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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 451 records · Page 25
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NASA NTRS1994

The chromospheric structure of the cool giant star g Herculis

Non-Local Thermodynamic Equilibrium (LTE) calculations of semiempirical chromospheric models are presented for 30 g Her (M6 III). This star is one of the coolest (T(sub eff) = 3250 K) SRb (semiregular) variable stars and has a mass perhaps as great as 4 solar mass. Chromospheric features we have observed in its spectrum include Mg II h and k; C II) UV0.01, which is sensitive to electron density; Mg I lambda 2852; Ca II H, K, and IRT; Ca I lambda 4227 and lambda 6573; Al II) UV 1; and H alpha. We pay special attention to fitting the C II intersystem lines and the Mg II resonance lines but use all the other features as constraints to some extent. The equations of radiative transfer and statistical equilibrium are solved self-consistently for H I, H(-), H2, He I, C I, C II, Na I, Mg I, Mg II, Al I, Al II, Ca I, and Ca II with the equivalent two-level technique. To simplify these calculations, a one-dimensional hydrostatic, plane-parallel atmosphere is assumed. We investigate 10 separate 'classical' chromospheric models, differing most importantly in total mass column density above the temperature minimum. Synthetic spectra from these models fit some but not all of the observations. These comparisons are discussed in detail. However, we find that no single-component classical model in hydrostatic equilibrium is able to reproduce both the Mg II line profiles and the relative strengths of the CII) lines. In all these models, chromospheric emission features are formed relatively close to the star (approximately less than 0.05 R(sub *). The circumstellar environment has a thick, cool component overlying the Mg II emission region, which is relatively static and very turbulent. Finally, we find that thermalization in the Mg II h and k lines in the coolest giant stars is controlled by continuum absorption from Ca I 4p 4p3 P0 bound-free opacity and not collisional de-excitation as is the case for warmer K giants.

Luttermoser, Donald G.↗
NASA NTRS1994

Rapid computation of spectrally integrated non-local thermodynamic equilibrium limb emission

The interpretation of infrared radiance measurements made by satellite-borne limb-scanning broadband radiometers requires accurate and computationally fast techniques with which to evaluate the equation of radiative transfer. This requirement is made even more stringent when analyzing measurements of non-local thermodynamic equilibrium (non-LTE) emission from the terrestrial mesosphere and lower thermosphere. In principle, line-by-line calculations which explicitly account for the departure from thermodynamic equilibrium in both the source functions and the transmittances are necessary. In this paper we extend the emissivity growth approximation (EGA) technique developed for local thermodynamic equilibrium (LTE) limb radiance for the molecular oxygen dayglow (1.27 micrometers and 762 nm), ozone and carbon dioxide in the 9- to 11-micrometer spectral interval, carbon monoxide (4.6 micrometers), nitric oxide (5.3 micrometers), and the carbon dioxide bands (15 micrometers) are presented. Using the non-LTE form of the EGA, the spectrally integrated limb emission is calculated for 35 tangent heights in the mesosphere and lower thermosphere (a total of 1200 atmospheric layers) with line-by-line accuracy in approximately 0.35 s of CPU time on readily available desktop computer hardware, while the corresponding line-by-line calculations may require several minutes. The non-LTE EGA technique will allow kinetic temperature and minor constituend retrieval algorithms to readily include non-LTE efects limited only by the a priori knowledge of the departure from LTE in the observed bands.

Mlynczak, Martin G.↗
NASA NTRS1995

Instabilities and the transport of polarized astrophysical maser radiation

Time-dependent, radiative instabilities in the creation and transport of polarized astrophysical maser radiation in the presence of a magnetic field are calculated. The instabilities are similar to and occur under the same conditions as those found previously by Scappaticci & Watson for unpolarized maser radiation. The common limits in which the Zeeman splitting is much greater than, and much less than, the spectral line breadths are both considered in the current investigation. The resulting fluctuations in the emergent radiation are potentially relevant for the OH 1665 MHz masers which have been reported to fluctuate on timescales of 1000 s and which tend to be polarized. Instabilities occur and alter the transport of maser radiation only under a quite limited range of conditions. In particular, we find here that the instabilities do not occur for conditions that are appropriate for astrophysical masers with small Zeeman splittings such as the SiO and H2O masers. The time-independent, numerical solutions to the GKK equations of radiative transfer that have been obtained in previous investigations are thus essentially always valid except within a narrow range of conditions relevant for the OH masers.

Wallin, Bradley K.↗
NASA NTRS2000

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Gould, Dana C.↗
NASA NTRS2001

Thermal Conductivity of Ceramic Thermal Barrier and Environmental Barrier Coating Materials

Thermal barrier and environmental barrier coatings (TBC's and EBC's) have been developed to protect metallic and Si-based ceramic components in gas turbine engines from high temperature attack. Zirconia-yttria based oxides and (Ba,Sr)Al2Si2O8(BSAS)/mullite based silicates have been used as the coating materials. In this study, thermal conductivity values of zirconia-yttria- and BSAS/mullite-based coating materials were determined at high temperatures using a steady-state laser heat flux technique. During the laser conductivity test, the specimen surface was heated by delivering uniformly distributed heat flux from a high power laser. One-dimensional steady-state heating was achieved by using thin disk specimen configuration (25.4 mm diam and 2 to 4 mm thickness) and the appropriate backside air-cooling. The temperature gradient across the specimen thickness was carefully measured by two surface and backside pyrometers. The thermal conductivity values were thus determined as a function of temperature based on the 1-D heat transfer equation. The radiation heat loss and laser absorption corrections of the materials were considered in the conductivity measurements. The effects of specimen porosity and sintering on measured conductivity values were also evaluated.

Zhu, Dong-Ming↗
NASA NTRS2009

X-ray Reflected Spectra from Accretion Disk Models. I. Constant Density Atmospheres

We present new models for illuminated accretion disks, their structure and reprocessed emission. We consider the effects of incident X-rays on the surface of an accretion disk by solving simultaneously the equations of radiative transfer, energy balance and ionization equilibrium over a large range of column densities. We assume plane-parallel geometry and azimuthal symmetry, such that each calculation corresponds to a ring at a given distance from the central object. Our models include recent and complete atomic data for K-shell of the iron and oxygen isonuclear sequences. We examine the effect on the spectrum of fluorescent Ka line emission and absorption in the emitted spectrum. We also explore the dependence of the spectrum on the strength of the incident X-rays and other input parameters, and discuss the importance of Comptonization on the emitted spectrum.

Garcia, Javier↗
NASA NTRS2013

Measurement of Electromagnetic Energy Flow Through a Sparse Particulate Medium: A Perspective

First-principle analysis of the functional design of a well-collimated radiometer (WCR) reveals that in general, this instrument does not record the instantaneous directional flow of electromagnetic energy. Only in special cases can a sequence of measurements with a WCR yield the magnitude and direction of the local time-averaged Poynting vector. Our analysis demonstrates that it is imperative to clearly formulate the physical nature of the actual measurement afforded by a directional radiometer rather than presume desirable measurement capabilities. Only then can the directional radiometer be considered a legitimate part of physically based remote sensing and radiation-budget applications. We also emphasize the need for a better understanding of the nature of measurements with panoramic radiometers.

directional radiometry↗
NASA NTRS2021

Constrained Inversion of a Microwave Snowpack Emission Model Using Dictionary Matching: Applications for GPM Satellite

This article presents a new algorithmic framework for multilayer inversion of the dense media radiative transfer (DMRT) equations of snowpack emission, with particular emphasis on the role of high-frequency microwave channels above 60 GHz. The approach relies on dictionary matching and locally constrained least squares. The results demonstrate that the algorithm can invert the DMRT model and retrieve depth, density, and grain size of a single-layer snowpack when dependencies of density and grain size on depth are properly accounted for. However, as the number of layers increases, the sensitivity of the inversion to observation noise grows markedly. Using observations, over the Great Plains in the United States, from the microwave imager onboard the global precipitation measurement (GPM, 10-166 GHz) core satellite, the initial results demonstrate that under a clear-sky condition and no vegetation canopy, the algorithm is capable to retrieve the snow depth and water equivalent of seasonal snow with a mean absolute error (MAE) of less than 0.15 m--when compared to the high-resolution analysis data from the SNOw Data Assimilation System (SNODAS).

Snow↗
NASA NTRSDate not supplied

Spectral Gap Filling Method Using the Spectral Information from CLARREO-Pathfinder Measured Earth-Reflected Solar Spectra to Support CPF-CERES Intercalibration

The high-accuracy Earth-reflected solar spectral radiances from CLARREO Pathfinder (CPF) will serve as in-orbit benchmark measurements for intercalibrating other satellite imagers. The CPF team is developing a state-of-the-art intercalibration method to calibrate the shortwave channel (300-5000 nm) of the CERES instrument against the CPF reference with an uncertainty of 0.3%. Because the CPF instrument only covers spectral range from 350 nm to 2300 nm, the team has developed a spectral extension method to fill in the gaps between the spectral domains of CPF and the CERES shortwave channel. The method solely relies on using the hyperspectral information from the CPF wavelengths to predict the radiances below 350 nm and above 2300 nm. To quantify the relationship between the CPF spectrum and the non-overlapping portions of the spectrum between CPF and CERES, the team has simulated a large ensemble of spectra that cover the spectral range for both CPF and CERES. A hyperspectral bidirectional reflectance model for land surface based on thousands of measured land surface reflectance has been developed. This land surface model as well as the Cox-Munk model for ocean surface are used in the spectral gap filling. Various water/ice clouds, aerosols, atmosphere profiles and surfaces were used to simulate Earth-reflected radiances from 200 nm to 15 um under different solar and sensor geometries. The targeted uncertainty for the CPF-extended broadband CERES radiances is less than 0.1%. The previously derived training spectra were updated to replace the Kurucz solar irradiance model with the TSIS-1 Hybrid Solar Reference Spectrum. The influence of the scalar assumption in radiative transfer model equations on the uncertainty in estimating the broadband radiances was also investigated.

Hyperspectral↗
NASA NTRS1992

Principles of the radiosity method versus radiative transfer for canopy reflectance modeling

The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.

Gerstl, Siegfried A. W.↗
NASA NTRS2020

Spectral Spherical Harmonics Discrete Ordinate Method

A new method for modeling the radiative transfer in inhomogeneous three-dimensional media illuminated by a Gaussian beam is described. This approach, called the Spectral Spherical Harmonics Discrete Ordinate Method (SSHDOM), uses the Fourier expansion method to transform the three-dimensional radiative transfer into an one-dimensional equation in the spectral domain, and the Spherical Harmonics Discrete Ordinate Method (SHDOM) for its solution. Specifically, (i) the source function is represented in the spectral domain through a spherical harmonic expansion, (ii) the spectral one-dimensional radiative transfer equation is integrated along discrete ordinates through a spatial grid, and (iii) the solution method is based on the Picard iteration. Both SSHDOM and SHDOM algorithms are implemented in a common computer code.

Gaussian beam↗
NASA NTRS2008

Stochastic Transport Theory for Investigating the Three-Dimensional Canopy Structure from Space Measurements

Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data.

Huang, Dong↗
NASA NTRS1999

Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces

We describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,,v.giss.nasa.gov/-crmim/brf.html and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.

Mishchenko, Michael I.↗
NASA NTRS1959

APPLICATION OF VARIATIONAL METHODS TO RADIATION HEAT-TRANSFER CALCULATIONS

A variational method is presented for solving a class of integral equations which arise in radiation heat-transfer problems. First, to demonstrate the formulation of radiation problems in terms of integral equations, consideration is given to a system consisting of two nonblack, finite, parallel plates. After a general description of the variational method, its use is illustrated by application to the parallel-plate system. Comparisons are made which show very good agreement with exact solutions.

E. M. Sparrow↗
NASA NTRS1983

Flare loop radiative hydrodynamics. I - Basic methods

The study presented here has two goals. The first is to examine the role of energy transport mechanisms in flare dynamics, for instance, thermal cone conduction in the corona and radiative transfer in the chromosphere. The second is to provide diagnostics of flare energization processes by predicting the evolutionary behavior of concurrent emissions from all regions of the flaring atmosphere. To attain these ends, a numerical method is developed for the simultaneous solution of thy continuity, momentum, and energy equations; the time-dependent atomic rate equations describing ionization and excitation; and the radiative transfer equations. With the physical model and computational methods used here, all components of the plasma move as a single fluid and in the initial studies are assumed to have a common kinetic temperature. The plasma is constrained to move in one dimension along the axis of a loop of nonuniform cross section, the geometry of which is defined by a sufficiently strong magnetic field.

Mcclymont, A. N.↗
NASA NTRS1994

Equilibrium structure of solar magnetic flux tubes: Energy transport with multistream radiative transfer

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium. This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers. A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations.

Hasan, S. S.↗
NASA NTRS2012

Improved Finite-Volume Method for Radiative Hydrodynamics

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy for such simulations on structured and unstructured grids compared to more conventional approaches. Results will be shown for shock radiation during hypersonic reentry. Issues of parallelization within a radiation sweep will also be discussed.

Wray, Alan↗
NASA NTRS1979

Radiation transfer through a model sunspot

A cylindrically symmetric model for a sunspot atmosphere using the similarity principle of Schlueter and Temesvary for the magnetic field configuration is presented. The equations of magnetostatic equilibrium are used, augmented by a radial Evershed flow. The LTE radiative transfer equations for the Stokes vector were solved under a variety of conditions for a ray emerging from a typical penumbral point. The contribution from isolated lines to the broadband circular polarization in sunspot penumbrae is evaluated using a more realistic model sunspot atmosphere than has hitherto been considered. Results indicate that the inclusion of a velocity field along the magnetic field vector is unable to give a net circular polarization of sufficient magnitude, although the variation with the angle between the line-of-sight and the magnetic field vector is in qualitative agreement with observations. The corresponding results for the net linear polarization are satisfactory.

Landman, D. A.↗