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DOE OSTI2020

TRT Compton Scattering Data: Comparisons between LLNL and LANL: Pointwise

This memo is one of a pair of reports comparing Compton scattering data in the context of thermal radiation transport (TRT). This document focuses on Pointwise (PW) data while the other report focuses on Multigroup (MG) data. These complementary analyses, via PW comparisons, show if the same physics are used and if fundamental bugs are present, and, via MG comparisons, quantify macroscopic Compton effects such as mean amplification factors. No averaging of Compton data over photon energy is done for the PW comparisons, while lab-dependent numerical resolution choices become relevant for the MG comparisons. This document plots and quantifies differences in PW Compton scattering data between LANL and LLNL for four disparate temperatures on a logarithmically-spaced energy grid. PW comparisons means we use the received LLNL data as-is, without any averaging or integration over energy. In addition to LANL-to-LLNL comparisons, we investigate the impact of numerical choices on LANL PW data. For the purposes of this comparison, we neglect induced scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

TRT Compton Scattering Data: Comparisons between LLNL and LANL: Multigroup

This memo is one of a pair of reports comparing Compton scattering data in the context of thermal radiation transport (TRT). This document focuses on Multigroup (MG) data while the other report focuses on Pointwise (PW) data. These complementary analyses, via PW comparisons, show if the same physics are used and if fundamental bugs are present, and, via MG comparisons, quantify macroscopic Compton effects such as mean amplification factors. No averaging of Compton data over photon energy is done for the PW comparisons, while lab-dependent numerical resolution choices become relevant for the MG comparisons. For this MG-comparison report, we make and document the numerical assumptions we use to convert LLNL PW data into MG data. This document plots and quantifies differences in Compton scattering data between MG LANL and LLNL for four disparate temperatures on a logarithmically-spaced photon-energy grid. In addition to LANL and LLNL data, we add a third and fourth independent vote from data generated by Brooks Kinch (LANL postdoc). For the purposes of these comparisons, we neglect induced scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

A novel MC TRT method: vectorizable variance reduction for the energy spectra

Data produced up to now gives us confidence that we will continue to see variance reduction behavior at amenable runtimes as we move this test bed forward. This method has characteristics of event and history based Monte Carlo transport, without the bulky modifications required by event based Monte Carlo while avoiding some overhead.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Moment-based adaptive time integration for thermal radiation transport

Here, in this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Nonlinear Elimination Applied to Radiation Diffusion

We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2024

A Survey of Multimaterial Treatments for Thermal Radiative Transfer

Arbitrary Lagrangian-Eulerian methods are a popular choice for hydrodynamic modeling in radiation (rad-hydro) simulations. Because these methods involve a relaxation step that moves the mesh relative to material boundaries, multimaterial spatial zones are generally present. Accurate treatments of these zones are needed to resolve various physical phenomena of interest for inertial confinement fusion applications. However, these codes are often paired with single-material, deterministic thermal radiative transfer (TRT) codes that are oblivious to the material compositions of each zone. These single-material TRT codes can only accept homogenized material properties (opacities, specific heats, etc.) from the hydrodynamic code and output homogenized solutions. After each TRT time step, the multimaterial hydrodynamic code must dehomogenize the quantities computed by the TRT package in order to update subzonal material temperatures. The process by which hydrodynamic codes perform this dehomogenization has not been well documented in previous literature, and the methods can vary significantly from code to code. The purpose of this paper is to document, study, and compare existing techniques used for rad-hydro simulations as well as present a new method with potentially promising results. We summarize several methods and give comparisons on infinite-medium problems as well a finite-medium problem for two of the methods.

42 ENGINEERING↗

DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Improved treatment of multi-material cells in thermal radiation transport codes

High-energy-density physics simulations with non-conformal meshes of materials require a multi-material (MM) closure that affects the thermal radiation transport (TRT). We propose a set of novel closures that work for an arbitrary number of materials, both grey and multigroup energy discretizations, and any angular discretization (such as Sn, IMC, or diffusion). For each spatial cell, our closures let each species (ion and electron) of each material have its own temperature, density, and internal energy, but use a single radiation distribution that interacts with all materials within the cell. Our closures maintain energy conservation, do not incur increased computational cost in the TRT solve itself, are compatible with single-material TRT solvers, and do not make any temperature-equilibrium assumptions. Here we test our closures on a wide range of increasingly realistic problems and find them to be robust.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

The production and separation of 161 Tb with high specific activity at the University of Utah

Targeted radiotherapy (TRT) is an increasingly prominent area of research in nuclear medicine, particularly in the context of treating cancerous tumors. One radionuclide of considerable interest for TRT is terbium-161 (t 1/2 = 6.95 days), which undergoes beta emission and shares similar decay properties as 177 Lu (FDA-approved as LUTATHERA® and PLUVICTO®). Besides beta emission, 161 Tb also emits a significant number of conversion and Auger electrons further enhancing its therapeutic potential. Terbium-161 can be produced using nuclear reactors through an indirect neutron capture reaction, $^{160}_{64}$Gd(n,γ) $^{161}_{64}$Gd → (3.7 min, β – ) $^{161}_{65}$Tb, from 160 Gd targets. However, a key challenge in utilizing 161 Tb for TRT lies in effectively separating target and product materials to attain high specific activity for radiolabeling. Here, we detail the production of no-carrier added 161 Tb using low flux research reactors (mean thermal (< 0.625 eV) neutron flux: 1.356 ×10 12 n • cm –2 • s –1 ) like the University of Utah TRIGA Reactor, using enriched 160 Gd 2 O 3 targets (1.5 ± 0.3 µCi of 161 Tb per mg of 160 Gd target per hour of irradiation). We also developed a separation technique based on cation exchange and extraction chromatography, suitable for mCi level irradiations with targets exceeding 200 milligrams. In a simulated full-scale irradiation, 161 Tb was successfully isolated from large mass targets using cation exchange (AG 50W-X8, with 2-hydroxyisobutyric acid at 70 mM, pH 4.75) and extraction chromatography (LN Resin, 0.5 – 0.75 M HNO 3 ) methods. Here, this resulted in high apparent molar activities of [ 161 Tb]Tb-DOTA (113 ± 3 MBq/nmol), demonstrating high purity 161 Tb relevant for potential future preclinical applications.

161Tb↗

DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗

DOE OSTI2020

Discretization Writeup for Grey Flux-Limited Radiation Diffusion

This report documents the time and space discretizations for grey flux-limited diffusion applied to the thermal radiative transfer (TRT) equations. We begin with a description of the physics being solved before moving into the diffusion approximation. Once we have the TRT system, we show a finite-volume-inspired discretization from Jim Morel (Texas A&M University, NUEN 627 class notes, lecture 8). As systems become hotter they emit more photons in the form of blackbody radiation. Because average photon energy of the blackbody source is proportional to the temperature of the system, we call these thermal photons or thermal radiation. As material temperatures increase, increasing fractions of the total energy in the system go into the radiation field. In addition, radiation can deposit energy and momentum non-locally, making it an important phenomenon for heating and impulse. In order to accurately study systems at high temperatures, we wish to add the physics of thermal radiation to our hydrodynamic system. In practice, coupling radiation and hydrodynamics is often done by operator-splitting each timestep into two consecutive, non-overlapping phases: (1) update the hydrodynamics for a fixed radiation state (2) update the radiation and internal energy for an otherwise fixed hydrodynamic state. Because of this clean separation of physics updates, in this report we show only the latter phase, which involves solely the TRT equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Fully Implicit Monte Carlo (FIMC) (September 2019-September 2020 Progress Report)

This research is focused on applying the NLem method to the full thermal radiative transfer (TRT) equations in the context of a Monte Carlo solution strategy. A framework has been developed for obtaining a solution to the TRT equations using the nonlinear elimination method (NLem) method. Current efforts are focused of the development and verification of the required Monte Carlo algorithm, diffusion algorithm, and material energy solver. Once all three pieces have been verified, the algorithms will then be coupled into a fully functioning method for applying NLem to the TRT equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Limited effects of tannin supplementation on the dairy cattle fecal microbiome with modulation of metabolites

Tannins are plant secondary metabolites that bind organic carbon (C) and nitrogen (N), potentially altering substrate bioavailability for enteric fermentation in ruminants. This interaction may reduce greenhouse gas (GHG) emissions and influence nitrogen partitioning. Given tannins' resistance to ruminal degradation and persistence through the gastrointestinal tract, this study investigated the effects of a tannin-based feed additive on fecal microbial diversity, fecal chemical composition, and GHG emissions. Twenty-four early- to mid-lactation dairy cows were randomized to receive either a tannin-based feed additive (TRT; containing condensed and hydrolyzable tannins from Schinopsis quebracho-colorado [Schltdl.]) or a control diet (CON) for 64 days. Cows were blocked by parity, dry matter intake, milk yield, body weight, and days in milk. Fecal samples were collected on days 0, 16, 32, and 64 and analyzed using 16S rRNA gene amplicon sequencing. Fecal C, N, and indole-3-lactate were measured, and GHG emissions (N2O, CH4, CO2) were assessed via 14-day laboratory incubation. A total of 1,538 amplicon sequence variants were identified, with Firmicutes as the dominant phylum. Fecal phylogenetic diversity showed a significant treatment × day interaction (p < 0.01), with TRT cows exhibiting reduced microbial diversity from day 16 to 64. Fecal C and N concentrations were significantly lower (p < 0.01) in TRT cows on day 16, while indole-3-lactate levels were higher on day 64 (p = 0.02). GHG emissions did not differ significantly between treatments. The tannin-based feed additive influenced fecal microbial community structure and select chemical parameters but did not significantly affect GHG emissions from feces. These findings suggest that dietary tannins may modulate gut microbial ecology with minimal impact on downstream manure-related emissions.

Klein, Matthew L↗

NASA NTRS2024

Airfoil Table Modification for Improved Calculation of Ingenuity Rotor Performance

To better characterize the behavior of the Ingenuity helicopter, multiple test campaigns were conducted. These tests included the Engineering Design Model 1 (EDM1) tests and the Transonic Rotor Test (TRT), both of which assessed Ingenuity rotor performance at various conditions. Using a comprehensive rotorcraft analysis tool, CAMRAD II, test setups of the two different Ingenuity test campaigns were simulated. The EDM1 test used coaxial test stand which focused on varying collective at various feasible Martian atmospheric densities and the TRT test used a single rotor test stand which focused on varying RPM to assess performance at different blade tip Mach numbers. Initial CAMRAD II analyses yielded performance results which differed significantly from experimental results. To reconcile the experimental results and the CAMRAD II analyses, modifications were made to the input airfoil decks for CAMRAD II. After several iterations of modifications, a specific method of modification was found that more accurately predicted experimental behavior at all tested densities for the coaxial rotor. This same modification was less successful for the single rotor test results. There are a number of differences between coaxial and single rotor aerodynamics and between the two test stands (hub and control system); also, there is a small influence of RPM (mainly tip Mach number) on dimensionless performance. These differences may be causing the coaxial rotor modifications not being successful for the single rotor.

Airfoil↗

NASA NTRSDate not supplied

Performance Analysis and Data Processing for the Mars Sample Recovery Helicopter in the Jet Propulsion Laboratory 25-ft Space Simulator

On April 19, 2021, Ingenuity became the first helicopter to fly on Mars at Jezero Crater, completing a total of 72 flights by the end of its mission. The success of Ingenuity resulted in various research efforts to further explore Mars via vertical flight, including two optimized Ingenuity-sized helicopters proposed to retrieve samples for the 2028 Mars Sample Return mission. To aid in the design process for the two proposed Sample Retrieval Helicopters, both heritage and optimized, increased diameter rotors were tested at the NASA Jet Propulsion Laboratory in the 25-ft Space Simulator. Three test campaigns were performed using the Ingenuity rotors and optimized Sample Retrieval Helicopter (SRH) rotors for several rotor speeds, densities, configurations, and collectives to identify performance limitations. These three test campaigns included the Ingenuity Engineering Design Model 1 (EDM-1) with and without a cruciform box, Transonic Rotor Test (TRT) rig, and SRH Dual Rotor Test (DRT). Experimental setup, test matrix, data processing, data quality, and performance results for EDM-1, TRT, and DRT campaigns are presented and discussed. Experimental results from the test campaigns will aid in future experimental methods and validation efforts for planetary rotorcraft exploration.

Data Processing↗

DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗