.X

SAND2021-3051 O CUBIT is a full-featured software toolkit for robust generation of two- and three-dimensional finite element meshes (grids) and geometry preparation. Its main goal is to reduce the time required to generate meshes - particularly large hex meshes of complicated, interlocking assemblies. It is a solid-modeler-based preprocessor that meshes volumes and surfaces for finite element analysis. CUBIT also includes state-of-the-art smoothing algorithms and provides an extensive suite of tools for geometry decomposition and mesh generation. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Stimpson, Clint↗

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Rotational symmetry relation for efficient response function generation in the coarse mesh transport method COMET

The coarse mesh transport code COMET is a continuous energy hybrid stochastic-deterministic neutronics solver with high fidelity and formidable computation speed in solving reactor core problems. Its method is based on the incident flux expansion theory. In this work, we take advantage of the local geometric symmetry in many reactor cores lattices (e.g., fuel lattices and reflector blocks) to develop relations among the flux response expansion coefficients for symmetric surfaces to further improve the computational efficiency of the COMET response function generation tool (method). This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle. The relations for the response coefficients for the symmetric surfaces can be then written as the Kronecker product of those transformation matrices. The method is implemented into COMET and tested on two advanced high temperature reactor (AHTR) full-length single assembly benchmark problems. The COMET results using the response function library based on the symmetry relations were compared to those using the library directly generated by continuous energy Monte Carlo for all surfaces. It was found that the eigenvalues and stripe-wise fission densities using the two libraries are in statistical agreement as expected. This indicates that the new method maintains the high fidelity of the original COMET method while improving the computational efficiency in the response function generation by 270% to 400%, depending on the local geometric symmetry. This method also reduces the size of the response function library by the same magnitude (270% to 400%). (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Cubit for MCNP Unstructured Mesh Analysis of Oktavian Benchmarks

The Monte Carlo N-Particle (MCNP) transport code developed by Los Alamos National Laboratory (LANL) can be used to transport various particles across user defined three dimensional (3D) geometries. Traditionally, these geometries are created as constructive solid geometry (CSG), involving the use of Boolean operators on defined surfaces to create 3D regions known as cells. A newer method of geometry definition in the MCNP code is unstructured mesh (UM) embedded within a CSG cell using the universe and fill repeated-structure features. An MCNP UM calculation requires an MCNP input file and mesh geometry file. The MCNP code cannot be used to generate UM geometry models. A computer-aided design (CAD) software is typically used to construct a solid geometry model, and a CAD file is then imported into a mesh generation software to prepare and generate a mesh model. Some mesh generation software packages have the ability to create a solid geometry and thus a separate CAD software for creating a CAD model is not needed. In this work, Cubit, a geometry creation and meshing software developed by Sandia National Laboratories, is used to construct UM models for MCNP simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Validation of Oregon State University High Temperature Test Facility Experiments Using Pronghorn

The OSU High Temperature Test Facility is a quarter-scale diameter, 1/64 scale volume test facility meant to replicate thermophysical phenomena in the prototypical General Atomics Modular High Temperature Gas Reactor. Tests pertaining to conduction cooldown events were performed from 2016-2019, providing a large database by which computational methods that are applicable to different length scales can be validated. One of these codes is Pronghorn, which is a coarse-meshed, porous-based subchannel thermal hydraulics code based on the MOOSE application, with the intention of better capturing the physics of both conduction and convection heat transfer within the OSU HTTF core. The goal of this summer project is to develop the framework by which Pronghorn can perform validation exercises of the HTTF core for benchmarking, by generating a mesh appropriate to the geometry of the HTTF core, developing input decks that accurately capture the initial and boundary conditions, materials, and relevant equations to the physics seen in the HTTF core, and using a postprocessor to compare simulation results to various experimental data. While validation of codes is a multi-year project, a mesh has been generated and tested in Pronghorn that meets mass conservation and basic heat transfer principles. The next step is to accurate depict the fluid inlet and outlet boundary conditions, which will be performed using computational fluid dynamics software.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

CrossLink: Meshing a 3D part from a STEP file [Slides]

This example shows how to use CrossLink to create a mesh for a 3D geometry part read in from a STEP file. A STEP file (Standard for the Exchange of Product data) is a common file format used for 3D modelling that can be written out from a CAD program (e.g., Creo Parametric). Being able to read and mesh STEP file geometries is essential for meshing parts from engineering models. Creating the mesh typically involves: (1) Importing the geometry; (2) Creating geometry groups; (3) Assigning curves and surfaces to the geometry groups; (4) Building a topology; (5) Applying geometric and mesh constraints; and (6) Generating the final mesh. Current issues with this process in CrossLink include: (1) The GUI does not display trimmed surfaces; (2) The user must manually create and assign geometry groups; and (3) The user must be aware of duplicate curves and surfaces from the CAD model.

97 MATHEMATICS AND COMPUTING↗

On-the-fly response function generation method for composite coarse mesh

The hybrid stochastic deterministic transport code COMET, based on the incident response expansion theory, is used to model reactor cores with high fidelity and formidable computational speed. COMET models a reactor core using a library of incident flux response expansion coefficients that are pre computed for all the unique lattice cells (e.g., fuel assemblies, reflector blocks, etc.) in the core. In order to further improve its computational efficiency in pre-calculating the response library a new response function generation method is developed to compute the response functions for the composite coarse meshes made of a smaller set of unique lattices on the fly within the COMET's deterministic transport core sweep. The efficiency is achieved by eliminating a number of unique lattices that can be made up from the reduced set of unique meshes on the fly. The numerical process consists of the following steps. First, the boundary condition on composite coarse mesh boundaries is projected onto the expansion basis to compute the incident flux moments on external surfaces of all the basic (reduced set of unique) coarse meshes. Secondly, the deterministic sweeping solver in COMET is used to converge on the outgoing/incoming flux expansion moments crossing interfaces between the basic coarse meshes. Thirdly, the response functions for the composite coarse meshes are constructed as a superposition on the fly. The new response function generation method was tested on 88 composite coarse meshes consisting of CANDU fuel bundles and moderator blocks. It was found that response functions generated by the new method agree very well with those generated by direct Monte Carlo calculations. The average and maximum relative differences in the surface-to-surface response coefficients computed by the two methods are 0.10% and 0.20%, respectively. Similarly, the average and maximum relative differences in the response fission densities are 0.13% and 0.43%, respectively. These discrepancies are within one standard deviation of the stochastic uncertainties. The new method is five times faster than the original direct Monte Carlo method. The size of the response function library for the new method is five times smaller than that for the original method, leading to significantly less requirement for the computer hard drive space and memory. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Geometry Mesher

This program implements tetrahedral meshing for implicitly-defined geometries, focusing on meshing unions of geometric primitives like spheres and cylinders. This enables users to quickly generate quality meshes of truss lattice and filament structures.

Watts, SethE [Lawrence Livermore National Laborato↗

An extrapolation method to remove spurious stress concentration in micromechanical analyses of composites using pixel-based meshes

It is easier to generate a finite element mesh of complicated geometries with voxel-based meshes compared to conformal meshes. However, the local stresses in voxel-based meshes are higher owing to artificial stress concentration caused due to jagged lines that approximate a curve. Here, we propose a method that accounts for this anomaly which would lead to accurate prediction of maximum von Mises stress in voxel-based meshes. The method is based on the variation of reciprocal of stresses and associated numerical gradient. The prediction of the proposed method is compared against the results of a conformal mesh by considering four two-dimensional example problems. The accuracy of the proposed method is verified using different mesh densities, material properties, and integration schemes. The proposed method was also implemented on a conformal mesh to verify that it filters out just the spurious stress concentration and not the realistic stress concentration.

36 MATERIALS SCIENCE↗

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Here, this paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

42 ENGINEERING↗

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

97 MATHEMATICS AND COMPUTING↗

Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media

A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. Here, the CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.

97 MATHEMATICS AND COMPUTING↗

Coupled beam-target-moderator optimization for the Second Target Station

To support the design of the Second Target Station, that aims to provide the world’s highest peak brightness of cold neutrons, studies that optimize the dimensions of the target and moderators are invaluable. In this work, we investigate the influence of the target dimensions and beam profile on the performance and optimal size of the moderators. We perform optimization runs with detailed MCNP6.2 simulations using high-fidelity unstructured mesh geometries generated from parametrized CAD models. We demonstrate that small changes in target height do not influence the moderator performance if the beam dimensions are chosen adequately. We quantify the effect of beam footprint and target width on the moderator performance and show that the optimal moderator dimensions are insensitive to limited changes in target and beam profile.

Dakota↗