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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Numerical Solution of the Radiative Transfer Equation: X-Ray Spectral Formation from Cylindrical Accretion onto a Magnetized Neutron Star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative transfer equation according to the expected physical conditions of the systems under study. Aims. We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system pi using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth pi produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions. The algorithm has been implemented in the XPEC package for X-ray fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (approx > 10(exp 12) G). This latter case is expected to be of typical accreting systems such as X-ray pulsars and supergiant fast X ray transients.

Fairnelli, R.↗
NASA NTRS1972

A general relaxation method for inverse solution of the full radiative transfer equation.

The relaxation method for the inverse solution of the full radiative transfer equation is generalized to solve for all atmospheric parameters which appear in the integrand as functions or functionals, without any a priori information related to the expected solution. The method is illustrated by examples in the earth's atmosphere for the determination of water vapor mixing ratio profiles from observations in the 6.3-micron band.

Chahine, M. T.↗
NASA NTRS1995

Temperature Distributions in Semitransparent Coatings: A Special Two-Flux Solution

Radiative transfer is analyzed in a semitransparent coating on an opaque substrate and in a semitransparent layer for evaluating thermal protection behavior and ceramic component performance in high temperature applications. Some ceramics are partially transparent for radiative transfer, and at high temperatures internal emission and reflections affect their thermal performance. The behavior is examined for a ceramic component for which interior cooling is not provided. Two conditions are considered: (1) the layer is heated by penetration of radiation from hot surroundings while its external surface is simultaneously film cooled by convection, and (2) the surface is heated by convection while the semitransparent material cools from within by radiant emission leaving through the surface. By using the two-flux method, which has been found to yield good accuracy in previous studies, a special solution is obtained for these conditions. The analytical result includes isotropic scattering and requires only an integration to obtain the temperature distribution within the semitransparent material. Illustrative results are given to demonstrate the nature of the thermal behavior.

Siegel, Robert↗
NASA NTRS1974

Solution of the radiative transfer theory problems by the Monte Carlo method

The Monte Carlo method is used for two types of problems. First, there are interpretation problems of optical observations from meteorological satellites in the short wave part of the spectrum. The sphericity of the atmosphere, the propagation function, and light polarization are considered. Second, problems dealt with the theory of spreading narrow light beams. Direct simulation of light scattering and the mathematical form of medium radiation model representation are discussed, and general integral transfer equations are calculated. The dependent tests method, derivative estimates, and solution to the inverse problem are also considered.

Marchuk, G. I.↗
NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗
NASA NTRS1993

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Menart, J. A.↗
NASA NTRS1973

Exact analytical solution to a transient conjugate heat-transfer problem

An exact analytical solution is found for laminar, constant-property, slug flow over a thin plate which is also convectively cooled from below. The solution is found by means of two successive Laplace transformations when a transient in the plate and the fluid is initiated by a step change in the fluid inlet temperature. The exact solution yields the transient fluid temperature, surface heat flux, and surface temperature distributions. The results of the exact transient solution for the surface heat flux are compared to the quasi-steady values, and a criterion for the validity of the quasi-steady results is found. Also the effect of the plate coupling parameter on the surface heat flux are investigated.

Sucec, J.↗
NASA NTRS2006

Two Phase Flow Modeling: Summary of Flow Regimes and Pressure Drop Correlations in Reduced and Partial Gravity

The purpose of this report is to provide a summary of state-of-the-art predictions for two-phase flows relevant to Advanced Life Support. We strive to pick out the most used and accepted models for pressure drop and flow regime predictions. The main focus is to identify gaps in predictive capabilities in partial gravity for Lunar and Martian applications. Following a summary of flow regimes and pressure drop correlations for terrestrial and zero gravity, we analyze the fully developed annular gas-liquid flow in a straight cylindrical tube. This flow is amenable to analytical closed form solutions for the flow field and heat transfer. These solutions, valid for partial gravity as well, may be used as baselines and guides to compare experimental measurements. The flow regimes likely to be encountered in the water recovery equipment currently under consideration for space applications are provided in an appendix.

Balasubramaniam, R.↗
NASA NTRS1983

An integral solution procedure for radiative transfer in concentric cylindrical media

A complete integral formulation is developed for radiative transfer in emitting and absorbing media contained between infinitely long, concentric cylinders with black surfaces. The resulting flux equation is used to state both the gray and nongray radiative equilibrium problems that are solved numerically with controlled error. The results are compared with those from other approaches, both approximate and geometrically limiting, to check and put into perspective the present and prior work. The nongray solution is unique for concentric cylindrical media. The independent parameters of optical thickness and radius ratio are varied to study the emissive power (temperature) distribution, total heat flux, and the required computational time.

Pandey, D. K.↗
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.↗