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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 415 records · Page 23
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NASA NTRS1972

Statistical versus nonstatistical temperature inversion methods

Vertical temperature profiles are derived from radiation measurements by inverting the integral equation of radiative transfer. Because of the nonuniqueness of the solution, the particular temperature profile obtained depends on the numerical inversion technique used and the type of auxiliary information incorporated in the solution. The choice of an inversion algorithm depends on many factors; including the speed and size of computer, the availability of representative statistics, and the accuracy of initial data. Results are presented for a numerical study comparing two contrasting inversion methods: the statistical-matrix inversion method and the nonstatistical-iterative method. These were found to be the most applicable to the problem of determining atmospheric temperature profiles. Tradeoffs between the two methods are discussed.

Smith, W. L.↗
NASA NTRS1973

A non-LTE study of silicon line formation in early-type main-sequence atmospheres.

We have computed populations of 16 levels of Si III-V and radiation fields in all connecting transitions; in particular the first six Si III triplet levels, including the 4553 line, and the first six Si IV levels including 4089. The computations were done for four non-LTE H-He model atmospheres, provided by Auer and Mihalas. Estimates of corresponding MK types are B1.5 V, B0.5 V, O9 V, and O6. Solutions were obtained by iterating the linearized equations of radiative transfer and statistical equilibrium, except that for less important lines an approximate equivalent two-level atom treatment was used. Continuous opacities of C, N, O, and Ne were included. All abundances were solar values.

Kamp, L. W.↗
NASA NTRS1974

Model calculations for diffuse molecular clouds

A steady state isobaric cloud model is developed. The pressure, thermal, electrical, and chemical balance equations are solved simultaneously with a simple one dimensional approximation to the equation of radiative transfer appropriate to diffuse clouds. Cooling is mainly by CII fine structure transitions, and a variety of heating mechanisms are considered. Particular attention is given to the abundance variation of H2. Inhomogeneous density distributions are obtained because of the attenuation of the interstellar UV field and the conversion from atomic to molecular hyrodgen. The effects of changing the model parameters are described and the applicability of the model to OAO-3 observations is discussed. Good qualitative agreement with the fractional H2 abundance determinations has been obtained. The observed kinetic temperatures near 80 K can also be achieved by grain photoelectron heating. The problem of the electron density is solved taking special account of the various hydrogen ions as well as heavier ones.

Glassgold, A. E.↗
NASA NTRS1974

Viscous, radiating hypersonic flow about a blunt body

The viscous, radiating hypersonic flow past an axisymmetric blunt body is analyzed based on the Navier-Stokes equations, plus a radiative equation of transfer derived from the Milne-Eddington differential approximation. The fluid is assumed to be a perfect gas with constant specific heats, a constant Prandtl number of order unity, a viscosity coefficient varying as a power of the temperature, and an absorption coefficient varying as the first power of the density and as a power of the temperature. The gray gas assumption is invoked, thereby making the absorption coefficient independent of the spectral frequency. Limiting forms of the solutions are studied as the freestream Mach number freestream Reynolds number and the temperature ratio across the shock wave, go to infinity, and as the Bouguer number and the density ratio across the shock wave go to zero. The method of matched asymptotic expansions is used in the analysis, and it is shown that there is a far-field precursor, composed of two regions, in which the fluid mechanics can be neglected for all practical purposes but included for completeness.

Passamaneck, R. S.↗
NASA NTRS1973

Optical transmission in a circumstellar dust cloud

It is shown from the equation of radiative transfer that the visual attenuation of an optically thick, spherically symmetric circumstellar cloud of dust can be small compared to that produced by an equal optical depth of interstellar dust. The reasons for this are the moderately large albedos of the grains and their tendency to emphasize forward scattering.

Jones, T. W.↗
NASA NTRS1974

Gravitational Stokes parameters

The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.

Anile, A. M.↗
NASA NTRS1974

Scattering and absorption from poly-dispersed aerosols

Results from numerical computations of the diffuse sky radiances and degree of polarization are given. These results were obtained by solving the equation of radiative transfer in the formulation of Eschelbach. In these computations, multiple scattering and absorption by aerosol particles were considered. In addition, results from experimental measurements of the complex refractive index of aerosol samples at different relative humidities are presented. From the radiation flux divergences which were computed based on the determined properties of atmospheric aerosol particles, atmospheric heating rates were derived which were found to be comparable to the heating rates by water vapor.

Bullrich, K.↗
NASA NTRS1975

Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere

The intensity of sunlight multiply scattered in model atmospheres is derived from the equation of radiative transfer by an analytical small-angle approximation. The approximate analytical solutions are compared to rigorous numerical solutions of the same problem. Results obtained from an aerosol-laden model atmosphere are presented. Agreement between the rigorous and the approximate solutions is found to be within a few per cent. The analytical solution to the problem which considers an aerosol-laden atmosphere is then inverted to yield a phase function which describes a single scattering event at small angles. The effect of noisy data on the derived phase function is discussed.

Weinman, J. A.↗
NASA NTRS1976

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

Kamp, L. W.↗
NASA NTRS1975

The effect of atmospheric haze on images of the earth's surface

The adding method to solve the equation of radiative transfer has been applied to a sunlit haze above a reflecting surface. The method was modified to include the effect of inhomogeneities on the underlying surface whose dimensions are less than the mean free path of the photons in the haze. Numerical examples of surface-feature contrast degradation due to haze are presented. This analysis renders it feasible to determine the optical thickness of hazes from haze-degraded images of the ground and also provides a technique to restore ground-image contrast, which has been obscured by haze, in photoelectrically scanned images.

Odell, A. P.↗
NASA NTRS1976

The ionization of a low-density intercloud medium by a single O star

The ionization structure of hydrogen in a cloud-containing low-density gas surrounding an O star is calculated, emphasizing how UV photons cause the ionization of hydrogen in regions which are totally obscured from the star by neutral clouds. Particular consideration is given to the ionization of such obscured regions by diffuse Lyman continuum radiation produced when H(+) recombines directly to the ground state. The assumed physical structure of the cloud-containing neighborhood of an O star is discussed, a method is outlined for expressing the emission and absorption properties of the neutral clouds and their shadows in terms of effective volume emissivities and absorption coefficients on a line of sight, and equations of radiative transfer are derived for diffuse and stellar radiation in a cloud-containing H II region. Reradiation of Lyman continuum photons from the ionized boundary layer of a neutral cloud or shadow is analyzed. The expected emission measure across a large cloud-containing H II region is determined and found to compare well with that obtained from observations of H-alpha emission around runaway O stars. It is shown that the hydrogen in cloud shadows may be completely ionized by diffuse radiation within approximately half the Stroemgren radius, depending on the extent of that radius, the average frequency of the Lyman continuum radiation from the star, and the average cloud size.

Elmegreen, B. G.↗
NASA NTRS1977

Application of statistical inversion to ground-based microwave remote sensing of temperature and water vapor profiles

Surface-based observations of downwelling microwave thermal emission are related to temperature and humidity profiles via a standard integral equation of radiative transfer. Both in clear and in cloudy atmospheres, statistical inversion techniques are used to retrieve profiles from a data vector of brightness observations and surface meteorological constraints. For the clear case, accuracy predictions and profile retrievals are illustrated for: (1) single frequency angular scanned data; (2) multi-frequency angular scanned data; and (3) multi-frequency zenith data. For the last case predicted and achieved accuracies were compared in a recently conducted radiometric experiment. Retrievals of cloud contaminated radiometric data are elaborated.

Westwater, E. R.↗
NASA NTRS1978

Aerothermodynamic environment for Jovian entry with silica heat shield

Solutions are presented for the stagnation-region shock-layer equations, including radiative transfer with spectral lines and silica ablation during Jovian entry. Results for variations of entry angle, sphere-cone configuration, and atmospheric model are given. The effect of silica ablation on the radiative and convective surface heating is correlated with the ratio of the wall to free-stream mass flux. Correlations are also given for spectral distributions. The effect of newly obtained SiO radiation properties on the surface heating is examined.

Green, M. J.↗
NASA NTRS1978

Error analysis of an aircraft-mounted backscatter ultraviolet experiment

An experiment has been proposed to measure the zenith sky intensity and directly transmitted solar flux density at several wavelengths in the near ultraviolet from an aircraft platform located at about 15 km. From these measurements, the vertical distribution of ozone above the platform is to be inferred, by inversion of the equation of radiative transfer. The present study is an analysis of the errors to be expected in a real experiment, due to atmospheric fluctuations, numerical procedures, and ignorance of various parameters necessary for the calculation of the intensities and fluxes to be expected. These errors are found to vary from 17% at the shorter wavelengths to about 3% at the longer wavelengths used. It is shown elsewhere (Twomey et al., 1977) that unacceptable levels of instability and non-uniqueness of results will be found if the error levels in the measurements upon which we wish to invert exceed 3%. On the basis of this, it is concluded that with the present instrumentation and the present knowledge of necessary ancillary parameters, this experiment will not be feasible.

Rabinoff, R.↗
NASA NTRS1980

The effect of earth's atmosphere on contrast reduction for a nonuniform surface albedo and 'two-halves' field

The paper presents a model for contrast reduction by atmospheric haze developed for the 'two-halves' field of the earth's surface and other geometries of the earth's surface albedo. The model is based on a simplified solution of the equation of radiative transfer in two dimensions, resulting in a method for calculation of the upward zenith intensity in the atmosphere as a function of the distance from the border between the two half planes, for an unabsorbing atmosphere. The adjacency effect between two infinitesimal areas of different albedos is calculated; the resultant simplified solution is used to develop expressions for the line-spread function of the atmosphere and the modulation transfer function. The line-spread function is used to calculate the point spread function, which can be used to compute the intensity above any surface with given spatial dependence of the reflectivity.

Mekler, Y.↗
NASA NTRS1981

Cyclotron emission from AM Herculis

The cyclotron absorption coefficients in the ordinary and extraordinary modes are calculated for the shock heated region of AM Her. The equations of radiative transfer are solved and the intensity of the emitted UV radiation determined as a function of angle. The average spectrum is shown to have deviations from the previously predicted Rayleigh-Jeans spectrum and the magnetic field of AM Her is deduced to be roughly 5 x 10 to the 7th power gauss.

Chanmugam, G.↗
NASA NTRS1980

Modified radiative transfer theory for a two-layer random medium

Modified radiative transfer (MRT) equations appropriate for electromagnetic wave propagation in bounded random media are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The MRT equations are then solved with the first-order renormalization approximation to obtain analytical results for the backscattering cross sections of a two-layer random medium with arbitrary three-dimensional correlation functions. The coherent effects of the MRT theory are illustrated and comparisons are made with backscattering cross sections obtained with the first Born approximation to the wave equation.

Zuniga, M. A.↗
NASA NTRS1980

Radiative transfer in dusty nebulae. III - The effects of dust albedo

The effects of an albedo of internal dust, such as ionization structure and temperature of dust grain, were studied by the quasi-diffusion method with an iterative technique for solving the radiative heat transfer equations. It was found that the generalized on-the-spot approximation solution is adequate for most astrophysical applications for a zero albedo; for a nonzero albedo, the Eddington approximation is more accurate. The albedo increases the average energy of the diffuse photons, increasing the ionization level of hydrogen and heavy elements if the Eddington approximation is applied; the dust thermal gradient is reduced so that the infrared spectrum approaches blackbody spectrum with an increasing albedo.

Petrosian, V.↗