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DOE OSTI2024

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell’s equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE Φ and TM Φ polarizations on the finite element (primal) mesh. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE Φ polarized fields, (E z , E ρ , B Φ ) and (2) D and H of TM Φ polarized fields, (D Φ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). Here, a cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMΦ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Computational modeling of phononic pseudocrystal isolators

Methods for the efficient computational prediction of the performance of phononic pseudocrystals (structured materials capable of blocking extraordinary ranges of frequency) in COMSOL and other comparable finite element method codes are set forth. These methods include boundary conditions that make possible halving the size of the computational domain. Also included is an introduction of elastic energy density methods for assessing the extinction of elastic waves within the patterned region.

Swift, Stephen Hales↗

DOE OSTI2024

Operator product expansion for radial lattice quantization of 3D ϕ 4 theory

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3D Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the quantum finite elements method to implement radially quantized critical ϕ 4 theory on simplicial lattices approaching R × S 2 . Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions Δ ε and Δ T as well as ratios of the operator product expansion coefficients f σ σ ε and f σ σ T of the first spin-0 and spin-2 primary operators ε and T of the 3D Ising CFT. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Effective field theory for radiative corrections to charged-current processes. II. Axial-vector coupling

Here we discuss the hadronic structure-dependent radiative corrections to the axial-vector coupling that controls single-nucleon weak charged-current processes—commonly denoted by 𝑔 𝐴 . We match the Standard Model at the GeV scale onto chiral perturbation theory at next-to-leading order in the one-nucleon sector, in the presence of electromagnetic and weak interactions. As a result, we provide a representation for the corrections to 𝑔 𝐴 in terms of infrared finite convolutions of simple kernels with the single-nucleon matrix elements of time-ordered products of two and three quark bilinears (vector, axial-vector, and pseudoscalar). We discuss strategies to determine the required nonperturbative input from data, lattice-QCD (+QED), and possibly hadronic models. This work paves the way for a precise comparison of the values of the ratio 𝑔 𝐴 ⁡/𝑔 𝑉 extracted from experiment and from lattice QCD, which constrain physics beyond the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Predicting Mechanical Properties from Microstructure Images in Fiber-Reinforced Polymers Using Convolutional Neural Networks

Evaluating the mechanical response of fiber-reinforced composites can be extremely time-consuming and expensive. Machine learning (ML) techniques offer a means for faster predictions via models trained on existing input–output pairs and have exhibited success in composite research. This paper explores a fully convolutional neural network modified from StressNet, which was originally used for linear elastic materials, and extended here for a non-linear finite element (FE) simulation to predict the stress field in 2D slices of segmented tomography images of a fiber-reinforced polymer specimen. The network was trained and evaluated on data generated from the FE simulations of the exact microstructure. The testing results show that the trained network accurately captures the characteristics of the stress distribution, especially on fibers, solely from the segmented microstructure images. The trained model can make predictions within seconds in a single forward pass on an ordinary laptop, given the input microstructure, compared to 92.5 h to run the full FE simulation on a high-performance computing cluster. These results show promise in using ML techniques to conduct fast structural analysis for fiber-reinforced composites and suggest a corollary that the trained model can be used to identify the location of potential damage sites in fiber-reinforced polymers.

Sun, Yixuan (ORCID:0000000311093380)↗

DOE OSTI2024

A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS

The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $ω$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $ω$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $τ$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.

Nek5000↗

DOE OSTI2025

Automated Redox Titrations via Interdigitated Electrode Arrays: Application to the Mediated Electron Transfer Interrogation of Charge and Rate on Electrodeposited Polymers

Mediated electron transfer (MET) plays a crucial role in energy storage and conversion technologies such as redox targeting flow batteries (RTFBs), yet its experimental investigation often requires labor-intensive and low-throughput setups. To address this, we developed a microfabricated interdigitated electrode array (IDA) platform that enables automated, high-throughput electrochemical redox titration measurement to be performed to study the MET process. Our redox titration method enables simultaneous measurement of the charge capacity and rate of MET processes on a material or surface. Automated redox titration (ART) facilitates systematic investigation of the MET process across a broad parameter space, exemplified through the study of polypyrrole (PPy) and a pyrene-4,5,9,10-tetrone azo group-based polymer (PTAP), both redox-active polymers relevant to various energy storage applications. Using PPy as a model material, 500 redox titration measurements were conducted within 50 h, varying the electrode gap widths, polymer charging potentials, voltammetric scan rates, and electrolyte concentrations. Finite-element simulations confirmed the electrochemical responses and elucidated the kinetics of the MET reactions. Our automated methodology was further tested with PTAP, revealing a surprising charging potential dependence on the rate of MET. The automation, flexibility, and scalability of our redox titration platform pave the way not only for advanced studies of MET processes relevant to RTFBs, but also with implications in the understanding of next-generation energy storage materials, molecular electrocatalysis, and biosensing.

electrochemical analysis↗

DOE OSTI2025

Rapid Commissioning of Large Machine Tools Using Finite Element-Based Correction of Geometric Errors

Large computer numerical control (CNC) machine tools derive their stiffness from monolithic cast iron bases or weldments that are sometimes integral to machine motion systems like box ways or guideways. However, the sheer size of castings and even floor flatness deviations result in dimensional errors in these systems, which manifest as machine motion errors. Typical geometric alignment processes rely on an iterative approach, where measurements are taken to assess alignment (straightness, squareness, and parallelism), followed by adjustment of the machine supports (fixators or leveling pads), which can take weeks even for an experienced operator. Conversely, a novel method is proposed to shorten the correction time by eliminating the trial-and-error process in favor of a more deterministic approach guided by a finite element (FE) method. A feasibility study is conducted on a CNC polymer hybrid machine, with a steel weldment frame, supported by six leveling pads. An FE model of the frame is utilized to obtain recommended leveling pad adjustments, based on measurement of machine errors taken using a laser tracker. After a single adjustment cycle, measurements reveal that geometric errors of the machine tool are reduced from 2.22 mm of flatness deviation to 0.32 mm, achieving an 85.6% reduction. Furthermore, the entire process including measurement, adjustment, and assessment is completed in just 6 h by two operators who are not professional service engineers. In conclusion, this methodology demonstrates feasibility for scaling up, especially to large, high-precision CNC machine tools with bases mounted by fixators, offering the capability for bidirectional adjustment.

42 ENGINEERING↗

DOE OSTI2026

Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics

Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.

Materials science↗

DOE OSTI2025

Metallurgical Analysis and Forward Modeling of Weld Distortion in SMR Containment Vessels

This work aimed to apply Sandia’s expertise in metallurgy and modeling to enable the use of hybrid laser arc welding for building nuclear reactor containment structures, via a collaboration with Holtec International. Experimental observations were coupled with finite element analysis to resolve microstructure development, mechanical properties, distortion, and residual stress in welds relevant to the production of the Holtec SMR-160. High residual stresses were observed in welds that were not subjected to preheat. Meanwhile, the microstructure of the welds generally exhibited a narrow heat affected zone relative to conventional arc welds. FEA appeared to be effective in simulating the thermal/mechanical conditions that occur during hybrid laser arc welding of simplified and instrumented test welds. Subsequently, FEA was used to perform sensitivity analyses for various weld geometries that would be prohibitively costly to assess with physical experiments. Insights from the study were used to inform Holtec’s welding process, and successful production welds were performed in 2025.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Fatigue life prediction of powder bed fused–laser beam AlSi10Mg: Incorporating critical defects via crystal plasticity modelling

The current study provides a microstructurally-based computational framework to predict the fatigue life of additive manufactured (AM), i.e., powder bed fused–laser beam (PBF-LB), AlSi10Mg specimens using the crystal plasticity finite element method (CPFEM). The fractography analysis, electron backscatter diffraction (EBSD), uniaxial and cyclic responses, and fatigue life of specimens were used to inform the computational framework. CPFE simulation was used to compute fatigue indicator parameters (FIPs) as fatigue driving forces. A new fatigue criterion is introduced based on FIPs, which was calibrated using experimental fatigue data. The proposed fatigue measure was evaluated versus the specimens with critical defects of various sizes and locations subjected to different stress amplitudes. The results show that the developed framework can capture the fatigue life of samples with different critical defect locations and sizes along with different stress amplitudes for both high-cycle fatigue (HCF) and very high-cycle fatigue (VHCF) regimes.

Additive manufacturing↗

DOE OSTI2025

Three and Two Phase Rotating Field Inductive Couplers for Wireless Power Transfer with One Phase per Layer Windings

Multiphase inductive wireless charging coils have been proposed recently to improve coupler surface power density, reduce component stress and size, and provide near-constant power delivery to charge mobile electric systems. Several aspects for the fundamental characterization of multiphase coils are explored up to six phases including approximate mutual inductance with size and turn variation, induced voltage, and output power estimation. The relative component stress and size of passive components for resonant operation are compared between the multiphase variants. A combination of an experimentally validated 3D electromagnetic finite element analysis (FEA) and power electronic co-simulations are used to validate the estimated quantities approximated with a mixture of analytical equations and an artificial neural network model for mutual inductance. A novel three-phase transmitter, two-phase receiver coil pair is also proposed for electric vehicle charging to reduce the number of connections and compensation complexity on the vehicle-side with improved power output compared to a two-phase configuration.

Lewis, Donovin D. [University of Kentucky]↗

DOE OSTI2025

SAM User's Guide

The System Analysis Module (SAM) is a modern system analysis tool being developed at Argonne National Laboratory for advanced non-LWR safety analysis. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for Sodium-cooled Fast Reactors (SFR), Lead-cooled Fast Reactors (LFR), and Molten Salt Reactors (MSR) or Fluoride-cooled High-temperature Reactors (FHR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage the modern advanced software environments and numerical methods. This document provides a user’s guide, which will help users understand the input description and core capabilities of the SAM code. A brief overview of the code is presented, as well as how to obtain and run it. The input syntax for various parts of the code is provided. Additionally, a number of example problems, starting with simple unit component problems to problems with increasing complexity, are provided. Because the code is still under active development, this SAM User’s Guide will evolve with periodic updates.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

An Inverse Heat Conduction Algorithm Used to Calculate the Temperatures on the Inner and Outer Cylindrical Surfaces of an HMX-based PBX Explosive Annulus

In this work, a new Inverse Heat Conduction (IHC) algorithm is applied to estimate the surface temperatures at twelve locations on the inner and outer cylindrical boundaries of an HMX-based Plastic Bonded Explosive (PBX) annulus. This IHC algorithm was developed in references using a set of Direct Heat Conduction (DHC) solutions and a temperature correction method. The DHC solutions were calculated using a Galerkin based finite element (FE) method. This HMX based PBX annulus was used in the Large Scale Annular Cookoff (LSAC) experiment, Shot 5. The reason Shot 5 was chosen as a prototype mathematical model for this study is that the temperature was measured at eighteen locations in the midplane of the HMX-based PBX annulus. In addition, this annulus underwent an experimental thermal ignition and a deflagration that caused a thermal explosion and the disassembly of the experiment. The objective of this study is to describe how the application of the temperature correction algorithm produced the convergence of the DHC solutions to the measured temperatures at twelve internal locations in the midplane of the HMX-based PBX annulus.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Develop a new integrated macro→micro←nano (MMN) multiscale modeling framework to optimize high strength aluminum alloys and processes for vehicle light-weighting

Bending tests provide a means to study plane strain fracture performance of 6000 series aluminum alloys. Metrics from bending tests have been correlated with self-pierce riveting (SPR) performance of a high strength AA6111 automotive aluminum alloy in previous works. Using the ORNL HPC resources, this project developed an innovative macro→micro←nano (MMN) multiscale microstructure-based finite element (FE) code to further understanding of the relationship between microstructure and fracture properties of high-strength 6000-series alloys. This work started with microstructural characterization in both mesoscale and nanoscale and bending performance characterization of AA6111 HS2-T6 alloy at Ford, the MMN framework was applied to this alloy to simulate 3-point VDA bending. From the results of the macro-modeling of 3-point VDA bending, the critical region of fracture was identified, and the region geometry was used to construct the micro-model. The fracture criterion of micron-scale precipitates and aluminum matrix which contains submicron and nano particles (AL-SMP-NP) in the micro-model was calibrated and validated by comparing simulated and measured bending results. With the AL-SMP-NP fracture strain obtained, the fracture strain of Al-matrix containing nano particles (ALNP) will similarly be determined by a submicron scale-model using an edge-constrained FE modeling approach developed by Hu et al. With the ALNP fracture strain obtained, the fracture strain of Al-matrix containing no particles will similarly be determined by a nano scale-model using an edge-constrained FE modeling approach. After the MMN framework is built and fracture criterion calibrated, nano-model FE simulations with virtual microstructures was performed to obtain a reduced order model (ROM) of the fracture criterion of the ALNP as a function of volume fraction, size, and distribution of the nanoparticle. This nano→submicron→micro modeling part allows exploration of the influence of different material nanostructures from different process conditions on the bending properties within the multiscale bending simulation framework and the ROM of material bendability as a function of nanoparticle size and shape was established. This obtained reduced order model (ROM) could help guide the design and selection of materials to improve existing SPR process models that could replace trial-and-error rivet/die selection and help to design new rivet/die combinations capable of robustly joining new higher strength 6000 5 series alloys in automotive body structures. This would enable lightweighting of Ford vehicles leading to greater fuel efficiency and reduce manufacturing time and energy.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A stable potential-based time-domain method for wideband elec- tromagnetic analysis

In previous research, the frequency-domain A-ϕ formulation has been validated using the finite element method for electromagnetic simulations of low-frequency and multi- scale problems, demonstrating excellent numerical accuracy, good matrix condition, and high computational efficiency. Time- domain simulations provide significant advantages for modeling wideband problems and are crucial for multiphysics applications. In this paper, the frequency-domain A-ϕ formulation is extended to the time domain. The central difference scheme is employed for temporal discretization to ensure both accuracy and stability. A numerical example is presented to demonstrate the capability of the proposed time-domain method in wideband electromagnetic analysis.

Mekonnen, Minyichil↗

DOE OSTI2024

Kinetic Plasma Simulation in the MOOSE Framework: Verification of Electrostatic Particle In Cell Capabilities

In magnetic confinement nuclear fusion reactors, the interaction between the plasma edge and plasma facing components is extremely important. At the plasma edge, a kinetic representation such as particle-in-cell (rather than a fluid representation) is required to accurately capture the plasma behavior. General purpose particle-in-cell plasma simulation capabilities have been developed in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. This new capability is a part of the development of a new MOOSE-based framework for modeling plasma facing components, the Fusion ENergy Integrated multiphys-X (FENIX) framework. In this work, the verification of foundational particle-in-cell capabilities in FENIX is presented. This new plasma simulation capability has three main components: moving particles in discrete steps on the finite element mesh, mapping charge density from the particle's location to the finite element mesh, and solving for the electrostatic potential based on the charge density mapped from particles to the mesh. In this paper, simple verification problems demonstrating each of these new capabilities are presented, and future work includes electromagnetic capabilities and Monte Carlo collisions with neutral gas particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A mechanistic interpretation of Nelson curves for PVP failures under high temperature hydrogen attack

As an empirically established design criterion, Nelson curves that relate the service temperature and the allowable hydrogen partial pressure have been developed and utilized for more than sixty years in pressure vessels and piping (PVP) safety design. Despite a relatively clear thermodynamic understanding of the high-temperature-hydrogen-attack (HTHA) problem, the detailed fracture process on the microstructural length scales, however, remains elusive, and a quantitative assessment of the PVP lifetime under HTHA from the available creep fracture dataset is still not possible. This work develops a microstructure-informed and micromechanics-based model by incorporating a synergy between hydrogen transport and intergranular-cavity-based fracture process. Based on the available creep lifetime data of C-0.5Mo steels, we are able to calibrate material constitutive parameters, and then conduct nonlinear finite element simulations that reveal a real-time stress-induced hydrogen diffusional transport along grain boundaries, coupled with a microstructure-explicit failure process, from which Nelson curves can be computed. Such failure analyses allow us to delineate two distinct regimes on the Nelson curves, i.e., dislocation-creep-controlled or grain boundary diffusion-assisted cavity growth. More importantly, we found that a small change of the pipe thickness and applied stresses can significantly shift these lifetime curves. However, these two parameters are usually not provided in Nelson curves, thus limiting their usage in material selection and safety design. In conclusion, this discrepancy can clearly be mitigated by extensive parametric studies from our micromechanical modeling/simulation framework.

36 MATERIALS SCIENCE↗