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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Compton Scattering by Static and Moving Media: The Transfer Equation and its Moments - Part 1

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering, as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first angular moments, both in the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in Epsilon/m(sub e), T(sub e)/m(sub e), and V, where Epsilon is the photon energy, T(sub e) and m(sub e) are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second order in V should usually be retained, because if the radiation energy density is sufficiently large, compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second order in V can be as important as the effects described by the terms that are first order in V, even when V is small. The system- and fluid-frame equations that we derive are correct to first order in Epsilon/m(sub e). Our system-frame equations, which are correct to second order in V, may be used when V is not too large. Our fluid-frame equations, which are exact in V, may be used when V approaches 1. Both sets of equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V(sup 2) is greater than 3T(sub e)/m(sub e).

Psaltis, Dimitrios↗
NASA NTRS1994

Radiation from advanced solid rocket motor plumes

The overall objective of this study was to develop an understanding of solid rocket motor (SRM) plumes in sufficient detail to accurately explain the majority of plume radiation test data. Improved flowfield and radiation analysis codes were developed to accurately and efficiently account for all the factors which effect radiation heating from rocket plumes. These codes were verified by comparing predicted plume behavior with measured NASA/MSFC ASRM test data. Upon conducting a thorough review of the current state-of-the-art of SRM plume flowfield and radiation prediction methodology and the pertinent data base, the following analyses were developed for future design use. The NOZZRAD code was developed for preliminary base heating design and Al2O3 particle optical property data evaluation using a generalized two-flux solution to the radiative transfer equation. The IDARAD code was developed for rapid evaluation of plume radiation effects using the spherical harmonics method of differential approximation to the radiative transfer equation. The FDNS CFD code with fully coupled Euler-Lagrange particle tracking was validated by comparison to predictions made with the industry standard RAMP code for SRM nozzle flowfield analysis. The FDNS code provides the ability to analyze not only rocket nozzle flow, but also axisymmetric and three-dimensional plume flowfields with state-of-the-art CFD methodology. Procedures for conducting meaningful thermo-vision camera studies were developed.

Farmer, Richard C.↗
DOE OSTI2022

Non-equilibrium plasma generation via nano-second multi-mode laser pulses

The formation and growth of plasma kernels generated via nano-second mode-beating laser pulses is investigated here via a non-equilibrium self-consistent computational model. Chemically reactive Navier–Stokes equations are used to describe the hydrodynamics, and non-equilibrium effects are taken into account with a two-temperature model. Inverse Bremsstrahlung and multiphoton ionization are included self-consistently in the model via a coupled solution of the plasma governing equations and the radiative transfer equation (that describes the laser beam propagation and attenuation). A self-consistent approach (despite carrying additional challenges) minimizes the empiricism and it allows for a more accurate description since it prevents both the utilization of artificial plasma seeds to trigger the breakdown and the implementation of tuning parameters to simulate the laser-energy deposition. The advantages of this approach are confirmed by the good agreement between the numerically predicted and the experimentally measured plasma boundary evolution and absorbed energy. This also holds true for the periodic plasma kernel structures that, as suggested by the experiments and confirmed by the simulations presented here, are connected to the modulating frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Application of satellite data in variational analysis for global cyclonic systems

The goal of the research is a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity were defined. The research performed during the second year fall into four areas: sensitivity studies involving Model 1; evaluation of Model 2; reformation of Model 1 for greater compatibility with Model 2; development of Model 3 (radiative transfer equation); and making the model more responsive to the observations.

Achtemeier, G. L.↗
NASA NTRS2016

A Quasi-Global Approach to Improve Day-Time Satellite Surface Soil Moisture Anomalies through the Land Surface Temperature Input

Passive microwave observations from various spaceborne sensors have been linked to the soil moisture of the Earth's surface layer. A new generation of passive microwave sensors are dedicated to retrieving this variable and make observations in the single theoretically optimal L-band frequency (1-2 GHz). Previous generations of passive microwave sensors made observations in a range of higher frequencies, allowing for simultaneous estimation of additional variables required for solving the radiative transfer equation. One of these additional variables is land surface temperature, which plays a unique role in the radiative transfer equation and has an influence on the final quality of retrieved soil moisture anomalies. This study presents an optimization procedure for soil moisture retrievals through a quasi-global precipitation-based verification technique, the so-called Rvalue metric. Various land surface temperature scenarios were evaluated in which biases were added to an existing linear regression, specifically focusing on improving the skills to capture the temporal variability of soil moisture. We focus on the relative quality of the day-time (01:30 pm) observations from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), as these are theoretically most challenging due to the thermal equilibrium theory, and existing studies indicate that larger improvements are possible for these observations compared to their night-time (01:30 am) equivalent. Soil moisture data used in this study were retrieved through the Land Parameter Retrieval Model (LPRM), and in line with theory, both satellite paths show a unique and distinct degradation as a function of vegetation density. Both the ascending (01:30 pm) and descending (01:30 am) paths of the publicly available and widely used AMSR-E LPRM soil moisture products were used for benchmarking purposes. Several scenarios were employed in which the land surface temperature input for the radiative transfer was varied by imposing a bias on an existing regression. These scenarios were evaluated through the Rvalue technique, resulting in optimal bias values on top of this regression. In a next step, these optimal bias values were incorporated in order to re-calibrate the existing linear regression, resulting in a quasi-global uniform LST relation for day-time observations. In a final step, day-time soil moisture retrievals using the re-calibrated land surface temperature relation were again validated through the Rvalue technique. Results indicate an average increasing Rvalue of 16.5%, which indicates a better performance obtained through the re-calibration. This number was confirmed through an independent Triple Collocation verification over the same domain, demonstrating an average root mean square error reduction of 15.3%. Furthermore, a comparison against an extensive in situ database (679 stations) also indicates a generally higher quality for the re-calibrated dataset. Besides the improved day-time dataset, this study furthermore provides insights on the relative quality of soil moisture retrieved from AMSR-E's day- and night-time observations.

soil moisture↗
NASA NTRS1994

The role of advection in the quasi-static approximation

We discuss the question of the form of the radiative transfer equation in an expanding envelope when a quasi-static approximation is applied. We find that the radiative transfer equation written in the fluid's rest frame must include the `advection' term.

Pistinner, Shlomi↗
NASA NTRS1996

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗
NASA NTRS1985

Limb effects in satellite temperature sounding

To date, operational satellite temperature retrievals from the TIROS-N/NOAA A-G series of satellites and a large percentage of those produced for research purposes have used statistical techniques to estimate limb effects in satellite-observed radiances. In this study, temperature profiles were derived using the radiative transfer equation in a form which properly takes into account the angle of observation. These temperature profiles were then compared to those derived using the radiative transfer equation with 'nadir radiances' produced by a statistical limb correction technique similar to those now used operationally. This comparison revealed significant differences in the derived temperature profiles at large viewing angles, particularly in the case of strong meridional temperature gradients. Overall, the results suggest that for the calculation of temperature profiles from nonnadir observations, the more proper physical solution is the preferred procedure for deriving temperature fields.

Le Marshall, J. F.↗
NASA NTRS2019

A Fast All-Sky Radiation Model for Solar Applications with Narrowband Irradiances on Tilted Surfaces (FARMS-NIT): Part II. The Cloudy-Sky Model

The Fast All-sky Radiation Model for Solar applications with Narrowband Irradiances on Tilted surfaces (FARMSNIT) reported in Part I of this study is enhanced to include the requirements for cloudy-sky conditions. Surface radiances in 2002 narrow-wavelength bands from 0.28 to 4.0 μm are analytically computed by solving the radiative transfer equation for five independent photon paths accounting for clear-sky absorption, Rayleigh scattering, and cloud absorption and scattering. The Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS) is used to provide the optical thickness of the clear-sky atmosphere. Unlike Part I, which approximates the computation of aerosol scattering using the single-scattering phase function, the cloud transmittance and reflectance are efficiently retrieved from a comprehensive look-up table pre-computed by a 32-stream DIScrete Ordinates Radiative Transfer (DISORT) model for possible cloud conditions as well as solar and viewing geometries. A resolution analysis is performed to assess the optimal balance between the computational efficiency and accuracy in the development of the look-up table. Model simulations by DISORT and TMYSPEC are used to evaluate the performance of FARMS-NIT under cloudy-sky conditions. Compared to DISORT, FARMS-NIT yields 2–3% uncertainties on average, but it substantially reduces the computational time because of the independent computation of cloud properties and the implementation of the look-up table. In contrast to TMYSPEC, which uses successive steps to empirically compute plane-of-array (POA) irradiances and spectral irradiances, FARMS-NIT directly solves spectral radiances from the radiative transfer equation, which profoundly increases the accuracy in surface irradiances, especially over inclined photovoltaics (PV) panels.

Xie, Yu↗
NASA NTRS1985

Theory of microwave remote sensing

Active and passive microwave remote sensing of earth terrains is studied. Electromagnetic wave scattering and emission from stratified media and rough surfaces are considered with particular application to the remote sensing of soil moisture. Radiative transfer theory for both the random and discrete scatterer models is examined. Vector radiative transfer equations for nonspherical particles are developed for both active and passive remote sensing. Single and multiple scattering solutions are illustrated with applications to remote sensing problems. Analytical wave theory using the Dyson and Bethe-Salpeter equations is employed to treat scattering by random media. The backscattering enhancement effects, strong permittivity fluctuation theory, and modified radiative transfer equations are addressed. The electromagnetic wave scattering from a dense distribution of discrete scatterers is studied. The effective propagation constants and backscattering coefficients are calculated and illustrated for dense media.

Tsang, L.↗
NASA NTRS1980

Radiative transfer theory for passive microwave remote sensing of a two-layer random medium with cylindrical structures

A model of the vegetation layer as a two-layer random medium with a small correlation length l sub rho in the horizontal direction, and a large correlation length l sub z in the vertical direction, is presented for fields with cylindrical structures. As l sub z approaches infinity, closed form solutions are derived for the brightness temperatures; the kernels in the scattering terms of the radiative transfer equations result in delta functions showing that forward scattering is dominant over all other directions. The results are compared with the Gaussian quadrature method data for numerical solution of the radiative transfer equations.

Chuang, S. L.↗
NASA NTRS1984

Radiative transfer theory for active remote sensing of a layer of nonspherical particles

The radiative transfer theory is applied to calculate the scattering by a layer of randomly positioned and oriented nonspherical particles. The scattering amplitude functions of each individual particle are calculated with Waterman's T matrix method, which utilizes vector spherical wave functions for expansion of incident, scattered, and surface fields. The orientation of the particles is described by a probability density function of the Eulerian angles of rotation. A rotation matrix is used to relate the T matrix of the principal frame to that of the natural frame of the particle. The extinction matrix and phase matrix of the radiative transfer equations are expressed in terms of the T matrix elements. The extinction matrix for nonspherical particles is generally nondiagonal. There are only two attenuation rates in a specified direction of propagation. The radiative transfer equations are solved by an iterative method to first order in albedo. Numerical results are illustrated as functions of incidence angle and frequency with applications to active remote sensing.

Tsang, L.↗
NASA NTRS2018

An Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. II: Approach Based on the Dyson and Bethe-Salpeter Equations

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scattering expansion of the total field, we derive the Dyson equation for the coherent field and the ladder approximated Bethe–Salpeter equation for the dyadic correlation function. Then, under the far-field assumption for sparsely distributed particles, the Dyson equation is reduced to the Foldy integral equation for the coherent field, while the iterated solution of the Bethe–Salpeter equation ultimately yields the vector radiative transfer equation.

Electromagnetic scattering↗
NASA NTRS2002

A New Look Into the Treatment of Large Drops in Radiative Transfer

One of the weakest links in conventional cloud radiation models is the way a size distribution of cloud particles is mathematically handled: one averages measured drop concentrations over space, evaluates the extinction and scattering cross sections using the mean drop size distribution function and solves the radiative transfer equation with average characteristics. This technique assumes that all drop sizes are well represented in ary given interval along the direction of photon travel. But the concentration of large drops can be so law that this assumption is significantly violated. This is clearly seen if one examines of how the appearance of drops changes with the scale. In the poster we demonstrate the results of our analysis of FSSP data acquired during FIRE'87 and both FSSP and DC1 data from cloud IOP in Spring 2000. The analysis shows that, in general, the average number of drops observed in an interval along the direction of photon travel is proportional to the interval's length (or scale) powered to a drop scaling exponent. For small droplets the scaling exponent is equal to 1, as predicted by a conventional radiative transfer model. However, for large drops, the scaling exponent can fall distinctly below 1. Since the solution of radiative transfer equation depends on the drop scaling exponent, its deviation from unity can lead to a systematic bias in estimation of cloud radiative properties. We discuss the importance of the scaling exponent for the characteristics of the small-scale drop size variability for large and small droplets. Most of the existing cloud radiation models, however, are insensitive to this parameter.

Marshak, Alexander↗
NASA NTRS1992

Application of radiative image transfer theory to the assessment of the overall OTF and contrast degradation of an image in an inhomogeneous turbulent and turbid atmosphere

A perturbation-theoretic approximation of the radiative transfer equation which neglects photon dispersion is used as a modeling basis for the propagation of the image of a self-luminous target through a turbulent atmosphere which also possesses inhomogeneously distributed turbidity along the propagation path. A contrast ratio is then introduced which provides an indicator of the relative contribution of the unscattered or coherent image component to that of the scattered or incoherent image component. Analytical expressions are then derived for the contrast ratio from the approximate form of the radiative transfer equation in the case of an inhomogeneously dispersed Joss thunderstorm rain distribution in the presence of turbulence. The case is clearly demonstrated for the need to consider a measure of the points of demarcation at which the dominant roles of the scattering processes due to turbidity and turbulence are exchanged. Such a measure can provide a performance parameter for the application of adaptive optics methods that are specific to the particular dominant scattering mechanism given the prevailing target size, total propagation length and overall propagation parameters.

Manning, Robert M.↗
NASA NTRS1979

On the Angular Variation of Solar Reflectance of Snow

Spectral and integrated solar reflectance of nonhomogeneous snowpacks were derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface was considered and for subsurface multiple scattering, an approximate solution of the radiative transfer equation was studied. Solar radiation incident on the snowpack was decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol and molecular scattering were included in the calculation of incident solar radiation. Illustrative numerical results were given for a case of North American winter atmospheric conditions. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation was in qualitative agreement with available observations.

Chang, A. T. C.↗