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NASA NTRS1987

A probabilistic model of brittle crack formation

Probability of a brittle crack formation in an elastic solid with fluctuating strength is considered. A set Omega of all possible crack trajectories reflecting the fluctuation of the strength field is introduced. The probability P(X) that crack penetration depth exceeds X is expressed as a functional integral over Omega of a conditional probability of the same event taking place along a particular path. Various techniques are considered to evaluate the integral. Under rather nonrestrictive assumptions, the integral is reduced to solving a diffusion-type equation. A new characteristic of fracture process, 'crack diffusion coefficient', is introduced. An illustrative example is then considered where the integration is reduced to solving an ordinary differential equation. The effect of the crack diffusion coefficient and of the magnitude of strength fluctuations on probability density of crack penetration depth is presented. Practical implications of the proposed model are discussed.

Chudnovsky, A.↗

NASA NTRS1975

A dynamic model for the time evolution of the modulated cosmic ray spectrum

A recently developed model predicts an energy dependent phase lag in the modulated cosmic ray density U(t) given by U(t) approximately equal to US (t - tau) where US is the solution to the Fokker-Planck equation under time independent conditions and tau is the average time spent by particles inside the modulating region. The delay times tau are functions of modulating parameters R (the radius of the modulating cavity), V (the solar wind velocity), and K (the effective average diffusion-coefficient which is a function of energy). This model is applied to predict the time evolution of the modulated cosmic ray proton spectrum over a simulated solar cycle. A modulation produced mostly by varying R over the solar cycle is less consistent with the observations.

Ogallagher, J. J.↗

NASA NTRS1988

Growth and characterization of Hg(1-x)Cd(x)Se alloys

A detailed evaluation of the influence of growth conditions on the radial and axial compositional variations in directionally solidified Hg(1-x)Cd(x)Se alloys was performed. The measured axial compositional profiles were fitted to theoretical profiles to determine the effective solute (CdSe) diffusion coefficient (D) for the Hg(1-x)Cd(x)Se system. The value for D was estimated to be 3.0 + or - 0.5 x 10 to the -5th sq cm/s and did not appear to be significantly affected by the rate of crystal growth. The axial crystal uniformity was shown to be highly growth-rate dependent, with the faster growth rates producing crystals of more uniform composition in the axial direction. The magnitude of the radial variations was also shown to be highly growth-rate dependent, with the slower growth rates producing crystals of greater radial uniformity. This translation rate dependence of the radial uniformity is discussed in terms of lateral solute diffusion and convective interfacial fluid flows.

Andrews, R. N.↗

NASA NTRS1993

Evaporation of LOX under supercritical and subcritical conditions

The evaporation of LOX under supercritical and subcritical conditions was studied experimentally and theoretically. In experiments, the evaporation rate and surface temperature were measured for LOX strand vaporizing in helium environments at pressures ranging from 5 to 68 atmospheres. Gas sampling and chromatography analysis were also employed to profile the gas composition above the LOX surface for the purpose of model validation. A comprehensive theoretical model was formulated and solved numerically to simulate the evaporation process of LOX at high pressures. The model was based on the conservation equations of mass, momentum, energy, and species concentrations for a multicomponent system, with consideration of gravitational body force, solubility of ambient gases in liquid, and variable thermophysical properties. Good agreement between predictions and measured oxygen mole fraction profiles was obtained. The effect of pressure on the distribution of the Lewis number, as well as the effect of variable diffusion coefficient, were further examined to elucidate the high-pressure transport behavior exhibited in the LOX vaporization process.

Yang, A. S.↗

NASA NTRS2005

The Dynamics of Miscible Interfaces: Simulations

This research project focuses on the dynamics of interfacial regions between miscible fluids. While much attention has focused on immiscible interfaces in the past, miscible interfaces have been explored to a much lesser degree, so that there are many open questions regarding their dynamics at this time. Among the more pressing issues is the role that nonconventional stresses can play in such interfacial regions. Such stresses are typically not accounted for in efforts to model the dynamics of miscible flows. Our research aims to clarify under which circumstances these stresses do have to be taken into account, and what quantitative approaches are most suitable in this regard. In order to address these issues, we have focused on conducting linear stability analyses and nonlinear simulations for capillary tube and Hele-Shaw flows, and to compare the results with corresponding experiments performed in the labs of our co-investigators Prof. Maxworthy at USC, and Dr. Balasubramaniam at NASA. Over the duration of the project we have, among other things, focused on the effects of variable diffusion coefficients in such flows, and specifically on their influence in the growth of instabilities. Furthermore, our three-dimensional spectral element simulations have made good progress, so that we have come to a point where we can conduct more detailed comparisons with experimental observations. We are currently focusing our efforts on reproducing the tip-splitting instability observed by Maxworthy. Finally, we have discovered a new core-annular flow instability in the Stokes flow regime during the last year. This represents a significant finding, as this instability does not have an immiscible counterpart.

Meiburg, Eckart↗

NASA NTRS2004

Non-Additive Voltametric Currents From a Mixture of Two, Three and Four Redox-Active Compounds and Electroanalytical Implications

We have published recently the effect of dissimilar diffusion coefficients on the size of the voltammetric waves from a mixture of two redox-active compounds. Similarly, at the potential range where three redox-active species, decamethylferrocene (dMeFc), ferrocene (Fc) and N-methylphenothiazine (MePTZ), are oxidized simultaneously with rates controlled by linear diffusion, electrogenerated radicals diffusing outwards from the electrode react with the original species diffusing towards the electrode from the bulk; thus, Fc(+) reacts with dMeFc producing Fc and dMeFc(+), while MePTZ(+) reacts both with dMeFc producing MePTZ and dMeFc(+), and with Fc producing MePTZ and Fc(+). These reactions replace dMeFc with Fc at the second plateau, and both dMeFc and Fc with MePTZ at the third plateau. Since the diffusion coefficients of the three species are not equal, the mass-transfer limited currents of the second and the third oxidation wave plateaus change by approx. 10%. Numerical simulations of the experimental voltamograms support this mechanism. Similar results were also obtained for a mixture of four redoxactive compounds. The implications of this non-additive nature of currents on: (a) the use of internal voltammetric standards for quantitative analysis of a mixture of redox-active compounds; and, (b) the half wave potentials (E1/2) of the 2nd, 3rd and 4th waves for qualitative analysis, will be discussed.

Dass, Amala↗

NASA NTRS1999

Effects of g-Jitter on Diffusion in Binary Liquids

The microgravity environment offers the potential to measure the binary diffusion coefficients in liquids without the masking effects introduced by buoyancy-induced flows due to Earth s gravity. However, the background g-jitter (vibrations from the shuttle, onboard machinery, and crew) normally encountered in many shuttle experiments may alter the benefits of the microgravity environment and introduce vibrations that could offset its intrinsic advantages. An experiment during STS-85 (August 1997) used the Microgravity Vibration Isolation Mount (MIM) to isolate and introduce controlled vibrations to two miscible liquids inside a cavity to study the effects of g-jitter on liquid diffusion. Diffusion in a nonhomogeneous liquid system is caused by a nonequilibrium condition that results in the transport of mass (dispersion of the different kinds of liquid molecules) to approach equilibrium. The dynamic state of the system tends toward equilibrium such that the system becomes homogeneous. An everyday example is the mixing of cream and coffee (a nonhomogeneous system) via stirring. The cream diffuses into the coffee, thus forming a homogeneous system. At equilibrium the system is said to be mixed. However, during stirring, simple observations show complex flow field dynamics-stretching and folding of material interfaces, thinning of striation thickness, self-similar patterns, and so on. This example illustrates that, even though mixing occurs via mass diffusion, stirring to enhance transport plays a major role. Stirring can be induced either by mechanical means (spoon or plastic stirrer) or via buoyancy-induced forces caused by Earth s gravity. Accurate measurements of binary diffusion coefficients are often inhibited by buoyancy-induced flows. The microgravity environment minimizes the effect of buoyancy-induced flows and allows the true diffusion limit to be achieved. One goal of this experiment was to show that the microgravity environment suppresses buoyancy-induced convection, thereby mass diffusion becomes the dominant mechanism for transport. Since g-jitter transmitted by the shuttle to the experiment can potentially excite buoyancy-induced flows, we also studied the effects of controlled vibrations on the system.

Duval, Walter M. B.↗

NASA NTRS2013

Modeling Analysis for NASA GRC Vacuum Facility 5 Upgrade

A model of the VF5 test facility at NASA Glenn Research Center was developed using the direct simulation Monte Carlo Hypersonic Aerothermodynamics Particle (HAP) code. The model results were compared to several cold flow and thruster hot fire cases. The main uncertainty in the model is the determination of the effective sticking coefficient -- which sets the pumping effectiveness of the cryopanels and oil diffusion pumps including baffle transmission. An effective sticking coefficient of 0.25 was found to provide generally good agreement with the experimental chamber pressure data. The model, which assumes a cold diffuse inflow, also fared satisfactorily in predicting the pressure distribution during thruster operation. The model was used to assess other chamber configurations to improve the local effective pumping speed near the thruster. A new configuration of the existing cryopumps is found to show more than 2x improvement over the current baseline configuration.

cryopumping↗

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 NTRS1978

A core origin for group IVA iron meteorites - A reply to Moren and Goldstein

Because uncertainties in experimental data are large, one has considerable latitude in choosing the input parameters needed to calculate iron meteorite cooling rates. The best way to test input parameters is by examining their ability to yield the observed properties of the meteorites. Our phase diagram yields fits to kamacite profiles that are superior to those based on the Moren-Goldstein phase diagram. Our method of allowing for the effect of P on the Ni diffusion coefficient takes into account the enhancement in this effect with decreasing temperature; Moren and Goldstein use a relationship derived for a temperature of 1100 C, well outside the 700-350 C range where kamacite growth occurs. Use of our input parameters yields cooling rates in IVA irons that are independent of composition, consistent with a core origin. Since the fractionation of siderophiles in group IVA also indicates a core origin, we conclude that this is the correct model for this group.

Willis, J.↗

NASA NTRS1985

The large scale dynamics of the outer heliosphere and the long-term modulation of galactic cosmic rays

The network of cosmic ray observatories reaching across the heliosphere has given new insight into the process of solar modulation, establishing that the decreases occur principally in the outer heliosphere and are produced by interplanetary flow systems; that the hysteresis effects appear to be produced by changes in the rigidity dependence of the diffusion coefficient and that the predicted effects on the cosmic ray gradients associated with the reversal of the solar magnetic field polarity are not observed.

Mcdonald, F. B.↗

NASA NTRS1981

On the transport and propagation of relativistic electrons in galaxies

Analytic solutions to the time-dependent equation describing the transport of relativistic electrons that are being convected and diffused, and may be either gaining or losing energy, are described. The calculations yield a body of solutions from which specific ones can be chosen for the modelling of synchrotron radiation in the Galaxy and in other galaxies. The solutions allow for (1) spatially varying convection velocity; (2) an energy and spatially dependent diffusion coefficient; (3) adiabatic acceleration effects; (4) a term describing spatially dependent synchrotron loss and/or Fermi acceleration; (5) an injection source for the electrons that may be impulsive, steady-state, or variable-injection; (6) a spatial injection or spatially more diffuse source; (7) arbitrary energy dependence of the injection source; and (8) spatial and energy boundaries where the spatial or energy form of the convection, diffusion, and energy supply terms in the basic equation can change character.

Lerche, I.↗

NASA NTRS1988

Venus - Surface electromagnetic properties

Pioneer Venus high-angle radar imaging data are used here to correct values of the specular power reflection coefficient for the effects of diffusely scattering small-scale surface roughness. A value of 5.0 + or - 0.9 is found for the average dielectric permittivity of the rolling plains and lowlands, suggesting that most of the Venus surface is overlain by at most only a few cm of soil or dust. The unexpectedly high values of power reflection coefficient are confirmed by observations of correspondingly low values of radiothermal emission. Thus there can be little doubt that most of the highlands contain significant amounts of a conducting mineral near the surface.

Pettengill, Gordon H.↗

NASA NTRS1993

Advances in Studies of Electrode Kinetics and Mass Transport in AMTEC Cells (abstract)

Previous work reported from JPL has included characterization of electrode kinetics and alkali atom transport from electrodes including Mo, W, WRh(sub x), WPt(sub x)(Mn), in sodium AMTEC cells and vapor exposure cells, and Mo in potassium vapor exposure cells. These studies were generally performed in cells with small area electrodes (about 1 to 5 cm(sup 2)), and device geometry had little effect on transport. Alkali diffusion coefficients through these electrodes have been characterized, and approximate surface diffusion coefficients derived in cases of activated transport. A basic model of electrode kinetic at the alkali metal vapor/porous metal electrode/alkali beta'-alumina solid electrolyte three phase boundary has been proposed which accounts for electrochemical reaction rates with a collision frequency near the three phase boundary and tunneling from the porous electrode partially covered with adsorbed alkali metal atoms. The small electrode effect in AMTEC cells has been discussed in several papers, but quantitative investigations have described only the overall effect and the important contribution of electrolyte resistance. The quantitative characterization of transport losses in cells with large area electrodes has been limited to simulations of large area electrode effects, or characterization of transport losses from large area electrodes with significant longitudinal temperature gradients. This paper describes new investigations of electrochemical kinetics and transport, particularily with WPt(sub 3.5) electrodes, including the influence of electrode size on the mass transport loss in the AMTEC cell. These electrodes possess excellent sodium transport properties making verification of device limitations on transport much more readily attained.

electrode kinetics alkali atom transport transport↗

NASA NTRS1984

Simulations of the stratocumulus-topped boundary layer with a third-order closure model

A third order closure model is proposed by Andre et al. (1982), in which the time rate of change terms, the relaxation and rapid effects for the pressure related terms, and the clipping approximation are included along with the quasi-normal closure, to study turbulence in a cloudy layer which is cooled radiatively from above. A spurious oscillation which is strongest near the inversion occurs. An analysis of the problem shows that the oscillation arises from the mean gradient and buoyancy terms of the triple moment equations; these terms are largest near the cloud top. The oscillation is physical, rather than computational. In nature the oscillation is effectively damped, by a mechanism which apparently is not included in our model. In the stably stratified layer just above the mixed layer top, turbulence can excite gravity waves, whose energy is radiated away. Because the closure assumption for the pressure terms does not take into account the transport of wave energy, the model generates spurious oscillations. Damping of the oscillations is possible by introducing diffusion terms into the triple moment equations. With a large enough choice for the diffusion coefficient, the oscillation is effectively eliminated. The results are quite sensitive to the ad hoc eddy coefficient.

Moeng, C. H.↗

NASA NTRS1987

Crack diffusion coefficient - A candidate fracture toughness parameter for short fiber composites

In brittle matrix composites, crack propagation occurs along random trajectories reflecting the heterogeneous nature of the strength field. Considering the crack trajectory as a diffusive process, the 'crack diffusion coefficient' is introduced. From fatigue crack propagation experiments on a set of identical SEN polyester composite specimens, the variance of the crack tip position along the loading axis is found to be a linear function of the effective 'time'. The latter is taken as the effective crack length. The coefficient of proportionality between variance of the crack trajectory and the effective crack length defines the crack diffusion coefficient D which is found in the present study to be 0.165 mm. This parameter reflects the ability of the composite to deviate the crack from the energetically most efficient path and thus links fracture toughness to the microstructure.

Mull, M. A.↗

NASA NTRS1977

Numerical simulation of the Gulf Stream and Mid-Ocean eddies

Oceanographic field measurements have revealed intense, transient mesoscale motions in many parts of the world ocean. The circulation of the western North Atlantic, considered in the present study as a rectangular basin, is simulated with a primitive equation model that has five levels and a horizontal grid size of 37 km. The model ocean is driven by a 2.5 gyre pattern of steady zonal wind stress and by a Newtonian-type surface heating. Two cases are considered: the first uses a Laplacian formulation for the subgrid-scale lateral diffusions of heat and momentum; the second uses a highly scale-selective biharmonic formulation for these diffusions. An analysis of the heat transport, in the biharmonic experiment, shows that the horizontal transport of heat by eddies is much larger than the subgrid-scale horizontal heat diffusion. In the Gulf Stream region, the eddy heat transport is comparable to the effect of a lateral diffusion coefficient of 10 to the 7th sq cm/s.

Semtner, A. J., Jr.↗

NASA NTRS1978

Prediction of moisture and temperature changes in composites during atmospheric exposure

The effects of variations in diffusion coefficients, surface properties of the composite, panel tilt, ground reflection, and geographical location on the moisture concentration profiles and average moisture content of composite laminates were studied analytically. A heat balance which included heat input due to direct and sky diffuse solar radiation, ground reflection, and heat loss due to reradiation and convection was used to determine the temperature of composites during atmospheric exposure. The equilibrium moisture content was assumed proportional to the relative humidity of the air in the boundary layer of the composite. Condensation on the surface was neglected. Histograms of composite temperatures were determined and compared with those for the ambient environment.

Tompkins, S. S.↗