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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Investigation of supersonic chemically reacting and radiating channel flow

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Mani, Mortaza↗
NASA NTRS1985

Multidimensional Modeling of Atmospheric Effects and Surface Heterogeneities on Remote Sensing

The overall goal of this project is to establish a modeling capability that allows a quantitative determination of atmospheric effects on remote sensing including the effects of surface heterogeneities. This includes an improved understanding of aerosol and haze effects in connection with structural, angular, and spatial surface heterogeneities. One important objective of the research is the possible identification of intrinsic surface or canopy characteristics that might be invariant to atmospheric perturbations so that they could be used for scene identification. Conversely, an equally important objective is to find a correction algorithm for atmospheric effects in satellite-sensed surface reflectances. The technical approach is centered around a systematic model and code development effort based on existing, highly advanced computer codes that were originally developed for nuclear radiation shielding applications. Computational techniques for the numerical solution of the radiative transfer equation are adapted on the basis of the discrete-ordinates finite-element method which proved highly successful for one and two-dimensional radiative transfer problems with fully resolved angular representation of the radiation field.

Gerstl, S. A. W.↗
NASA NTRS1994

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗
NASA NTRS1989

Variational objective analysis for cyclone studies

Significant accomplishments during 1987 to 1988 are summarized with regard to each of the major project components. Model 1 requires satisfaction of two nonlinear horizontal momentum equations, the integrated continuity equation, and the hydrostatic equation. Model 2 requires satisfaction of model 1 plus the thermodynamic equation for a dry atmosphere. Model 3 requires satisfaction of model 2 plus the radiative transfer equation. Model 4 requires satisfaction of model 3 plus a moisture conservation equation and a parameterization for moist processes.

Achtemeier, Gary L.↗
NASA NTRS1991

Thomson scattering in a magnetic field. I - Field along z

The Monte Carlo method is used here to solve the radiative transfer equation for Thomson scattering in a constant magnetic field perpendicular to the atmosphere. Emergent radiation and polarization are presented for various atmospheric thicknesses. The circular polarization peaks at frequencies near the cyclotron, omega(c), and for propagation direction along the field. At low field strengths, the circular polarization is roughly proportional to omega(c)/omega; the linear polarization is proportional to the square of omega(c)/omega and the amount of circular polarization present at each scatter and is therefore much smaller than the circular polarization. The linear polarization is large for propagation direction perpendicular to the magnetic field and at frequencies near the cyclotron and in the strong-field limit. The position angle of the linear polarization undergoes a rotation of 90 deg at a value of omega(c)/omega near the square root of three.

Whitney, Barbara A.↗
NASA NTRS1996

Two-Flux Method for Transient Radiative Transfer in a Semitransparent Layer

The two-flux method was used to obtain transient solutions for a plane layer including internal reflections and scattering. The layer was initially at uniform temperature, and was heated or cooled by external radiation and convection. The two-flux equations were examined as a means for evaluating the radiative flux gradient in the transient energy equation. Comparisons of transient temperature distributions using the two-flux method were made with results where the radiative flux gradient was evaluated from the exact radiative transfer equations. Good agreement was obtained for optical thicknesses from 0.5 to 5 and for refractive indices of 1 and 2. Illustrative results obtained with the two-flux method demonstrate the effect of isotropic scattering coupled with changing the refractive index. For small absorption with large scattering the maximum layer temperature is increased when the refractive index is increased. For larger absorption the effect is opposite, and the maximum temperature decreases with increased refractive index .

Siegel, Robert↗
NASA NTRS2000

Forward Monte Carlo Computations of Polarized Microwave Radiation

Microwave radiative transfer computations continue to acquire greater importance as the emphasis in remote sensing shifts towards the understanding of microphysical properties of clouds and with these to better understand the non linear relation between rainfall rates and satellite-observed radiance. A first step toward realistic radiative simulations has been the introduction of techniques capable of treating 3-dimensional geometry being generated by ever more sophisticated cloud resolving models. To date, a series of numerical codes have been developed to treat spherical and randomly oriented axisymmetric particles. Backward and backward-forward Monte Carlo methods are, indeed, efficient in this field. These methods, however, cannot deal properly with oriented particles, which seem to play an important role in polarization signatures over stratiform precipitation. Moreover, beyond the polarization channel, the next generation of fully polarimetric radiometers challenges us to better understand the behavior of the last two Stokes parameters as well. In order to solve the vector radiative transfer equation, one-dimensional numerical models have been developed, These codes, unfortunately, consider the atmosphere as horizontally homogeneous with horizontally infinite plane parallel layers. The next development step for microwave radiative transfer codes must be fully polarized 3-D methods. Recently a 3-D polarized radiative transfer model based on the discrete ordinate method was presented. A forward MC code was developed that treats oriented nonspherical hydrometeors, but only for plane-parallel situations.

Battaglia, A.↗
NASA NTRS1993

Radiation/convection coupling in rocket motors and plumes

The three commonly used propellant systems - H2/O2, RP-1/O2, and solid propellants - primarily radiate as molecular emitters, non-scattering small particles, and scattering larger particles, respectively. Present technology has accepted the uncoupling of the radiation analysis from that of the flowfield. This approximation becomes increasingly inaccurate as one considers plumes, interior rocket chambers, and nuclear rocket propulsion devices. This study will develop a hierarchy of methods which will address radiation/convection coupling in all of the aforementioned propulsion systems. The nature of the radiation/convection coupled problem is that the divergence of the radiative heat flux must be included in the energy equation and that the local, volume-averaged intensity of the radiation must be determined by a solution of the radiative transfer equation (RTE). The intensity is approximated by solving the RTE along several lines of sight (LOS) for each point in the flowfield. Such a procedure is extremely costly; therefore, further approximations are needed. Modified differential approximations are being developed for this purpose. It is not obvious which order of approximations are required for a given rocket motor analysis. Therefore, LOS calculations have been made for typical rocket motor operating conditions in order to select the type approximations required. The results of these radiation calculations, and the interpretation of these intensity predictions are presented herein.

Farmer, R. C.↗
NASA NTRS1989

IR emission from circumstellar envelopes of C-rich stars

The reliability of a theoretical model that solves the radiative transfer equation in dust clouds surrounding a central star is checked. In particular, it is found that both classical scattering by dust and the back-heating effects are negligible in the radiative transfer when envelopes similar to IRC+10216 are taken into consideration. In addition, new fits of IRC+10216 spectra are presented which were obtained, when the source is in different luminosity phases, under the assumption that amorphous carbon grains are in the circumstellar envelope. The same model is currently used to simulate the emission from carbon-rich sources showing the silicon carbide feature at 11.3 microns.

Blanco, A.↗
NASA NTRS1976

Solution of the comoving-frame equation of transfer in spherically symmetric flows. IV - Frequency-dependent source functions for scattering by atoms and electrons

A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles.

Mihalas, D.↗
NASA NTRS2001

Numerical Investigation of Radiative Heat Transfer in Laser Induced Air Plasmas

Radiative heat transfer is one of the most important phenomena in the laser induced plasmas. This study is intended to develop accurate and efficient methods for predicting laser radiation absorption and plasma radiative heat transfer, and investigate the plasma radiation effects in laser propelled vehicles. To model laser radiation absorption, a ray tracing method along with the Beer's law is adopted. To solve the radiative transfer equation in the air plasmas, the discrete transfer method (DTM) is selected and explained. The air plasma radiative properties are predicted by the LORAN code. To validate the present nonequilibrium radiation model, several benchmark problems are examined and the present results are found to match the available solutions. To investigate the effects of plasma radiation in laser propelled vehicles, the present radiation code is coupled into a plasma aerodynamics code and a selected problem is considered. Comparisons of results at different cases show that plasma radiation plays a role of cooling plasma and it lowers the plasma temperature by about 10%. This change in temperature also results in a reduction of the coupling coefficient by about 10-20%. The present study indicates that plasma radiation modeling is very important for accurate modeling of aerodynamics in a laser propelled vehicle.

Liu, J.↗
NASA NTRS1978

Microwave emission from polar firn

The microwave emission from a half-space medium, characterized by coordinate dependent scattering and absorbing centers, was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. Rayleigh scattering phase functions and scattering induced polarization of the radiation were included in the calculation. Using the scattering and extinction data of polar firn the brightness temperature was calculated for the 1.55 cm wavelength. This study was the first quantitative comparison of the results of numerical calculation using the actual measured information of crystal size with the observed data.

Chang, A. T. C.↗
NASA NTRS1987

Relationships between vegetation indices, radiation absorption, and net photosynthesis evaluated by a sensitivity analysis

A two-stream approximation to the radiative-transfer equation is used to calculate the vegetation indices (simple ratio and normalized difference), the fraction of incident photosynthetically active radiation (PAR) absorbed by the canopy, and the daily mean canopy net photosynthesis under clear-sky conditions. The model calculations are tested against field observations over wheat, cotton, corn, and soybean. The relationships between the vegetation indices and radiation absorption or net photosynthesis are generally found to be curvilinear, and changes in the soil reflectance affected these relationships. The curvilinearity of the relationship between normalized differences and PAR absorption decreases as the magnitude of soil reflectance increases. The vegetation indices might provide the fractional radiation absorption with some a priori knowledge about soil reflectance. The relationship between the vegetation indices and net photosynthesis must be distinguished for C3 and C4 crops. Effects of spatial heterogeneity are discussed.

Choudhury, Bhaskar J.↗
NASA NTRS1993

Calculation of the angular radiance distribution for a coupled atmosphere and canopy

The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Gauss-Seidel algorithm has been widely applied in atmospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extinction coefficients of upward single scattering radiation and unscattered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.

Liang, Shunlin↗
NASA NTRS1996

Precision and Radiosonde Validation of Satellite Gridpoint Temperature Anomalies. Part I; MSU Channel 2: MSU Channel 2 - Pt. 1

In Part 1 of this study, monthly 2.5 deg. gridpoint anomalies in the TIROS-N (Television and Infrared Operational Satellite-N) series Microwave Sounding Unit (MSU) channel 2 brightness temperatures during 1979-88 are evaluated with multiple satellites and radiosonde data for their climate temperature monitoring capability. The MSU anomalies we computed about a 10-year mean annual cycle at each grid point, with the MSUs intercalibrated to a common arbitrary level. The intercalibrations remove relative biases between instruments of up to several tenths of a degree celsius. The monthly gridpoint anomaly agreement between concurrently operating satellites reveals single-satellite precision on generally better than 0.07 C in the tropics and better than 0.15 C at higher latitudes. Monthly anomalies in radiosonde channel 2 brightness temperatures computed with the radiative transfer equation compare very closely to the MSU measured anomalies in all climate zones, with correlations generally from 0.94 to 0.98 and standard errors of 0.15 C in the tropics to 0.30 C at high latitudes. Simplification of these radiative transfer calculations to a static weighting profile applied to the radiosonde temperature profile leads to an average degradation of only 0.02 deg. in the monthly skill. In terms of a more traditionally measured quantity, the MSU channel 2 anomalies match best with either the radiosonde 100-20-kPa or 100-15-kPa layer anomalies. No significant spurious trends were found in the 10-yr satellite dataset compared to the radiosondes that would indicate a calibration drift in either system. Thus, sequentially launched, overlapping passive microwave radiometers provide a useful system for monitoring intraseasonal to interannual climate anomalies and offer hope for monitoring of interdecadal trends from space. The Appendix includes previously unpublished details of the MSU gridpoint anomaly dataset construction. Part II of this study addresses the removal from channel 2 of the temperature influence above the 30-kPa level, providing a sharper and thus potentially more useful weighting function for monitoring lower tropospheric temperatures.

Spencer, Roy W.↗
NASA NTRS1977

A novel methodology for radiative transfer in a planetary atmosphere. I - The functions a exponent m and b exponent m of anisotropic scattering

The original problem of anisotropic scattering in an atmosphere illuminated by a unidirectional source is replaced by an analogous formulation where the incident light is omnidirectional. A radiative-transfer equation for the omnidirectional case is obtained in which the direction of illumination plays no role and the source-function analog, Sobolev's (1972) source function Phi exponent m, contains only a single integral term. For radiation incident on the top or the bottom of the atmosphere, this equation involves the functions b exponent m and h exponent m, respectively, with m corresponding to the order of the harmonic component of the scattered radiation field; these two functions are shown to be only one through some simple reciprocity relations. The transfer problem is then reformulated for the function a exponent m, in which case the source-function analog (Sobolev's function D exponent m) involves incident direction.

Fymat, A. L.↗
NASA NTRS2013

Time-Dependent Photoionization of Gaseous Nebulae: The Pure Hydrogen Case

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full timedependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionizationthermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and nonlinearly from the illuminated face of the cloud to the ionization front (IF). IFthermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solution. Moreover, even the time average of ionization and temperature is different from any steady-state case. This time average is characterized by overionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is a large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of nonlinear propagation times for thermal frontsIFs and equilibration times.

Seyfert↗
NASA NTRS2007

Effect of an Opaque Reflecting Layer on the Thermal Behavior of a Thermal Barrier Coating

A parametric study using a two-flux approximation of the radiative transfer equation was performed to examine the effects of an opaque reflective layer on the thermal behavior of a typical semitransparent thermal barrier coating on an opaque substrate. Some ceramic materials are semitransparent in the wavelength ranges where thermal radiation is important. Even with an opaque layer on each side of the semitransparent thermal barrier coating, scattering and absorption can have an effect on the heat transfer. In this work, a thermal barrier coating that is semitransparent up to a wavelength of 5 micrometers is considered. Above 5 micrometers wavelength, the thermal barrier coating is opaque. The absorption and scattering coefficient of the thermal barrier was varied. The thermal behavior of the thermal barrier coating with an opaque reflective layer is compared to a thermal barrier coating without the reflective layer. For a thicker thermal barrier coating with lower convective loading, which would be typical of a combustor liner, a reflective layer can significantly decrease the temperature in the thermal barrier coating and substrate if the scattering is weak or moderate and for strong scattering if the absorption is large. The layer without the reflective coating can be about as effective as the layer with the reflective coating if the absorption is small and the scattering strong. For low absorption, some temperatures in the thermal barrier coating system can be slightly higher with the reflective layer. For a thin thermal barrier coating with high convective loading, which would be typical of a blade or vane that sees the hot sections of the combustor, the reflective layer is not as effective. The reflective layer reduces the surface temperature of the reflective layer for all conditions considered. For weak and moderate scattering, the temperature of the TBC-substrate interface is reduced but for strong scattering, the temperature of the substrate is increased slightly.

Spuckler, Charles M.↗