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DOE OSTI2025

CFD modeling of turbulent air flow in self-heated gyroid TPMS structures: Thermal-hydraulic performance and validation

The application of mathematically derived geometries, such as triply periodic minimal surface (TPMS) lattices, has garnered significant interest across various fields, including the nuclear sector, due to their superior thermal-hydraulic characteristics for heat transfer compared to traditional plain or finned tubes. Here, this study validates a computational fluid dynamics (CFD) model, evaluates different turbulence models and CFD model settings, and performs uncertainty quantification to provide a comprehensive analysis. Despite extensive research on CFD modeling of TPMS lattices, such as gyroid and diamond geometries, there is a notable lack of publicly available literature providing comprehensive details on numerical analysis aspects, including convergence and methodological best practices. This study embarks on a benchmark analysis of a gyroid geometry to evaluate its thermal-hydraulic performance under turbulent flow conditions and scrutinize various CFD model configurations. The main contributions of this work include validating the CFD model, assessing and comparing different turbulence models, and enhancing pressure drop and temperature prediction capabilities. The results aim to support the development of methodologies needed to benchmark and enhance numerical analysis techniques for TPMS lattices. This work seeks to complement the existing body of knowledge, support the development of TPMS reactor concepts, and improve best practices for CFD modeling of TPMS lattices, ultimately advancing methodologies to support future applications in this domain.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

In this work, we propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

The Euler characteristic as a basis for teaching topology concepts to crystallographers

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V – E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χ m ) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χ m has an elegant topological interpretation through the concept of orbifolds. Alternatively, χ m can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss–Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Implementation of ACTS into sPHENIX Track Reconstruction

Abstract sPHENIX is a high energy nuclear physics experiment under construction at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory (BNL). The primary physics goals of sPHENIX are to study the quark-gluon-plasma, as well as the partonic structure of protons and nuclei, by measuring jets, their substructure, and heavy flavor hadrons in $$p$$ p $$+$$ + $$p$$ p , p + Au, and Au + Au collisions. sPHENIX will collect approximately 300 PB of data over three run periods, to be analyzed using available computing resources at BNL; thus, performing track reconstruction in a timely manner is a challenge due to the high occupancy of heavy ion collision events. The sPHENIX experiment has recently implemented the A Common Tracking Software (ACTS) track reconstruction toolkit with the goal of reconstructing tracks with high efficiency and within a computational budget of 5 s per minimum bias event. This paper reports the performance status of ACTS as the default track fitting tool within sPHENIX, including discussion of the first implementation of a time projection chamber geometry within ACTS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Precision string phenomenology

Calabi-Yau compactifications of the E 8 × E 8 heterotic string provide a promising route to recovering the four-dimensional particle physics described by the Standard Model. While the topology of the Calabi-Yau space determines the overall matter content in the low-energy effective field theory, further details of the compactification geometry are needed to calculate the normalized physical couplings and masses of elementary particles. In this work, we present numerical computations of physical Yukawa couplings in a number of heterotic models in the standard embedding and demonstrate the existence of natural hierarchies, a coveted feature in string model building. Published by the American Physical Society 2025

Berglund, Per (ORCID:0000000316754133)↗

DOE OSTI2025

VoroClust

SAND2025-11465O VoroClust, also known as Voronoi Clustering, is a fast, density-based unsupervised clustering algorithm applicable to high-resolution and high-dimensional data. It operates as quickly as distance-based clustering methods while effectively capturing complex regional geometries, matching the performance of current density-based methods. VoroClust employs a data-centered sphere cover to reduce computational demands while preserving data topology. It propagates clusters outward from local density peaks. Although supervised machine learning is powerful for applications like image classification and segmentation, it requires comprehensive, consistent datasets, which many applications lack. Unsupervised clustering algorithms analyze the structure of each dataset rather than relying on similarities with other examples, making them well-suited for practical applications with insufficient or inappropriate data for supervised learning. 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.

Ebeida, Mohamed [Sandia National Lab. (SNL-CA), Li↗

DOE OSTI2024

Inverse design for waveguide dispersion with a differentiable mode solver

Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However, existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work, we develop gradient back-propagation through a general-purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ∼100x compared to exhaustive search and identifying new designs for broadband optical frequency doubling of laser sources in the 1.3–1.4 µm wavelength range. Furthermore, we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.

Gray, Dodd (ORCID:000000030469599X)↗

DOE OSTI2024

Wasatch Fault Structure from Machine Learning Arrival Times and High-Precision Earthquake Locations

Abstract On 18 March 2020, a magnitude 5.7 earthquake hit the Salt Lake valley in the state of Utah, United States. Using a dense geophone deployment and machine learning (ML), an additional several thousand events were detected and located. Currently, both the mainshock and the majority of the aftershocks are suspected to have occurred on or near a deeper portion of the Salt Lake segment of the Wasatch fault—part of a large range-bounding fault system thought to be capable of generating an Mw 7.2 earthquake. However, a small subset of aftershocks may have occurred on a portion of the more steeply, eastward dipping, and poorly understood West Valley fault. Unfortunately, the catalog locations and lack of focal mechanisms for this subset of aftershocks provide only a crude constraint on the true fault structure. To better illuminate fault structure, we relocate the ML-generated catalog with a range of magnitudes from −2 to 4.6, using: (1) NonLinLoc, a nonlinear location algorithm, (2) source-specific station terms, and (3) waveform coherence. We further compute first-motion focal mechanisms for 68 events. Results of the relocation suggest a simpler, minimally listric Wasatch fault geometry, contrary to what has been previously proposed. We also find that analysis of the focal mechanisms and waveform similarity indicates minimal event similarity throughout the Magna sequence, suggesting a highly complex and heterogeneous rupture zone, as opposed to rupture on a single plane. These findings suggest an increased seismic hazard due to the overall shallowness of the earthquake sequence and highly varied rupture mechanisms.

Geochemistry & Geophysics↗

DOE OSTI2024

Optimization Studies of Radiation Shielding for PIP-II Project at Fermilab

The Proton Improvement Plan-II (PIP-II) at Fermilab represents a significant advancement in the quest to answer some of the most profound questions about our universe using the world's most intense high-energy neutrino beam. The project requires the construction of a new addition to the Fermilab accelerator complex – an 800-MeV high-intensity superconducting linear accelerator. Ensuring the safety and regulatory compliance of this ambitious project is paramount, necessitating thorough dose rate assessments under both normal operational and accidental scenarios to align with the Fermilab Radiological Control Manual (FRCM) standards. Our approach included a shielding optimization used for the simulations with the Monte Carlo code MARS [1,2,3] to incorporate new magnet and collimator designs, essential for reflecting the current state of PIP-II infrastructure. The implementation of high-resolution detector planes, despite their computational demands, enabled us to gather detailed radiation field data crucial for optimizing shielding configurations. To overcome the significant computational demands, we developed a branching code that drastically reduced simulation runtimes while maintaining statistical integrity. This was achieved through geometry splitting and the application of Russian Roulette techniques, tailored to prioritize regions of interest based on predefined importances and weight limits.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Optimization Studies of Radiation Shielding for PIP-II Project at Fermilab

Makovec, Alajos↗

DOE OSTI2026

Modeling Marangoni Convection using a Velocity-Time Relationship

The Waste Treatment and Immobilization Plant (WTP) at the U.S. Department of Energy’s (DOE’s) Handford site is designed to treat 56 million gallons of radioactive waste through vitrification. The melting vessels physical and chemical integrity is essential to maintain, as failure has a high safety and financial penalty. Monofrax® K-3 refractory, the material widely used for the melting vessel, undergoes significant corrosion over time, concentrated at the triple-point junction between the gaseous atmosphere, refractory, and glass melt, producing a characteristic neck-like profile that significantly limits refractory service life. Accurate prediction of the corrosion within the melter can be used to prevent this and extend the lifetime of the melters. A computational fluid dynamics (CFD) model was previously developed, and predicted subsurface refractory corrosion, but failed to predict the neck-line profile observed experimentally. To address this limitation, the glass-melt meniscus geometry at the glass-refractory interface was estimated from experimentally measured neck profiles and wettability experiments. A curve was fitted to the neck profile to identify the triple point location, and the meniscus shape was characterized by a contact angle of 1°. A velocity profile accounting for Marangoni convection-driven corrosion was derived from the estimated meniscus geometry. Surface tension measurements from LORPM14R1 glasses of varying composition were coupled with K-3 coupon dissolution rates to establish a surface tension–time relationship. This analytical velocity-time model was integrated into the existing CFD framework to improve prediction of the neck corrosion profile. Work was done in a computational setting with national collaboration, resulting in professional development through presentational and technical writing growth.

36 - MATERIALS SCIENCE↗

DOE OSTI2022

An Adaptive Geometry-Free Thermo-Mechanical Model for Directed Energy Deposition Process Modeling

This presentation describes a novel, geometry-free thermo-mechanical model with adaptive subdomain con- struction to accurately predict the thermal conditions, distortions, and residual stresses throughout the directed energy deposition (DED) process. A novel finite element workflow is designed to con- duct the numerical analysis, based on the multi-app and data transfer capabilities in the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE). Unlike with traditional methods, the part geometry in this model is not predefined. Instead, it is a combined effect of the processing parameters and material properties. At each time step, the model utilizes a subdomain construction paradigm to model the material deposition. A specialized mesh adaptivity scheme is incorporated to provide an accurate prediction while reducing the overall computational cost. The results generated by the proposed model show general agreement with the experimental measurements for the single track scan with varying processing parameters and demonstrate reasonable predictions for higher material buildups.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Evaluation of Spray and Combustion Models for Simulating Dilute Combustion in a Direct-Injection Spark-Ignition Engine

Dilute combustion in spark-ignition engines has the potential to improve thermal efficiency by mitigating knock and by reducing throttling and wall heat losses. However, ignition and combustion processes can become unstable for dilute operation due to a lowered laminar flame speed, resulting in excessive cycle-to-cycle variability (CCV) of the combustion process. To compensate for the slower combustion in less reactive mixtures, a modified intake port geometry can be employed to generate a strong tumble flow in the cylinder and elevate turbulence levels around the spark plug, thereby promoting a faster transition to turbulent deflagration. Consequently, optimizing combustion chamber geometry and operating strategy is crucial to maximizing the benefits of using dilute combustion with enhanced in-cylinder turbulence across a wide range of operating conditions. Computational fluid dynamics (CFD) simulations can be utilized for virtual engine optimization tasks, but this would require the models to be truly predictive regarding the impact of changes to the engine design and operational parameters.In this study, multicycle large-eddy simulations (LES) are performed for a direct-injection spark-ignition engine to investigate the model performance in predicting engine combustion characteristics with respect to changes in the intake configuration. A tumble plate that blocks the lower part of the intake port inlet is used to vary the tumble. A set of CFD models that have been recently developed are employed, which takes into account the drag of nonspherical droplets, flash-boiling behavior of liquid sprays, spray-wall interaction, surrogate formulation of a research-grade E10 gasoline, and fast chemical kinetic solvers. Simulation results are compared to experimental engine data in terms of cylinder pressure, apparent heat release rate, mass fraction burned timing, and flame images. It is found that LES employing the state-of-the-art CFD models are capable of properly predicting the spray processes and reproducing the measured mean cylinder pressure for the case with the tumble plate. On the other hand, the LES over-predicts the combustion rate during the early combustion stage and under-estimates the CCV, and these discrepancies become larger when the tumble plate is removed.

computational fluid dynamics simulation↗

DOE OSTI2020

Synthesis, characterization, and computational modeling of 6,6'-(((2-hydroxyethyl)azanediyl)bis(methylene))bis(2,4-di-tert-butylphenol) modified group 4 metal alkoxides

The coordination behavior of the tridentate alkoxy ligand 6,6'-(((2-hydroxyethyl)azanediyl)bis(methylene)) bis(2,4-di-tert-butylphenol) (termed H 3 -AM-DBP 2 ) with group 4 metal alkoxides ([M(OR) 4 ]) in a 1:1 ratio was previously found to generate [(ONep)Ti(κ 4 (O,O’,O”,N)-AM-DBP2)] and [(OR)Zr(κ 4 (μ-O,O’,O”,N)-AM-DBP 2 )] 2 (M = Zr, Hf). Additional studies revealed that increasing the stoichiometric ratio to 1:2 H3-AM-DBP 2 :[M(OR) 4 ] led to the isolation of [(ONep)Ti(κ 4 (μ-O,O’,O”,N)-AM-DBP2)(μ-ONep)Ti(ONep) 3 ] (1)•tol, [(OBu t)Zr(κ 4 (μ-O,O’,O”,N)-AM-DBP2)(μ-OBu t)Zr(OBu t )3] (2) and [(OBu t)Hf(κ 4 (μ-O,O’,O”,N)-AM-DBP2)(μ-OBu t )Hf(OBu t ) 3 ] (3). The asymmetric dinuclear complexes of 1-3 resemble the chelation of a [M(OR) 4 ] moiety to a “(OR)M(κ 4 (O,O’,O”,N)-AM-DBP 2 )” fragment. The metal complexed by the AM-DBP 2 ligand has a pseudo octahedral geometry while the other metal adopts an intermediate trigonal bipyramidal (TBP-5)/square base pyramidal (SBP-5) geometry for 1 but a distorted SBP-5 for both 2 and 3. The structure and properties of 1-3 were analyzed by computational modeling and fully characterized by standard analytical methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

PyCDFT: A Python package for constrained density functional theory

In this paper, we present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn–Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Weight function procedure for reduced order fracture analysis of arbitrary flaws in cylindrical pressure vessels

Fracture mechanics calculations using the finite element method can be computationally expensive, which makes them challenging to use in engineering evaluations of flaws in pressure vessels. The weight function (WF) technique is a reduced order fracture modeling method that is widely used to greatly reduce these computational costs. Its computational efficiency is essential for use in probabilistic fracture mechanics evaluations of embrittled nuclear reactor pressure vessels (RPVs), due to the large number of sampled flaws that must be evaluated. Although the WF technique is general, it is typically used only for axis-aligned flaws. Recent discoveries of off-axis flaws in operating nuclear reactors have necessitated detailed simulations of such flaws and the interactions between neighboring flaws. This paper presents a generalized WF approach applicable for analyzing arbitrary flaw geometries in thick-walled cylindrical vessels, including surface-breaking and subsurface flaws, which can either axis-aligned or off-axis, and can account for interactions with other flaws. Herein, this approach is demonstrated on representative simulations of multiple flaw geometries in a RPV subjected to transient loading conditions. In all cases, the WF technique gives good comparison with benchmark results from direct simulation with greatly reduced computational effort.

42 ENGINEERING↗

DOE OSTI2020

Entanglement islands in higher dimensions

It has been suggested in recent work that the Page curve of Hawking radiation can be recovered using computations in semi-classical gravity provided one allows for ``islands" in the gravity region of quantum systems coupled to gravity. The explicit computations so far have been restricted to black holes in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically construct a five-dimensional asymptotically AdS geometry whose boundary realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole in equilibrium with a bath. We also numerically find two types of extremal surfaces: ones that correspond to having or not having an island. The version of the information paradox involving the eternal black hole exists in this setup, and it is avoided by the presence of islands. Thus, recent computations exhibiting islands in two-dimensional gravity generalize to higher dimensions as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗