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Results for “Radiative transfer equation”

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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Transfer of polarized radiation in self-absorbed synchrotron sources. I - Results for a homogeneous source

The solution to the equation of transfer of polarized radiation in a steady-state homogeneous rarefied medium is applied to self-absorbed synchrotron sources. Relativistic electrons (independent of the presence of any cold plasma) can quite easily produce in such sources significant Faraday rotation and/or conversion of linear to circular polarization. Structural inhomogeneities do not obviate the importance of these phenomena in compact nonthermal sources. Contrary to the calculation of Pacholczyk and Swihart (1975), the circular polarization for a homogeneous source changes sign just below the self-absorption turnover as the source becomes opaque, even when polarization conversion dominates; however, for a physically realistic source, structural inhomogeneity may alter this behavior. The observational evidence bearing upon these effects is reviewed.

Jones, T. W.↗
NASA NTRS1978

Solution of the comoving-frame equation of transfer in spherically symmetric flows. V - Multilevel atoms

The coupled radiative transfer and statistical equilibrium equations for multilevel ionic structures in the atmospheres of early-type stars are solved. Both lines and continua are treated consistently; the treatment is applicable throughout a transonic wind, and allows for the presence of background continuum sources and sinks in the transfer. An equivalent-two-level-atoms approach provides the solution for the equations. Calculations for simplified He (+)-like model atoms in parameterized isothermal wind models indicate that subordinate line profiles are sensitive to the assumed mass-loss rate, and to the assumed structure of the velocity law in the atmospheres.

Mihalas, D.↗
NASA NTRS1983

The equivalence of three techniques for estimating ground reflectance from LANDSAT digital count data

The equivalence of three separate investigations that related LANDSAT digital count (DC) to ground measured reflectance (R) was demonstrated. One investigator related DC data to the cosZ, where Z is the solar zenith angle, for surfaces of constant R. The second investigator corrected the DC data to the solar zenith angle of 39 degrees before relating to surface R. Both of these investigators used LANDSAT 1 and 2 data from overpass dates 1972 through 1977. A third investigator calculated the relation between DC and R based on atmospheric radiative transfer theory. The equation coefficients obtained from these three investigators for all four LANDSAT MSS bands were shown to be equivalent although differences in ground reflectance measurement procedures have created coefficient variations among the three investigations. These relations should be useful for testing atmospheric radiative transfer theory.

Richardson, A. J.↗
NASA NTRS2002

Heat Transfer in High-Temperature Fibrous Insulation

The combined radiation/conduction heat transfer in high-porosity, high-temperature fibrous insulations was investigated experimentally and numerically. The effective thermal conductivity of fibrous insulation samples was measured over the temperature range of 300-1300 K and environmental pressure range of 1.33 x 10(exp -5)-101.32 kPa. The fibrous insulation samples tested had nominal densities of 24, 48, and 72 kilograms per cubic meter and thicknesses of 13.3, 26.6 and 39.9 millimeters. Seven samples were tested such that the applied heat flux vector was aligned with local gravity vector to eliminate natural convection as a mode of heat transfer. Two samples were tested with reverse orientation to investigate natural convection effects. It was determined that for the fibrous insulation densities and thicknesses investigated no heat transfer takes place through natural convection. A finite volume numerical model was developed to solve the governing combined radiation and conduction heat transfer equations. Various methods of modeling the gas/solid conduction interaction in fibrous insulations were investigated. The radiation heat transfer was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. A genetic-algorithm based parameter estimation technique was utilized with this model to determine the relevant radiative properties of the fibrous insulation over the temperature range of 300-1300 K. The parameter estimation was performed by least square minimization of the difference between measured and predicted values of effective thermal conductivity at a density of 24 kilograms per cubic meters and at nominal pressures of 1.33 x 10(exp -4) and 99.98 kPa. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements at other densities and pressures. The numerical model was also validated by comparison with a transient thermal test simulating reentry aerodynamic heating conditions.

Daryabeigi, Kamran↗
NASA NTRS1983

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Strelkov, S. A.↗
NASA NTRS2004

Higher-Order Finite Elements for Computing Thermal Radiation

Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other unrealistic physical conditions are assumed. Instead, the equations of radiative heat transfer are integrated numerically over the parent finite elements by use of a computationally efficient Gaussian integration scheme.

Gould, Dana C.↗
NASA NTRS1995

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗
DOE OSTI2023

A reduced-order modeling of a tubular solar reactor for long duration thermochemical energy storage

The storage of solar energy in a solid form, referred to as a “solar fuel”, can be achieved through a process known as endothermic solar thermochemistry. This process transforms the absorbed solar energy into a stable and retrievable form that can be stored for extended periods of time. This paper presents a low–order heat transfer model of a counter–current tubular falling bed reactor designed to produce thermally reduced magnesium manganese oxide pellets for long duration thermochemical energy storage. The energy required for the endothermic reduction was supplied by concentrated solar energy or renewable electricity via indirect heating of the gas and solid reactants flowing in a ceramic tube. The counter-current gas flow enhances the mixing of the solid particles with the heat recuperation zone, allowing the gas and particles to enter and exit the tubular reactor close to room temperature. Further, the reactor was vertically oriented and was heated circumferentially by an adjustable level heat flux along a finite segment of its length. The temperature distribution of the reactor in response to transient changes along the tube was modeled by considering conduction, convection, and radiation heat transfer. Governing equations for the heat transfer model were solved by discretizing the reactor tube into a finite number of control volumes and using an energy balance for the heat exchange between the reactor wall, gas, and particles within the control volume. The energy absorbed during this endothermic reaction was modeled numerically by fitting the data of the chemical conversion rate with the corresponding temperature of particles in the heating zone. The numerical model has been experimentally validated using a reactor prototype made of a 121.92 cm alumina tube heated by a 7kW electric tube–furnace. The alumina tube receives magnesium manganese oxide pellets of 3.66±0.516 mm in diameter from the top, and a counter–current gas flow from the bottom. The reactor wall temperature was monitored by six thermocouples installed along the reactor tube length. The experimental procedure was numerically simulated, and the temperature variation along the reactor tube was compared with a matrix of experimental runs for a range of particles mass flowrates (0.75–1.25g/s) and corresponding gas flowrates (36–65 SLPM). The reactor system was heated gradually from room temperature to a steady state temperature of 1673K, and then cooled down to room temperature. The heating and cooling processes were simulated, and the numerical and experimental results were compared throughout processes. The numerical model showed similar trends to the experimental results, with an error of 0.69 to 7.9% for the particle inlet and 0.7 to 7.9% for the gas inlet during steady-state operation. The proposed numerical model can be implemented as a simplified physical model to design a feedback control system to regulate reactor temperature.

14 SOLAR ENERGY↗
NASA NTRS1976

Laser induced fluorescence applied to turbulent reacting flows

The saturated fluorescence method makes use of the great simplifications which occur when under conditions of intense radiation the excitation process becomes saturated. A description is presented of the saturated fluorescence method, taking into account rate equations and saturation, radiative transfer, the two-level system, a multilevel system, and measurements under saturation conditions. The detectability limits of the method are investigated. Fluorescence trapping is found to place an upper limit on the number density of the fluorescing species that can be measured without signal loss. Turbulence places time and spatial constraints on the measurements, but otherwise poses no difficulties. Saturated laser induced fluorescence spectroscopy appears to be a most promising method for measuring species concentrations in flames.

Daily, J. W.↗
NASA NTRS1980

Tropical cyclone outer surface winds derived from satellite microwave sounder data

Upper tropospheric temperature anomalies are detected in brightness temperature data from the Nimbus 6 Scanning Microwave Spectrometer (SCAMS). Brightness temperature anomalies are related to surface pressure anomalies through the radiative transfer and hydrostatic equation. Surface wind speeds at outer radii are then estimated using the gradient wind equation and a shearing parameter. The method is first tested using simulated satellite data constructed from temperature, pressure and height data recorded by aircraft reconnaissance of four hurricanes. Wind speeds in the 80-95 kPa region are estimated with 2-3 m/sec accuracy. Next, 55.45 GHz SCAMS data over eight typhoons during 1975 are used to estimate the radii of 15.4 m/sec (30 kt) and 27.5 m/sec (50 kt) winds. Accuracies of about + or - 80 and + or - 70 km, respectively, are found. It is suggested that the technique be further tested using data from the Microwave Sounding Unit on board the TIROS-N and NOAA 6 satellites.

Kidder, S. Q.↗
NASA NTRS1984

Modeling the middle atmosphere circulation

Some of the motivations for constructing models of the middle atmosphere circulation are given. These are as follows: (1) to provide a better understanding of middle atmosphere dynamics; (2) to study the coupling of middle atmosphere dynamics with radiation and chemistry; (3) to study the sensitivity of tropospheric climate modeling and/or weather forecasting to changes in the middle atmosphere; (4) to better understand the limitations of more simplified models; (5) to supply a proxy for atmospheric data for diagnostic analysis; and finally, (6) for forecast-analysis of data. Different types of models are discussed in relation to their anticipated use. Various model simplifications, such as using the quasi-geostrophic set of equations and simplified radiative transfer, are discussed as are some of the consequences of these simplifications. Some of the accomplishments of middle atmosphere circulation modeling are presented as are some of the difficulties in existing models. Finally, some of the problems in constructing and verifying middle atmosphere circulation models are discussed.

Geller, M. A.↗
NASA NTRS1990

Simulated and observed 37 GHz emission over Africa

A model for simulating polarized 37-GHz microwave emissions from vegetated surfaces is proposed. An equation expressing the radiative transfer is solved using a two-point Gauss quadrature method. Surface temperature, reflectance, normalized difference, and polarized brightness temperatures are obtained from processed multispectral satellite data. The model simulations are evaluated against satellite data collected between January 1982 and December 1983 along a transect going from rain forest to hot desert over Africa (0 deg to 20 deg N, 11 deg E). It is found that the temporal variation of the average brightness temperature matches closely the surface temperature. The seasonal variation of the polarization difference is confined within the latitude band of 8 deg to 18 deg N, but the normalized difference continues to show seasonal variation south of 8 deg N. The relations between the polarization difference and the normal difference and between the polarization difference and the reflectance are considered to be nonlinear and almost linear, respectively.

Choudhury, B. J.↗
NASA NTRS1992

Chemical vapor deposition fluid flow simulation modelling tool

Accurate numerical simulation of chemical vapor deposition (CVD) processes requires a general purpose computational fluid dynamics package combined with specialized capabilities for high temperature chemistry. In this report, we describe the implementation of these specialized capabilities in the spectral element code NEKTON. The thermal expansion of the gases involved is shown to be accurately approximated by the low Mach number perturbation expansion of the incompressible Navier-Stokes equations. The radiative heat transfer between multiple interacting radiating surfaces is shown to be tractable using the method of Gebhart. The disparate rates of reaction and diffusion in CVD processes are calculated via a point-implicit time integration scheme. We demonstrate the use above capabilities on prototypical CVD applications.

Bullister, Edward T.↗
NASA NTRS1994

Fast two-stream method for computing diurnal-mean actinic flux in vertically inhomogeneous atmospheres

Based on a derivation of the two-stream daytime-mean equations of radiative flux transfer, a method for computing the daytime-mean actinic fluxes in the absorbing and scattering vertically inhomogeneous atmosphere is suggested. The method applies direct daytime integration of the particular solutions of the two-stream approximations or the source functions. It is valid for any duration of period of averaging. The merit of the method is that the multiple scattering computation is carried out only once for the whole averaging period. It can be implemented with a number of widely used two-stream approximations. The method agrees with the results obtained with 200-point multiple scattering calculations. The method was also tested in runs with a 1-km cloud layer with optical depth of 10, as well as with aerosol background. Comparison of the results obtained for a cloud subdivided into 20 layers with those obtained for a one-layer cloud with the same optical parameters showed that direct integration of particular solutions possesses an 'analytical' accuracy. In the case of the source function interpolation, the actinic fluxes calculated above the one-layer and 20-layer clouds agreed within 1%-1.5%, while below the cloud they may differ up to 5% (in the worst case). The ways of enhancing the accuracy (in a 'two-stream sense') and computational efficiency of the method are discussed.

Filyushkin, V. V.↗
NASA NTRS2001

Jet Stability and the Generation of Superluminal and Stationary Components

We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component instead of being ejected from the core. Their oblique nature should also result in distinct polarization properties. Those appearing closer to the core show small apparent motions and a very slow secular decrease in brightness and could be identified as stationary components. Those appearing farther downstream are weaker and can reach superluminal apparent motions. The existence of these trailing components indicates that not all observed components necessarily represent major perturbations at the jet inlet; rather, multiple emission components can be generated by a single disturbance in the jet. While the superluminal component associated with the primary perturbation exhibits a rather stable pattern speed, trailing components have velocities that increase with distance from the core but move at less than the jet speed. The trailing components exhibit motion and structure consistent with the triggering of pinch modes by the superluminal component. The increase in velocity of the trailing components is an indirect consequence of the acceleration of the expanding fluid, which is assumed to be relativistically hot; if observed, such accelerations would therefore favor an electron-positron (as opposed to proton rest mass) dominated jet.

Agudo, Ivan↗
NASA NTRS1992

Radiative equilibrium in rapidly expanding shells

The equation of radiative equilibrium for rapidly expanding spherical shells including the special relativistic terms is discussed, and a temperature-correction procedure for the solution of this equation is given. The temperature-correction scheme combines a partial linearization approach with the approximate Lambda-operator iteration method. For some test problems, the temperature structures of atmospheres in radiative equilibrium in the Lagrangian frame are calculated. The effects of the velocity field on the temperature stratification and the luminosity are also discussed. We find that the temperature structure of a moving photosphere in radiative equilibrium in the Lagrangian frame differs significantly from that of a static photosphere and that, at least, all first-order terms, in particular the advection and aberration terms, have to be included consistently both in the radiative transfer and the energy equation in studies of supernovae atmospheres and other high-speed radiating flows.

Hauschildt, P. H.↗