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NASA NTRS1991

Void probability as a function of the void's shape and scale-invariant models

The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.

Elizalde, E.↗

NASA NTRS1992

Void probability as a function of the void's shape and scale-invariant models

Elizalde, E.↗

NASA NTRS1994

The evolution of voids in the adhesion approximation

We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 128(exp 3) particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H(sub 50) = 1 scals approximately as bar D(z) = bar D(sub zero)/(1+2)(exp 1/2), where bar D(sub zero) approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordialpotential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is strongly epoch dependent, with void topologies generally simplifying with time. This means that as voids grow older they become progressively more empty and have less structure within them. We evaluate the genus measure both for individual voids as well as for the entire ensemble of voids predicted by CDM model. As a result we find that the topology of voids when taken together with the void spectrum is a very useful statistical indicator of the evolution of the structure of the universe on large scales.

Sahni, Varun↗

NASA NTRS2013

Fuzzy Reasoning to More Accurately Determine Void Areas on Optical Micrographs of Composite Structures

Accomplishing the best-performing composite matrix (resin) requires that not only the processing method but also the cure cycle generate low-void-content structures. If voids are present, the performance of the composite matrix will be significantly reduced. This is usually noticed by significant reductions in matrix-dominated properties, such as compression and shear strength. Voids in composite materials are areas that are absent of the composite components: matrix and fibers. The characteristics of the voids and their accurate estimation are critical to determine for high performance composite structures. One widely used method of performing void analysis on a composite structure sample is acquiring optical micrographs or Scanning Electron Microscope (SEM) images of lateral sides of the sample and retrieving the void areas within the micrographs/images using an image analysis technique. Segmentation for the retrieval and subsequent computation of void areas within the micrographs/images is challenging as the gray-scaled values of the void areas are close to the gray-scaled values of the matrix leading to the need of manually performing the segmentation based on the histogram of the micrographs/images to retrieve the void areas. The use of an algorithm developed by NASA and based on Fuzzy Reasoning (FR) proved to overcome the difficulty of suitably differentiate void and matrix image areas with similar gray-scaled values leading not only to a more accurate estimation of void areas on composite matrix micrographs but also to a faster void analysis process as the algorithm is fully autonomous.

Dominquez, Jesus A.↗

NASA NTRS1983

Ultrasonic attenuation of a void-containing medium for very long wavelengths

Ultrasonic longitudinal through-thickness attenuation in an isotropic medium due to scattering by randomly distributed voids is considered analytically. The attenuation is evaluated on the assumption of no interaction between voids. The scattered power is assumed to be entirely lost, thus accounting for the ultrasonic attenuation. The scattered power due to the presence of a void is described in terms of the scattering cross section of the void. An exact solution exists for the scattering cross section of a spherical void. An approximate solution for the scattering cross section of an ellipsoidal void is developed based on the so-called Born approximation commonly used in quantum mechanics. This approximate solution is valid for k sub p a sub i 1, where k sub p is the wave number of the incident longitudinal wave and a sub i is the largest dimension of the void. It is found that the shape of the void has negligible effect on the scattering cross section and that only the volume of the void is important. Thus, it is noted that in cases where k sup p a sub i 1, the exact scattering cross section of a spherical void having the same volume as an arbitrarily shaped void can be used for evaluating ultrasonic attenuation.

Williams, J. H., Jr.↗

NASA NTRS1984

Ultrasonic attenuation of a void-containing medium for very long wavelengths

Ultrasonic longitudinal through-thickness attenuation in an isotropic medium due to scattering by randomly distributed voids is considered analytically. The attenuation is evaluated on the assumption of no interaction between voids. The scattered power is assumed to be entirely lost, thus accounting for the ultrasonic attenuation. The scattered power due to the presence of a void is described in terms of the scattering cross section of the void. An exact solution exists for the scattering cross section of a spherical void. An approximate solution for the scattering cross section of an ellipsoidal void is developed based on the so-called Born approximation commonly used in quantum mechanics. This approximate solution is valid for k sub p a sub i much less than 1, where k sub p is the wave number of the incident longitudinal wave and a sub i is the largest dimension of the void. It is found that the shape of the void has negligible effect on the scattering cross section and that only the volume of the void is important. Thus, it is noted that in cases where k sub p a sub i is much less than 1, the exact scattering cross section of a spherical void having the same volume as an arbitrarily shaped void can be used for evaluating ultrasonic attenuation. Previously announced in STAR as N83-28466

Williams, J. H., Jr.↗

NASA NTRS1999

Theory of Dust Voids in Plasmas

Dusty plasmas in a gas discharge often feature a stable void, i.e., a dust-free region inside the dust cloud. This occurs under conditions relevant to both plasma processing discharges and plasma crystal experiments. The void results from a balance of the electrostatic and ion drag forces on a dust particle. The ion drag force is driven by a flow of ions outward from an ionization source and toward the surrounding dust cloud, which has a negative space charge. In equilibrium the force balance for dust particles requires that the boundary with the dust cloud be sharp, provided that the particles are cold and monodispersive. Numerical solutions of the one-dimensional nonlinear fluid equations are carried out including dust charging and dust-neutral collisions, but not ion-neutral collisions. The regions of parameter space that allow stable void equilibria are identified. There is a minimum ionization rate that can sustain a void. Spatial profiles of plasma parameters in the void are reported. In the absence of ion-neutral collisions, the ion flow enters the dust cloud's edge at Mach number M = 1. Phase diagrams for expanding or contracting voids reveal a stationary point corresponding to a single stable equilibrium void size, provided the ionization rate is constant. Large voids contract and small voids expand until they attain this stationary void size. On the other hand, if the ionization rate is not constant, the void size can oscillate. Results are compared to recent laboratory and microgravity experiments.

Goree, J.↗

NASA NTRS1993

Experimental study of void formation during aluminum solidification in reduced gravity

Void formation due to volumetric shrinkage and liquid/vapor reorientation during aluminum solidification was observed in real time by using a radiographic viewing system in normal and reduced gravity. An end-chill directional solidification furnace with water quench was designed and constructed to solidify aluminum samples during the approximately 16 sec of reduced gravity (+/-0.02g) achieved by flying an aircraft through a parabolic trajectory. In the first series of tests the aluminum was contained in a vacuum sealed, pyrolytic boron nitride crucible. An ullage space was present during each test. Void formation was recorded for two cases: a nonwetting system, and a wetting system where wetting occurred between the aluminum and the crucible lid. The void formation in the nonwetting case was similar in normal and reduced gravity, with a single vapor cavity forming at the top of the crucible. In the wetting case during reduced gravity surface tension caused two voids to form in the top corners of the crucible, but during normal gravity only one large void formed across the top. In the second series of tests the aluminum was contained in a pyrolytic boron nitride crucible that was placed in a stainless steel container and sealed in an environment of argon plus 4 percent hydrogen. An ullage space was present during each test. Void formation was recorded for two cases: a nonwetting system, and a wetting system where wetting occurred between the aluminum and one side wall and the lid. The void for nation in the nonwetting case was similar in normal and reduced gravity, with a single vapor cavity forming at the top of the crucible, although the meniscus became more convex in reduced gravity. In the wetting case the aluminum did not climb up the corners in 1g, and one large symmetric void resulted at the top when the aluminum had solidified. In the wetting case during reduced gravity the molten aluminum was drawn up the wetted wall and partially across the lid by a capillary underpressure; however, on the nonwetting wall the aluminum moved down. One void resulted along the nonwetting side of the container continuing to the top on the same side.

Chiaramonte, Francis Paul, III↗

NASA NTRS1999

Friction stir welding process to repair voids in aluminum alloys

The present invention provides an in-process method to repair voids in an aluminum alloy, particularly a friction stir weld in an aluminum alloy. For repairing a circular void or an in-process exit hole in a weld, the method includes the steps of fabricating filler material of the same composition or compatible with the parent material into a plug form to be fitted into the void, positioning the plug in the void, and friction stir welding over and through the plug. For repairing a longitudinal void (30), the method includes machining the void area to provide a trough (34) that subsumes the void, fabricating filler metal into a strip form (36) to be fitted into the trough, positioning the strip in the trough, and rewelding the void area by traversing a friction stir welding tool longitudinally through the strip. The method is also applicable for repairing welds made by a fusing welding process or voids in aluminum alloy workpieces themselves.

Rosen, Charles D.↗

NASA NTRS2013

Quantifying Effects of Voids in Woven Ceramic Matrix Composites

Randomness in woven ceramic matrix composite architecture has been found to cause large variability in stiffness and strength. The inherent voids are an aspect of the architecture that may cause a significant portion of the variability. A study is undertaken to investigate the effects of many voids of random sizes and distributions. Response surface approximations were formulated based on void parameters such as area and length fractions to provide an estimate of the effective stiffness. Obtaining quantitative relationships between the properties of the voids and their effects on stiffness of ceramic matrix composites are of ultimate interest, but the exploratory study presented here starts by first modeling the effects of voids on an isotropic material. Several cases with varying void parameters were modeled which resulted in a large amount of variability of the transverse stiffness and out-of-plane shear stiffness. An investigation into a physical explanation for the stiffness degradation led to the observation that the voids need to be treated as an entity that reduces load bearing capabilities in a space larger than what the void directly occupies through a corrected length fraction or area fraction. This provides explanation as to why void volume fraction is not the only important factor to consider when computing loss of stiffness.

Goldsmith, Marlana B.↗

NASA NTRS1994

Voids and constraints on nonlinear clustering of galaxies

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R equal to or less than 10/h Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales equal to or less than 10/h Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling (such scaling implies that the N-point correlation functions for N greater than 2 depend only on pairwise products of the two-point function xi(r)) However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of 'voids' with density rho less than 0.2 -/rho. This statistic reveals a paucity of very bright galaxies (L greater than L asterisk) in the 'voids.' Underdensities are equal to or greater than 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and Cold Dark Matter (CDM)-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (omega = 0.4, h = 0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the 'standard' CDM model (omega = 1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model (omega = 0.4, h = 0.6 lambda(sub 0) = 0.6, b = 1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M less than M asterisk = -19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.

Vogeley, Michael S.↗

NASA NTRS1999

Effect of Marangoni Convection Generated by Voids on Segregation During Low-G and 1-G Solidification

Solidification experiments, especially microgravity solidification experiments are often hampered by the evolution of unwanted voids or bubbles in the melt. Although these voids and/or bubbles are highly undesirable, there are currently no effective means of preventing their formation or eliminating their adverse effects, particularly, during low-g experiments. Marangoni Convection caused by these voids can drastically change the transport processes in the melt and, therefore, introduce enormous difficulties in interpreting the results of the space investigations. Recent microgravity experiments by Matthiesen, Andrews, and Fripp are all good examples of how the presence of voids and bubbles affect the outcome of costly space experiments and significantly increase the level of difficulty in interpreting their results. In this work we examine mixing caused by Marangoni convection generated by voids and bubbles in the melt during both 1-g and low-g solidification experiments. The objective of the research is to perform a detailed and comprehensive combined numerical-experimental study of Marangoni convection caused by voids during the solidification process and to show how it can affect segregation and growth conditions by modifying the flow, temperature, and species concentration fields in the melt. While Marangoni convection generated by bubbles and voids in the melt can lead to rapid mixing that would negate the benefits of microgravity processing, it could be exploited in some terrestrial processing to ensure effective communication between a melt/solid interface and a gas phase stoichiometry control zone. Thus we hope that this study will not only aid us in interpreting the results of microgravity solidification experiments hampered by voids and bubbles but to guide us in devising possible means of minimizing the adverse effects of Marangoni convection in future space experiments or of exploiting its beneficial mixing features in ground-based solidification.

Kassemi, M.↗

NASA NTRS1990

A study of void effects on the interlaminar shear strength of unidirectional graphite fiber reinforced composites

A study was conducted to evaluate the effect of voids on the interlaminar shear strength (ILSS) of a polyimide matrix composite system. The graphite/PRM-15 composite was chosen for study because of the extensive amount of experience that has been amassed in the processing of this material. Composite densities and fiber contents of more than thirty different laminates were measured along with ILSS. Void contents were calculated and the void geometry and distribution were noted using microscopic techniques such as those used in metallography. It was found that there was a good empirical correlation between ILSS and composite density. The most acceptable relationship between the ILSS and density was found to be a power equation which closely resembles theoretically derived expressions. An increase in scatter in the strength data was observed as the void content increased. In laminates with low void content, the void appears to be more segregated in one area of the laminate. It was found that void free composites could be processed in matched metal die molds at pressures greater than 1.4 and less than 6.9 MPa.

Bowles, Kenneth J.↗

NASA NTRS1995

The Local Ly(alpha) Forest: Association of Clouds with Superclusters and Voids

The Goddard High Resolution Spectrograph aboard the Hubble Space Telescope was used with the G160M grating to obtain high-resolution (6.2 A) spectra of three very bright active galactic nuclei located behind voids in the nearby distribution of bright galaxies (i.e., CfA and Arecibo redshift survey regions). A total of eight definite (greater than or equal to 4 sigma) Ly(alpha) absorption lines were discovered ranging in equivalent width from 26 to 240 mA at Galactocentric velocities 1740-7740 km/s. Of these eight systems, we locate seven in supercluster structures and one, in the sight line of Mrk 501 at 7740 km/s, in a void. In addition, one of two tentative (3-4 sigma) Ly(alpha) absorption lines are found in voids. Thus, the voids are not entirely devoid of matter, and not all Ly(alpha) clouds are associated with galaxies. Also, since the path lengths through voids and superclusters probed by our observations thus far are nearly equal, there is some statistical evidence that the Ly(alpha) clouds avoid the voids. The nearest galaxy neighbors to these absorbing clouds are 0.45-5.9 Mpc away, too far to be physically associated by most models. The lower equivalent width absorption lines (W(sub lambda) less than or equal to 100 mA) are consistent with random locations with respect to galaxies and may be truly intergalactic, similar to the bulk of the Ly(alpha) forest seen at high z. These results on local Ly(alpha) clouds are in full agreement with those found by Morris et al. (1993) for the 3C 273 sight line but are different from the results for higher equivalent width systems where closer cloud-galaxy associations were found by Lanzetta et al. (1994). Pencil-beam optical and 21 cm radio line observations of the area of sky surrounding Mrk 501 fail to find faint galaxies near the velocities of the Ly(alpha) clouds in that sight line. Specifically, for the 'void absorption' system at 7740 km/s, we find no galaxy at comparable redshift to the absorber within 100 h(sub 75)(sup -1) kpc (H(sub 0) = 75 h(sub 75) km/s Mpc(sup -1)) with an absolute magnitude of B less than or equal to - 16 and no object with H I mass greater than or equal to 7 x 10(exp 8) h(sub 75)(sup -2) M(solar) within 500 h(sub 75)(sup -1) kpc. Thus, neither a faint optical galaxy nor a gas-rich, optically dim or low surface brightness galaxy is present close to this absorber.

Stocke, John T.↗

NASA NTRS1998

Void Management in MEPHISTO and Other Space Experiments

The second flight of NASA's Shuttle Flight experiment program known as MEPHISTO suffered from a void in the liquid portion of the sample, even though a piston arrangement was in place to keep the ampoule filled. In preparations for the next flight of the MEPHISTO furnace an animated computer program, called MEPHISTO Volume Visualizer (MVV), was written to help avoid the formation of unwanted voids. A piston system on MEPHISTO has the ability to move approximately 5 mm in compression, to accommodate expansion of the solid during heating; then from the completely compressed position, the piston can move up to 25 mm in towards the sample, effectively making the ampoule smaller and hopefully eliminating any voids. Due to the nature of the piston design and ampoule and sample arrangement, the piston has gotten stuck during normal directional solidification; this creates the risk of a void. To eliminate such a void, the liquid in the hot zones of the furnace can be heated, thereby expanding the liquid and consuming any void. The problem with this approach is that if the liquid is heated too much an overpressure could result, breaking the ampoule and ending the experiment catastrophically. The MVV has been found to be a useful tool in the assessment of the risks associated with the formation of a void and the additional heating of the liquid in the hot zone of this Bridgman type furnace. The MVV software will be discussed and copies available; it is written in the Delphi 2 programming language and runs under Windows 95 and NT. The strategies used in other flight experiments, such as the Isothermal Dendritic Growth Experiment, will also be presented.

deGroh, Henry C., III↗

NASA NTRS2001

Effect of Marangoni Convection Generated by Voids on Segregation During Low-G and 1-G Solidification

Solidification experiments, especially microgravity solidification experiments, are often compromised by the evolution of unwanted voids or bubbles in the melt. Although these voids and/or bubbles are highly undesirable, there is currently no effective means of preventing their formation or of eliminating their adverse effects, particularly during microgravity experiments. Marangoni convection caused by these voids can drastically change the transport processes in the melt. Recent microgravity experiments by Matthiesen (1) Andrews (2) and Fripp (3) are perfect examples of how voids and bubbles can affect the outcome of costly space experiments and significantly increase the level of difficulty in interpreting their results. Formation of bubbles have caused problems in microgravity experiments for a long time. Even in the early Skylab mission an unexpectedly large number of bubbles were detected in the four materials processing experiments reported by Papazian and Wilcox (4). They demonstrated that while during ground-based tests bubbles were seen to detach from the interface easily and float to the top of the melt, in low-gravity tests no detachment from the interface occurred and large voids were grown in the crystal. More recently, the lead-tin-telluride crystal growth experiment of Fripp et al.(3) flown aboard the USMP-3 mission has provided very interesting results. The purpose of the study was to investigate the effect of natural convection on the solidification process by growing the samples at different orientations with respect to the gravitational field. Large pores and voids were found in the three solid crystal samples processed in space. Post-growth characterization of the compositional profiles of the cells indicated considerable levels of mixing even in the sample grown in the hot-on-top stable configuration. The mixing was attributed to thermocapillary convection caused by the voids and bubbles which evolved during growth. Since the thermocapillary convection is orientation-independent, diffusion-controlled growth was not possible in any of the samples, even the top-heated one. These results are consistent with recent studies of thermocapillary convection generated by a bubble on a heated surface undertaken by Kassemi and Rashidnia (5-7) where it is numerically and experimentally shown that the thermocapillary flow generated by a bubble in a model fluid (silicone oil) can drastically modify the temperature field through vigorous mixing of the fluid around it, especially under microgravity conditions.

Kassemi, M.↗

NASA NTRS1991

An investigation of voids formation mechanisms and their effects on freeze and thaw processes of lithium and lithium fluoride

The mechanisms of void formation during the cooldown and freezing of lithium coolant within the primary loop of SP-100 type systems are investigated. These mechanisms are: (1) homogeneous nucleation; (2) heterogeneous nucleation; (3) normal segregation of helium gas dissolved in liquid lithium; and (4) shrinkage of lithium during freezing. To evaluate the void formation potential due to segregation, a numerical scheme that couples the freezing and mass diffusion processes in both the solid and liquid regions is developed. The results indicated that the formation of He bubbles is unlikely by either homogeneous or heterogeneous nucleation during the cooldown process. However, homogeneous nucleation of He bubbles following the segregation of dissolved He in liquid lithium ahead of the solid-liquid interface is likely to occur. Results also show that total volume of He void is insignificant when compared to that of shrinkage voids. In viewing this, the subsequent research focuses on the effects of shrinkage void forming during freezing of lithium on subsequent thaw processes are investigated using a numerical scheme that is based on a single (solid/liquid) cell approach. The cases of lithium-fluoride are also investigated to show the effect of larger volume shrinkage upon freezing on the freeze and thaw processes. Results show that a void forming at the wall appreciably reduces the solid-liquid interface velocity, during both freeze and thaw, and causes a substantial rise in the wall temperature during thaw. However, in the case of Li, the maximum wall temperature was much lower than the melting temperature of PWC-11, which is used as the structure material in the SP-100 system. Hence, it is included that a formation of hot spots is unlikely during the startup or restart of the SP-100 system.

El-Genk, Mohamed S.↗

NASA NTRS1993

Characterization of voids formed during liquid impregnation of nonwoven multifilament glass networks as related to composite processing

A technique based on matching the refractive index of an invading liquid to that of a fiber mat was used to study entrapment of air ('voids') that occurs during forced in-plane radial flow into nonwoven multifilament glass networks. The usefulness of this technique is demonstrated in quantifying and mapping the air pockets. Experiments with a series of fluids with surface tensions varying from 28 x 10(exp -3) to 36 x 10(exp -3) N/m, viscosities from 45 x 10(exp -3) to 290 x 10(exp -3) Pa.s, and inlet flow rates from 0.15 x 10(exp -6) to 0.75 x 10(exp -6) m(exp 3)/s, showed that void content is a function of the capillary number characterizing the flow process. A critical value of capillary number, Ca = 2.5 x 10(exp -3), identifies a zone below which void content increases exponentially with decreasing capillary number. Above this critical value, negligible entrapment of voids is observed. Similar experiments carried out on surface treated nonwoven mats spanning a range of equilibrium contact angles from 20 deg to 78 deg showed that there is a critical contact angle above which negligible entrapment is observed. Below this value, there is no apparent effect of contact angle on the void fraction - capillary number relationship described earlier. Studies on the effect of filament wettability, and fluid velocity and viscosity on the size of the entrapment (voids) were also carried out. These indicate that larger sized entrapments which envelop more than one pore are favored by a low capillary number in comparison to smaller, pore level bubbles. Experiments were carried out on deformed mats - imposing high permeability spots at regular intervals on a background of low permeability. The effect of these spatial fluctuations in heterogeneity of the mat on entrapment is currently being studied.

Mahale, Anant D.↗