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DOE OSTI2021

SAS4A/SASSYS-1 Lead Verification Test Suite

SAS4A/SASSYS-1 is a simulation tool used to perform deterministic analyses of anticipated events as well as design basis and beyond design basis accidents for advanced liquid-metal-cooled nuclear reactors. With its origin as SAS1A in the late 1960s, the SAS series of codes has been under continuous use and development for over forty-five years and represents a critical investment in safety analysis capabilities for the U.S. Department of Energy. Although SAS4A/SASSYS-1 was developed to support the analysis of any liquid-metal-cooled nuclear reactor, it has primarily been utilized to design and analyze Sodium Fast Reactors (SFRs). As a result, most of the verification basis for SAS4A/SASSYS-1 utilizes sodium as a coolant and geometry descriptions that are typical of a SFR facility. In this work, new verification problems are defined to extend the applicability of the SAS4A/SASSYS-1 verification basis into Lead Fast Reactor (LFR) design space. A review of the existing SAS4A/SASSYS-1 SFR verification test suite is performed to determine the number of test cases that are SFR specific. SFR specific test cases are replicated using lead as a coolant and system layouts that are representative of LFRs. This report provides definitions and reference solutions for seven new test cases that scope lead-specific features and capabilities of the software. For a verification test to be considered acceptable, comparisons of analytical solutions to SAS4A/SASSYS-1 predictions must produce negligible or justifiable errors. All LFR specific test cases are found to be acceptable.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Results of the Micromorphic Upscaling Workflow for the PSAAP III Year 3 Report

Predicting the mechanical response and failure of heterogeneous materials has proven difficult. Multiscale numerical methods based in higher order continuum theories attempt to bridge the gap between microscale and macroscale structural behavior. Micromorphic continuum theories have shown promise. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling workflows. These include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This work discusses micromorphic upscaling efforts of the University of Colorado Boulder PSAAP III multidisciplinary simulation center (MSC). Verification studies are presented that compare the accuracy of the upscaling workflow with analytical solutions for a trivial stress state and homogeneous material using direct numerical simulations (DNS) conducted in the Ratel finite element method (FEM) and GEOS material point method (MPM) codes. These verification studies consider upscaling using the Micromorphic Filter for a “single filter domain”. Finally, DNS of a heterogeneous composite material is upscaled using a “multiple filter domain” method.

36 MATERIALS SCIENCE↗

DOE OSTI2023

GnarlyX: Eulerian multi-material hydrodynamics coupled to equation of state and hyperelastic, plastic constitutive models

GnarlyX is a new hydrocode for direct numerical simulations of the microstructural behavior of high explosives at the mesoscale. We summarize the computational framework for multidimensional, Eulerian multi-material hydrodynamics coupled to EOS and hyperelastic, plastic constitutive models. We present 1D verification tests of multi-material only and combined multimaterial and strength capabilities with comparisons to exact solutions of shock states resulting from an incident shock impacting the material interface of PBX9502 and aluminum. We show that GnarlyX performs well in capturing the resulting shock waves in examining numerical convergence with exact solutions. In later work, we will summarize the thermomechanics and multi-dimensional, parallel computing capabilities in GnarlyX with multi-dimensional verification tests.

42 ENGINEERING↗

DOE OSTI2022

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. As some additional changes have been made to the ARC software since this point all versions between release 3012 and 3266 can be considered verified as version 3253 was used for all updates in this revision. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the methodology used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative noting that DIF3D will properly notify the user when the peaking values it is providing are potentially incorrect.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Verification of the DIF3D Software to Support Fast Reactor Analysis (Rev. 3)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Code-verification techniques for the method-of-moments implementation of the combined-field integral equation

Code verification plays an important role in establishing the credibility of computational simulations by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, the numerical solution to integral equations incurs multiple interacting sources of numerical error, as well as other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the combined-field integral equation. Here, we demonstrate the effectiveness of these approaches for cases with and without coding errors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Modeling of Macroscopic Dynamics in Three-Dimensional Plasma Configurations (Final Technical Report)

A numerical simulation-based study to investigate the stability properties of inherently three-dimensional plasma magnetic configurations is presented. These configurations, called stellarators and heliotrons, use external helical coils to provide the twisting magnetic field that is required to confine ionized plasma particles. In contrast to the tokamak configuration, which nominally has the property of axisymmetry, electrical current does not need to be induced in stellarator and heliotron plasma. Experiments have shown that these three-dimensional configurations are remarkably robust to macroscopic instability, even when driven to relatively high levels of plasma pressure. Our understanding of how the plasma is able to withstand macroscopic instability will be enhanced by the work proposed here. The effort will generalize existing numerical modeling capability, and it will apply the new capability to model macroscopic dynamics in these three-dimensional configurations. The development work has been applied to the NIMROD simulation code (https://nimrodteam.org) that was originally based on axisymmetric problem domains. It has been generalized to accommodate the three-dimensional shaping of the plasma volume in stellarators and heliotrons. Its use of equilibrium data has also been generalized, and the implementation allows different numerical representation of the magnetic field. Analysis has been performed to inform the selection of numerical methods, and a method to accelerate the iterative solution of the necessary algebraic systems has been developed and implemented. Verification of the new NIMSTELL code on benchmark problems has also been an important part of the effort.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Software Quality Assurance for EBR-II Fuels Irradiation and Physics Database (FIPD)

The Fuels Irradiation and Physics Database (FIPD) is an ongoing DOE project on archival of the EBR-II metal-alloy fuel irradiation experiments. As part of its use in support of license applications, the Quality Assurance Program Plan (QAPP) was drafted and endorsed by NRC in an effort to demonstrate its compliance with regulatory expectations. Software Quality Assurance (SQA) for the physics portion of FIPD is intended to qualify the calculated quantities such as fuel and cladding temperatures, neutron fluence and axially varying burnup estimates for irradiated fuel elements. This report covers the initial evaluation of SQA status of three neutron physics and thermo-fluid codes (REBUS, RCT and SE2RCT) that form the basis of calculated quantities for as-irradiated characteristics of the tested metallic fuel elements. The report also introduces an SQA plan to address the identified deficiencies. The REBUS, RCT, and SE2RCT codes are all part of the Argonne Reactor Code (ARC) code system. There is considerable knowledge and experience on REBUS and RCT but relatively less on SE2RCT. During FY2021, efforts focused on an assessment of how the data in the EBR-II Physics and Analysis DataBase (PADB) is generated with SE2RCT and used in FIPD. Additional tasks included considerations of uncertainties for power estimates in REBUS and RCT calculations and their impact on the combined RCT methodology. The RCT software usage in FIPD was assessed this year and the input/output details studied. A “requirements” document was created that identifies the key features of the RCT software being used in FIPD that need to have SQA documentation. A brief discussion on the history of RCT and its input is included in this report along with the basic SQA roadmap laid out in the requirements document. The SE2RCT software usage in FIPD is still being studied noting that there is no current manual. As part of the work done this year, two bugs were identified in the SE2RCT software which have a minor impact on the accuracy of the results it produces. No requirements document has been created, but one identified feature of SE2RCT being used that needs verification was its fuel pin temperature calculation. The work completed this year confirms that the approximations which will be included in the software verification report for SE2RCT are accurate. In addition to software quality assurance work for RCT and SE2RCT, an automated verification framework is proposed to simplify the software quality assurance process. The purpose of this framework is to streamline code verification and documentation while minimizing repetitive tasks for code developers and reviewers. The reduction of repeated input (between reference solution, software, and documentation input) throughout the SQA process reduces potential for human errors during the preparation of the supporting software quality records. The automation of the verification and documentation process proposed for this project leverages the existing verification structure already in place for the SAS4A/SASSYS-1 code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

HARD: A performance portable radiation hydrodynamics code based on FleCSI framework

Hydrodynamics And Radiation Diffusion (HARD) is an open-source application for high-performance simulations of compressible hydrodynamics with radiation-diffusion coupling. Built on the FleCSI (Bergen et al., 2021 [1]) (Flexible Computational Science Infrastructure) framework, HARD expresses its computational units as tasks whose execution can be orchestrated by multiple back-end runtimes, including Legion (Bauer et al., 2012 [2]), MPI (Forum, 1994 [3]), and HPX (Kaiser et al., 2020 [4]). Node-level parallelism is handled through Kokkos (Edwards et al., 2014 [5]), providing a single-source, portable code base that runs efficiently on laptops, small homogeneous clusters, and the largest heterogeneous supercomputers currently available. To ensure scientific reliability, HARD includes a regression test suite that automatically reproduces canonical verification problems such as the Sod and LeBlanc shock tubes, and the Sedov blast wave, comparing numerical solutions against known analytical results. The project is distributed under an OSI-approved license, hosted on GitHub, and accompanied by reproducible build scripts and continuous integration workflows. This combination of performance portability, verification infrastructure, and community-focused development makes HARD a sustainable platform for advancing radiation hydrodynamics research across multiple domains.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Verification of the PERSENT Software

Ongoing commercial design activities require a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system and substantial work has been done to verify its accuracy on several identified commercial needs. This manuscript details the verification work done on PERSENT which relies upon the DIF3D code for its forward and adjoint flux solution. Previous work identified the PERSENT features required to be verified to support commercial design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying PERSENT’s ability to correctly calculate four key quantities: perturbation worth distributions, kinetics parameters, sensitivity coefficients, and cross section uncertainty quantification. This manuscript provides the verification tasks and their results with respect to these quantities needed for commercial design activities. For the perturbation worth distributions, hand calculations are deployed to verify the PERSENT calculated results. Similarly, hand calculation of the PERSENT computed kinetics parameters is also used to verify the PERSENT results. In both of these, the input to PERSENT is manipulated to ensure the hand calculation exactly matches the equations PERSENT is calculating. The sensitivity coefficients involve calculating the derivatives of a parameter (such as reactivity worth), with respect to the cross section data. Direct finite difference calculations with DIF3D are used to verify the PERSENT calculated results. For the uncertainty quantification, manufactured input to PERSENT is used to allow an exact hand calculation to reproduce the PERSENT calculated results. The work detailed in this report verified that significant issues were identified for earlier versions of PERSENT for sensitivity coefficients which were corrected in this work and thus version 12.1.0 of PERSENT must be used to reproduce all of the verified work in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Taylor wave solution for a general equation of state

This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Verification and Validation Activities of Molten Salt Reactors Multiphysics Coupling Schemes at Idaho National Laboratory

This paper presents the latest verification and validation activities in molten salt reactor modeling and simulation performed at Idaho National Laboratory. Multiphysics solutions are obtained by coupling the neutronics code Griffin, the thermal hydraulics code Pronghorn, and the system analysis code SAM, under the MOOSE framework. We present various multiphysics coupling schemes with these codes for molten salt reactor problems and provide verification and validation results. First, we present verification test results of the Griffin-Pronghorn coupled scheme for the CNRS benchmark. Then validation test results are presented for the Griffin-SAM coupled scheme for the pump startup and coast down transients of the Molten Salt Reactor Experiment. Finally, the Griffin-Pronghorn-SAM coupled scheme is demonstrated for the Molten Salt Reactor Experiment reactivity insertion transient using a domain-overlapping coupling algorithm between Pronghorn and SAM. The results of these various coupling schemes demonstrate the ability to capture the effect of fuel flow and the various feedback mechanisms important to MSRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Earthquake-induced impact of base-isolated buildings: theory, numerical modeling, and design solutions

Earthquake shaking more intense than that used to size the horizontal clearance between a base–isolated building and near–rigid perimeter moat wall will result in hard impact, producing high–frequency, high–amplitude acceleration response in the structure and supported equipment. Herein this paper provides a design solution for the damaging effects of hard impact by installing a compliant engineered element in the load path between the base–isolated building and the moat wall, resulting in soft impact and a much smaller acceleration response. The engineered element assumed herein is a commercial–off–the–shelf marine fender with mechanical properties determined by physical testing. The attachment of a flexible engineered element, with well–defined stiffness and damping, to a near–rigid moat wall, simplifies the numerical modeling of the building–moat wall system and eliminates the need to bound the lateral stiffness of the wall for impact calculations. The simple model of the engineered element can be implemented in commercial finite element codes. Theory is developed for two–sided impact of a single–degree–of–freedom oscillator. Analytical solutions are derived for the shifted first–mode frequency of the impacted oscillator and for its free–vibration response. The shifted first–mode frequency is a function of the composite lateral stiffness of the isolator–engineered element assembly and its earthquake–induced displacement. Local peaks in the spectral response of the impacted oscillator form at odd integer multiples of the shifted first–mode frequency. The analytical solutions can be used to verify, in part, the numerical model used for impact analysis.

42 ENGINEERING↗

DOE OSTI2024

Giant Uniaxial Magnetocrystalline Anisotropy in SmCrGe 3

Explore the source record for details and available documents.

Xu, Mingyu↗

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 OSTI2025

MOOSE-based Tritium Migration Analysis Program, Version 8 (TMAP8) for advanced open-source tritium transport and fuel cycle modeling

Tritium management is critical for the safety, sustainability, and economics of fusion energy systems, and advanced and reliable modeling tools help accelerate the development of tritium technologies. This paper presents the Tritium Migration Analysis Program, Version 8 (TMAP8), an open-source, MOOSE-based application developed to provide state-of-the-art tritium transport and fuel cycle modeling capabilities. TMAP8 aims to expand the capabilities of previous versions (i.e., TMAP4 and TMAP7) by leveraging modern computational techniques, ensuring high software quality assurance standards (key to building trust), and enabling multispecies, multiscale, and multiphysics simulations for integrated tritium transport modeling in complex geometries. This paper outlines TMAP8’s scope and rigorous development practices, emphasizing its transparency, accessibility, modularity, and reliability. We present the current suite of verification and validation cases based on those from TMAP4, demonstrating TMAP8’s accuracy and reliability against analytical solutions and experimental data. Additionally, the paper showcases TMAP8’s integrated fuel cycle modeling capabilities, highlighting its applicability at various scales and levels. The TMAP8 code and documentation are openly available, promoting collaborative development and widespread adoption within the fusion community. Future work will soon expand TMAP8’s verification and validation suite to include those from TMAP7 and other recent experimental studies for validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗