A new approach to the homogenization of heterogeneous media for neutron diffusion calculations
Mathematical formulation for homogenization of heterogeneous media for neutron diffusion transport theory
DIFFUSION THEORY↗
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Modelling the solution growth of TGS crystals in low gravity
The experimental growth of triglycine sulfate (TGS) crystals from aqueous solution is modeled here in two dimensions using the PHOENICS finite volume code. Simulations are carried out for steady, impulsive, and periodic accelerations in order to determine tolerable acceleration levels. Scaling arguments are used to estimate the times required for thermal and solutal variations from the initial equilibrium state to be diffusively transported throughout the system, and to obtain order of magnitude information on the relative magnitudes of diffusive and convective transport. The computed concentration fields reflect the features of the concentration distributions found experimentally during experiments conducted aboard Spacelab 3 in 1985.
Nadarajah, Arunan↗
Radial diffusion of low-energy plasma ions in Saturn's magnetosphere
Radial diffusion of low-energy plasma ions in Saturn's magnetosphere is investigated using a comprehensive set of equations for radial diffusion that incorporate distributed sources and sinks of ions. The results of calculations indicate that the radial-diffusion transport of low-energy O(+) ions with a source in the neutral H2O cloud of the satellites Dione and Tethys can account for Voyager observations of thermal heavy ions in Saturn's magnetosphere. The source rate was calculated to be about 10 to the 26th O(+) ions/sec, in good agreement with the sputtering calculations of Johnson et al. (1989). It is estimated that, due to fast radial diffusion, the residence time of O(+) ions in the Dione-Tethys torus is about 30 days, sufficiently short to account for the plasma density observed there. The densities of hot H(+) and N(+) resulting from the ionization and pickup of Titan's neutral clouds in the outer magnetosphere can also be accounted for within the framework of diffusive ion transport.
Barbosa, D. D.↗
Cosmic ray transport - Modulation and the anomalous component
Cosmic ray transport research is reviewed for the 1987-1990 time period, focusing on diffusive transport. Problems discussed include the diffusion model, anomalous components, radial gradient and north south anisotropy, short term modulation, long-term solar modulation, and charge sign dependent modulation.
Evenson, Paul↗
The Cool Flames Experiment
A space-based experiment is currently under development to study diffusion-controlled, gas-phase, low temperature oxidation reactions, cool flames and auto-ignition in an unstirred, static reactor. At Earth's gravity (1g), natural convection due to self-heating during the course of slow reaction dominates diffusive transport and produces spatio-temporal variations in the thermal and thus species concentration profiles via the Arrhenius temperature dependence of the reaction rates. Natural convection is important in all terrestrial cool flame and auto-ignition studies, except for select low pressure, highly dilute (small temperature excess) studies in small vessels (i.e., small Rayleigh number). On Earth, natural convection occurs when the Rayleigh number (Ra) exceeds a critical value of approximately 600. Typical values of the Ra, associated with cool flames and auto-ignitions, range from 104-105 (or larger), a regime where both natural convection and conduction heat transport are important. When natural convection occurs, it alters the temperature, hydrodynamic, and species concentration fields, thus generating a multi-dimensional field that is extremely difficult, if not impossible, to be modeled analytically. This point has been emphasized recently by Kagan and co-workers who have shown that explosion limits can shift depending on the characteristic length scale associated with the natural convection. Moreover, natural convection in unstirred reactors is never "sufficiently strong to generate a spatially uniform temperature distribution throughout the reacting gas." Thus, an unstirred, nonisothermal reaction on Earth does not reduce to that generated in a mechanically, well-stirred system. Interestingly, however, thermal ignition theories and thermokinetic models neglect natural convection and assume a heat transfer correlation of the form: q=h(S/V)(T(bar) - Tw) where q is the heat loss per unit volume, h is the heat transfer coefficient, S/V is the surface to volume ratio, and (T(bar) - Tw ) is the spatially averaged temperature excess. This Newtonian form has been validated in spatially-uniform, well-stirred reactors, provided the effective heat transfer coefficient associated with the unsteady process is properly evaluated. Unfortunately, it is not a valid assumption for spatially-nonuniform temperature distributions induced by natural convection in unstirred reactors. "This is why the analysis of such a system is so difficult." Historically, the complexities associated with natural convection were perhaps recognized as early as 1938 when thermal ignition theory was first developed. In the 1955 text "Diffusion and Heat Exchange in Chemical Kinetics", Frank-Kamenetskii recognized that "the purely conductive theory can be applied at sufficiently low pressure and small dimensions of the vessel when the influence of natural convection can be disregarded." This was reiterated by Tyler in 1966 and further emphasized by Barnard and Harwood in 1974. Specifically, they state: "It is generally assumed that heat losses are purely conductive. While this may be valid for certain low pressure slow combustion regimes, it is unlikely to be true for the cool flame and ignition regimes." While this statement is true for terrestrial experiments, the purely conductive heat transport assumption is valid at microgravity (mu-g). Specifically, buoyant complexities are suppressed at mu-g and the reaction-diffusion structure associated with low temperature oxidation reactions, cool flames and auto-ignitions can be studied. Without natural convection, the system is simpler, does not require determination of the effective heat transfer coefficient, and is a testbed for analytic and numerical models that assume pure diffusive transport. In addition, mu-g experiments will provide baseline data that will improve our understanding of the effects of natural convection on Earth.
Pearlman, Howard↗
Hypervelocity atmospheric flight: Real gas flow fields
Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.
Howe, John T.↗
Hypervelocity atmospheric flight: Real gas flow fields
Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.
Howe, John T.↗
Two-Dimensional Transport Studies for the Composition and Structure of the Io Plasma Torus
The overall objective of this project is to investigate the roles of local and spatially extended plasma sources created by Io, plasma torus chemistry, and plasma convective and diffusive transport in producing the long-lived S(+), S(++) and O(+) radial ribbon structures of the plasma torus, their System III longitude and local-time asymmetries, their energy sources and their possible time variability. To accomplish this objective, two-dimensional [radial (L) and System III longitude] plasma transport equations for the flux-tube plasma content and energy content will be solved that include the convective motions for both the east-west electric field and co-rotational velocity-lag profile near Io s orbit, radial diffusion, and the spacetime dependent flux-tube production and loss created by both neutral-plasma and plasma-ion reaction chemistry in the plasma torus. For neutral-plasma chemistry, the project will for the first time undertake the calculation of realistic three-dimensional, spatially-extended, and time-varying contributions to the flux-tube ion-production and loss that are produced by Io's corona and extended neutral clouds. The unknown two-dimensional spatial nature of diffusion in the plasma transport will be isolated and better defined in the investigation by the collective consideration of the foregoing different physical processes. For energy transport, the energy flow from hot pickup ions (and a new electron source) to thermal ions and electrons will be included in investigating the System III longitude and local-time temperature asymmetries in the plasma torus. The research is central to the scope of the NASA Sun-Earth Connection Roadmap in Quest II Campaign 4 "Comparative Planetary Space Environments" by addressing key questions for understanding the magnetosphere of planets with high rotation rates and large internal plasma sources and, in addition, is of considerable importance to the NASA Solar System Exploration Science Theme. In this regard, Jupiter is the most extreme example with its rapid rotation and with its inner Galilean satellite Io providing the dominant plasma source for the magnetosphere.
Smyth, William H.↗
Transport into the south polar vortex in early spring
Estimates of the mean circulation and diffusive transport of ozone and other species into the Antarctic polar vortex during the spring of 1987 are made using data from the Airborne Antarctic Ozone Experiment. Measurements of long-lived tracers of tropospheric origin remained relatively constant at the levels of the maximum rate of decline of ozone during September. At lower levels in the stratosphere some evidence exists to support intrusions of tropospheric or low latitude air. Given the distribution in latitude and height of these tracers measured from the ER-2 aircraft, it can be inferred that the Lagrangian or diabatic mean circulation was zero or downward over Antarctica during the period of the ozone decline. The observation of a decline in ozone therefore requires a photochemical sink for ozone. The magnitude of the required photochemical sink must be sufficient to offset the transport of ozone into the polar region and produce the observed decline. Quasi-isentropic mixing and downward motion are coupled and are difficult to estimate from a single tracer. The full suite of measured tracers and auxiliary information are brought together to provide an estimate of the rate at which air is cycled through the polar vortex during spring. Estimates of large scale transport of potential vorticity and ozone from previous years are generally consistent with the data from the airborne experiment in suggesting a relatively slow rate of mass flow through the polar vortex in the lower stratosphere during September.
Hartmann, D.↗
Modeling arcjet space thrusters
The UTSI arcjet model is used to compare the performance of a hydrogen and an ammonia arcjet in the same configuration and at the same electrical power. The predicted specific impulse is 50 percent higher for the hydrogen propellant. Numerical studies made of the effect of transport properties on the performance of a hydrogen arcjet indicate that diffusive transport is very significant even in the supersonic part of the flow, and that relatively small changes in transport properties can have a significant effect on performance. These studies also show that nonequilibrium recombination chemistry can have a large effect on the transport coefficients. This leads to the conclusion that finite rate chemical calculations are necessary if accurate arcjet performance is to be calculated.
Rhodes, Robert↗
Denouement of Jovian radiation belt theory
Predictions of theoretical models of Jupiter's radiation belts are compared with Pioneer 10 measurements. A brief quasi-historical review is given of the evolution of the basic theoretical ideas with emphasis on the three physical processes that were believed to be dominant in the Jovian electron fluxes: radial-diffusion transport, limitation of particle fluxes by plasma wave turbulence, and particle losses from collisional sweep-up by the Galilean satellites. Pioneer 10 data on the inner zone are discussed which yield the clearest evidence for radial diffusion being the dominant transport process, the synchrotron flux density is estimated using Pioneer 10 measurements, and the observed outer-zone electron fluxes are favorably compared with the qualitative and quantitative predictions of the whistler-mode stable-trapping model. The outer-zone electron-precipitation flux is estimated, and it is suggested that precipitation could affect the structure of the Jovian ionosphere. Satellite sweep-up is shown to be less severe than had been anticipated.
Coroniti, F. V.↗
Poly/vinyl alcohol/ membranes for reverse osmosis
A description is presented of the results of studies of the water and salt transport properties of PVA membranes, taking into account radiation crosslinked PVA membranes, diffusive salt permeability through PVA membranes, and heat treated PVA membranes. The experimental findings support an occurrence of independent water, and salt permeation processes. It is suggested that the salt permeation is governed by a solution-diffusion transport mechanism. The preparation of thin skinned, asymmetric PVA membranes is also discussed. The employed method has a certain similarity to the classical phase inversion method, which is widely applied in the casting of asymmetric reverse osmosis membranes. Instead of using a gelling bath composed of a nonsolvent for the membrane material and miscible with the solvent from which the membrane is cast, a 'complexing' bath is used, which is a solution of a complexing agent in water.
Katz, M. G.↗
A transport model of the turbulent scalar-velocity
Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables.
Amano, R. S.↗
Transport models of the turbulent velocity-temperature products for computations of recirculating flows
Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables.
Amano, R. S.↗
Mathematical model of water transport in Bacon and alkaline matrix-type hydrogen-oxygen fuel cells
Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.
Prokopius, P. R.↗
Propagation of solar cosmic rays in the solar wind.
The theory of the propagation of solar cosmic rays in the solar wind is reviewed, with particular emphasis on the diffusive transport during the decay phase of events. Recent evidence is shown to corroborate the prediction that the diffusion coefficient is small for protons with energies of the order of 1 Mev. It is concluded that the transport equation explains the principal phenomena quite well, in that most effects are reasonably understood.
Jokipii, J. R.↗
Variations in eddy diffusion and associated transport processes
Variation in the eddy diffusion coefficient constitutes a momentum source. This variation near the turbopause affects both the composition and the wind and temperature fields of the thermosphere. Two types of calculations are carried out, for horizontal winds considered self-consistently in a three-dimensional dynamic model and horizontal winds artificially suppressed to simulate a one-dimensional model. Momentum transfer associated with variations in eddy diffusion coefficients represents the source function in the analysis presented. It is shown that for long-term variations in the thermosphere, the compositional dependence on variations in eddy diffusion coefficients can be entirely different in one and three dimensional models with horizontal winds included. Horizontal winds can greatly reduce the effects of eddy diffusion in general and the ratio between He and O amplitudes in particular.
Mayr, H. G.↗
Latitudinal variation of tropospheric ozone in a photochemical model
A zonally, vertically, and annually averaged numerical model of trace gases in the troposphere is used to examine the variation of ozone as a function of latitude. Processes included in the ozone budget are a source due to downward transport of ozone from the stratosphere, deposition at earth's surface, north-south diffusive transport, and photochemical reactions. Sensitivity of calculated ozone concentrations to the latitude variation and magnitude of the stratospheric source is presented. The model indicates a net photochemical source of ozone in the Northern Hemisphere and a net chemical sink in the tropical latitudes. Calculated variation of ozone concentration with latitude is in qualitative agreement with observations.
Hameed, S.↗