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NASA NTRS1993

Rational trigonometric approximations using Fourier series partial sums

A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.

Geer, James F.↗

NASA NTRS1994

Evolution of dynamo-generated magnetic fields in accretion disks around compact and young stars

Geometrically thin, optically thick, turbulent accretion disks are believed to surround many stars. Some of them are the compact components of close binaries, while the others are throught to be T Tauri stars. These accretion disks must be magnetized objects because the accreted matter, whether it comes from the companion star (binaries) or from a collapsing molecular cloud core (single young stars), carries an embedded magnetic field. In addition, most accretion disks are hot and turbulent, thus meeting the condition for the MHD turbulent dynamo to maintain and amplify any seed field magnetic field. In fact, for a disk's magnetic field to persist long enough in comparison with the disk viscous time it must be contemporaneously regenerated because the characteristic diffusion time of a magnetic field is typically much shorter than a disk's viscous time. This is true for most thin accretion disks. Consequently, studying magentic fields in thin disks is usually synonymous with studying magnetic dynamos, a fact that is not commonly recognized in the literature. Progress in studying the structure of many accretion disks was achieved mainly because most disks can be regarded as two-dimensional flows in which vertical and radial structures are largely decoupled. By analogy, in a thin disk, one may expect that vertical and radial structures of the magnetic field are decoupled because the magnetic field diffuses more rapidly to the vertical boundary of the disk than along the radius. Thus, an asymptotic method, called an adiabatic approximation, can be applied to accretion disk dynamo. We can represent the solution to the dynamo equation in the form B = Q(r)b(r,z), where Q(r) describes the field distribution along the radius, while the field distribution across the disk is included in the vector function b, which parametrically depends on r and is normalized by the condition max (b(z)) = 1. The field distribution across the disk is established rapidly, while the radial distribution Q(r) evolves on a considerably longer timescale. It is this evolution that is the subject of this paper.

Stepinski, Tomasz F.↗

NASA NTRS1994

The stability of two-phase flow over a swept-wing

We use numerical and asymptotic techniques to study the stability of a two-phase air/water flow above a flat porous plate. This flow is a model of the boundary layer which forms on a yawed cylinder and can be used as a useful approximation to the air flow over swept wings during heavy rainfall. We show that the interface between the water and air layers can significantly destabilize the flow, leading to traveling wave disturbances which move along the attachment line. This instability occurs for lower Reynolds numbers than in the case of the absence of a water layer. We also investigate the instability of inviscid stationary modes. We calculate the effective wavenumber and orientation of the stationary disturbance when the fluids have identical physical properties. Using perturbation methods we obtain corrections due to a small stratification in viscosity, thus quantifying the interfacial effects. Our analytical results are in agreement with the numerical solution which we obtain for arbitrary fluid properties.

Coward, Adrian↗

NASA NTRS1995

Krylov methods for compressible flows

We investigate the application of Krylov methods to compressible flows, and the effect of implicit boundary conditions on the implicit solution of nonlinear problems. Two defect-correction procedures, namely, approximate factorization (AF) for structured grids and ILU/GMRES for general grids, are considered. Also considered here are Newton-Krylov matrix-free methods that we combined with the use of mixed discretization schemes in the implicitly defined Jacobian and its preconditioner. Numerical experiments that show the performance of our approaches are then presented.

Tidriri, M. D.↗

NASA NTRS1994

Unsteady aerodynamics of vortical flows: Early and recent developments

The development of aerodynamic theories of streaming motions around bodies with unsteady vortical and entropic disturbances is reviewed. The basic concepts associated with such motions, their interaction with solid boundaries and their noise generating mechanisms are described. The theory was first developed in the approximation wherein the unsteady flow is linearized about a uniform mean lfow. This approach has been extensively developed and used in aeroelastic and aeroacoustic calculations. The theory was recently extended to account for the effect of distortion of the incident disturbances by the nonuniform mean flow around the body. This effect is found to have a significant influence on the unsteady aerodynamic force along the body surface and the sound radiated in the far field. Finally, the nonlinear characteristics of unsteady transonic flows are reviewed and recent results of linear and nonlinear computations are presented.

Atassi, H. M.↗

NASA NTRS1996

High temperature coarsening of Cr2Nb precipitates in Cu-8 Cr-4 Nb alloy

A new high-temperature-strength, high-conductivity Cu-Cr-Nb alloy with a CrNb ratio of 2:1 was developed to achieve improved performance and durability. The Cu-8 Cr4 Nb alloy studied has demonstrated remarkable thermal and microstructural stability after long exposures at temperatures up to 0.98 T(sub m). This stability was mainly attributed to the slow coarsening kinetics of the Cr2Nb precipitates present in the alloy. At all temperatures, the microstructure consists of a bimodal and sometimes trimodal distribution of strengthening Cr2Nb precipitates, depending on precipitation condition, i.e. from liquid or solid solution, and cooling rates. These precipitates remain in the same size range, i.e. large precipitates of approximately I pm, and small precipitates less dm 300 nm, and effectively pin the grain boundaries thus retaining a fine grain size of 2.7 micro-m after 100 h at 1323 K. (A relatively small number of Cr-rich and Nb-rich particles were also present.) This grain boundary pinning and sluggish coarsening of Cr2Nb particles explain the retention of good mechanical properties after prolonged holding at very high temperatures, e.g., 75% of the original hardness after aging for 100 h at 1273 K. Application of LSW-based coarsening models indicated that the coarsening kinetics of the large precipitates are most likely governed by grain boundary diffsion and, to a lesser extent, volume diffusion mechanisms.

Anderson, Kenneth Reed↗

NASA NTRS1998

Aeroheating Predictions for X-34 Using an Inviscid-Boundary Layer Method

Radiative equilibrium surface temperatures and surface heating rates from a combined inviscid-boundary layer method are presented for the X-34 Reusable Launch Vehicle for several points along the hypersonic descent portion of its trajectory. Inviscid, perfect-gas solutions are generated with the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and the Data-Parallel Lower-Upper Relaxation (DPLUR) code. Surface temperatures and heating rates are then computed using the Langley Approximate Three-Dimensional Convective Heating (LATCH) engineering code employing both laminar and turbulent flow models. The combined inviscid-boundary layer method provides accurate predictions of surface temperatures over most of the vehicle and requires much less computational effort than a Navier-Stokes code. This enables the generation of a more thorough aerothermal database which is necessary to design the thermal protection system and specify the vehicle's flight limits.

Riley, Christropher J.↗

NASA NTRS1998

Aeroheating Predictions for X-34 Using an Inviscid-Boundary Layer Method

Riley, Christopher J.↗

NASA NTRS2001

Ventifact Formation in the Mojave Desert: Field Analogs for Martian Processes

Two field studies in the Mojave Desert, California, shed light on processes of ventifact formation. The field sites are located on a ridge at Little Cowhole Mountain, which lies approximately 12 km south of Baker, and on an unnamed ridge situated along the northern boundary of the Mojave River Sink (Rasor Road site). The rocks at Little Cowhole Mountain are a blue-grey marble/dolomite, whereas those at Rasor Road are Miocene volcanic rocks (basalt). At both sites the abrasive agent is a fine-grained aeolian sand which was probably derived largely from the Mojave River. There are minimal modem inputs of sand to either site: abrasion occurs as a result of unique climatic and topographic conditions which allow pre-existing sand to be recycled from one aspect of the ridge to the other. Climatic conditions are well suited for ventifact formation. Owing, to the dry climate (marked by low average relative humidity, infrequent dew, and low annual rainfall), rates of chemical weathering are low. Where resurfacing of the rocks by sand abrasion proceeds at a rate greater than weathering, the ventifacts are considered "active." Active ventifacts are found atop and straddling the ridge crests, in the zone of maximum wind velocity and sediment supply. Inactive ventifacts occur where modem weathering Processes exceed abrasion rates; principally on the basal two-thirds of the hillslope, where wind velocity and sediment supply are lower. At intermediate locations between the slope base and crest, ventifacts are either active or inactive, depending on local conditions. The presence of relict ventifacts at the study sites, as well as elsewhere in the eastern Mojave Desert, suggests that the conditions for venti fact formation must have been more intense and extensive in the past. Together, the studies illustrate that the processes that interact to form ventifacts are highly complex, and must be studied at many scales. Small-scale effects, such as local topography, plant cover, or even the spatial distribution of boulders, strongly influence the formation of each individual ventifact. Mesoscale effects (hillslope form, total availability of sediment, seasonality of winds, etc.) determine the distribution of overall erosional energy and the location of active and relict forms.

Laity, J. E.↗

NASA NTRS2001

Beagle 2: The Next Exobiology Mission to Mars

Beagle 2 is a 60 kg probe (with a 30 kg lander) developed in the United Kingdom for inclusion on the European Space Agency's 2003 Mars Express. Beagle 2 will deliver to the Martian surface a payload which consists of a high percentage of science instruments to landed spacecraft mass. Beagle 2 will be launched in June, 2003 with Mars Express on a Soyuz-Fregat rocket from the Baikonur Cosmodrome in Kazakhstan. Beagle 2 will land on Mars on December 26, 2003 in the Isidis Planitia basin (approximately 10 degrees N and 275 degrees W), a large sedimentary basin that overlies the boundary between ancient highlands and northern plains. Isidis Planitia, the third largest basin on Mars, which is possibly filled with sediment deposited at the bottom of long-standing lakes or seas, offers an ideal environment for preserving traces of life. Beagle 2 was developed to search for organic material and other volatiles on and below the surface of Mars in addition to the study of the inorganic chemistry and mineralogy. Beagle 2 will utilize a mechanical mole and grinder to obtain samples from below the surface, under rocks and inside rocks. A pair of stereo cameras will image the landing site along with a microscope for examination of surface and rock samples. Analyses will include both rock and soil samples at various wavelengths, X-ray spectrometer and Mossbauer spectrometer as well as a search for organics and other light element species (e.g. carbonates and water) and measurement of their isotopic compositions. Beagle 2 has as its focus the goal of establishing whether evidence for life existed in the past on Mars at the Isidis Planitia site or at least establishing if the conditions were ever suitable. Carbonates and organic components were first recognized as existing on Mars when they were found in the Martian meteorite Nakhla. Romanek et al showed the carbonates in ALH84001 were formed at low temperatures. McKay et al noted possible evidence of early life on Mars within the ALH84001 meteorite. Thomas-Keprta et al showed the magnetite biomarkers in ALH84001's carbonates are indistinguishable from those formed by magnetotactic bacteria found on Earth. Gibson et al showed there was significant evidence for liquid water and biogenic products present on Mars across a 3.9 billion year period. A mechanical arm (PAW) operates from the lander and is used for science operations along with sample acquisition. Instruments attached to the PAW include: stereo cameras, Mossbauer instrument, X-ray fluorescence instrument, microscope, environmental sensors, rock corer/grinder, a spoon, mirror, brushes, a mole attachment for acquisition of subsurface to depths of 1 to 2 meters and an illumination device. Each camera has 14 filters which have been optimized for mineralogy composition, dust and water vapor detection. The microscope's camera is designed for viewing the size and shape of dust particles, rock surfaces, microfossils, and characteristics of the samples prior to introduction into the gas analysis package (GAP). The camera has a resolution of 4 microns/pixel, features four color capability (red, green, blue and UV (ultraviolet) fluoresence), a depth of focus of 40 micrometers and translation stage of +3 millimeters. The heart of the Beagle 2's life detection package is the gas analysis package (GAP), which consists of a mass spectrometer with collectors at fixed masses for precise isotopic ratio measurements and voltage scanning for spectral analysis. Primary aim of the GAP is to search for the presence of bulk constituents, individual species, and isotopic fractionations for both extinct and extent life along with studying the low-temperature geochemistry of the hydrogen, carbon, nitrogen and oxygen components on Mars from both the surface and atmosphere. GAP is a magnetic sector mass spectrometer with the range of 1 to 140 amu which can be operated in both the static and dynamic modes. A triple Faraday collector array will be used for C, N and O ratios along with a double Faraday array for H/D. Pulse counting electron multiplier will be utilized for noble gases and selected organics. Anticipated detection limits are at the picomole level for operation in the static mode of operation and high precision isotopic measurements will be made in the dynamic mode. Sample processing and preparation system consists of reaction vessels along with references. Sample ovens capable of being heated are attached to the manifold for sample combustion. Surface, subsurface materials and interior rock specimens will be combusted in pure oxygen gas at various temperature intervals to release organic matter and volatiles. Combustion process will permit detection of all forms and all atoms of carbon present in the samples. A chemical processing system is capable of a variety of conversion reactions. Gases are manipulated either by cryogenic or chemical reactions and passed through the gas handling portion of the vacuum system. There are two modes of operation: quantitative analysis and precise isotopic measurements. Additional information is contained in the original extended abstract.

Gibson, Everett K., Jr.↗

NASA NTRS1998

Numerical Simulations of an Unsteady Rocket Launch from the AH-64D Apache Longbow Helicopter

Rocket and missile firings from attack helicopters can cause main engine compressor stall. Studies of this phenomenon suggest that the main engine ingests either the plume from the rockets or the rocket blast waves. This creates surges at the inlet face, causing a loss of power in the main engine. The objective of this project is to set-up a computational fluid dynamics (CFD) simulation of the AH-64D Apache Longbow helicopter during a rocket launch, in order to qualitatively study the fluid dynamics of the problem. This project presents a progression of three unsteady Navier-Stokes solutions. The first unsteady solution involves only a rocket launch from its launch canister. The second solution is a launch from a canister mounted on the Apache's wing-pylon assembly. The last solution includes the Apache main engine and fuselage. The computations use a series of structured, overset grid systems, which allow for a rocket moving in a prescribed path. The method implements a Roe upwind scheme with LU-SGS (lower-upper factored symmetric Gauss-Seidel). A rotor pressure disk model approximates the helicopter rotor, while the rocket engine exit properties are applied as a prescribed boundary condition. Although the project is only at the half-way point, the first and second CFD simulations suggest the possibility of pressure wave interference. Sudden surges in pressure occur from two sources: at rocket start-up, and as the rocket leaves the canister. Wave patterns set-up by these sources appear to propagate to the location of the engine inlet. However the simplified geometry simulation with the main engine needs to be performed before coming to a conclusion.

Okamoto, Kevin↗

NASA NTRS1999

The Effect of Viscosity on the Spherical Stability of Oscillating Gas Bubbles

Gas bubbles driven in radial oscillations are subject to an instability of the spherical shape that is opposed by surface tension and viscosity. An exact linear formulation for the study of the phenomenon has been available for many years, but its complexity has discouraged a detailed investigation. With the recent theory of sonoluminescence of Lohse and co-workers, there has been a renewed interest in the problem and new data have become available. This paper presents a numerical method for the solution of the pertinent equations and compares the theory with these new data. The coupling of the strong nonlinearity of the bubble radial oscillations with the parametric mechanism of the surface instability results in a very complex structure for the stability boundary. Nevertheless, a good agreement between theory and data is found. A comparison with earlier approximate models is also made.

Hao, Y.↗

NASA NTRS2006

Improvements in Raman Lidar Measurements Using New Interference Filter Technology

Narrow-band interference filters with improved transmission in the ultra-violet have been developed under NASA-funded research and used in the Raman Airborne Spectroscopic Lidar (RASL) in ground-based, upward-looking tests. Measurements were made of atmospheric water vapor, cirrus cloud optical properties and carbon dioxide that improve upon any previously demonstrated using Raman lidar. Daytime boundary and mixed layer profiling of water vapor mixing ratio up to an altitude of approximately 4 h is performed with less than 5% random error using temporal and spatial resolution of 2-minutes and 60 - 210, respectively. Daytime cirrus cloud optical depth and extinction-to-backscatter ratio measurements are made using 1 -minute average. Sufficient signal strength is demonstrated to permit the simultaneous profiling of carbon dioxide and water vapor mixing ratio into the free troposphere during the nighttime. A description of the filter technology developments is provided followed by examples of the improved Raman lidar measurements.

Whiteman, David N.↗

NASA NTRS1998

Extension of the Polar Coronal Hole Boundary into Interplanetary Space

White-light measurements made by the Mk III Mauna Loa K-coronameter and the SOHO LASCO C2 and C3 coronagraphs, extending from 1.15 to 30 Ro, have been combined to show that the boundaries of polar coronal holes, as determined by measurements of path-integrated density, extend approximately radially into interplanetery space.

polar coronal radio occultation↗

NASA NTRS2007

Clay Bearing Units in the Region around Mawrth Vallis: Stratigraphy, Extent, and Possible Alteration Fronts

The largest exposure of phyllosilicates on Mars occurs on the highland plains around Mawrth Vallis. This exposure extends for about 300 km southward from the edge of the dichotomy boundary, covering an area greater than 200 x 300 kilometers over an elevation range of approximately 2000 meters. At least two different types of hydrated phyllosilicates (Fe/Mg-rich and Al-rich phyllosilicates) have been identified in OMEGA data based on absorption bands near 2.3 and 2.2 micrometers, respectively. These clay-bearing units are associated with layered, indurated light-toned units with complex spatial and stratigraphic relationships, and are unconfomably overlain by a darker, indurated, more heavily cratered unit. Ongoing analysis of OMEGA (approximately 1 kilometer/pixel) and CRISM multi-spectral (MSP, 200 meters/pixel) data reveal hydrated minerals with absorptions at approximately 2.2 or 2.3 micrometers in locations up to 300 kilometers away from the borders of the previously identified extent of clay-bearing units. We seek to: 1) further constrain the mineralogy of the hydrated species identified in [5], and 2) understand spatial and stratigraphic relationships between the different hydrated minerals and the cratered plains units in which they are found. In this work we perform mineralogical and stratigraphic comparisons between units to test whether these extended units may be related, in order to establish a broad zone of alteration.

Dobrea, E. Z. Noe↗

NASA NTRS2012

X-Ray Spectra from MHD Simulations of Accreting Black Holes

We present the results of a new global radiation transport code coupled to a general relativistic magneto-hydrodynamic simulation of an accreting, nonrotating black hole. For the first time, we are able to explain from first principles in a self-consistent way the X-ray spectra observed from stellar-mass black holes, including a thermal peak, Compton reflection hump, power-law tail, and broad iron line. Varying only the mass accretion rate, we are able to reproduce the low/hard, steep power-law, and thermal-dominant states seen in most galactic black hole sources. The temperature in the corona is T(sub e) ~ 10 keV in a boundary layer near the disk and rises smoothly to T(sub e) greater than or approximately 100 keV in low-density regions far above the disk. Even as the disk's reflection edge varies from the horizon out to approximately equal to 6M as the accretion rate decreases, we find that the shape of the Fe Ka line is remarkably constant. This is because photons emitted from the plunging region are strongly beamed into the horizon and never reach the observer. We have also carried out a basic timing analysis of the spectra and find that the fractional variability increases with photon energy and viewer inclination angle, consistent with the coronal hot spot model for X-ray fluctuations.

Schnittman, Jeremy D.↗

NASA NTRS2017

Invariant Imbedded T-Matrix Method for Axial Symmetric Hydrometeors with Extreme Aspect Ratios

The single-scattering properties (SSPs) of hydrometeors are the fundamental quantities for physics-based precipitation retrievals. Thus, efficient computation of their electromagnetic scattering is of great value. Whereas the semi-analytical T-Matrix methods are likely the most efficient for nonspherical hydrometeors with axial symmetry, they are not suitable for arbitrarily shaped hydrometeors absent of any significant symmetry, for which volume integral methods such as those based on Discrete Dipole Approximation (DDA) are required. Currently the two leading T-matrix methods are the Extended Boundary Condition Method (EBCM) and the Invariant Imbedding T-matrix Method incorporating Lorentz-Mie Separation of Variables (IITM+SOV). EBCM is known to outperform IITM+SOV for hydrometeors with modest aspect ratios. However, in cases when aspect ratios become extreme, such as needle-like particles with large height to diameter values, EBCM fails to converge. Such hydrometeors with extreme aspect ratios are known to be present in solid precipitation and their SSPs are required to model the radiative responses accurately. In these cases, IITM+SOV is shown to converge. An efficient, parallelized C++ implementation for both EBCM and IITM+SOV has been developed to conduct a performance comparison between EBCM, IITM+SOV, and DDSCAT (a popular implementation of DDA). We present the comparison results and discuss details. Our intent is to release the combined ECBM IITM+SOV software to the community under an open source license.

Pelissier, Craig↗

NASA NTRS1990

Ground observations of magnetospheric boundary layer phenomena

Several classes of traveling vortices in the dayside ionosphere convection have been detected and tracked using the Greenland magnetometer chain (Friis-Christensen et al., 1988, McHenry et al., 1989). One class observed during quiet times consists of a continuous series of vortices moving generally antisunward for several hours at a time. The vortices' strength is seen to be approximately steady and neighboring vortices rotate in opposite directions. Sondrestrom radar observations show that the vortices are located at the ionospheric convection reversal boundary. Low altitude DMSP observations indicate the vortices are on field lines which map to the inner edge of the low latitude boundary layer. Because the vortices are conjugate to the boundary layer, repeat in a regular fashion and travel antisunward, it is argued that this class of vortices is caused by the Kelvin-Helmholtz instability of the inner edge of the magnetospheric boundary layer.

Mchenry, Mark A.↗