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At least 1,333 records · Page 74
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NASA NTRS1972

A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate

A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.

Dow, J. W.↗
NASA NTRS1971

The present state of gamma-ray astronomy.

The current state of gamma-ray astronomy is reviewed in terms of the most recent experimental results that define, in either measured fluxes or upper limits, the cosmic photon spectrum in the energy range from 0.5 MeV to 10,000 TeV. Methods of research developed during the last 10 yr are discussed and specific results are cited. Cosmic gamma rays have been observed in two regions of the spectrum - from 0.5 to 6 MeV and from about 50 MeV to several hundred mega-electronvolts. Above 50 MeV, a strong concentration of intensity is observed in a band of directions around the galactic equator. In both spectral regions a diffuse background gamma ray flux, apparently isotropic and of extragalactic origin, is observed. Evidence of 50 MeV gamma-ray pulses from the Crab pulsar has been reported. No definite evidence of any other discrete gamma-ray source besides the galaxy itself has been observed at any energy.

Clark, G.↗
NASA NTRS1974

Implications of the reported low energy electron gradients

A recently reported measurement of a small electron gradient in the energy range from 1.9 to 8.4 MeV by Webber et al. (1973) is interpreted in terms of a large local value of the scattering mean free path for these particles. The possibility that the scattering mean free path may be large throughout the modulation region is then investigated under the assumption of an azimuthally symmetric modulation region of 5 AU extent, the applicability of the diffusion-convection-adiabatic energy loss transport equation, and a galactic origin for the low-energy electrons. The implications for the solar modulation of electrons and the interstellar electron spectrum are discussed.

Lezniak, J. A.↗
NASA NTRS1975

Bidirectional plant canopy reflection models derived from the radiation transfer equation

A collection of bidirectional canopy reflection models was obtained from the solution of the radiation transfer equation for a horizontally homogeneous canopy. A phase function is derived for a collection of bidirectionally reflecting and transmitting planar elements characterized geometrically by slope and azimuth density functions. Two approaches to solving the radiation transfer equation for the canopy are presented. One approach factors the radiation transfer equation into a solvable set of three first-order linear differential equations by assuming that the radiation field within the canopy can be initially approximated by three components: uniformly diffuse downwelling, uniformly diffuse upwelling, and attenuated specular. The solution to these equations, which can be iterated to any degree of accuracy, was used to obtain overall canopy reflection from the formal solution to the radiation transfer equation. A programable solution to canopy overall bidirectional reflection is given for this approach. The special example of Lambertian leaves with constant leaf bidirectional reflection and scattering functions is considered, and a programmable solution for this example is given. The other approach to solving the radiation transfer equation, a generalized Chandrasekhar technique, is presented in the appendix.

Beeth, D. R.↗
NASA NTRS1980

On the dynamics of agglomerating ensembles of clouds

It is shown that for dynamical time scales longer than 10 million years the ensemble of interstellar cold diffuse clouds may be described by equations of mass and momentum conservation where the pressure has the form p/v-squared/ where /v-squared/ is the mass averaged square velocity dispersion. Equilibrium cloud spectra are derived and an equation of state obtained. The equation of state undergoes a phase transition at a critical density close to the local interstellar gas density. At higher densities, more massive clouds are formed and the cloud fluid softens. It is suggested that this mechanism may naturally regulate the interstellar gas density if star formation is very efficient in the cooler high-density systems.

Cowie, L. L.↗
NASA NTRS1981

Analytical description of charged particle transport along arbitrary guiding-field configurations

Focused particle transport is analyzed in terms of partial differential equations which are applicable to arbitrary spatial variations of the mean free path and the focusing length. A distribution function for transport is written in two forms of the Boltzmann equation and a coefficient of spatial diffusion is defined. Changes from a nearly coherent propagation of flare particles in regions of strong focusing near the sun to ordinary diffusion in the outer solar system are described as supercoherent transitions. A solution to the steady state problem is developed and results are presented for a monopolar guiding field configuration with isotropic diffusion gradually giving way to anisotropy in a region suggestive of a collimated beam of particles streaming away from its source.

Earl, J. A.↗
NASA NTRS1982

Ion temperature variations in the daytime high-latitude F region

The Schunk and Sojka (1981a, b) high latitude ionospheric model is improved through the inclusion of thermal conduction and diffusion terms in the ion energy equation, permitting the study of daytime, high latitude F layer temperature variations in a region poleward of the auroral oval. It is found that ion temperature variation with solar cycle, season and geomagnetic activity closely follows the neutral atomic oxygen variation, and that meridional electric fields of more than 40 mV/m can cause larger ion temperature changes than those due to solar cycle, seasonal or geomagnetic activity variations. In the presence of meridional electric fields, there is an upward flow of heat from the lower ionosphere that also acts to raise ion temperatures at high altitudes. Zonal electric fields affect ion temperature indirectly, through electron density changes.

Schunk, R. W.↗
NASA NTRS1983

The diffusivity of hydrogen in Nb stabilized stainless steel

The evolution of hydrogen from 347 stainless steel has been studied by using a real time dynamic technique under ultrahigh vacuum conditions. Auger electron spectroscopy was used to determine the surface composition as a function of time and temperature. The surface film on the electropolished samples was found to be approximately 15 A thick and consisted of a carbon-oxygen complex and a metal oxide (FexOy). Upon heating to 400 C, the carbon-oxygen complex desorbed as CO and the remaining oxygen and carbon began to incorporate. Also at this temperature sulfur began to diffuse out of the bulk to the surface and at approximately 800 C formed a complete monolayer. At 900 C, carbon and oxygen virtually disappeared, leaving the monolayer of sulfur as the only surface contaminant. The hydrogen diffusivity was found to follow closely the equation D = 7.01 x 10 to the -7th exp(-48.0/RT) sq m per second over the entire temperature range studied, thus indicating that hydrogen evolution is not significantly affected by the changing surface composition. The somewhat higher value of the diffusivity obtained in this work compared to past measurements in austenitic stainless steels may indicate the importance of sample preprocessing and ultrahigh vacuum conditions in minimizing the effects of surface layers.

Outlaw, R. A.↗
NASA NTRS1986

Losses in Channels with Increased External Turbulence

An approximate method for determining the effect of the level of turbulence on the aerodynamic characteristics of convergent and diffuser channels is examined. A momentum equation for the boundary layer is in the method, introducing external flow turbulence on the basis of experimental values of the coefficient of friction and the form factor. It is found that at significant levels of external turbulence, losses must be considered not only in the boundary layer but also in the central region of the channel.

Zaryankin, A. Y.↗
NASA NTRS1986

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗
NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗
NASA NTRS1989

Computations of turbulent evaporating sprays

A computational study of turbulent evaporating sprays is reported. The major focus is to examine the sensitivity of the vaporization behavior of turbulent sprays to the transient liquid-phase processes. Three models considered to represent these processes are the thin skin, infinite diffusion, and diffusion limit models. Favre-averaged equations with k-epsilon-g turbulence model are employed for the gas phase. The Lagrangian approach with a stochastic separated flow method is used for the liquid phase where the effects of gas turbulence on droplet trajectories and interphase transport rates are considered using random-walk computations. Also the variable-property effects are considered in detail. Results indicate that, depending upon the boiling temperature and heat of vaporization of the fuel considered, the vaporization behavior of turbulent sprays may be quite sensitive to the modeling of transient liquid-phase processes. Thus, it is important that for most hydrocarbon fuels these processes be adequately represented in any comprehensive spray computations. The present results also provide further support to the conclusions of earlier studies which have been based on simplified spray configurations.

Aggarwal, S. K.↗
NASA NTRS1991

A simplified treatment of SiB's land surface albedo parameterization

The earlier presented surface albedo parameterization is simplified by assuming that the reflectance of direct solar radiation is a simple function of solar zenith angle. The function chosen contains three parameters that vary with vegetation type, greenness, and leaf area index. Tables of parameter values are presented. Using these tables, SiB's (Simple Biosphere model) absorbances of direct solar radiation can be reproduced with an average relative error of less than 0.5 percent. Finally, the direct reflectance function is integrated over zenith angle to produce an equation for the surface reflectance of diffuse radiation.

Koster, Randal D.↗
NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗
NASA NTRS1991

Convective instability in superposed fluid and anisotropic porous layers

The onset of thermal convection due to heating from below in a system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity is studied. The linear perturbation equations are solved numerically. It is found that the effects of anisotropy on the onset of thermal convection are most profound for small values of the depth ratio xi (ratio of fluid layer thickness to porous layer thickness), since in that case, the onset of convection corresponds to significant motion in both layers. For fixed vlues of the vertical permeability in the porous medium, decreasing the value of zeta (ratio of horizontal to vertical permeability) leads to stabilization of the superposed layer configuration because of increased resistance to motion in the porous medium. For larger values of xi, the onset of motion is increasingly confined to the fluid layer, with the transport of heat through the porous layer occurring primarily by conduction. Accordingly, the influence of zeta on the stability characteristics for larger xi is less significant than the effects of an anisotropic thermal conductivity.

Chen, Falin↗
NASA NTRS1992

Magnetic field decay in isolated neutron stars

Three mechanisms that promote the loss of magnetic flux from an isolated neutron star - Ohmic decay, ambipolar diffusion, and Hall drift - are investigated. Equations of motions are solved for charged particles in the presence of a magnetic field and a fixed background of neutrons, while allowing for the creation and destruction of particles by weak interactions. Although these equations apply to normal neutrons and protons, the present interpretations of their solutions are extended to cover cases of neutron superfluidity and proton superconductivity. The equations are manipulated to prove that, in the presence of a magnetic force, the charged particles cannot be simultaneously in magnetostatic equilibrium and chemical equilibrium with the neutrons. The application of the results to real neutron stars is discussed.

Goldreich, Peter↗
NASA NTRS1995

Solar structure inversion with LOWL data

Inversion results for the radial hydrostatic structure of the Sun, using six months of oscillation data obtained with the LOWL instrument, are presented. Both low and intermediate degree modes are used, thus avoiding the systematic errors that might have occurred in previous inversions by merging more than one data set. Using modes of between 0 deg and 90 deg and frequencies of between 1.5 mHz and 3.5 mHz, the variations with depth of the speed of sound, the density and the pressure were inferred for radii of between 0.05 and 0.85 stellar radius. It was found that in this region, the sound speed was within 0.15% of that of a model constructed using an equation of state that incorporated helium diffusion. The density difference between the Sun and the model was less than 0.8%. Given the small error bars on the inversion results, these differences are considered as being significant.

Basu, Sarbani↗
NASA NTRS1985

Diffusion and solubility of oxygen in silver

The diffusion and solubility of oxygen in Ag in the temperature range between 412 and 862 C was determined. The following interpolation formula was found for the solubility: L = 8.19.1/100.exp(-11 860/RT)Mol O2/g.At.Ag.at 1/.5. The process obeys the Sieverts square root law within the limits of error. The dissolution of oxygen in Ag may be accompanied by the dissociation of the oxygen molecules into atoms. The tests on Ag-foils reveal that below a temperature of about 500 C a higher solubility is simulated by the adsorption of oxygen. The diffusion coefficient of oxygen in silver obeys the following equation: D = 2.72.1/100.exp(-11 000/RT)sq cm/s. The relatively low activation energy of 11 kcal/g.At suggests that the diffusion of oxygen takes places over interstitial sites.

Eichenauer, W.↗