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At least 37 records · Page 2

Mathematical modeling of moving boundary problems in thermal energy storage

The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

Solomon, A. D.↗

Systematic over-estimation of lattice thermal conductivity in materials with electrically-resistive grain boundaries

Reducing the thermal conductivity κ of a material via nano-structuring to create small grain sizes is one of the most common strategies to improve thermoelectric materials. In such polycrystalline materials heat carrying phonons are scattered at the grain boundaries, which directly improves the thermoelectric quality factor and ultimately the figure-of-merit zT. In some cases, however, such as in Mg 3 Sb 2 , SnSe, and Mg 2 Si an opposite trend is found where higher lattice thermal conductivity reported in small grain polycrystalline material than in large grain or single crystal materials. This unphysical result indicates a problem with the conventional use of the Wiedemann–Franz law. Here, we trace this problematic finding to the electrical resistance at the grain boundaries, which leads to an overestimation of the phonon or lattice contribution of the thermal conductivity κ L . In materials with significant grain boundary electrical resistance, the estimated electronic contribution to the thermal conductivity LσT is low because the measured electrical conductivity σ is low. However within the grain electrons may still be transporting more heat than the total conductivity suggests, leading to an overestimation of κ L if the conventional κ L = κ – LσT is used with the measured values of κ and σ. Here, the overestimation of κL in small-grain samples is shown to be pervasive across a broad range of thermoelectric materials, including Mg 3 Sb 2 , Mg 2 Si, PbTe, PbSe, SnSe, (Hf,Zr)CoSb, CoSb 3 , and Bi 2 Te 3 alloys, and a correction is necessary to properly understand and predict their charge and heat transport.

36 MATERIALS SCIENCE↗

Laboratory studies of baroclinic instability at small Richardson number

As part of the support program for the Atmospheric General Circulation Experiment, laboratory studies of baroclinic and other convective instabilities were performed for a thin layer of fluid between thermally conducting horizontal discs. There were three types of modes identified. The first has a spiral-arm appearance, and exists for large enough horizontal thermal forcing, weak enough static stability, and large enough rotation. The source of this wave is shown to be the Eady mode of instability. The second mode is due to convective instability in the thermal boundary layers which exist due to the thermally conducting horizontal boundaries. Finally, for strong enough negative static stability, thermal convection of the Benard type appears. The most significant result is that the symmetric (Solberg) mode was not found, even though the infinite-plane theory predicts this mode under certain experimental conditions.

Miller, T. L.↗

Thermomechanics coupling to Monte Carlo particle transport on unstructured mesh geometries using Cardinal

Geometry deformation due to thermal expansion influences neutron transport in many systems. Studying this phenomenon involves coupling models for neutronics, thermal hydraulics, and solid mechanics. To enable high fidelity modeling of these coupled physics, new capabilities were introduced in Cardinal, coupling OpenMC Monte Carlo particle transport models with MOOSE thermomechanical physics on unstructured moving-mesh geometries. In this work, we present a fully open-source capability leveraging on-the-fly mesh skinning to automatically regenerate OpenMC geometry, which allows multiphysics feedback from temperature, density, and geometry changes. The new capability is verified using an analytic benchmark slab problem, which couples S 2 neutron transport with thermal conduction, convective boundary conditions, Doppler-broadened cross sections, and nonlinear thermal expansion effects along the heated slab. Cardinal reproduces the analytic solutions for the neutron flux, heating, k eff , and temperature with demonstrated convergence in various error terms including mesh resolution and cross section temperature library spacing. For the nominal benchmark conditions and with a fine mesh, maximum relative errors for neutron flux, temperature, and heating are lower than 1%, while errors in integral quantities such as k eff and slab length are within 1 pcm and 48 µm, respectively. This work (i) presents a new numerical approach to thermomechanics coupling with OpenMC models, (ii) is the first (to our knowledge) to utilize a mechanical partial differential equation (PDE) solution to solve the (Griesheimer and Kooreman, 2022) analytic benchmark, and (iii) develops this verified capability within an open-source package.

97 - MATHEMATICS AND COMPUTING↗

Uncertainty Determination for Aeroheating in Uranus and Saturn Probe Entries by the Monte Carlo Method

The 2013-2022 Decaedal survey for planetary exploration has identified probe missions to Uranus and Saturn as high priorities. This work endeavors to examine the uncertainty for determining aeroheating in such entry environments. Representative entry trajectories are constructed using the TRAJ software. Flowfields at selected points on the trajectories are then computed using the Data Parallel Line Relaxation (DPLR) Computational Fluid Dynamics Code. A Monte Carlo study is performed on the DPLR input parameters to determine the uncertainty in the predicted aeroheating, and correlation coefficients are examined to identify which input parameters show the most influence on the uncertainty. A review of the present best practices for input parameters (e.g. transport coefficient and vibrational relaxation time) is also conducted. It is found that the 2(sigma) - uncertainty for heating on Uranus entry is no more than 2.1%, assuming an equilibrium catalytic wall, with the uncertainty being determined primarily by diffusion and H(sub 2) recombination rate within the boundary layer. However, if the wall is assumed to be partially or non-catalytic, this uncertainty may increase to as large as 18%. The catalytic wall model can contribute over 3x change in heat flux and a 20% variation in film coefficient. Therefore, coupled material response/fluid dynamic models are recommended for this problem. It was also found that much of this variability is artificially suppressed when a constant Schmidt number approach is implemented. Because the boundary layer is reacting, it is necessary to employ self-consistent effective binary diffusion to obtain a correct thermal transport solution. For Saturn entries, the 2(sigma) - uncertainty for convective heating was less than 3.7%. The major uncertainty driver was dependent on shock temperature/velocity, changing from boundary layer thermal conductivity to diffusivity and then to shock layer ionization rate as velocity increases. While radiative heating for Uranus entry was negligible, the nominal solution for Saturn computed up to 20% radiative heating at the highest velocity examined. The radiative heating followed a non-normal distribution, with up to a 3x variation in magnitude. This uncertainty is driven by the H(sub 2) dissociation rate, as H(sub 2) that persists in the hot non-equilibrium zone contributes significantly to radiation.

Palmer, Grant↗

Wide‐Field Bond Quality Evaluation Using Frequency Domain Thermoreflectance with Deep Neural Network Feature Reconstruction

Heterogeneous integration of microelectronic components provides a pathway to improve circuit/component performance; however, this comes with assembly challenges, in particular due to complex interfaces via subsurface bump bonds. The ability of these bonds to transmit electrical signals and conduct heat to the carrier substrate limits component performance. In this work, hyperspectral frequency‐domain thermoreflectance (FDTR) imaging is demonstrated as a robust technique for evaluating the quality of subsurface indium bump bonds in a surrogate microelectronic sample. By performing microscale FDTR imaging with coarse motion image stitching, thermal phase maps that cover a 4 mm by 4 mm field‐of‐view with subsurface feature sensitivity at depths greater than 50 µm are obtained. The resulting FDTR hyperspectral data contains more than three million pixels and reveal the quality of subsurface microbump arrays. Wide‐field analysis of bonded versus gap regions is enabled by deep neural network feature reconstruction, that after training, rapidly provides an interpretable representation of bond quality. Utility of noisy higher frequency FDTR phase maps, i.e., near the computationally predicted sensing depth limit, results in an average prediction error of 11%. Taken together, FDTR with neural network‐based analysis demonstrates subsurface bond monitoring at length scales relevant for heterogeneously integrated microelectronics.

FDTR↗

Enhancing Thermal Transport in Polymeric Composites Via Engineered Noncovalent Filler–Polymer Interactions

Understanding thermal transport mechanisms in polymeric composites allows us to expand the boundaries of thermal conductivity in them, either increasing it for more efficient heat dissipation or decreasing it for better thermal insulation. But, these mechanisms are not fully understood. Systematic experimental investigations remain limited. Practical strategies to tune the interfacial thermal resistance (ITR) between fillers and polymers and the thermal conductivity of composites remain elusive. Here, we studied the thermal transport in representative polymer composites, using polyethylene (PE) or polyaniline (PANI) as matrices and graphite as fillers. PANI, with aromatic rings in its backbone, interacts with graphite through strong noncovalent π–π stacking interactions, whereas PE lacks such interactions. We can then quantify how π–π stacking interactions between graphite and polymers enhance thermal transport in composites. PE/graphite and PANI/graphite composites with the same 1.5% filler volume fractions show a ∼22.82% and ∼34.85% enhancement in thermal conductivity compared to pure polymers, respectively. Calculated ITRs in PE/graphite and PANI/graphite are ~6 x 10 -8 m 2 KW -1 and ~1 x 10 -8 m 2 KW -1 , respectively, highlighting how π–π stacking interactions reduce ITR. Molecular dynamics (MD) simulations suggest that π–π stacking interactions between PANI chains and graphite surfaces enhance alignment of PANI's aromatic rings with graphite surfaces. This allows more carbon atoms from PANI chains to interact with graphite surfaces at a shorter distance compared to PE chains. Finally, our work indicates that tuning the π–π stacking interactions between polymers and fillers is an effective approach to reduce the ITR and enhance the thermal conductivity of composites.

atoms↗

Defects vibrations engineering for enhancing interfacial thermal transport in polymer composites

To push upper boundaries of thermal conductivity in polymer composites, understanding of thermal transport mechanisms is crucial. Despite extensive simulations, systematic experimental investigation on thermal transport in polymer composites is limited. To better understand thermal transport processes, we design polymer composites with perfect fillers (graphite) and defective fillers (graphite oxide), using polyvinyl alcohol (PVA) as a matrix model. Measured thermal conductivities of ~1.38 ± 0.22 W m -1 K -1 in PVA/defective filler composites is higher than those of ~0.86 ± 0.21 W m -1 K -1 in PVA/perfect filler composites, while measured thermal conductivities in defective fillers are lower than those of perfect fillers. We identify how thermal transport occurs across heterogeneous interfaces. Thermal transport measurements, neutron scattering, quantum mechanical modeling, and molecular dynamics simulations reveal that vibrational coupling between PVA and defective fillers at PVA/filler interfaces enhances thermal conductivity, suggesting that defects in polymer composites improve thermal transport by promoting this vibrational coupling.

42 ENGINEERING↗

Overturn of magma ocean ilmenite cumulate layer: Implications for lunar magmatic evolution and formation of a lunar core

We explore a model for the chemical evolution of the lunar interior that explains the origin and evolution of lunar magmatism and possibly the existence of a lunar core. A magma ocean formed during accretion differentiates into the anorthositic crust and chemically stratified cumulate mantle. The cumulative mantle is gravitationally unstable with dense ilmenite cumulate layers overlying olivine-orthopyroxene cumulates with Fe/Mg that decreases with depth. The dense ilmenite layer sinks to the center of the moon forming the core. The remainder of the gravitationally unstable cumulate pile also overturns. Any remaining primitive lunar mantle rises to its level of neutral buoyancy in the cumulate pile. Perhaps melting of primitive lunar mantle due to this decompression results in early lunar Mg-rich magmatism. Because of its high concentration of incompatible heat producing elements, the ilmenite core heats the overlying orthopyroxene-bearing cumulates. As a conductively thickening thermal boundary layer becomes unstable, the resulting mantle plumes rise, decompress, and partially melt to generate the mare basalts. This model explains both the timing and chemical characteristics of lunar magmatism.

Hess, P. C.↗

Thermal conductivity and its relation to atomic structure for symmetrical tilt grain boundaries in silicon

We perform a systematic study of thermal resistance and conductance of tilt grain boundaries (GBs) in Si using classical molecular dynamics. The GBs studied are naturally divided into three groups according to the structural units forming the GB core. In this work we find that, within each group, the GB thermal conductivity strongly correlates with the excess GB energy. All three groups predict nearly the same GB conductivity extrapolated to the high-energy limit. This limiting value is close to the thermal conductivity of amorphous Si, suggesting similar heat transport mechanisms. While the lattice thermal conductivity decreases with temperature, the GB conductivity slightly increases. However, at high temperatures it turns over and starts decreasing if the GB structure undergoes a premelting transformation. Analysis of vibrational spectra of GBs resolved along different directions sheds light on the mechanisms of their thermal resistance. The existence of alternating tensile and compressive atomic environments in the GB core gives rise to localized vibrational modes, frequency gaps creating acoustic mismatch with lattice phonons, and anharmonic vibrations of loosely bound atoms residing in open atomic environments.

36 MATERIALS SCIENCE↗

Multiscale Modeling of Grain Boundaries in ZrB2: Structure, Energetics, and Thermal Resistance

A combination of ab initio, atomistic and finite element methods (FEM) were used to investigate the structures, energetics and lattice thermal conductance of grain boundaries for the ultra high temperature ceramic ZrB2. Atomic models of idealized boundaries were relaxed using density functional theory. Information about bonding across the interfaces was determined from the electron localization function. The Kapitza conductance of larger scale versions of the boundary models were computed using non-equilibrium molecular dynamics. The interfacial thermal parameters together with single crystal thermal conductivities were used as parameters in microstructural computations. FEM meshes were constructed on top of microstructural images. From these computations, the effective thermal conductivity of the polycrystalline structure was determined.

Lawson, John W.↗

A direct approach to finding unknown boundary conditions in steady heat conduction

The capability of the boundary element method (BEM) in determining thermal boundary conditions on surfaces of a conducting solid where such quantities are unknown was demonstrated. The method uses a non-iterative direct approach in solving what is usually called the inverse heat conduction problem (IHCP). Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on a surface where such data is readily available, the algorithm computes the temperature field within the object and any unknown thermal boundary conditions on surfaces where thermal boundary values are unavailable. A two-dimensional, steady-state BEM program was developed and was tested on several simple geometries where the analytic solution was known. Results obtained with the BEM were in excellent agreement with the analytic values. The algorithm is highly flexible in treating complex geometries, mixed thermal boundary conditions, and temperature-dependent material properties and is presently being extended to three-dimensional and unsteady heat conduction problems. The accuracy and reliability of this technique was very good but tended to deteriorate when the known surface conditions were only slightly over-specified and far from the inaccessible surface.

Martin, Thomas J.↗

Martian thermal boundary layers: Subhourly variations induced by radiative-conductive heat transfer within the dust-laden atmosphere-ground system

Radiative-conductive heat transfer has been investigated for the ground-atmosphere system of the planet Mars. The basic goal was the quantitative determination of time dependent vertical distributions of temperature and static stability for Southern-Hemispheric summer season and middle and polar latitudes, for both dust-free and dust-laden atmospheric conditions. The numerical algorithm which models at high spatial and temporal resolution the thermal energy transports in the dual ground-atmosphere system, is based on solution of the applicable heating rate equation, including radiative and molecular-conductive heat transport terms. The two subsystems are coupled by an internal thermal boundary condition applied at the ground-atmosphere interface level. Initial data and input parameters are based on Mariner 4, 6, 7, and 9 measurements and the JPL Mars Scientific Model. Numerical experiments were run for dust-free and dust-laden conditions in the midlatitudes, as well as ice-free and ice-covered polar regions. Representative results and their interpretation are presented. Finally, the theoretical framework of the generalized problem with nonconservative Mie scattering and explicit thermal-convective heat transfer is formulated, and applicable solution algorithms are outlined.

Pallmann, A. J.↗

The influence of boundary and edge-plasma modeling in computations of axisymmetric vertical displacement

A number of previously published studies apply extended-MHD computations to model macroscopic dynamics of tokamak vertical displacement events (VDEs). The characteristic plasma-wall contact and resistive-wall diffusion imply sensitivity to boundary conditions in a general sense, but which conditions have significant influence depends on how the plasma is modeled. This work examines these dependencies by comparing results of axisymmetric extended-MHD computations with different sets of boundary conditions, plasma thermal-conduction models, and wall resistivity values. The geometry and plasma parameters of the computations represent a modest-sized tokamak. The forced-displacement scenario and computational setup are similar to those used in previous 3D computations. The results show that for a given wall resistivity, the VDE time-scale is most sensitive to variations in the boundary and thermal-conduction parameters that affect electron thermal transport. The electrical conductivity depends on electron temperature, and the dependence on thermal transport stems from its influence on the electrical circuit that includes the open-field halo current. Lastly, conditions that lead to hotter, broader halo regions slow the evolution. Significant sensitivity to the boundary condition on plasma flow-velocity exists when electron thermal conduction is restricted and electron energy loss is convective, which is expected for conditions at the entrance of the magnetic presheath.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ThermoPI—an Online Tool to Calculate Heat Transfer Through Foam Insulation

Thermal insulation materials with ultra-low effective thermal conductivity are crucial for a multitude of applications. Over the years, a significant amount of experimental work has been dedicated to creating new insulation materials with low thermal conductivity. Similarly, substantial efforts have been made to enhance the theoretical understanding of thermal transport mechanisms in thermal insulation materials and to push the boundaries of lower thermal conductivity. However, ample room remains for enhancing the thermal resistivity of closed-cell foam insulations. To aid in the development of ultra-low effective thermal conductivity foam insulations, Oak Ridge National Laboratory has introduced a unique online tool, ThermoPI. This tool calculates not only the effective thermal conductivity but also the thermal conductivity components for porous materials, including gases, solids, and radiative, based on the materials’ structural information (e.g., porosity, pore size, gas species, pressure, solid species, pore geometry, and temperature).This tool collected and improved the existing theoretical models for thermal insulation materials’ gas, solid, and radiative thermal conductivity. These improved models have been validated with experimental data. Effective medium theory and sound velocity softening effects are considered for solid thermal conductivity. The built-in solid materials include polystyrene, polyurethane, polyethylene, and silica. Users are allowed to input new solid materials that are not built inside the tool. For gas thermal conductivity, the subcontinuum Knudsen effect is considered. In addition to several built-in gases, users can input new gases. For solid and radiative thermal conductivity calculations, several models are available to select, and the tool can determine the best model to choose based on the materials that users input. Users are also allowed to change selections manually. In addition, the tool can also calculate the effect of interfacial resistance on the overall thermal conductivity of layered materials. This work will elaborate on the tool and discuss how it can guide the development of new insulation products.

Shrestha, Som [ORNL] (ORCID:0000000183993797)↗

Effect of wall temperature spatial variations on aerodynamic heating to an actively cooled aircraft

The design of cooled skin panels, which requires consideration of many parameters such as heat load, skin thickness, panel size, tube spacing, tube size, temperature limits, coolant flow, etc., must minimize weight and thermal stresses. A design procedure for such panels has been developed by Bell Aerospace Company (Helenbrook and Anthony, 1971). This design procedure assumes a uniform heating rate to the panel, i.e., the variation of aerodynamic heating rate due to the cyclic wall temperature distribution, which results from the discrete coolant tube locations in such a panel, has been neglected. This study was made to determine if these variations were sufficiently large to cause variations in aerodynamic heating rate which would require coupling of boundary layer and conductive thermal analysis solutions.

Jones, R. A.↗