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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16

Milky Way white dwarfs as sub-GeV to multi-TeV dark matter detectors

Here, we show that Milky Way white dwarfs are excellent targets for dark matter (DM) detection. Using Fermi and H.E.S.S. Galactic center gamma-ray data, we investigate sensitivity to DM annihilating within white dwarfs into long-lived or boosted mediators and producing detectable gamma rays. Depending on the Galactic DM distribution, we set new constraints on the spin-independent scattering cross section down to 10 -45 -10 -41 cm 2 in the sub-GeV DM mass range, which is multiple orders of magnitude stronger than existing limits. For a generalized NFW DM profile, we find that our white dwarf constraints exceed spin-independent direct detection limits across most of the sub-GeV to multi-TeV DM mass range, achieving sensitivities as low as about 10 -46 cm 2 . In addition, we improve earlier versions of the DM capture calculation in white dwarfs, by including the low-temperature distribution of nuclei when the white dwarf approaches crystallization. This yields smaller capture rates than previously calculated by a factor of a few up to two orders of magnitude, depending on white dwarf size and the astrophysical system.

79 ASTRONOMY AND ASTROPHYSICS↗

Surface Merging Technique to Design GA-Optimized Heat Sinks

High-power density inverters require efficient and small heat dissipation systems. For liquid cooling systems, an effective heat sink design is important to enable higher heat transfer and keep the pressure drop within reasonable limits. A heat sink geometry generated from an extruded, 1D fast Fourier transform can achieve more even temperature distribution and improved heat transfer than a conventional heat sink. Building on this concept, this paper proposes a new heat sink geometry creation algorithm. Instead of one plane profile being extruded, multiple plane profiles, each created from the fast Fourier transform method, are subsequently merged by smooth surfaces along the flow direction of the heat sink. Thus, a 3D heat sink geometry is created that enables 3D coolant flow and efficient heat transfer. The volume of this design was reduced by 50% compared with pin fin heat sinks. Compared with extruded 1D fast Fourier transform heat sinks, the proposed design showed an approximately 5% device temperature reduction and a 20% pressure drop reduction.

Barua, Himel↗

A Code-Agnostic Driver Application for Coupled Neutronics and Thermal-Hydraulic Simulations

While the literature has numerous examples of Monte Carlo and computational fluid dynamics (CFD) coupling, most are hard-wired codes intended primarily for research rather than as standalone, general-purpose applications. In this work, we describe an open source application, ENRICO, that enables coupled neutronic and thermal-hydraulic simulations between multiple codes that can be chosen at runtime (as opposed to a coupling between two specific codes). The application has been designed such that the control flow logic, domain mapping, nonlinear fixed-point iteration, solution transfers, and convergence checks are all agnostic to the underlying physics solvers used. Special emphasis has also been placed on enabling efficient execution on distributed-memory computing environments. The transfer of solution fields between solvers is performed in memory rather than through filesystem I/O. Additionally, solvers can be configured to run on overlapping or disjoint sets of processes. To date, coupling with the OpenMC and Shift Monte Carlo codes, the Nek5000 CFD code, and a simplified heat diffusion and subchannel solver has been implemented in ENRICO. We present results for coupled simulations of a single light-water reactor fuel assembly based on the NuScale reactor using various combinations of the physics solvers. For this problem, the coupled simulations are shown to converge in about four Picard iterations. A comparison of the heat source and temperature distributions computed by ENRICO using OpenMC coupled with Nek5000 and Shift coupled with Nek5000 illustrates remarkable agreement between the codes.

42 ENGINEERING↗

Final Technical Report Wireless Microsensors System for Monitoring Deep Subsurface Operations

This final technical report describes the main findings of the project Wireless Microsensors System for Monitoring Deep Subsurface Operations (FE0031850). The project was part of the U.S. Department of Energy National Energy Technology Laboratory FOA 1998 program to develop new sensor systems for direct observation of parameters associated with CO2 injection and to provide data collection without being disruptive to operations. The overall DOE program was aimed at developing and validating innovative transformational sensor systems, amenable for integration with autonomous intelligent monitoring systems, that are capable of being deployed within the casing annulus and do not have casing perforation or wires/cables in the annulus for installation, power supply, or data transmission needs. Project accomplishments included 1) design and fabrication of a wireless downhole sensor system to monitor parameters for CO2 storage, 2) field testing of the sensor system in two legacy oil & gas wells, and 3) development of an analysis approach that validates the measurements and demonstrates the application of the technology to depict CO2 movement in the subsurface. The project leveraged new sensor technologies along with specialized wellbore telemetry, deployment, and analysis methods designed to address the challenges and risks related to CO2 storage in the subsurface. Results from field testing were a mixture of successes and challenges. The temperature sensor rings, installation procedures in legacy oil & gas wells, wireless powering demonstration, automated data collection, and material compatibility were successful. The wireless data transfer through cement to the wellhead via the sensor relays was not functional beyond the first relay. Consequently, work in the last year of the project included some additional testing of data transmission through different materials along with modeling and analysis of field data for CO2 monitoring applications. This work suggested there are options like polymer cements and open hole annuli that may allow point-to-point transmission along the borehole. The techno-economic analysis suggests that the sensor system is ~40% less expensive than fiber optic distributed temperature system. Modeling of CO2 storage applications suggests temperature can provide an indicator of CO2 saturation but would be best combined with pressure sensors.

47 OTHER INSTRUMENTATION↗

Toward local core outlet temperature monitoring in gas-cooled nuclear reactors using distributed fiber-optic temperature sensors

Gas-cooled nuclear reactors operate at temperatures up to 950 °C with significant spatial variations in power generation and coolant flow through hundreds of parallel flow channels, resulting in complex mixing at the core outlet. The high temperatures and complex mixing can damage downstream components, challenge reactor calorimetry for power determination, and result in significant conservatism in calculated peak fuel temperatures, which ultimately limits the total power output. Directly measuring each gas stream individually is unrealistic using single point thermocouples, requiring more robust sensing techniques. Fiber-optic sensors are resilient to high temperatures (up to 1,000 °C) and radiation damage. Moreover, distributed measurements can be made along the length of one fiber, making them potential candidates for monitoring local core outlet temperatures to improve core calorimetry and identify hot channels. Here, to the authors’ knowledge, this manuscript is the first to report spatially distributed fiber optic temperature measurements to quantify mixing at the outlet of a relevant orifice plate under prototypic temperature and flow regimes to assess the feasibility of using fiber-optic sensors for distributed measurements of coolant temperature in gas-cooled reactors. A single optical fiber captured dynamic changes in local temperatures, whereas the mixed outlet temperature exhibited a muted response and could not identify which channels were responsible for the change in the mixed outlet temperature. The discussion focuses on potential challenges for deploying distributed optical fibers in gas-cooled reactors, including the effects of vibrations, radiation-induced signal attenuation and drift, and routing of the fiber while minimizing flow obstructions.

42 ENGINEERING↗

A framework to measure the properties of intergalactic metal systems with two-point flux statistics

ABSTRACT The abundance, temperature, and clustering of metals in the intergalactic medium are important parameters for understanding their cosmic evolution and quantifying their impact on cosmological analysis with the Ly α forest. The properties of these systems are typically measured from individual quasar spectra redward of the quasar’s Ly α emission line, yet that approach may provide biased results due to selection effects. We present an alternative approach to measure these properties in an unbiased manner with the two-point statistics commonly employed to quantify large-scale structure. Our model treats the observed flux of a large sample of quasar spectra as a continuous field and describes the one-dimensional, two-point statistics of this field with three parameters per ion: the abundance (column density distribution), temperature (Doppler parameter), and clustering (cloud–cloud correlation function). We demonstrate this approach on multiple ions (e.g. ${\rm C\, \small {\rm IV}}$ , ${\rm Si\, \small {\rm IV}}$ , and ${\rm Mg\, \small {\rm II}}$ ) with early data from the Dark Energy Spectroscopic Instrument (DESI) and high-resolution spectra from the literature. Our initial results show some evidence that the ${\rm C\, \small {\rm IV}}$ abundance is higher than previous measurements and evidence for abundance evolution over time. The first full year of DESI observations will have over an order of magnitude more quasar spectra than this study. In a future paper, we will use those data to measure the growth of clustering and its impact on the Ly α forest, as well as test other DESI analysis infrastructure such as the pipeline noise estimates and the resolution matrix.

79 ASTRONOMY AND ASTROPHYSICS↗

Transition to Online Cable Insulation Condition Monitoring

Nuclear power plant cables were originally qualified for 40 year life and generally have not required specific test verification to assure service availability through the initial plant qualification period. However, license renewals to 60 and 80 years of operation require a cable aging management program that depends on some form of test and verification to assure fitness for service. Environmental stress (temperature, radiation, chemicals, water, and mechanical) varies dramatically within a nuclear power plant and, in some cases, cables have degraded and required repair or replacement before their qualified end-of-life period. In other cases, cable conditions have been mild and dependable cable performance confirmed to extend well beyond the initial qualified life. Most offline performance-based testing requires cables to be de-coupled and de-energized for specially trained technicians to perform testing. These offline tests constitute an expensive operational burden that limits the economic viability of nuclear power plants. Although initial investment may be higher, new online test practices are emerging as options or complements to offline testing that avoid or minimize the regularly scheduled offline test burden. These online methods include electrical and fiber-optic partial discharge measurement, spread spectrum time or frequency domain reflectometry, distributed temperature profile measurements, and local interdigital capacitance measurement of insulation characteristics. Introduction of these methods must be supported by research to confirm efficacy plus either publicly financed or market driven investment to support the start-up expense of cost-effective instrumentation to monitor cable condition and assure reliable operation. This work summarizes various online cable assessment technologies plus introduces a new cable motor test bed to assess some of these technologies in a controlled test environment.

Glass, Samuel W.↗

Heat load measurements for the PIP-II pHB650 cryomodule

This study presents a brief overview of the 1st and 2nd phases and an in-depth analysis of the 3rd phase heat load testing performed on the pHB650 (prototype High Beta 650 MHz) cryomodule at PIP2IT (PIP-II Injector Test Facility), with a focus on both the results and the methodological advancements that have improved testing efficiency and accuracy. A key challenge identified in the testing campaign is the higher-than-expected heat loads observed in the first PIP-II (Proton Improvement Plan II) prototype cryomodules (pSSR1 and pHB650) tested at PIP2IT. Elevated heat loads are concerning given the fixed capacity of the PIP-II cryoplant that is currently being installed at Fermilab. However, understanding the sources of these elevated heat loads offers a critical opportunity to implement effective heat load mitigations on upcoming PIP-II cryomodules to stay within the available capacity of the PIP-II cryoplant. The study includes a summary of test results, descriptions of measurement procedures, and key observations on parameters directly and indirectly related to heat load measurements. Direct observations include measured heat loads and the effectiveness of JT heat exchanger under varying conditions, while indirect observation analyze factors such as the temperature distribution on the two-phase pipe and relief piping under varying conditions. Thermal acoustic oscillations (TAO) were identified during testing, which was mitigated by replacing the original G10 stem with a stainless steel stem equipped with wipers for the cryomodule cooldown valve. A major innovation during pHB650 Phase 3 testing was the development of an automated Python script to streamline data acquisition, analysis, and reporting of heat load results. This script automatically retrieved data from ACNET (Accelerator Control Network), performed heat load calculations, and generated detailed reports featuring plots and tables. This advancement significantly reduced manual labor and enhanced the thoroughness of data analysis compared to earlier campaigns. The heat load test reports were promptly uploaded to the electronic logbook shortly after each test, enabling rapid feedback and collaboration between the SRF and cryogenic teams. The heat load measurements included various components: HTTS (high-temperature thermal shield), LTTS (low-temperature thermal shield), 2K isothermal and non-isothermal heat loads. Results were recorded both within the cryomodule and between the bayonet can supply and return. Measurements were conducted under different operating conditions such as "standard", "linac", and "simulated dynamic". Additionally, HTTS and LTTS heat loads were calculated in real time, allowing for the tracking of thermal stability and identification of changes during testing, both in steady-state and transient conditions. The results of this testing campaign not only provide valuable insights into the performance of the pHB650 cryomodule but also highlight best practices and lessons learned that will inform future cryomodule testing at PIP2IT. These include adopting automated tools for data analysis, refining real-time measurement capabilities, and emphasizing detailed pre-test planning. The framework established in this campaign aims to set an improved standard for cryomodule testing and heat load reporting in future cryomodule test campaigns.

Porwisiak, D. [Fermilab; Wroclaw Tech. U.]↗

High-Resolution Thermal Profiling of a High-Power Diode Laser Facet During Aging

Here, we study the facet temperature distribution of a high-power diode laser over its lifetime using a noncontact, high spatial resolution CCD-based thermoreflectance technique. Based on the known correlation between non-radiative defects and heating, thermal maps can provide valuable information regarding the formation and evolution of small point defects that are at or near the facet during aging. In the laser under study in this work we measure the appearance of local hot spots on the facet, including concentrated hot spots that appear just before or just after COD and are correlated with loss of local light emission. The locations of these hot spots do not exhibit morphology changes in high-resolution SEM imaging of the facet, indicating that the related defects are too small to be observable in SEM or are located at some depth under the facet. Prior to COD, we measure a gradual facet temperature increase accompanied by a gradual optical power decrease and gradual facet optical absorption increase, indicating gradual degradation of the laser.

47 OTHER INSTRUMENTATION↗

Computational fluid dynamics investigations of flow, heat transfer, and oxidation in heat recovery steam generator

Modern heat recovery steam generators (HRSGs) operate at elevated temperatures, leading to the formation of oxides inside the tubes of heat exchangers (HXs). This oxide growth reduces the heat recovery efficiency. Moreover, after reaching a certain critical thickness, some oxide scales detach from the tube surface (exfoliation), causing erosion damage to the components downstream. Predicting the metal temperature distribution and associated oxide thickness in the HXs of an HRSG can aid in mitigating these problems. Here, a computational fluid dynamics (CFD) model was developed within the commercial code STAR-CCM+ for the prediction of fluid flow, conjugate heat transfer, and associated oxidation in HRSGs. Moreover, a new Porous Media Model (PMM) method was developed to model the fin effect on the heat transfer in HX, which can substantially reduce the prohibitive computational costs of fin meshes. The developed CFD model was used to conduct a high-fidelity simulation of a real-scale HRSG to investigate flow, heat transfer, and oxide growth. The calculated oxide thickness on different tubes can be used to identify HX regions that require oxide-resistant coatings to prevent exfoliation and ensuing damages. Furthermore, this CFD framework can serve as a reference for future studies that intend to model and investigate high-temperature oxidation in HXs used for any applications.

42 ENGINEERING↗

MHD simulations of cold bubble formation from 2/1 tearing mode during massive gas injection in a tokamak

Massive gas injection (MGI) experiments have been carried out in many tokamaks to study disruption dynamics and mitigation schemes. Two events often observed in those experiments are the excitation of the m = 2, n = 1 magnetohydrodynamic mode, and the formation of cold bubble structure in the temperature distribution before the thermal quench (TQ). Here m is the poloidal mode number, n the toroidal mode number. The physics mechanisms underlying those phenomena, however, have not been entirely clear. In this work, our recent NIMROD simulations of the MGI process in a tokamak have reproduced the main features of both events, which has allowed us to examine and establish the causal relation between them. In these simulations, the 3/1 and 2/1 islands are found to form successively after the arrival of impurity ion cold front at the corresponding q = 3 and q = 2 rational surfaces. At the interface between impurity and plasma, a local thin current sheet forms due to an enhanced local pressure gradient and moves inward following the gas cold front, this may contribute to the formation of a dominant 2/1 mode. Following the growth of the 2/1 tearing mode, the impurity penetration into the core region inside the q = 2 surface gives rise to the formation of the cold bubble temperature structure and initiates the final TQ. Here, a subdominant 1/1 mode developed earlier near the q = 1 surface alone does not cause such a cold bubble formation, however, the exact manner of the preceding impurity penetration depends on the nature of the 1/1 mode: kink-tearing or quasi-interchange.

2/1 tearing mode↗

A Forward Time Stepping Heat Conduction Model for Spot Melt Additive Manufacturing

Solidification dynamics are crucial for determining microstructure development in additively manufactured parts. Multiphysics models based on finite element or finite volume methods may help gain insight for complicated phenomena such as fluid flow, keyholing, and porosity but are too computationally expensive to use for simulating actual builds. Recent analytic and semi-analytic solutions for moving heat sources in a semi-infinite three-dimensional space provide a way to accurately estimate the solidification conditions for entire builds. The downside to these methods is that, unlike finite element or finite volume methods, they cannot use the temperature distribution of the previous timesteps to march the solution forward in time. This paper provides the mathematical formulation and implementation of a forward time stepping (FTS) approach to an existing semi-analytic solution. The speed and accuracy of the two methods are then compared for various scan patterns. The result is that, for spot melts, the forward time-stepping model provides improvements in both speed and accuracy. This is especially true for longer simulations, where the simulation can be orders of magnitude faster. Finally, the longest simulation analyzed in this paper was roughly 30× faster when using the forward time-stepping model versus the straightforward implementation of the semi-analytic solution.

36 MATERIALS SCIENCE↗

Numerical simulation of falling film sensible heat transfer over round horizontal tubes

Numerical simulations are performed to explore the heat transfer characteristics of falling films over horizontal round tubes with uniform heat flux imposed for a range of Reynolds numbers spanning the droplet, jet, and sheet regimes. Simulations results agree well with available experimental measurements. The study analyzes the local as well as average heat transfer behavior under the different flow modes. The numerical results show that the local Nusselt number (Nu) distribution depends on the flow features in each mode and varies substantially in all directions for the respective mode. In the droplet mode, the Nu value varies significantly as the droplet impinges and the remnant liquid-bridge retracts (peak instantaneous Nu near 6), followed by wave propagation over the tube surface with peak Nu around 0.25. For the jet modes, the local maximum in the heat transfer occurs off-center to the impingement location with magnitudes of peak Nu = 3.1 for the inline jet mode and Nu = 2.7 for the staggered jet mode, while on the rest of the tube surface, it has an inverse relation with the liquid film thickness. Substantial variations in the heat transfer value are also recorded in the middle of the two impinging jets with Nu = 0.95 in the inline jet mode where the neighboring jets do not interact, and Nu = 0.60 in the crest region of the staggered jet mode where the neighboring jets interact with each other. In the sheet mode, the Nu was seen to depend on the thickness of the liquid waves traversing over the tube surface. Lower Nu values were recorded beneath the crest location of the liquid waves, which increases (1.4–11.6% depending on circumferential location) abruptly in magnitude at the advancing fronts of the waves. The temperature distribution in the liquid film in each of the modes was examined to evaluate the mechanism of heat transfer process. This study also compares the local heat transfer coefficient distribution with the analytical heat transfer models derived to predict heat transfer performance over horizontal tube surfaces.

42 ENGINEERING↗

Radio-Frequency Rapid Thermal Processing Enabling Spatial Phase Transformation and Nanocrystallization of Soft Magnetic Amorphous Alloys

Thermal processing of soft magnetic amorphous and nanocrystalline alloys is explored under the influence of radio-frequency induction-heating techniques. Direct induction-heating concepts based on longitudinal and transverse flux heating are examined and the details of electromagnetic fields interaction with metallic strips are discussed by analytical calculations as well as finite element analysis. Initial experimental results confirming spatial control of phase transformations and nanocrystallization within a single strip of Finemet Fe-based amorphous ribbons are reported. Here, the degree to which primary and secondary crystallization temperature are achieved depends on the spacing between the ribbon relative to the induction coil as well as the coil design and configuration. For transverse coil configurations, the local temperature and therefore microstructural evolution is different across the lateral dimension of processed ribbons, with reduced gap sizes producing enhanced peak temperatures and larger temperature distributions with greater spatial variation in microstructure. In addition, indirect susceptor-based induction heating under tension is performed and the impact of microstructure is demonstrated. Herein, potential for exploiting spatially optimized phase transformations is illustrated through electromagnetic field–assisted processing in a scalable manufacturing process with amorphous and nanocrystalline soft magnetic alloys.

36 MATERIALS SCIENCE↗

Dynamics of Intra-Cell Thermal Front Propagation in Lithium-Ion Battery Safety Issues

Thermal runaway (TR), a critical failure mode in lithium-ion batteries (LIBs), poses significant safety risks and hinders wider application of LIBs. TR typically begins at a localized heat source and spreads across the cell. Understanding thermal front propagation (TFP) characteristics, such as front and velocity, is crucial for assessing energy release and temperature distribution for battery hazardous estimation. Recent studies assume that TR within cells propagates at a near-constant velocity, based on the reaction kinetics and thermal properties. Here, in this study, an intra-battery TR model is further proposed and it indicates that TFP velocity stabilizes when the front is distanced from the heat source. Theoretical estimates for propagation velocity and front are developed and validated through numerical simulations and experimental tests from the NREL Battery Failure Databank. The energy release rate during TFP and the impact of preheating based on a point heat source are explored. This work clarifies the long-standing clouds of the thermal font propagation behaviors within the single cell, highlights the power and beauty of mathematics modeling to describe the complicated thermal behaviors, and provides important guidelines for thermal hazardous understanding for next-generation batteries.

25 ENERGY STORAGE↗

Thermophysical Properties of Mixtures of Thorium and Uranium Nitride

Abstract The miscibility, lattice parameter, and thermophysical properties of (Th 0.2 U 0.8 )N and (Th 0.5 U 0.5 )N have been investigated. It is shown that additions of thorium nitride (ThN) to uranium nitride (UN) increases the thermophysical performance of the mixed nitride fuel form in comparison to reference UN. In the more dilute limit, additions of ThN serve as a burnable neutronic poison and reduces the change in k eff over the lifecycle of the fuel. At higher concentrations, additions of ThN serve as a significant fertile source of 233 U. Where appropriate, comparisons to previous work on UN + PuN mixtures are made, as this is a comparable fuel form for potential fast reactor concepts, and a suitable point of contrast in the possible design space afforded by mixed (Th x U 1 − x )N fuel forms. The data from this work are the input parameters for finite element modeling of the temperature distribution in a compact reactor. The results of modeling and simulation of this core design are shown for the case of steady-state operation and during double, adjacent heat pipe failure.

Parker, S. S. (ORCID:000000018597440X)↗

Optimization of the FRIB beam dump: a hybrid genetic algorithm and reinforcement learning approach

The operational envelope of high-power-density systems, such as particle accelerators and advanced nuclear energy systems, is critically constrained by the need to manage extreme thermal loads. To address this, we present a novel hybrid optimization framework combining a genetic algorithm (GA) with a soft actor-critic (SAC) deep reinforcement learning agent. This framework was applied to a practical high-heat-flux problem: redesigning the beam dump at the Facility for Rare Isotope Beams (FRIB) for a power upgrade from 20 kW to 50 kW. The resulting design, validated by three-dimensional conjugate heat transfer simulations, suppresses hazardous hot spots and yields a markedly more uniform temperature distribution. This provides a robust operating margin, increasing the average power-handling capability by 72% relative to the current design, demonstrating the framework’s potential to solve complex thermal management challenges in both accelerator technology and advanced nuclear systems.

Accelerator↗

Predicting mesoscale spectral thermal conductivity using advanced deterministic phonon transport techniques

We present a review, demonstration and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale. We focus primarily on the development and implementation of a unified methodology to enable predictive heat transport. We report on the current state of the art as it pertains to deterministic phonon transport methodologies, discussing various topics concerning phonons. In application, we focus on the Self-Adjoint Angular Flux (SAAF) formulation of the Boltzmann transport equation for phonons, and develop the spatial, angular, and material property discretization required to accurately simulate the predictive physics of heat transport in dielectrics. We discuss thermal interfacial resistance and present our formulation of the diffuse mismatch model for simulating phonon interactions at internal boundaries. We have recently developed a deterministic, spectral phonon transport method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$), using Bose-Einstein source terms coupled through an average material temperature. In this method, we introduce a closure term to the phonon transport system which acts as a redistribution function for the total energy of the system, and serves as a guide for the amount of non-equilibrium behavior occurring in the system. This method predicts thermal conductivity and equilibrium temperature distributions in homogeneous and heterogeneous materials using data generated by ab initio density functional theory methods. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. The equations associated with this method are solved via a modification of traditional source iteration. We compare the performance of source iteration applied to an existing uncoupled, traditional SAAF method to our new method and comment on the iterative performance of each. We observe ballistic and diffusive phonon scattering as acoustic thickness of the domain changes, and are able to make comparisons between the accuracy and efficiency of both methods.

36 MATERIALS SCIENCE↗