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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
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.↗
DOE OSTI2020

The Numerical Computation of Clear-Sky Transmittance and Reflectance of Solar Radiation for the Modeling of PV System Performance

Modeling of photovoltaics (PV) system performance requires numerical computation of plane-of-array (POA) irradiances that are influenced by atmospheric absorption and scattering. Clear-sky transmittance and reflectance of diffuse irradiance are essential for the understanding of solar radiation related to multiple reflection between land surface and clouds. This study analytically solves the radiative transfer equation for clear-sky conditions and numerically computes the transmittance and reflectance of diffuse irradiance as functions of the optical thickness of the atmosphere. The computation will be implemented in all-sky radiative transfer models to improve their computational efficiency.

14 SOLAR ENERGY↗
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.↗
DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
DOE OSTI2020

Collinear dual-pulse laser optical breakdown and energy deposition

A non-equilibrium model for laser-generated plasmas is used to represent collinear dual nano-second-pulse interactions. In the specific case considered, the breakdown is initiated with an ultraviolet (UV) laser pulse at 266 nm, which pre-ionizes the gas, and it is followed by a near-infrared (NIR) pulse at 1064 nm, which deposits significant energy into the ionized mixture. The model is validated against corresponding experiments, and simulation results are interrogated to understand key features of the plasma-kernel dynamics and the post-discharge hydrodynamics. The hydrodynamics of the non-equilibrium plasma is governed by the two-temperature Navier–Stokes equations accounting for both multiphoton ionization and inverse bremsstrahlung. The interaction between the laser beam and the plasma is modeled based on the radiative transfer equation. The temporal and spatial offsets of the two pulses can generate ionization kernels with different topology and dynamics. It is shown that the UV pre-ionization pulse can tailor the plasma region, leading to a larger ionized volume than would occur for a single-pulse breakdown, and it increases the efficiency of the energy deposition for the following NIR discharge. Vorticity in the early post-discharge phase is generated via baroclinic torque from the misalignment of the radial gradient of density (sudden gas expansion) and the strong pressure gradient (initiated by energy deposition from the laser beam). It is predicted that the collinear dual pulse can be designed to specify the plasma kernel size, shape, and maximum temperature in the breakdown phase, and the initial post-breakdown vorticity and plasma-core decay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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.↗
NASA NTRS1993

The effects of zonal atmospheric currents on the spectra of rotating early-type stars

We suggest the existence of zonal currents in the atmospheres of rapidly rotating stars analogous to those found in planetary atmospheres. The zonal flow is assumed to be characterized by 'thin' atmospheric, nearly geostrophic flow which does not change the gravity darkening and stellar shape determined by the underlying uniformly rotating model. The contribution that such flows make to the continuum spectra of such stars is investigated. The additional rotationally induced Doppler displacement resulting from such zonal wind belts can distort the rotationally broadened stellar lines leading to significant departures from the line profiles predicted by the classical model of rotating stars. Our estimates of the zonal flow velocity stem from the assumption of a relation between it and the latitudinal wavenumber of the zonal velocity field. It is thus possible to create barotropic atmosphere models which, in turn, enable the modeling of the stellar spectrum including important spectral lines. In addition, the radiative transfer equations for the Stokes parameters I and Q are solved for the locally plane-parallel atmospheres so that the polarization structure of the radiation field is determined. We find that the presence of zonal wind belts leads to significant changes in the photospheric polarization from those characteristic of a uniformly rotating model.

Cranmer, Steven R.↗
NASA NTRS1975

On the use of a finite difference method for solving anisotropic scattering problems

A new method of solving the radiative transfer equation is developed in which the scattering and absorption coefficients may have arbitrary variations with depth, and in which both internal (thermal) emission and incident radiation are allowed. Specular and diffuse reflection at both boundaries also is taken into account. The method begins by forming a paired set of coupled first-order differential equations for the symmetric and antisymmetric parts of the radiation field after writing the scattering integral as a numerical quadrature. These differential equations are broken into finite difference form, in which the symmetric and antisymmetric parts of the radiation field are found on alternate grid points. Numerical results for a number of test problems are shown, demonstrating that the method is very fast, that it returns specific intensities and fluxes that are accurate to at least a percent, and that it can be applied to optically thick problems.

Barkstrom, B. R.↗
NASA NTRS1978

Some effects of 8-12 micron radiant energy transfer on the mass and heat budgets of cloud droplets

In standard treatments of the mass and energy budget of cloud droplets, radiant energy transfer is neglected on the grounds that the temperature difference between the droplet and its surroundings is small. This paper includes the effect of radiant heating and cooling of droplets by using the Eddington approximation for the solution of the radiative transfer equation. Although the calculation assumes that the cloud is isothermal and has a constant size spectrum with altitude, the heating or cooling of droplets by radiation changes the growth rate of the droplets very significantly. At the top of a cloud with a base at 2500 m and a top at 3000 m, a droplet will grow from 9.5 to 10.5 microns in about 4 min, assuming a supersaturation ratio of 1.0013. Such a growth rate is more than 20 times the growth rate for condensation alone, and may be expected to have a significant impact on estimates of precipitation formation as well as on droplet spectrum calculations.

Barkstrom, B. R.↗