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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 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Phase-change Reconfigurable Optical WavEfront Synthesis System (PROWESS)

We report the design, fabrication, and testing of electrically tunable metasurface k-space filters based on the low-loss, high-contrast phase-change material GSST and a transparent Si electrode heating architecture. A 10x10 array of PCM elements integrated with Si heaters was fabricated via foundry processes, and used to actively control the crystallinity of a metasurface consisting of GSST nano antennae. By selectively varying the structural state of individual PCM elements, specific k-vectors of transmitted light can effectively be filtered out, resulting in improved imaging quality by reducing the scattered light that reaches a detector. Optimized doping profiles in the Si heaters allow for uniform, low power, reliable and repeatable switching of the GSST state. Compared to other k-space filters, this new architecture is completely transparent to the wavelength of interest and can be actively reconfigured in real time with high performance, low power consumption and a small footprint. The 10x10 array device is a proof-of-concept demonstration that can enable high-resolution arbitrary wavefront synthesis and correction in the future, with key applications in optical communications, beam steering, remote sensing, and adaptive optics.

phase change material↗
DOE OSTI2016

Conceptual System Design of a Supercritical CO{sub 2} cooled Micro Modular Reactor - 18492

Small modular reactor (SMR) concepts proposed in the past have compact size and a longer life reactor core than the conventional nuclear power plants. However, previous concepts based on the water-cooled technologies with a steam Rankine cycle have shown that the complete modularization is still technically challenging. This study suggests an innovative concept of a reactor directly cooled by supercritical carbon dioxide (S-CO{sub 2}) with S-CO{sub 2} Brayton cycle as a power conversion system, namely KAIST MMR (Micro Modular Reactor). To enhance neutron economy and maximize the fuel volume fraction of the core, a uranium carbide fuel controlled by drum type control rods was used in the fast-spectrum MMR. The core has long life (20 years) without refueling or reshuffling as well as inherent safety features. The reactor can be used as a distributed power source, and replace outdated fossil fuel power plants for small cities. Moreover, we propose a S-CO{sub 2} Brayton cycle as a power conversion system to achieve small, high performance and lightweight module. Thanks to the compact core and power conversion system, the entire system can be contained in a single module. The target of the system is to achieve small and compact system that can be transported via ground transportation of a single module containing the core and the power conversion system altogether. In order to meet this target single module s total weight is minimized in the order of 150 tons. The external size of a module is less than 7 m in length and 4 m in diameter. It produces 12 MWe electricity from 36 MWt reactor core. The S-CO{sub 2} Brayton cycle was optimized, and the cycle components were designed while maximizing the performance and minimizing the weight. A passive decay heat removal system utilizing shell and tube heat exchangers was also developed, and examined its performance with transient analysis code. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Modeling Radiolysis and Chemical Reactions during Dry Storage of Aluminum-clad Spent Nuclear Fuel

After aluminum-clad spent nuclear fuel (ASNF) is removed from the reactor, it is initially stored in spent fuel pools, which are specially designed water-filled basins that provide temporary cooling to reduce the temperature of the fuel assemblies and provide radiation shielding. ASNF continues to generate heat due to the radioactive decay of elements within the fuel, which persists for many years post-shutdown as the residual radioactive products decay into more stable elements. During the wet storage period, an oxyhydroxide layer composed of boehmite/bayerite forms on the surfaces of the aluminum cladding from exposure to water in the pools. Road-ready packaging for long-term disposition of the ASNF involves dry storage in helium backfilled DOE standard canisters (DSCs). When the ASNF is removed from water storage and dried, most of the water is removed, but some physisorbed and chemisorbed water remains in the oxyhydroxide layers. This residual water can produce hydrogen when exposed to radiation from the ASNF during dry storage. Predicting hydrogen accumulation over time in the DSCs is critical for long-term storage considerations. Previous modeling efforts have developed coupled computational fluid dynamics (CFD)-chemical models to simulate temperature, pressure, and gas phase concentrations within the DSCs. These models use the thermal field predicted by CFD as input to a radiolysis model for the gas phase and the surface oxyhydroxide layer chemistry. Given the long storage period of the DSCs and the impracticality of long-term experiments, a simulation-based approach is necessary to assess chemical evolution within the canisters. This study advances the development of a modeling framework designed to simulate the chemical evolution of spent fuel canisters. Both thermal and radiation-driven reactions are considered, with radiation kinetics quantified using G-values. Sensitivity analysis identifies key parameters influencing species composition. Reaction pathway diagrams offer insight into dominant species formation routes, enabling more effective comparisons between model predictions and experimental observations, particularly regarding the production of hydrogen. Results show that the model predicts significant hydrogen gas production with minimal oxygen generation, primarily due to hydrogen formation via boehmite pathways. These findings underscore the importance of accurately characterizing surface-bound species and radiolysis kinetics. A deeper understanding of these mechanisms is critical for evaluating the long-term safety of nuclear waste storage.

12 - MGMT OF RADIOACTIVE AND NON-RADIOACTIVE WASTE↗
NASA NTRS1989

A parametric heat transfer study for cryogenic ball bearings in SSME HPOTP

A numerical modeling is to examine the effects of coolant convective heat transfer coefficient and frictional heating on the local temperature characteristics of a ball element in Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP) bearing. The present modeling uses a control-volume based, finite-difference method to solve the non-dimensionalized heat conduction equation in spherical coordinate system. The dimensionless temperature is found as a function of Biot number, heat flux ratio between the two race contacts, and location in the ball. The current results show that, for a given cooling capability, the ball temperature generally increases almost linearly with the heat input from the race-contacts. This increase is always very high at one of the two contacts. An increase in heat transfer coefficient generally reduces the ball temperature and alleviates the temperature gradient, except for the regions very close to the race contacts. For a 10-fold increase of heat transfer coefficient, temperature decrease is 35 percent for the average over entire ball, and 10 percent at the inner-race contact. The corresponding change of temperature gradient displays opposing trends between the regions immediately adjacent to the contacts and the remaining portion of the ball. The average temperature gradient in the vicinity of both contacts increases approximately 70 to 100 percent. A higher temperature gradient produces excessive thermal stress locally which may be detrimental to the material integrity. This, however, is the only unfavorable issue for an increase of heat transfer coefficient.

Chyu, Mingking K.↗
DOE OSTI2018

Development and validation of a three pressure analysis (TPA) GT-Power model of the CFR F1/F2 engine for estimating cylinder conditions

The CFR engine is the widely accepted platform to test standard Research Octane Number (RON) and Motored Octane Number (MON) for determining anti-knock characteristics of motor fuels. With increasing interest in engine downsizing, up-torquing, and alternative fuels for modern spark ignition (SI) engines, there is a need to better understand the conditions that fuels are subjected to in the CFR engine during octane rating. To take into account fuel properties, such as fuel heat of vaporization, laminar flame speed and auto-ignition chemistry; and understand their impacts on combustion knock, it is essential to estimate accurate cylinder conditions. In this study, the CFR F1/F2 engine was modeled using GT-Power with the Three Pressure Analysis (TPA) and the model was validated for different fuels and engine conditions. The finite element cylinder model was applied to better estimate heat transfer and cylinder wall temperatures of the cast iron combustion chamber (piston, cylinder, and head) of the CFR engine under continuous standard knocking operation. Uncertainty of unburned gas temperature and cylinder wall temperatures estimation was analyzed depending on uncertainty in experimentally measured and prescribed model input parameters. The model was finally used to estimate the IVC conditions (trapped mass, residual gas fraction, and temperature), as well as unburned gas temperature and cylinder wall temperatures for various fuels throughout the engine cycle.

Choi, Seungmok↗
NASA NTRS2009

Testing of an Integrated Reactor Core Simulator and Power Conversion System with Simulated Reactivity Feedback

A Direct Drive Gas-Cooled (DDG) reactor core simulator has been coupled to a Brayton Power Conversion Unit (BPCU) for integrated system testing at NASA Glenn Research Center (GRC) in Cleveland, OH. This is a closed-cycle system that incorporates an electrically heated reactor core module, turbo alternator, recuperator, and gas cooler. Nuclear fuel elements in the gas-cooled reactor design are replaced with electric resistance heaters to simulate the heat from nuclear fuel in the corresponding fast spectrum nuclear reactor. The thermodynamic transient behavior of the integrated system was the focus of this test series. In order to better mimic the integrated response of the nuclear-fueled system, a simulated reactivity feedback control loop was implemented. Core power was controlled by a point kinetics model in which the reactivity feedback was based on core temperature measurements; the neutron generation time and the temperature feedback coefficient are provided as model inputs. These dynamic system response tests demonstrate the overall capability of a non-nuclear test facility in assessing system integration issues and characterizing integrated system response times and response characteristics.

Bragg-Sitton, Shannon M.↗
NASA NTRS2001

Thermal Analysis of a High-Speed Aircraft Wing Using p-Version Finite Elements

This paper presents the results of conceptual level thermal analyses of a High Speed Civil Transport (HSCT) wing using p-version finite elements. The work was motivated by a thermal analysis of a HSCT wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining a traditional finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Further study indicated using p-version finite elements might improve computation performance for this class of problem. Methods for determining internal radiation heat transfer were then developed and demonstrated on test problems representative of the geometry found in an aircraft wing structure. This paper presents the results of the application of these new methods to the analysis of a high speed aircraft wing. Results for both a wing box model as well as a full wing model are presented. 'Me reduced wing box model allows for a comparison of the traditional finite element method with mesh refinement (h-refinement) to the new p-version finite elements while the full wing model demonstrates the applicability and efficiency of p-version finite elements for large models.

Gould, Dana C.↗
DOE OSTI2021

Simulation of the PBX 9501 Self-Ignited Heavily Confined Cookoff Test

The PBX 9501 self-ignited thermally damaged explosive (SITX) test was carried out by Holmes et al. A 6-inch diameter sphere made of the PBX 9501 was heated inside a steel confinement vessel until it underwent a thermal explosion. This test provided measured temperature data that was used to define a boundary condition to carry out post-experiment finite element (FE) thermal simulations and comparisons of the FE thermal response with the experimental time to thermal ignition and internal temperature measurements at the center of the PBX 9501 sphere. Finite element models of this experiment were constructed using the heat transfer code Aria. A cookoff model for PBX 9501 was used to simulate the thermal decomposition of PBX 9501 and to predict the time to thermal ignition. An inverse heat conduction scheme was designed and applied to estimate a 1D temperature boundary condition.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2024

Implementation of the Glued Sphere Discrete Element Model for Non-Spherical Particles in MFiX Software

To enhance solver capabilities, simulation flexibility and model validation within the MFiX software, the U.S. Department of Energy (DOE) is funding efforts to develop and integrate the glued-sphere discrete element method into the latest version of MFiX as a dedicated computational module. The glued-sphere discrete element method is a numerical technique to depict the behavior of non-spherical particles in granular flows or particulate systems by representing them as a collection of component spheres. These spheres are bonded together to approximate the shape and mechanical/chemical properties of a more complex particle. The method effectively reuses the existing sphere-sphere collision algorithm, interphase momentum and heat transfer calculations utilized in the traditional discrete element method, extending these capabilities to non-spherical particles. Additionally, this method explicitly resolves intra-particle temperature and species distributions. The MFiX glued-sphere computational module includes tools for generating glued sphere configurations, a dedicated solver, and visualization capabilities in post-processing. More specifically within the computational module, collision detection and calculations were first performed on component spheres and then mapped onto non-spherical particles. The linear spring-dashpot model was utilized to simulate the sphere-sphere interactions.

Ke, Renjie↗
NASA NTRSDate not supplied

The Effects of Experimentally Induced Zircon Annealing on Melt Inclusion-Zircon Geochemistry: A Case Study of Archean Zircon From the Barberton Complex

Crystalline melt inclusions (MIs) in Archean zircons can potentially constrain the evolution of magmatic processes. However, to obtain a homogeneous glassy MI representative of the parent melt, devitrified MIs must be heated at temperatures above the liquidus. Although, it is well known that radiation damaged domains in MI-host zircon undergo temperature-time dependent annealing, the effects of annealing on zircon stable isotope and trace element compositions has received less attention. In this study, we heated multiple aliquots of low-magnetism zircons with relatively low levels of radiation damage (Deff<9.6x1014 α-events/mg) from a 3.304 Ga tonalite gneiss xenolith from the Barberton greenstone belt (sample B87-18; Kamo and Davis, 1994) in an internally-heated pressure vessel at 0.4GPa and 1000–1200°C. Zircons were imaged by SEM (CL, BSE) to determine the zoning patterns around the MIs. The radiation damage preserved in the heated and unheated zircons was determined by measuring broadening of the 3(SiO4) Raman stretching band of zircon (FWHM). Oxygen isotope ratios (δ18O), OH/O ratios, and trace and rare earth element (TREE) concentrations were measured in the zircons and MIs using SIMS. The FWHM and Raman shift of the zircon 3(SiO4) band show a systematic increase of zircon crystallinity with increasing experimental temperature. Despite increasing crystallinity, the 3(SiO4) FWHM is not correlated with δ18O(Zrn) values in the heated or unheated zircons, suggesting that δ18O was not altered by laboratory heating in these low initial radiation damage zircons. FWHM and OH/O are positively correlated in both heated and unheated zircons. The unheated zircons have the largest FWHM and OH/O (OH/OMAX=3.5×10-4) suggesting that H2O was lost during experimental heating due to the progressive annealing of radiation-damaged domains in the zircons. Zircon TREE concentrations and FWHM values are not correlated despite the presence of TREE altered domains in both the heated and unheated zircons. Our results demonstrate that pre-experimental zircon TREE concentrations and δ18O(Zrn) remain intact during laboratory heating of crystalline MIs in zircon, while secondary H2O hosted in radiation damaged domains is partially lost. Thus, MIs in low initial radiation damage Archean zircon are a potentially viable tool for constraining melt compositions.

Joseph P. Gonzalez↗
DOE OSTI2016

SU-G-TeP2-05: Development of a Thimble Calorimeter for Absorbed Dose to Water Characterized in MV Photons

Purpose: To develop a thimble sized polystyrene calorimeter for use from kV to MV photons, as a primary reference standard for applications from diagnostic CT imaging to therapy beam dose determination. Methods: A polystyrene calorimeter about 1.5 cm diameter embedded with small thermistors was characterized in a 6 MV photon beam from a clinical accelerator at 5 nominal dose rates from 0.8 to 4 Gy/min. Irradiations were delivered with beam on/off cycles first at 60 s and then at 20 s. Two sets of phantom conditions were evaluated: 1) in a 30 cm diameter polyethylene cylinder, and 2) in 10 cm depth of a 30 cm water phantom. The temperature waveforms were recorded and analyzed for temperature rise, arriving at a dose to polystyrene. This value is compared with the result of measurements under identical conditions using an ionization chamber calibrated for absorbed dose to water. Monte Carlo simulations were performed on the measurement systems to estimate such a ratio. Results: The ratio of the dose determined by the calorimeter to the dose reported by the ionization chamber was aggregated from all 5 dose rates. The 60 s results show a much elevated response in both phantoms compared to their respective expected results based on simulation. This deviation was reduced when the on/off cycles were shortened to 20 s. This behavior was possibly due to the heat conduction effects in the small calorimeter body. Finite element modeling is being conducted to simulate this effect. Conclusion: A small solid plastic calorimeter offers the convenience of a portable absorbed dose standard based on direct measurement of energy deposition, but comes at the expense of heat transfer complications which need to be characterized. This work offers preliminary evidence of the behavior and quantitative assessment of the issues to be resolved in future investigations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗
DOE OSTI2022

A Machine Learning-Assisted Framework to Control Thermally Anisotropic Building Envelopes in Residential Buildings

To curb the energy consumption of buildings and their related CO2 emissions, Oak Ridge National Laboratory (ORNL) has developed the thermally anisotropic building envelope (TABE) —a multi-layer design comprising insulation materials and metal foils connected to thermal loops. In this study, a machine learning-assisted framework was developed to control the TABE in residential buildings to reduce the computation load for future optimal rule-based control and application. First, a 2D finite element model was established in COMSOL to calculate the hourly heat flux through exterior walls installed with the TABE. Then, TABE wall heat fluxes were simulated for various given indoor and outdoor boundary conditions, as well as thermal loops fluid temperatures and flow rates. Since the finite element simulations are computationally expensive, an artificial neural network (ANN) was then trained to use as a proxy of the finite element (COMSOL) modeling. Finally, the trained ANN model was coupled with the EnergyPlus model to predict the energy consumption of a US Department of Energy prototype single-family house installed with the TABE. An optimal simple rule-based control was determined from predefined rules for a case study. The results demonstrate that the developed machine learning–assisted framework can reduce 99.9% of the computation time while efficiently managing residential building energy for installed TABE walls.

Shen, Zhenglai↗
DOE OSTI2017

Characterization of Flame Cut Heavy Steel: Modeling of Temperature History and Residual Stress Formation

Heavy steel plates are used in demanding applications that require both high strength and hardness. An important step in the production of such components is cutting the plates with a cost-effective thermal cutting method such as flame cutting. Flame cutting is performed with a controlled flame and oxygen jet, which burns the steel and forms a cutting edge. However, the thermal cutting of heavy steel plates causes several problems. A heat-affected zone (HAZ) is generated at the cut edge due to the steep temperature gradient. Consequently, volume changes, hardness variations, and microstructural changes occur in the HAZ. In addition, residual stresses are formed at the cut edge during the process. In the worst case, unsuitable flame cutting practices generate cracks at the cut edge. The flame cutting of thick steel plate was modeled using the commercial finite element software ABAQUS. The results of modeling were verified by X-ray diffraction-based residual stress measurements and microstructural analysis. The model provides several outcomes, such as obtaining more information related to the formation of residual stresses and the temperature history during the flame cutting process. In addition, an extensive series of flame cut samples was designed with the assistance of the model.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Design, fabrication, simulation, and testing of additively manufactured lattice-based copper heat sinks

Here, this study investigates the potential advantages of lattice structure-based bound metal material extrusion (MEX) 3D printing for fabricating high-performance copper heat sinks. Copper powder-filled polymer filaments, with a copper content of > 90 wt.%, were developed specifically for the bound metal MEX 3D printing process. Three types of structures—planar, strut, and surface lattices—were 3D printed to facilitate efficient heat transfer pathways within the heat sinks. Subsequent post-processing steps, including polymer removal and sintering, were performed to achieve dense copper parts. Hot isostatic pressing was further employed to enhance the sintered density from 93 to 98%. Finite element analysis (FEA) simulations were conducted to assess the heat transfer efficiency of the designs, and heat transfer experiments were performed using a custom setup to validate the simulation results. Additionally, this research explores the use of extended hold times during pre-sintering and a reduced atmosphere to enhance the %IACS values (electrical conductivity) and thermal performance of the bound metal MEX 3D printed copper heat sinks. The investigation combines experimental analysis, including simulations and heat transfer experiments, to gain insights into the structure-material property relationships and optimize the thermal performance of the printed heat sinks.

Ajjarapu, Kameswara Pavan Kumar [Oak Ridge Nationa↗
NASA NTRS1987

Heat generation in Aircraft tires under yawed rolling conditions

An analytical model was developed for approximating the internal temperature distribution in an aircraft tire operating under conditions of yawed rolling. The model employs an assembly of elements to represent the tire cross section and treats the heat generated within the tire as a function of the change in strain energy associated with predicted tire flexure. Special contact scrubbing terms are superimposed on the symmetrical free rolling model to account for the slip during yawed rolling. An extensive experimental program was conducted to verify temperatures predicted from the analytical model. Data from this program were compared with calculation over a range of operating conditions, namely, vertical deflection, inflation pressure, yaw angle, and direction of yaw. Generally the analytical model predicted overall trends well and correlated reasonably well with individual measurements at locations throughout the cross section.

Dodge, Richard N.↗
DOE OSTI2016

Environmentally Friendly Economical Sequestration of Rare Earth Metals from Geothermal Waters

The purpose of this work was to complete a proof of concept study to apply and validate a novel method developed by Tusaar for the capture and recovery of rare earth elements (known as REEs) and other critical and valuable elements from geothermal waters produced from deep within the earth. Geothermal water provides heat for power production at many geothermal power plants in the western United States. The target elements, the REEs, are vital to modern day electronics, batteries, motors, automobiles and many other consumer favorites and necessities. Currently there are no domestic sources of REEs while domestic and international demand for the products they are used in continues to rise. Many of the REEs are considered “strategically” important. A secure supply of REEs in the USA would benefit consumers and the country at large. A new method to recover these REEs from geothermal waters used at existing geothermal power plants around the country is a high priority and would benefit consumers and the USA. The result of this project was the successful development and demonstration of an integrated process for removal and recovery of the REEs from synthetic geothermal brines on a small laboratory scale. The work included preparation of model geothermal brines to test, selection of the most effective proprietary sorbent media to capture the REEs and testing of the media under a variety of potential operating conditions. Geothermal brines are generally very high in salt content and contain a wide range of elements and anions associated with the rock layers from which they are produced. Processing the geothermal water is difficult because it is corrosive and the dissolved minerals in the water precipitate easily once the temperature and pressure change. No commercial technologies have been shown to be effective or robust enough under these geothermal brine conditions to be commercially viable for removal of REEs. Technologies including ion exchange, traditional sorptive media and membrane concentration are too expensive, difficult or impossible to regenerate and easily rendered ineffective under these working conditions. The work completed during this project has demonstrated that a selective media that is robust and durable under the conditions associated with geothermal brines is possible. The initial economic analysis indicates that the process would not be financially viable at current market prices for REEs. The world market price for REEs has been turbulent over the past several years and are currently near historical lows. Historical trends and market forces suggest that the world price is stabilizing and will rise. At the same time, further development has the potential to reduce the costs associated with the technology. This work opened the door to the idea that a large scale process for removal and recovery of REEs from geothermal brines is possible. Upward price pressures coupled with technology improvements suggest that this process has the opportunity to be commercially successful at a point in the future.

15 GEOTHERMAL ENERGY↗
NASA NTRS1975

Finite-element solution for a combined radiative-conductive analysis with mixed diffuse-specular surface characteristics

The finite-element method has been applied to solve a combined radiative-conductive heat transfer problem for a large space telescope similar to those used in orbiting satellites. The derivation of the underlying matrices and associated solution algorithm for a 2-D triangular element is presented in detail. The resulting expressions for this triangular element typify such an analysis, which yields constitutive matrices when the heat equation is cast in the matrix form. The relevant matrices include those pertaining to thermal conductance, internal heat generation, radiative exchanges, and all possible external thermal loadings. Emphasis is placed on the treatment of non-linear radiative interchange between surfaces in an enclosure having mixed diffuse-specular surface characteristics. Essential differences in governing equations describing these distinctive surface characteristics are identified. Concluding remarks are drawn from an example simulating a Cassegrainian space telescope.

Lee, H.-P.↗