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NASA NTRS1987

Numerical solution of the radiation transport equation in disk geometry

An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

Spagna, George F., Jr.↗

NASA NTRS2014

Measuring the Coronal Properties of IC 4329A with NuSTAR

We present an analysis of an approximately 160 ks NuSTAR observation of the nearby bright Seyfert galaxy IC 4329A. The highquality broadband spectrum enables us to separate the effects of distant reflection from the direct coronal continuum, and to therefore accurately measure the high-energy cutoff to be E(sub cut) = 178 (+74 / −40) keV. The coronal emission arises from accretion disk photons Compton up-scattered by a thermal plasma, with the spectral index and cutoff being due to a combination of the finite plasma temperature and optical depth. Applying standard Comptonization models, we measure both physical properties independently using the best signal to noise obtained to date in an active galactic nucleus over the 3 - 79 keV band. We derive kT(sub e) = 37(+7 /−6) keV with tau = 1.25(+0.20 / −0.10) assuming a slab geometry for the plasma, and kT(sub e) = 33(+6 / −6) keV with tau = 3.41(+0.58 / −0.38) for a spherical geometry, with both having an equivalent goodness-of-fit.

X-rays: binaries↗

NASA NTRS2014

Measuring the Coronal Properties of IC 4329A with NuSTAR

finite plasma temperature↗

NASA NTRS1982

The latitude dependence of the variance of zonally averaged quantities

Geometric characteristics of the spherical earth are shown to be responsible for the increase of variance with latitude of zonally averaged meteorological statistics. An analytic model is constructed to display the effect of a spherical geometry on zonal averages, employing a sphere labeled with radial unit vectors in a real, stochastic field expanded in complex spherical harmonics. The variance of a zonally averaged field is found to be expressible in terms of the spectrum of the vector field of the spherical harmonics. A maximum variance is then located at the poles, and the ratio of the variance to the zonally averaged grid-point variance, weighted by the cosine of the latitude, yields the zonal correlation typical of the latitude. An example is provided for the 500 mb level in the Northern Hemisphere compared to 15 years of data. Variance is determined to increase north of 60 deg latitude.

North, G. R.↗

NASA NTRS1961

Comparison of Fission Electric Cell Geometries

Comparison has been made of the relative power-to-weight ratios calculated for fission-electric cell reactor power systems based upon cells of plane, cylindrical, and spherical geometry. It is demonstrated that for systems of equal power output, the choice of cell geometry does not greatly affect the total weight of the system.

POWER SUPPLY↗

NASA NTRS2015

Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry

The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.

Wilson, John W.↗

NASA NTRS1973

The influence of ozone and aerosols on the brightness and color of the twilight zone

The radiance and color of the twilight sky are calculated for single scattered radiation with the use of spherically symmetric models of the earth's atmosphere. Spherical geometry is used throughout the calculations with no plane parallel approximations. Refraction effects are taken into account through fine subdivision of the atmosphere into spherical shells of fixed index of refraction. Shell's law of refraction is used to calculate a direction of travel each time that a photon traverses the interface between layers. Five different models of the atmosphere were used: a pure molecular scattering atmosphere; molecular atmosphere plus ozone absorption; and three models with aerosol concentrations of 1, 3, and 10 times normal together with molecular scattering and ozone absorption. The results of the calculations are shown for various observation positions and local viewing angles in the solar plane for wavelengths in the range of 0.40 microns to 0.75 microns.

Adams, C. N.↗

NASA NTRS1993

Global-scale waves in the Venus atmosphere

The nature of global-scale waves that can exist in the atmosphere of Venus is examined. A linear three-dimensional model atmosphere with spherical geometry is used to study large-scale forced and free waves. Solutions are obtained numerically with grid points in the vertical and a spherical harmonic expansion in the horizontal. Observations have shown a global-scale traveling wave with phase speed near the cloud-top wind velocity. Global-scale wave modes are found to exist in the model at this velocity. When a radiative-dynamic cloud feedback is added to the model, the most unstable wave mode is found to have the same phase speed as the observed wave. The horizontal structure of this wave is consistent with the observed horizontal structure of the 'Y' feature seen in ultraviolet images of the Venus cloud top.

Smith, Michael D.↗

NASA NTRS2003

Radiant Extinction Of Gaseous Diffusion Flames

The absence of buoyancy-induced flows in microgravity (mu:g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and :g flames have been reported in experiments on candle flames [1, 2], flame spread over solids [3, 4], droplet combustion [5,6], and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (i) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation, and (ii) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the Aweak@ (low burning rate per unit flame area) :g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in :g will burn indefinitely [1]. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the :g experiments and modeling because: (i) It reduces the complexity by making the problem one-dimensional. (ii) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame. (iii) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in :g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in :g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Berhan, S.↗

NASA NTRS1974

The influence of ozone and aerosols on the brightness and color of the twilight sky

The radiance and color of the twilight sky are calculated for single scattered radiation with the use of spherically symmetric models of the earth's atmosphere. Spherical geometry is used throughout the calculations with no plane-parallel approximations. Refraction effects are taken into account through fine subdivision of the atmosphere into spherical shells of fixed index of refraction. Snell's law of refraction is used to calculate a new direction of travel each time that a photon traverses the interface between layers. Five different models of the atmosphere were used: a pure molecular scattering atmosphere; molecular atmosphere plus ozone absorption; and three models with aerosol concentrations of one, three, and ten times normal together with molecular scattering and ozone absorption. The results of the calculations are shown for various observation positions and local viewing angles in the solar plane for wavelengths in the range from 0.40 to 0.75 micron.

Adams, C. N.↗

NASA NTRS1979

Interfacial geometry and D-variation effects in two-phase systems

Numerical solutions of the governing diffusion equation for two-phase concentration dependent diffusion coefficients are examined. Solutions were also calculated for planar, cylindrical, and spherical geometries to compare the effect of interface geometries with those caused by concentration-dependent diffusion coefficients, and two methods of averaging D were considered to determine the best averaging method for different types of D-variations. The effects of interface-location criteria on mass conservation and convergence of interface location, diffusion coefficient variation in the alpha and beta-phases of a two-phase binary alloy system, effect of D(alpha) variation in a cylindrical couple on beta-phase thickness, and geometry and D-variation effects on the degree of homogenization were determined. It is concluded that typical D(alpha)-variations can have a greater influence on the kinetics of interdiffusion than the geometry.

Tenney, D. R.↗

NASA NTRS1999

Radiant Extinction of Gaseous Diffusion Flames

The absence of buoyancy-induced flows in microgravity (mu-g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and mu-g flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion, and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (1) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation; and (2) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the "weak" (low burning rate per unit flame area) mu-g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in mu-g will burn indefinitely. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the mu-g experiments and modeling because: (1) It reduces the complexity by making the problem one-dimensional; (2) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame; (3) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in mu-g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in mu-g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Berhan, Sean↗

NASA NTRS2001

Unsteady Spherical Diffusion Flames in Microgravity

The absence of buoyancy-induced flows in microgravity (mu-g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and (mu-g) flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion, and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (i) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation, and (ii) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the "weak" (low burning rate per unit flame area) mu-g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in mu-g will burn indefinitely. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the mu-g experiments and modeling because: (i) It reduces the complexity by making the problem one-dimensional; (ii) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame. (iii) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in mu-g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in mu-g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Atreya, Arvind↗

NASA NTRS2011

A Fractal Model for the Capacitance of Lunar Dust and Lunar Dust Aggregates

Lunar dust grains and dust aggregates exhibit clumping, with an uneven mass distribution, as well as features that span many spatial scales. It has been observed that these aggregates display an almost fractal repetition of geometry with scale. Furthermore, lunar dust grains typically have sharp protrusions and jagged features that result from the lack of aeolian weathering (as opposed to space weathering) on the Moon. A perfectly spherical geometry, frequently used as a model for lunar dust grains, has none of these characteristics (although a sphere may be a reasonable proxy for the very smallest grains and some glasses). We present a fractal model for a lunar dust grain or aggregate of grains that reproduces (1) the irregular clumpy nature of lunar dust, (2) the presence of sharp points, and (3) dust features that span multiple scale lengths. We calculate the capacitance of the fractal lunar dust analytically assuming fixed dust mass (i.e. volume) for an arbitrary number of fractal levels and compare the capacitance to that of a non-fractal object with the same volume, surface area, and characteristic width. The fractal capacitance is larger than that of the equivalent non-fractal object suggesting that for a given potential, electrostatic forces on lunar dust grains and aggregates are greater than one might infer from assuming dust grains are sphericaL Consequently, electrostatic transport of lunar dust grains, for example lofting, appears more plausible than might be inferred by calculations based on less realistic assumptions about dust shape and associated capacitance.

Collier, Michael R.↗

NASA NTRS1997

A Measurement of the Energy Spectra of Cosmic Rays from 20 to 1000 GeV Per Amu

The design features and operational performance from the test flight of the fourth generation of spherical geometry cosmic ray detectors developed at Bristol University (Bristol University Gas Scintillator 4 - BUGS-4) are presented. The flight from Ft. Sumner (NM) in Sept. 1993 was the premier flight of a large (1m radius) spherical drift chamber which also gave gas scintillation and Cerenkov signals. The combinations of this chamber with one gas and two solid Cerenkov radiators lead to a large aperture factor (4.5 m2sr), but low (approximately 3.5 g/sq cm) instrument mass over the energy sensitive range 1 to several hundred GeV/a. Moreover, one simple timing measurement determined the impact parameter which provided a trajectory (path length) correction for all detector elements. This innovative and efficient design will be of interest to experimental groups engaged in studies of energetic charged particles. Although there were technical problems on the flight, which were compounded by the total destruction of BUGS-4 by fire while landing in Oklahoma, there was a period of stable operation during which the instrument was exposed at float altitude (approximately 125,000 ft.) to high energy cosmic rays. We present the performance of the instrument as determined from the analysis of these data and an appraisal of its novel design features. Suggestions for design improvements in a future instrument are made.

Gregory, J. C.↗

NASA NTRS2017

Reconnection-Driven Coronal-Hole Jets with Gravity and Solar Wind

Coronal-hole jets occur ubiquitously in the Sun's coronal holes, at EUV and X-ray bright points associated with intrusions of minority magnetic polarity. The embedded-bipole model for these jets posits that they are driven by explosive, fast reconnection between the stressed closed field of the embedded bipole and the open field of the surrounding coronal hole. Previous numerical studies in Cartesian geometry, assuming uniform ambient magnetic field and plasma while neglecting gravity and solar wind, demonstrated that the model is robust and can produce jet-like events in simple configurations. We have extended these investigations by including spherical geometry,gravity, and solar wind in a nonuniform, coronal hole-like ambient atmosphere. Our simulations confirm that the jet is initiated by the onset of a kink-like instability of the internal closed field, which induces a burst of reconnection between the closed and external open field, launching a helical jet. Our new results demonstrate that the jet propagation is sustained through the outer corona, in the form of a traveling nonlinear Alfven wave front trailed by slower-moving plasma density enhancements that are compressed and accelerated by the wave. This finding agrees well with observations of white-light coronal-hole jets, and can explain microstreams and torsional Alfven waves detected in situ in the solar wind. We also use our numerical results to deduce scaling relationships between properties of the coronal source region and the characteristics of the resulting jet, which can be tested against observations.

Karpen, J. T.↗

NASA NTRS1988

Three-dimensional axisymmetric ball model for the PC-TAP program

Spherical-geometry solids' thermal modeling is presently undertaken with a three-dimensional FEM method that can be used in conjunction with the IBM-PC Thermal Analyzer Program (TAP). The elements of the model's nodal network are spherical triangles having approximately equivalent volumes for transient cases, thereby decreasing computer run times. Attention is given to results for the three test cases to which the model has been applied, which are compared with results from analytical closed-form solutions. Absolute temperature errors not greater than 1 percent are indicated by the comparisons.

Pidcoke, L. H.↗

NASA NTRS1973

Theoretical emergent Lyman alpha intensities from Mars.

The behavior of the Lyman alpha 1216-A intensity on Mars is presented for a range of atomic hydrogen density distributions below 200 km. Two sets of radiative transfer calculations have been performed. The first is based on spherical geometry and includes the effect of pure absorption of the resonance photons by CO2. The second set is based on the simpler plane parallel geometry and includes the effects of both pure absorption and a varying Doppler width associated with the planetary Lyman alpha line. From the plane parallel solutions, we are able to estimate and account for the effect of a varying Doppler width on our spherical model results. When pure absorption and a varying Doppler width are incorporated in the theory, the maximum change in the Lyman alpha disc intensity is a factor of about 2 over the range of hydrogen density models considered.

Strickland, D. J.↗