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Accelerating Innovative Energy Solutions Using Combustion Simulations

Combustion-based transportation, electricity generation, and industrial heating in manufacturing constitute the three largest sectors of energy demand. Some of the recent technology development in these sectors are: switching to low-carbon fuels for the transportation sector, increasing energy efficiency in the power sector, and capturing carbon emissions from conventional power generators. Several teams at the National Renewable Energy Laboratory have been actively advancing research in these areas by leveraging computational modeling of combustion processes across the heavy-duty land based transportation, aviation, and power generation sectors. This article summarizes some of these efforts, demonstrating the potential of advanced computational techniques to generate technological solutions that will transform the global energy system.

08 HYDROGEN

Assessment of Condition Monitoring Methods and Technologies for Inservice Inspection and Testing of Nuclear Power Plant Components

This report was prepared for the U.S. Nuclear Regulatory Commission (NRC) to explore the application of advanced technologies toward meeting the current and future regulatory requirements for maintenance and condition monitoring of structures, systems, and components. The advanced technologies considered in this work are advanced sensors and instrumentation, data analytics, machine learning and artificial intelligence (ML/AI), physics-based models, and digital twins (DT). The interest in the application of advanced technologies for condition monitoring in nuclear power plants continues to grow, and current and future licensees are expected to implement advanced technologies as part of their inservice inspection (ISI) and inservice testing (IST) programs. This report delineates the outcomes of an exploratory investigation into the implementation of advanced condition monitoring technologies to address ISI and IST requirements. A thorough review was conducted of the existing regulatory requirements for ISI and IST, along with an analysis of associated industry practices. Additionally, a state-of-the-art assessment was performed on advanced condition monitoring technologies frequently employed in non-nuclear sectors. This research incorporated two nuclear-specific case studies to illustrate the application of these technologies within the current nuclear fleet. The report provides an exhaustive discussion on the technical challenges, considerations, and opportunities associated with the deployment of advanced condition monitoring technologies. The following are key considerations in the application of advanced technologies for the ISI and IST of nuclear power plant components: • Developing adequate verification and validation procedures to confirm the functional and non-functional requirements, • Developing technical capabilities to conduct real-time asset condition monitoring, • Establishing guidance and protocol for modeling and simulation tools to continuously meet regulatory requirements, • Addressing trustworthiness, explainability, and interpretability of ML/AI methods, • Evaluating maintenance activities to maintain an adequate safety margin and avoid undesirable conditions, • Establishing cybersecure condition monitoring programs associated with a computer-based software system, and • Establishing standardized evaluation metrics for advanced condition monitoring programs. Interest in the use of advanced technologies for condition monitoring in ISI and IST programs continues to grow, and the technology is expected to experience rapid and wide industry adoption in the near future. Adoption of advanced technologies for condition monitoring could have novel and unique impacts on regulatory activities associated with ISI and IST programs. The NRC is continuing to explore the regulatory aspects of advanced technologies as part of ISI and IST programs by pursuing additional research in this technical area.

22 - GENERAL STUDIES OF NUCLEAR REACTORS

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Transient uncertainty quantification and Global Sensitivity Analysis of the open-source Molten Chloride Reactor Experiment (MCRE) using GP-PCA surrogate models

Uncertainties in the thermophysical properties of molten salts impact both the steady-state and transient behavior of Molten Salt Reactors (MSRs). In this work, we aim to quantify the influence of such uncertainties on the transient operation of the Molten Chloride Reactor Experiment (MCRE), utilizing the open-source specifications provided for this reactor. Seven representative transient scenarios are considered. For each scenario, we evaluate the impact of thermophysical property uncertainties on four key multiphysics model output variables of interest (VoIs): maximum power density, maximum fuel temperature, maximum reflector temperature, and average fuel velocity magnitude. In addition, we perform a Global Sensitivity Analysis (GSA) by computing Sobol’ indices for the uncertain input parameters to determine their contribution to the variability of each VoI. Conducting GSA is computationally intensive due to the large number of required evaluations of the high-fidelity multiphysics model. To mitigate this cost, we develop a surrogate modeling framework that combines Gaussian Process (GP) regression with Principal Component Analysis (PCA), enabling efficient sample generation for the GSA. Our results show that for energy-related VoIs, thermal conductivity is the dominant contributor to uncertainty. In contrast, for flow-related VoIs, density and dynamic viscosity are the primary sources of uncertainty. The specific heat of the fuel salt was found to play a secondary role in the transient analyses.

42 - ENGINEERING

Genetic programming for the nuclear many-body problem: a guide

Genetic Programming (GP) is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use GP to develop surrogate models to mitigate the computational costs of modeling atomic nuclei with ever increasing complexity. The computational burden escalates when uncertainty quantification is pursued, or when observables must be globally computed for thousands of nuclei. By studying three models in which the mean field depends on the total particle density self-consistently, we show that by constructing reduced order models supported by GP one can speed up many-body computations by several orders of magnitude with a negligible loss in accuracy.

dimensionality reduction

SULI Intern Final Report: Computationally Investigating Hydrogen Thermo-Diffusion in Yttrium Hydride Using Multiscale Methods

The renaissance of nuclear energy has arrived, heralding an age of abundant inexpensive clean energy, and renewed space exploration. In nuclear-powered spacecraft and microreactors, safety and size are of utmost importance. Yttrium Hydride (YHx) is being researched for its utility as a neutron moderator in nuclear reactors; the hydrogen in YHx slows down neutrons, enabling a continuous nuclear reaction in the reactor. This has the benefit of allowing reactors to be more safe, compact, and efficient. The goal of this effort is to computationally predict the coefficient of temperature-dependent hydrogen diffusion within YHx, the Soret coefficient. This parameter is essential for determining the safe operating modes of YHx moderators. Zirconium Hydride (ZrHx) is used in the Training, Research, Isotopes, General Atomics (TRIGA) reactor, is the reference material for these calculations. In this work, nanoscale atomic modeling in the Vienna Ab initio Simulation Package (VASP) is combined with the mesoscale finite element phase-field module in the Multiphysics Object-Oriented Simulation Environment (MOOSE); this culminates in a new multiscale computational method to simulate Soret diffusion of hydrogen in YHx. This data is useful for predicting experimental outcomes. This workflow involves convergence testing followed by static, Nudged Elastic Band (NEB), Quasi-Harmonic Approximation (QHA), and Molecular Dynamics (MD) calculations - linked with phase field simulation. NEB simulates hydrogen migration, while QHA and MD predict temperature-dependent properties. The static calculations align with literature, and preliminary NEB and QHA calculations yield accurate results. Once the atomic calculations are complete, we will incorporate Electron Backscatter Diffraction (EBSD) images and VASP-generated parameters into the phase field module to simulate intra- and intergranular transport of hydrogen in ZrHx and YHx. Future research will extend our approach to fuel-moderator materials systems such as Uranium-Yttrium Hydride (U-YHx). This work contributes to the development of advanced nuclear energy solutions for space travel.

36 - MATERIALS SCIENCE

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING

Mobility assessment of the BCC and carbide phases in the C-Nb, C-U and Nb-U systems

Uranium carbides with refractory metal additions are considered for Gen IV nuclear reactors and nuclear thermal propulsion as fuels for their high-temperature and corrosion resistant properties. Understanding kinetic effects that dictate microstructural evolution during fabrication and operating conditions is essential to advance technological development of these fuels. This work presents the development of an atomic mobility database for C-Nb-U systems based off available experimental data supported with ab-initio methods. The mobility assessments and uncertainty quantification (using Markov chain Monte Carlo) were conducted in the Kawin software. Carbon diffusion is considered dominant, as metal diffusion is much slower, with niobium diffusion being even slower and rate limiting than uranium metal. We provide a comprehensive and self-consistent thermo-kinetic database that is validated by diffusion couple simulations through Kawin. In conclusion, this enables prediction of microstructural and phase evolution critical for the development and lifetime assessment of next generation nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Upstreamness and downstreamness in input–output analysis from local and aggregate information

Abstract Ranking sectors and countries within global value chains is of paramount importance to estimate risks and forecast growth in large economies. However, this task is often non-trivial due to the lack of complete and accurate information on the flows of money and goods between sectors and countries, which are encoded in input–output (I–O) tables. In this work, we show that an accurate estimation of the role played by sectors and countries in supply chain networks can be achieved without full knowledge of the I–O tables, but only relying on local and aggregate information, e.g., the total intermediate demand per sector. Our method, based on a rank-1 approximation to the I–O table, shows consistently good performance in reconstructing rankings (i.e., upstreamness and downstreamness measures for countries and sectors) when tested on empirical data from the world input–output database. Moreover, we connect the accuracy of our approximate framework with the spectral properties of the I–O tables, which ordinarily exhibit relatively large spectral gaps. Our approach provides a fast and analytically tractable framework to rank constituents of a complex economy without the need of matrix inversions and the knowledge of finer intersectorial details.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Peak effect and dynamics of stripe- and pattern-forming systems on a periodic one-dimensional substrate

Here we examine the ordering, pinning, and dynamics of two-dimensional pattern-forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range attraction form anisotropic crystal, stripe, and bubble states. When the system is tuned across the stripe transition in the presence of a substrate, we find that there is a peak effect in the critical depinning force when the stripes align and become commensurate with the substrate. Under an applied drive, the anisotropic crystal and stripe states can exhibit soliton depinning and plastic flow. When the stripes depin plastically, they dynamically reorder into a moving stripe state that is perpendicular to the substrate trough direction. We also find that when the substrate spacing is smaller than the widths of the bubbles or stripes, the system forms pinned stripe states that are perpendicular to the substrate trough direction. The system exhibits multiple reentrant pinning effects as a function of increasing attraction, with the anisotropic crystal and large bubble states experiencing weak pinning but the stripe and smaller bubble states showing stronger pinning. We map out the different dynamic phases as a function of filling, the strength of the attractive interaction term, the substrate strength, and the drive, and demonstrate that the different phases produce identifiable features in the transport curves and particle orderings.

97 MATHEMATICS AND COMPUTING

Bias Correction and Statistical Downscaling of Future Solar Irradiance Projections Using the NSRDB

Assessing renewable energy resources under future climate scenarios has been highlighted to understand potential impacts of future climate change in renewable generation on the power sector. Climate model projection has been recognized by the renewable energy community as a useful data set to analyze the impacts of future climate change on renewable resources. However, future climate projections generated from general circulation models (GCMs) contain inherent biases that need to be corrected for accurate analysis of future projections of climate variables. In addition, the coarse spatiotemporal resolution of GCMs needs to be improved for regional climate studies. In this work, we develop statistical methods to downscale future projections of global horizontal irradiance (GHI) in a computationally efficient way. Our approach builds statistical downscaling models that correct bias of climate projection of GHI and downscale the future GHI projection from daily-scale to hourly-scale. The National Solar Radiation Database (NSRDB) is used to calibrate the statistical models and validate the downscaled GHI projections across the contiguous United State (CONUS). Preliminary results show that the statistical approach efficiently downscales climate projections of GHI with a nBIAS of 3%, nMAE of 34 % and nRMSE of 46% calculated against NSRDB for CONUS. This study describes the implemented methodology and initial results as well as future research to create high-resolution climate data sets for solar energy applications.

analytical models

On Compatible Transfer Operators in Nonsymmetric Algebraic Multigrid

The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction Π will almost certainly be nonorthogonal (and divergent) in any known standard product, meaning ∥Π∥ > 1. This introduces a new consideration, that one wants coarse-grid correction to be as close to orthogonal as possible, in an appropriate norm. In addition, due to nonorthogonality, Π may actually amplify certain error modes that are in the range of interpolation. Relaxation must then not only be complementary to interpolation, but also rapidly eliminate any error amplified by the nonorthogonal correction, or the algorithm may diverge. Here this paper develops analytic formulae on how to construct “compatible” transfer operators in nonsymmetric AMG such that ∥Π∥ = 1 in some standard matrix-induced norm. Discussion is provided on different options for the norm in the nonsymmetric setting, the relation between “ideal” transfer operators in different norms, and insight into the convergence of nonsymmetric reduction-based AMG.

97 MATHEMATICS AND COMPUTING

Argonne Leadership Computing Facility 2024 Operational Assessment Report

This Operational Assessment Report describes how the Argonne Leadership Computing Facility (ALCF) met or exceeded every goal set by DOE for the calendar year (CY) 2024. In CY 2024, the ALCF operated Polaris, an AMD and NVIDIA-based Hewlett Packard Enterprise (HPE) Apollo 6500 Gen10+ system that provides a powerful platform for breakthrough science and prepares applications and workloads for Aurora, Argonne National Laboratory’s Intel-HPE exascale computer. Since going into production in August 2022, Polaris has supported research teams from the DOE Exascale Computing Project (ECP), which concluded in 2024, and from ALCF’s Aurora Early Science Program (ESP). Polaris delivered a total of 2555.7K node-hours to 17 Innovative and Novel Computational Impact on Theory and Experiment (INCITE) 2024 projects and 601.6K node-hours to ASCR Leadership Computing Challenge (ALCC) projects (12 of which were awarded during the 2023–2024 ALCC year and 11 of which were awarded during the 2024–2025 ALCC year), as well as providing substantial time for Director’s Discretionary (DD) projects (966.2K node-hours). As Table ES.1 shows, Polaris performed exceptionally well in terms of overall availability (97.7 percent), scheduled availability (99.6 percent), and utilization (94.7 percent; Table 2.1). In CY 2024, ALCF supported more than 2,000 users. As of March 18, 2025, ALCF’s users have published 254 papers in peer-reviewed journals and technical proceedings.

97 MATHEMATICS AND COMPUTING

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max- k -SAT, Max- k -Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.

97 MATHEMATICS AND COMPUTING

Diffusion Limit–Preserving Lumped DFEMs on AMR Meshes

Here, we present sweep-compatible, novel upwinding recipes for the bilinear discontinuous (BLD) finite element method (FEM) that allows lumped BLD to be used on adaptive mesh refinement (AMR) meshes for thick transport applications without adding additional degrees of freedom at hanging nodes that exist on refinement boundaries. We analyze the properties of the upwinding and lumping that are needed for BLD to get the thick diffusion limit on such meshes, present results demonstrating locking with the wrong recipe, and present results showing error convergence and robustness properties for two diffusive problems on a variety of AMR meshes.

42 ENGINEERING