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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 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Exploring for Superhot Geothermal Targets in Magmatic Settings: 2022 Field Campaign at Newberry Volcano

This paper presents preliminary results from a subset of work carried out as part of a multinational research project entitled DErisking Exploration for multiple geothermal Plays in magmatic ENvironments (DEEPEN), supported by the U.S. Department of Energy (DOE) and Geothermica, a joint effort by EU member states and associated countries. The DEEPEN project will develop a customized approach to exploration for supercritical and superhot geothermal plays in magmatic systems, which will be applied to two demonstration sites. This paper summarizes field activities carried out at the U.S. demonstration site, Newberry Volcano in central Oregon. The objective of this work effort is to refine the subsurface model of Newberry Volcano, with special focus on deeper zones including the magmatic plumbing system and other key geologic elements. New data collection included gravity and wideband magnetotelluric (MT) surveys, as well as reinstallation of a seismic network. The National Renewable Energy Laboratory (NREL) and Enthalpion Energy LLC (Enthalpion) worked with the Deschutes National Forest Fort Rock District to use a low ground disturbance method of MT deployment to collect MT data inside the caldera and other restricted areas inside the National Volcanic Monument. This opened these areas to geophysical exploration for the first time in decades. Sites along and adjacent to the south rim of the volcano constituted the primary survey objectives. A team from Lawrence Berkeley National Laboratory (LBNL), the U.S. Geological Survey (USGS), and AltaRock also began the process of reinstalling the seismic network from the AltaRock enhanced geothermal system (EGS) demonstration in anticipation of further development activities at the site. The data ingestion, reduction, and analysis phase of the project is ongoing. We are currently processing the MT and gravity data and are developing a new, highly GPU-accelerated, 3D joint MT and gravity inversion to better localize the south rim/south flank conductive target and better understand its relationship to deep heat, fluid sources, and surface extrusive features. Joint inversions, which have not yet been undertaken at Newberry, will allow us to obtain constraints on the geologic model that cannot be determined from each method in isolation, improving our ability to image key geologic features at depth.

geophysics↗
NASA NTRS2008

Aerothermodynamic Testing and Boundary Layer Trip Sizing of the HIFiRE Flight 1 Vehicle

An experimental wind tunnel test was conducted in the NASA Langley Research Center s 20-Inch Mach 6 Air Tunnel in support of the Hypersonic International Flight Research Experimentation Program. The information in this report is focused on the Flight 1 configuration, the first in a series of flight experiments. This report documents experimental measurements made over a range of Reynolds numbers and angles of attack on several scaled ceramic heat transfer models of the Flight 1 payload. Global heat transfer was measured using phosphor thermography and the resulting images and heat transfer distributions were used to infer the state of the boundary layer on the vehicle windside and leeside surfaces. Boundary layer trips were used to force the boundary layer turbulent, and a brief study was conducted to determine the effectiveness of the trips with various heights. The experimental data highlighted in this test report were used to size and place the boundary layer trip for the flight test vehicle.

Berger, Karen T.↗
NASA NTRSDate not supplied

Plans for Ice Crystal Icing Tests Using a 3D Heated Test Article at the NASA Icing Research Tunnel

This presentation describes the plans for ice crystal icing and supercooled water icing tests to be conducted in Fall/Winter 2021 at the NASA Icing Research Tunnel. A test article, whose geometry is representative of an inter-compressor duct and strut region of a turbofan engine, has been designed and fabricated for the study of ice crystal icing physics tests. The Simulated Inter-compressor Duct Research Model (SIDRM) will have the ability to heat surfaces to simulate the warm surfaces of the inter-compressor duct within an engine. The test article is instrumented with heaters, heat flux gauges, thermocouples, and pressure taps to measure icing behavior. The aim of these tests is to generate ice shapes on the SIDRM test article under well-characterized conditions. The results of the testing with the SIDRM model will be used to provide icing physics and validation data for development of the engine icing simulation capabilities in GlennICE, the 3D ice prediction tool. This is intended to be a presentation only, and does not have an accompanying paper.

ice-crystal icing↗
NASA NTRS2009

Aerothermodynamic Characteristics of Boundary Layer Transition and Trip Effectiveness of the HIFiRE Flight 5 Vehicle

An experimental wind tunnel test was conducted in the NASA Langley Research Center s 20-Inch Mach 6 Tunnel in support of the Hypersonic International Flight Research Experimentation Program. The information in this report is focused on the Flight 5 configuration, one in a series of flight experiments. This report documents experimental measurements made over a range of Reynolds numbers and angles of attack on several scaled ceramic heat transfer models of the Flight 5 vehicle. The heat transfer rate was measured using global phosphor thermography and the resulting images and heat transfer rate distributions were used to infer the state of the boundary layer on the windside, leeside and side surfaces. Boundary layer trips were used to force the boundary layer turbulent, and a study was conducted to determine the effectiveness of the trips with various heights. The experimental data highlighted in this test report were used determine the allowable roughness height for both the windside and side surfaces of the vehicle as well as provide for future tunnel-to-tunnel comparisons.

Berger, Karen T.↗
DOE OSTI2025

Fitness for Service Assessment of a Corroded Heat Exchanger

Fermilab s Main Injector Accelerator has used shell & tube heat exchangers to cool various beamline components since its construction in the late 1990s. Many of the heat exchangers still around today are original to the machine. Untreated pond water has been used to exchange heat with the Low Conductivity Water. Throughout the lifetime of Fermilab s heat exchangers, they have undergone significant material degradation in the carbon steel end channels due to corrosion. Wall thickness measurements (per API 510) of each heat exchanger were used to generate a 3D model of the corroded surfaces. In order to continue their safe and reliable operation, ASME FFS-1/API 579 (Fitness-For-Service) was implemented to address their integrity. The assessments consisted of finite element analysis techniques outlined in ASME Section VIII Div. 2 (design by analysis methods for pressure vessels), in accordance with the requirements of ASME FFS-1 Part 4: General Metal Loss, Part 5: Local Metal Loss, and Part 9: Crack Like Flaws. The assessments concluded that each heat exchanger is coined Fit For Service . The Fitness-For-Service standard offers a unique opportunity to facilities and institutions within the DOE National Lab complex to properly and safely assess the integrity of aging equipment necessary to conduct science and research. This poster demonstrates the assessment process and techniques used to determine the heat exchangers are fit for service.

Humenik, Alex [Fermilab]↗
DOE OSTI2023

Wide-range continuous tuning of the thermal conductivity of La0.5Sr0.5CoO3-δ films via room-temperature ion-gel gating

Abstract Solid-state control of the thermal conductivity of materials is of exceptional interest for novel devices such as thermal diodes and switches. Here, we demonstrate the ability to continuously tune the thermal conductivity of nanoscale films of La 0.5 Sr 0.5 CoO 3- δ (LSCO) by a factor of over 5, via a room-temperature electrolyte-gate-induced non-volatile topotactic phase transformation from perovskite (with δ ≈ 0.1) to an oxygen-vacancy-ordered brownmillerite phase (with δ = 0.5), accompanied by a metal-insulator transition. Combining time-domain thermoreflectance and electronic transport measurements, model analyses based on molecular dynamics and Boltzmann transport equation, and structural characterization by X-ray diffraction, we uncover and deconvolve the effects of these transitions on heat carriers, including electrons and lattice vibrations. The wide-range continuous tunability of LSCO thermal conductivity enabled by low-voltage (below 4 V) room-temperature electrolyte gating opens the door to non-volatile dynamic control of thermal transport in perovskite-based functional materials, for thermal regulation and management in device applications.

42 ENGINEERING↗
NASA NTRS2010

Lunar Surface Stirling Power Systems Using Isotope Heat Sources

For many years, NASA has used the decay of plutonium-238 (Pu-238) (in the form of the General Purpose Heat Source (GPHS)) as a heat source for Radioisotope Thermoelectric Generators (RTGs), which have provided electrical power for many NASA missions. While RTGs have an impressive reliability record for the missions in which they have been used, their relatively low thermal to electric conversion efficiency and the scarcity of plutonium-238 (Pu-238) has led NASA to consider other power conversion technologies. NASA is considering returning both robotic and human missions to the lunar surface and, because of the long lunar nights (14.75 Earth days), isotope power systems are an attractive candidate to generate electrical power. NASA is currently developing the Advanced Stirling Radioisotope Generator (ASRG) as a candidate higher efficiency power system that produces greater than 160 W with two GPHS modules at the beginning of life (BOL) (~32% efficiency). The ASRG uses the same Pu-238 GPHS modules, which are used in RTG, but by coupling them to a Stirling convertor provides a four-fold reduction in the number of GPHS modules. This study considers the use of americium-241 (Am-241) as a substitute for the Pu-238 in Stirling- convertor-based Radioisotope Power Systems (RPS) for power levels from tens of watts to 5 kWe. The Am-241 is used as a substitute for the Pu-238 in GPHS modules. Depending on power level, different Stirling heat input and removal systems are modeled. It was found that substituting Am-241 GPHS modules into the ASRG reduces power output by about one-fifth while maintaining approximately the same system mass. In order to obtain the nominal 160 W of electrical output of the Pu-238 ASRG requires 10 Am-241 GPHS modules. Higher power systems require changing from conductive coupling heat input and removal from the Stirling convertor to either pumped loops or heat pipes. Liquid metal pumped loops are considered as the primary heat transportation on the hot end and water pumped loop/heat pipe radiator is considered for the heat rejection side for power levels above 1 kWe.

Schmitz, Paul C.↗
NASA NTRSDate not supplied

Material Characterization and Modeling of Room Temperature Vulcanizing Silicone

Room Temperature Vulcanizing silicone (RTV) is a high-temperature adhesive that has successfully been used as a gap-filler between Thermal Protection System (TPS) tiles for heatshields on numerous missions. It is also used to bond instrumentation plugs such as temperature and pressure sensors into the heatshields. While RTV has been traditionally assumed to be a non-porous and non-ablating material, numerous experiments have shown that RTV pyrolyzes and becomes highly porous as it is heated. Heating RTV has also shown swelling, or intumescence, which can pose unique problems that lead to roughness induced boundary-layer transition, surface oxide formation and contamination of heat shield sensors. Therefore, it is crucial to understand and model the intumescence phenomenon of RTV. As data for RTV material properties is limited, the first step in modeling RTV is to collect material properties such as pyrolysis mass-loss, microstructure change, virgin and char porosity, etc. which was performed in our initial study. Additionally, thermomechanical properties such as Young’s modulus and Poisson ratio are required for modeling the intumescence of RTV, which were taken from literature and the coefficient of thermal expansion was collected using in-situ heating and Micro Computed Tomography (µ-CT) in previous studies. Finally, numerous other properties such as pyrolysis gas properties, virgin and char thermal conductivity and specific heat were compiled from previous experiments and literature into a material database that can be used for simulations. In Porous Material Analysis Toolbox based on OpenFOAM (PATO) [4], structural mechanics coupled with material response was used for simulating the intumescence of RTV as it is heated. However, since the permeability of the material is very low, the pyrolysis gas creates an internal pressure build-up as the material is being heated, significantly contributing to the deformation of the material. To correctly characterize this phenomenon, additional physics models were implemented into PATO's stress analysis solver, and results were compared with RTV dilatometry test data as a preliminary verification case. Future work will include experiments of RTV at the Plasmatron X facility and the in-situ heating cell with µ-CT, and improvement of simulation tools to more accurately model RTV intumescence.

TPS↗
NASA NTRSDate not supplied

Material Properties and Modeling of Room Temperature Vulcanizing Silicone

Room Temperature Vulcanizing silicone (RTV) is a high-temperature adhesive that has successfully been used as a gap-filler between Thermal Protection System (TPS) tiles for heatshields on numerous missions. It is also used to bond instrumentation plugs such as temperature and pressure sensors into the heatshields. While RTV has been traditionally assumed to be a non-porous and non-ablating material, numerous experiments have shown that RTV pyrolyzes and becomes highly porous as it is heated. Heating RTV has also shown swelling, or intumescence, which can pose unique problems that lead to roughness induced boundary-layer transition, surface oxide formation and contamination of heat shield sensors. Therefore, it is crucial to understand and model the intumescence phenomenon of RTV. As data for RTV material properties is limited, the first step in modeling RTV is to collect material properties such as pyrolysis mass-loss, microstructure change, virgin and char porosity, etc. which was performed in our initial study. Additionally, thermomechanical properties such as Young’s modulus and Poisson ratio are required for modeling the intumescence of RTV, which were taken from literature and the coefficient of thermal expansion was collected using in-situ heating and Micro Computed Tomography (µ-CT) in previous studies. Finally, numerous other properties such as pyrolysis gas properties, virgin and char thermal conductivity and specific heat were compiled from previous experiments and literature into a material database that can be used for simulations. In Porous Material Analysis Toolbox based on OpenFOAM (PATO) [4], structural mechanics coupled with material response was used for simulating the intumescence of RTV as it is heated. However, since the permeability of the material is very low, the pyrolysis gas creates an internal pressure build-up as the material is being heated, significantly contributing to the deformation of the material. To correctly characterize this phenomenon, additional physics models were implemented into PATO's stress analysis solver, and results were compared with RTV dilatometry test data as a preliminary verification case. Future work will include experiments of RTV at the Plasmatron X facility and the in-situ heating cell with µ-CT, and improvement of simulation tools to more accurately model RTV intumescence.

PATO↗
NASA NTRS1961

Local Aerodynamic Heat Transfer and Boundary-Layer Transition on Roughened Sphere-Ellipsoid Bodies at Mach Number 3.0

A wind-tunnel investigation was made to determine heat-transfer distributions on three steel sphere-ellipsoid bodies with surface roughnesses of 5, 100, and 200 microinches. Tests were conducted in the Langley 9- by 6-foot thermal structures tunnel at a Mach number of 3.0, free-stream Reynolds numbers (based on model spherical diameter) of 4.25 x 10(exp 6) and 2.76 x l0(exp 6), and at a stagnation temperature of 650 F. Pressure distributions were obtained also on a fourth model. The results indicated that the combination of surface roughness and boundary-layer cooling tended to promote early transition and nullify the advantages attributable to the blunt shape of the model for reducing local temperatures. Good correlation between experimental heating rates and those calculated from laminar theory was achieved up to the start of boundary-layer transition. The correlation also was good with the values predicted by turbulent theory for surface stations downstream from the 45 deg. station.

Deveikis, William D.↗
NASA NTRSDate not supplied

Icing Physics Studies Using the 3D SIDRM Test Article: Aerodynamic and Supercooled Liquid Icing Analysis

In-flight icing is an important safety issue and is a factor that affects aircraft design and performance. Newer regulations are driving a need for improvements in airframe and engine icing simulation capability. Experimental data is required for development of icing physics models and simulation validation. To that end, this paper presents the analysis of the supercooled liquid icing data subset from tests conducted in 2022 at the NASA Icing Research Tunnel that studied both supercooled water and ice-crystal icing. The test article that was utilized replicated 3D geometrical features of an inter-compressor duct and strut region of a turbofan engine. The surfaces of the Simulated Inter-compressor Duct Research Model (SIDRM) can be heated to simulate the warm surfaces of the turbofan inter-compressor duct. The test article is instrumented with pressure taps, heaters, heat flux gauges, and thermocouples, while a 3D laser scanner, cameras, and a scale to measure ice mass were utilized to characterize the icing behavior. The aim of these tests was to generate ice accretions on the SIDRM test article under well-characterized supercooled liquid icing and ice crystal icing conditions. This paper discusses measurements related to aerodynamic testing and supercooled liquid icing tests that were conducted. Aerodynamic measurements were analyzed and compared to computational simulations and were found to be in good agreement for the range of airspeeds (50 to 230 knots) and angles of attack (0 to 4°) tested. Various parametric sweeps were conducted during the supercooled liquid icing portion of the test entry (cloud median volumetric diameter ranged from 15 to 90 µm, total air temperature from -3 to -17 °C, angle of attack from 0 to 4°, and accretion time from 5 to 20 min). These sweeps were performed to measure that parameter’s impact on ice accretion size, location (icing extent), characteristics (such as glaze/rime ice and shedding behavior), and test article surface temperature. Analysis of the test data showed that clouds composed of larger drops, colder air temperatures, smaller angles of attack, and longer spray times were the primary parameters that resulted in accretions with greater ice mass. Test article angle of attack and cloud droplet size influenced the location of ice accretion as these two parameters directly impact collection efficiency. With respect to icing characteristics, total air temperature dictated icing type, and smaller cloud drop size along with warmer air temperatures resulted in greater amounts of ice shedding. Surface temperature increased during ice accretion from the release of latent (fusion) heat, where total air temperature and cloud drop size impacted the amount of surface temperature change. The icing measurements collected during the SIDRM tests will be used to develop and validate 3D computational engine icing tools, such as GlennICE, that predictively assesses the onset and growth of ice. One of the goals of the sponsoring NASA project is to develop simulation models and tools that can assist in the design and certification of engines for flight in icing conditions in a cost effective way.

supercooled liquid icing↗
DOE OSTI2020

NMDQi Thermal-hydraulic Optimization, Analysis, and Scoping Tool (TOAST)

The Thermal-hydraulic Optimization, Analysis, and Scoping Tool (TOAST) is developed to support the thermal-hydraulic aspects for the design of optimal irradiation vehicles for the Nuclear Materials Discovery and Qualification initiative (NMDQi). TOAST is currently a MATLAB-based tool that utilizes a simplified steady-state analytical model where a radial thermal resistance circuit is utilized to account for conduction through up to 2 capsules, a gas gap, a thermal bond, a sample cladding, and a sample, as well as the convection from a water coolant outside the capsules. The geometry is discretized axially along the user-defined height of a basket with a user-defined number of points/nodes, essentially turning TOAST into a semi-2D heat transfer analysis utility for cylindrical irradiation vehicles with practically any configuration, solving for temperatures radially at multiple axial locations. TOAST utilizes a Graphical User Interface (GUI) in-which a user can define the geometrical layout, the materials utilized for each component, the coolant characteristics, and the required solution. The user can define the geometry by inputting the diameters, thicknesses, and heights for each component, whereas the materials are defined via the user-provided constant or variable thermal conductivities. The user can select the coolant's inlet temperature, pressure, and the pressure drop across the height of the problem (which is used to calculate the velocity of the flow). Finally, the user can choose to solve for a sample heat generation rate limit by inputting temperature limits for the sample and capsules or can choose to purely solve for the axial temperature distributions of each component by inputting a pre-selected heat generation rate. Either way, TOAST provides the user with axial temperature distributions of all the components including the coolant, and the heat generation rate limit as well as the maximum outlet coolant temperature. The user can also choose to do one of 6 sensitivity analyses in TOAST. The sensitivity analyses yield plots of the sensitivity of the heat generation rate limit, the maximum coolant temperature, and the pressure limit for the annular components due to perturbations in 1-2 unknown variables based on the selected sensitivity analysis. Benchmarks between computations in TOAST and equivalent 2D axis symmetric ABAQUS models are presented, showing that TOAST results are within less than 3% of ABAQUS results in most cases, and a maximum of 8% difference in some cases. The benchmarks also revealed that this uncertainty is tied to the selection of an appropriate Nusselt number correlation and appropriate thermal conductivities, which the user can do from the GUI. Regardless, TOAST is demonstrated as a computationally efficient, highly accessible, and accurate utility for optimization and scoping s of studies different irradiation vehicles.

42 ENGINEERING↗
DOE OSTI2020

Falling-film thermosyphons: Application to water harvesting from humid gas streams

Water harvesting from humid gas streams is central to fresh-water production, desalination, and particulate removal from combustion gas streams. Two-phase thermosyphons are well suited for these applications due to their very low thermal resistance, but have several operating limits at the high heat flows required for such applications. This work introduces the falling-film thermosyphon for large-scale condensation applications. Working fluid is pumped to the top of the evaporator to provide the evaporating liquid film on the inner tube wall, rather than by vapor condensation. The flooding, dry-out and pool-boiling limits are eliminated, resulting in significantly higher maximum heat fluxes for the same physical evaporator size. Furthermore, the condenser no longer needs to be located vertically above the evaporator, which allows for a standard steam condenser to be used. A model for the condensation process in humid air was developed that estimates the fluid and heat transfer and is confirmed experimentally. Further benefits include the use of a high-thermal-conductivity polymer material for the evaporator section to minimize corrosion, and the ability to impose a temperature boundary condition on the evaporator, which is made possible due to the elimination of a liquid pool.

42 ENGINEERING↗
DOE OSTI2021

Approach to nonlinear magnetohydrodynamic simulations in stellarator geometry

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-C 1 code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-C 1 . A C 1 coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-C 1 extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approach, including simulations of the heating, destabilization, and equilibration of a stellarator plasma with strongly anisotropic thermal conductivity, and of the relaxation of stellarator equilibria to integrable and non-integrable magnetic field configurations in realistic geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Development of a two-zone zero-dimensional mixing model for actively fueled prechamber engines

In this numerical work, a zero-dimensional, two-zone mixing model was developed and validated to capture the mixture preparation process of an actively fueled prechamber engine. The model was developed for ethanol-gasoline fuel blends but is applicable to various fuels of interest relevant to prechamber applications. The model was exercised to demonstrate the effects of boundary conditions, fuel composition, and residual content on the mixture stoichiometry predictions. The 0D model showed reasonable agreement in prechamber equivalence ratio predictions with higher fidelity computational fluid dynamics modeling, but the accuracy of model was constrained to the governing assumptions of the injection process. The modeling assumptions surrounding the non-dimensional injection of mass into the prechamber were scrutinized to identify key areas of model improvement. The results indicate heat transfer effects play a crucial role in the evaporation of the fuel within the confined auxiliary chamber, especially when considering fuels with high latent heat of vaporization. Additionally, the presence of fuel films that collect on the prechamber surfaces complicated the modeled evaporative cooling loses as the modeling suggests the films evaporate primarily by means of conduction from the boundary. Furthermore, the developed model serves as a simplified framework to generate calibration maps of prechamber fueling or run real time as an open loop control strategy such that desired prechamber mixture proportions are effectively targeted.

Zero-dimensional↗
DOE OSTI2021

Multiscale thermal properties prediction in the Multiphysics Object Oriented Simulation Environment (MOOSE) via a general Boltzmann solver [Poster]

The project objectives were: (1) Engineering-scale fuel performance modeling relies on accurate thermal properties; (2) Thermal properties are inherently multi-scale, arising from atomistic processes and interactions with a material’s microstructure; (3) Heat transport in solids via conduction occurs through transport and scattering of electrons and phonons; (4) Use the Boltzmann transport equation (BTE) to predict the macroscopic behavior of a materials system in terms of the microscopic dynamics of its heat carriers; and (5) This project establishes a new MOOSE (Multiphysics Object Oriented Simulation Environment) module, Boltzmann, dedicated to phonon and thermal electron transport.

36 MATERIALS SCIENCE↗
NASA NTRS1971

Zero-gravity transient thermal mixing simulation

The experimental program described is an outgrowth of independent investigations into alternate redesign concepts for the Apollo SM cryogenic oxygen storage system. The experiments were continued, after the redesign was established, to provide physical insight into transient thermal mixing in zero-gravity and to aid in the characterization of the system performance in flight. Zero-gravity heat transfer and fluid mixing were simulated experimentally through an analogy between unsteady heat conduction and species diffusion. To further support numerical analyses of the cryogenic oxygen storage system, the experimental investigation was extended to include a cubical tank geometry, representative of existing numerical models. In general, the transient flow patterns in the cubical tank are far more complex than those of the spherical tank and the extent of fluid mixing is significantly greater but less repeatable.

Lands, J. F., Jr.↗
NASA NTRS1980

The polarization and directivity of solar-flare hard X-ray bremsstrahlung from a thermal source

The polarization and directivity of hard X-ray bremsstrahlung from a thermal source consisting of a region in which a thermal flux drives a pair of steel collisionless conduction fronts were evaluated. The conduction fronts are symmetrically driven from a central region, heated by the flare energy dissipation process. By comparing results with similar calculations based on a nonthermal thick-target electron beam model of the source, it was aimed to determine the degree to which the observed polarization and directivity of solar flare hard X-rays favor either model. Results which exhibit significant polarization and directivity of the hard X-ray radiation emitted by the source are produced by using Maxwellian electron-phase-space distribution functions modified to take into account a directional heat flux and a steady direct current in the X-ray source, and a fully relativistic treatment of the bremsstrahlung emission process. The results are consistent with solar hard X-ray anisotropy and polarization observations to date, although these observations are too crude to be conclusive.

Emslie, A. G.↗