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NASA NTRS2004

Spectroscopy of the Perseus Cluster

We present preliminary results of a XMM-Newton 50 ks observation of the Perseus Cluster that provides an unprecedented view of the central 0.5 Mpc region. The projected gas temperature declines smoothly by a factor of 2 from a maximum value of approx. 7 keV in the outer regions to just above 3 keV at the cluster center. Over this same range, the heavy-element abundance rises slowly from 0.4 to 0.5 solar as the radius decreases from 14 ft. to 5 ft., and then it rises to a peak of almost 0.7 solar at 1&farcm;25 before declining to 0.4 at the center. Th global east-west asymmetry of the gas temperature and surface brightness distributions, approximately aligned with the chain of bright galaxies, suggests an ongoing merger, although the modest degree of the observed asymmetry certainly excludes a major merger interpretation. The chain of galaxies probably traces the filament along which accretion started some time ago and is continuing at the present time. A cold and dense (low-entropy) cluster core like Perseus is probably well "protected" against the penetration of the gas of infalling groups and poor clusters, whereas in non-cooling core clusters such as Coma and A1367, infalling subclusters can penetrate deeply into the core region. In Perseus, gas associated with infalling groups may be stripped completely at the outskirts of the main cluster and only compression waves (shocks) may reach the central regions. We argue, and show supporting simulations, that the passage of such a wave(s) can qualitatively explain the overall horseshoe shaped appearance of the gas temperature map (the hot horseshoe surrounds the colder, low-entropy core) as well as other features of the Perseus Cluster core. These simulations also show that as compression waves traverse the cluster core, they can induce oscillatory motion of the cluster gas that can generate multiple sharp "edges" on opposite sides of the central galaxy. Gas motions induced by mergers may be a natural way to explain the high frequency of "edges" seen in clusters with cooling cores.

Jones, Christine↗
NASA NTRS1972

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

Bossel, H. H.↗
NASA NTRS1982

Magnetic field studies by Voyager 2 - Preliminary results at Saturn

Results of Voyager 2 studies of the magnetosphere and planetary magnetic field of Saturn are presented. Magnetometer studies have confirmed the results obtained by Voyager 1, indicating the magnetic field to be that of a centered dipole of moment 0.21 gauss Saturn radii-cubed, tilted approximately 0.8 deg from the rotation axis and a maximum measured field intensity of 1187 nT at latitude 17.3 deg N just before periapsis. Voyager 2 observed multiple bow shock and magnetopause crossings during its inbound and outbound trajectories, which were complementary to those of Voyager 1, including magnetopause crossing at 18.5 Saturn radii on the inbound trajectory, and at 48.4-50.9 Saturn radii outbound indicative of magnetospheric expansion due to changing solar wind conditions. Throughout the outbound passage, the magnetospheric field was observed to be relatively steady and smooth, with no evidence for any azimuthal asymmetry or magnetic anomaly. Results thus are incapable of accounting for the observed periodic modulation of the Saturnian kilometric radio emissions.

Ness, N. F.↗
NASA NTRS1961

Exploratory Environmental Tests of Several Heat Shields

Exploratory tests have been conducted with several conceptual radiative heat shields of composite construction. Measured transient temperature distributions were obtained for a graphite heat shield without insulation and with three types of insulating materials, and for a metal multipost heat shield, at surface temperatures of approximately 2,000 F and 1,450 F, respectively, by use of a radiant-heat facility. The graphite configurations suffered loss of surface material under repeated irradiation. Temperature distribution calculated for the metal heat shield by a numerical procedure was in good agreement with measured data. Environmental survival tests of the graphite heat shield without insulation, an insulated multipost heat shield, and a stainless-steel-tile heat shield were made at temperatures of 2,000 F and dynamic pressures of approximately 6,000 lb/sq ft, provided by an ethylene-heated jet operating at a Mach number of 2.0 and sea-level conditions. The graphite heat shield survived the simulated aerodynamic heating and pressure loading. A problem area exists in the design and materials for heat-resistant fasteners between the graphite shield and the base structure. The insulated multipost heat shield was found to be superior to the stainless-steel-tile heat shield in retarding heat flow. Over-lapped face-plate joints and surface smoothness of the insulated multi- post heat shield were not adversely affected by the test environment. The graphite heat shield without insulation survived tests made in the acoustic environment of a large air jet. This acoustic environment is random in frequency and has an overall noise level of 160 decibels.

Goodman, George P.↗
NASA NTRS1979

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗
NASA NTRS2000

Multiresolution With Super-Compact Wavelets

The solution data computed from large scale simulations are sometimes too big for main memory, for local disks, and possibly even for a remote storage disk, creating tremendous processing time as well as technical difficulties in analyzing the data. The excessive storage demands a corresponding huge penalty in I/O time, rendering time and transmission time between different computer systems. In this paper, a multiresolution scheme is proposed to compress field simulation or experimental data without much loss of important information in the representation. Originally, the wavelet based multiresolution scheme was introduced in image processing, for the purposes of data compression and feature extraction. Unlike photographic image data which has rather simple settings, computational field simulation data needs more careful treatment in applying the multiresolution technique. While the image data sits on a regular spaced grid, the simulation data usually resides on a structured curvilinear grid or unstructured grid. In addition to the irregularity in grid spacing, the other difficulty is that the solutions consist of vectors instead of scalar values. The data characteristics demand more restrictive conditions. In general, the photographic images have very little inherent smoothness with discontinuities almost everywhere. On the other hand, the numerical solutions have smoothness almost everywhere and discontinuities in local areas (shock, vortices, and shear layers). The wavelet bases should be amenable to the solution of the problem at hand and applicable to constraints such as numerical accuracy and boundary conditions. In choosing a suitable wavelet basis for simulation data among a variety of wavelet families, the supercompact wavelets designed by Beam and Warming provide one of the most effective multiresolution schemes. Supercompact multi-wavelets retain the compactness of Haar wavelets, are piecewise polynomial and orthogonal, and can have arbitrary order of approximation. The advantages of the multiresolution algorithm are that no special treatment is required at the boundaries of the interval, and that the application to functions which are only piecewise continuous (internal boundaries) can be efficiently implemented. In this presentation, Beam's supercompact wavelets are generalized to higher dimensions using multidimensional scaling and wavelet functions rather than alternating the directions as in the 1D version. As a demonstration of actual 3D data compression, supercompact wavelet transforms are applied to a 3D data set for wing tip vortex flow solutions (2.5 million grid points). It is shown that high data compression ratio can be achieved (around 50:1 ratio) in both vector and scalar data set.

Lee, Dohyung↗
NASA NTRS2012

Three Dimensionally Interlinked, Dense, Solid Form of Single-Walled CNT Ropes

A 3D networked, dense form of single-walled carbon nanotubes (SWNT) has been made through isotropic shrinking of a gel-like SWNT-water paste by very slow evaporation. Approximately 35 g of Raw HiPco nanotubes were cleaned by the method of soft baking (250 C for 15 hours in air saturated with water vapor) in a glass beaker followed by leaching with concentrated hydrochloric acid. Typically, one liter of concentrated hydrochloric acid was added to the soft-baked voluminous mass in the same large beaker, and allowed to digest at room temperature with stirring overnight. The acid-digested SWNT slurry was filtered through a large porcelain Buchner funnel under atmospheric pressure. The slurry was continuously flushed, while still in the funnel, with a very slow but steady stream of deionized water employing a peristaltic pump. This process, referred to as gwashing, h continued until the filtrate water dripping from the Buchner funnel was clear, colorless, and neutral to a pH paper. This took about 15 liters of water to flow through the slurry over a day. At this point, the water pump was stopped and the SWNT-water slurry was allowed to drain the excess water for about 10 hours. The resulting thick paste of SWNT-neutral water was transferred to a beaker. The beaker was covered with aluminum foil with few holes and allowed to dry very slowly in a hood at room temperature. In about eight weeks, the sample gradually dried isotropically to a cylindrical dense mass referred to as a carbon nanotube block (CNB). There was no carbonaceous matter sticking to any of the glass surface where the SWNT-water paste made contact. The approximate dimensions of the cylindrical SWNT block that weighed 28 g were 1.5 in. (.3.8 cm) in diameter and 1.25 in. (.3.2 cm) in height. The bottom portion of the cylinder that was in contact with the beaker surface was slightly wider, indicating some resistance to shrinking. The cylindrical mass also consisted of several pores. The cylindrical mass was very tough and could not be broken with a small hammer using considerable force. The mass of the solid could be polished over a fine grain emery paper or even a smooth, stainless steel surface indicative of alignment at finer levels.

Smalley, Richard E.↗
NASA NTRS1994

Comet Shoemaker-Levy 9: Impact on Jupiter and plume evolution

The impact of fragments of Comet Shoemaker-Levy 9 on Jupiter and the resulting vapor plume expansion are investigated by conducting three-dimensional numerical simulations using the smoothed particle hydrodynamics (SPH) method. An icy body, representing the cometary fragments, with a velocity of 60 km/sec and a diameter of 2 km can penetrate to 350 km below the 1-bar pressure level in the atmosphere. Most of the initial kinetic energy of the fragment is transferred to the atmosphere between 50 km and 300 km below the 1-bar pressure level. The shock-heated atmospheric gas in the wake is totally dissociated and partially ionized. Scaling our SPH results to other sizes indicates that fragments larger than approximately 100 m in diameter can penetrate to below the visible cloud decks. The energy deposited in the atmosphere is explosively released in the upward expansion of the resulting plume. The plume preferentially expands upward rather than horizontally due to the density gradient of the ambient atmosphere. It rises greater than or equal to 10(exp 2) km in approximately 10(exp 2) sec. Eventually the total atmospheric mass ejected to above 1 bar is greater than or equal to 40 times the initial mass of the impactor. The plume temperature at a radius approximately 10(exp 3) km is greater than 10(exp 3) K for 10(exp 3) sec for a 2-km fragment. We predict that impact-induced plumes will be observable with the remote sensing instruments of the Galileo spacecraft. As the impact site rotates into the view of Earth some 20 min after the impact, the plume expansion will be observable using the Hubble Space Telescope (HST) and from visible and infrared instruments on groundbased telescopes. The rising plume reaches approximately 3000 km altitude in approximately 10 min and will be visible from Earth.

Takata, Toshiko↗
NASA NTRS2010

A Model for Backscattering from Quasi Periodic Corn Canopies at L-Band

In this study, a model for backscattering at L-band from a corn canopy is proposed. The canopy consists of a quasi-periodic distribution of stalks and a random distribution of leaves. The Distorted Born Approximation (DBA) is employed to calculate the single scattered return from the corn field. The new feature of the method is that the coherence of the stalks in the row direction is incorporated in the model in a systematic fashion. Since the wavelength is on the order of the distance between corn stalks in a row, grating lobe behavior is observed at certain azimuth angles of incidence. The results are compared with experimental values measured in Huntsville, Alabama in 1998. The mean field and the effective dielectric constant of the canopy are obtained by using the Foldy approximation. The stalks are placed in the effective medium in a two dimensional lattice to simulate the row structure of a corn field. In order to mimic a real corn field, a quasi-periodic stalk distribution is assumed where the stalks are given small random perturbations about their lattice locations. Corn leaves are also embedded in the effective medium and the backscattered field from the stalks and the leaves is computed. The backscattering coefficient is calculated and averaged over successive stalk position perturbations. It is assumed that soil erosion has smoothed the soil sufficiently so that it can be assumed flat. Corn field backscatter data was collected from cornfields during the Huntsville 98 experimental campaign held at Alabama A&M University Research Station, Huntsville, Alabama in 1998 using the NASA/GW truck mounted radar. Extensive ground truth data was collected. This included soil moisture measurements and corn plant architectural data to be used in the model. In particular, the distances between the stalks in a single row have been measured. The L-band radar backscatter data was collected for both H and V polarizations and for look angles of 15o and 45o over a two week period under varying soil moisture conditions. These measured backscattering values will be compared with the model backscattering values and a discussion of the results will be presented.

Lang, R.↗
NASA NTRS1994

Use of multiple gauges and microwave attenuation of precipitation for satellite verification

In this paper both a microwave attenuation measurement along a horizontal line and multiple point gauge measurements are analyzed as possible ground-truth designs to validate satellite precipitation retrieval algorithms at the field of view spatial level (typically about 20 km). The design consists of comparing a sequence of pairs of contemporaneous measurements taken from the ground and from space. The authors examine theoretically the variance of expected differences between the two systems. The line average measurement leads to a smaller mean-square error compared to the case of a single point gauge, since some of the small-scale variability of the rain field is smoothed away by the line integration. The multiple point gauge measurements also give smaller mean-square error than that of a single point gauge. The centroid of the line and point gauge configurations are considered to be located randomly inside the field of view for different overpasses. A space-time spectral formalism is used with a noise-forced diffusive rain field to find the mean-square error. By considering instantaneous ground and satellite measurement pairs over about 50 visits when raining, we can reduce the expected error to approximately 10% of the standard deviation of climatological variability. This is considered to be a useful level of tolerance for identifying biases in the retrieval algorithms. It is found that the multiple point gauges (especially two gauges) are the economical ground-truth design compared to the microwave attenuation based on the mean-square error comparison. The major finding of this study is that a significant improvement over the point gauge is obtained by adding a single additional piece of information; adding more gauges or extending the line of attenuation is not an important improvement.

Ha, Eunho↗
NASA NTRS1998

Development of the endolymphatic sac and duct in the Japanese red-bellied newt, Cynops pyrrhogaster

The development and maturation of the endolymphatic sac (ES) and duct (ED) were studied in the newt Cynops pyrrhogaster. The ES first appears as an oval capsule at the dorsal-medial tip of the otic vesicle at stage 39, about 11 days after oviposition. The ES consists of polymorphous epithelial cells with a minimum of cytoplasm. The intercellular space (IS) between the epithelial cells is narrow and has a smooth surface. At stage 44, the size of the ES increases as many vacuoles in the IS become filled. At stage 46, 18 days after oviposition, the ES elongates markedly and a slit-like lumen is found in the ES. The epithelium contains a few cell organelles which are scattered in the cytoplasm. The vacuoles in the IS are fused, which expands the IS. Two days later (stage 48), floccular material (endolymph) is present in the expanded lumen. The IS dilates and has a wide and irregular appearance. At stage 50, approximately 26 days after oviposition, the ES extends and expands significantly and crystals (otoconia) can now be seen in the widened lumen of the ES. The cytoplasm of the cuboidal epithelial cells contains an abundance of vesicles surrounded by ribosomes and Golgi complexes. Intercellular digitations are formed in the expanded IS. At stage 54, the ES forms a large bellow-like pouch. Numerous otoconia accumulate in the lumen. Free floating cells and cell debris can be seen in the lumen at this stage. The epithelial cells contain numerous cytoplasmic organelles which are evenly distributed in the cytoplasm. Granules are found in the apical and lateral cytoplasm. The IS is loose and displays a labyrinthine appearance. The primitive ED first appears as a connection between the ES and the saccule but no lumen is present inside at stage 39. At stage 46, a narrow lumen is formed in the ED, which corresponds to the formation of the ES lumen. At stage 50, as the ED extends, floccular material is seen in the lumen. At stage 54, the ED bears numerous microvilli on its luminal surface. Otoconia and endolymph are present in the ED. Tight junctions between the epithelial cells are formed at stage 46. A fully developed intercellular junctional complex is produced at stage 54. Based on the development of the ES and ED, the maturation of function of the ES and ED are discussed.

NASA Discipline Neuroscience↗
NASA NTRS2012

Modular Flooring System

The modular flooring system (MFS) was developed to provide a portable, modular, durable carpeting solution for NASA fs Robotics Alliance Project fs (RAP) outreach efforts. It was also designed to improve and replace a modular flooring system that was too heavy for safe use and transportation. The MFS was developed for use as the flooring for various robotics competitions that RAP utilizes to meet its mission goals. One of these competitions, the FIRST Robotics Competition (FRC), currently uses two massive rolls of broadloom carpet for the foundation of the arena in which the robots are contained during the competition. The area of the arena is approximately 30 by 72 ft (approximately 9 by 22 m). This carpet is very cumbersome and requires large-capacity vehicles, and handling equipment and personnel to transport and deploy. The broadloom carpet sustains severe abuse from the robots during a regular three-day competition, and as a result, the carpet is not used again for competition. Similarly, broadloom carpets used for trade shows at convention centers around the world are typically discarded after only one use. This innovation provides a green solution to this wasteful practice. Each of the flooring modules in the previous system weighed 44 lb (.20 kg). The improvements in the overall design of the system reduce the weight of each module by approximately 22 lb (.10 kg) (50 %), and utilize an improved "module-to-module" connection method that is superior to the previous system. The MFS comprises 4-by-4-ft (.1.2-by- 1.2-m) carpet module assemblies that utilize commercially available carpet tiles that are bonded to a lightweight substrate. The substrate surface opposite from the carpeted surface has a module-to-module connecting interface that allows for the modules to be connected, one to the other, as the modules are constructed. This connection is hidden underneath the modules, creating a smooth, co-planar flooring surface. The modules are stacked and strapped onto durable, commercially available drywall carts for storage and/or transportation. This method of storage and transportation makes it very convenient and safe when handling large quantities of modules.

Thate, Robert↗
NASA NTRS1992

Aerodynamic design of turbomachinery blading in three-dimensional flow - An application to radial inflow turbines

A computational method, based on a theory for turbomachinery blading design in three-dimensional inviscid flow, is applied to a parametric design study of a radial inflow turbine wheel. As the method requires the specification of swirl distribution, a technique for its smooth generation within the blade region is proposed. Excellent agreements have been obtained between the computed results from this design method and those from direct Euler computations, demonstrating the correspondence and consistency between the two. The computed results indicate the sensitivity of the pressure distribution to a lean in the stacking axis and a minor alteration in the hub/shroud profiles. Analysis based on Navier-Stokes solver shows no breakdown of flow within the designed blade passage and agreement with that from design calculation; thus the flow in the designed turbine rotor closely approximates that of an inviscid one. These calculations illustrate the use of a design method coupled to an analysis tool for establishing guidelines and criteria for designing turbomachinery blading.

Yang, Y. L.↗
NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth Observing System) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of "radiative smoothing" of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. "Offbeam" Lidar returns are now being used to estimate the cloud "radiative Green's function", (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the "Independent Pixel Approximation" or IPA. This and other measurements of 3D transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international "Intercomparison of 3D Radiation Codes" or I3RC, program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗
NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM (atmospheric radiation measurement) are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth observing system) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of 'radiative smoothing' of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. 'Offbeam' Lidar returns are now being used to estimate the cloud 'radiative Green's function' (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the 'Independent Pixel Approximation' or IPA. This and other measurements of 3D (three dimensional) transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international 'Intercomparison of 3D Radiation Codes' (I3RC) program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗
NASA NTRS2003

Characterization of a Ultra-high Temperature Ceramic Composite

Ultra-high temperature ceramics (UHTC) are of interest for hypersonic vehicle leading edge applications. Monolithic UHTCs are of concern because of their low fracture toughness and brittle behavior. UHTC composites (UHTCC) are being investigated as a possible approach to overcome these deficiencies. In this study a small sample of a UHTCC was evaluated by limited mechanical property tests, furnace oxidation exposures, and oxidation exposures in a flowing environment. The composite was prepared from a carbon fiber perform using ceramic particulates and a preceramic polymer. The as-received composite plate was non-uniform from front to back surface. Plate dimensions were 150 x 150 x 6 mm. The back surface had a fibrous, uniform appearance; XRD analysis revealed the presence of Sic and C. The front surface was smooth and non-uniform in appearance with evidence of a coarse grain structure produced by a liquid phase; XRD analysis revealed the presence of HfB2. Microcracks were present throughout the thickness as one might expect from a carbon fiber reinforced composite with attendant large thermal expansion mismatch between the matrix phases and the fibers. The HfB2 phase on the front surface was comparable in thickness to a fiber ply or about 0.6 mm, and surface microcracks were evident. Limited four point flexural tests were carried out at span to depth ratios of approximately 14 and 16 with markedly different results. Tests were run with the front or the back surface in tension. At the shorter span to depth failures occurred under a loading pin for both orientations. At a span to depth of 16 failures occurred in the center of the span with fracture clearly initiating from a tensile failure. Ultimate flexural strength, strain at ultimate stress, stress and strain at deviation from linear elastic behavior are reported. Strains at ultimate stress ranged from about 0.6 to 0.7 % for the back surface in tension, and 0.4 to 0.6 for the front surface in tension. At constant span to depth the strain at ultimate stress was about 0.2% greater for the back surface in tension and the ultimate strength was also higher. Strengths were in line with predictions from theory. Furnace oxidation studies were carried out at 1627 and 1927OC in a static furnace environment using ten minute cycles and one, five, and ten cycles. Limited oxidation studies were also carried out in a flowing oxyacetylene torch environment. Specimens were photographed, and weight and dimensional changes were determined. XRD and SEM characterizations were performed. Weight losses were attributed primarily to carbon fiber oxidation. The composite survived the torch test with little visible distress. Further details will be determined once metallographic studies are completed.

Levine, Stanley R.↗
NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗
NASA NTRS1972

Nonlinear estimation theory applied to the interplanetary orbit determination problem.

Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.

Tapley, B. D.↗