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NASA NTRS1993

The interstellar abundances of tin and four other heavy elements

Spectra recorded at 1150-1600 A with an instrumental resolution near 16 km/s were obtained with the Goddard High-Resolution Spectrograph on board the HST. The gaseous interstellar abundances of five heavy elements along the light paths to 23 Ori, 15 Mon, 1 Sco, Pi Sco, and Pi Aqr were determined from the observations. The 1400.450 A line of Sn II was detected and identified toward three stars; at Z = 50, tin is the first element from the fifth row of the periodic table to be identified in the interstellar medium. One spectral line of each of Cu II (Z = 29) and Ga II (Z = 31), three lines of Ge II (Z = 32), and two lines of Kr I (Z = 36) were also detected toward some or all of the five stars. The depletions of these five heavy elements generally decrease monotonically with increasing atomic number toward each of the six stars, and tin is generally undepleted within the observational errors. The depletions of 26 elements from the interstellar gas in an average dense interstellar cloud appear to correlate with the elemental 'nebular' condensation temperatures more closely than with the first ionization potentials.

Hobbs, L. M.↗

NASA NTRS1994

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Baumeister, Kenneth J.↗

NASA NTRS1993

Massively parallel computation of RCS with finite elements

One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary steps expected to result in a robust low i/o system for very large finite element problems.

Parker, Jay↗

NASA NTRS1993

Multi-band reflector antenna with double-ring element frequency selective subreflector

Frequency selective subreflectors (FSS) are often employed in the reflector antenna system of a communication satellite or a deep space exploration vehicle for multi-frequency operations. In the past, FSS's have been designed for diplexing two frequency bands. For example, the Voyager FSS was designed to diplex S and X bands and the TDRSS FSS was designed to diplex S and Ku bands. Recently, NASA's CASSINI project requires an FSS to multiplex four frequency (S/X/Ku/Ka) bands. Theoretical analysis and experimental verifications are presented for a multi-band flat pannel FSS with double-ring elements. Both the exact formulation and the thin-ring approximation are described for analyzing and designing this multi-ring patch element FSS. It is found that the thin-ring approximation fails to predict the electrically wide ring element FSS's performance. A single screen double-ring element FSS is demonstrated for the tri-band system that reflects the X-band signal while transmitting through the S- and Ku-band signals. In addition, a double screen FSS with non-similar double-ring elements is presented for the Cassini's four-band system which reflects the X- and Ka-band signals while passing the S- and Ku-band signals. To accurately predict the FSS effects on a dual reflector antenna's radiation pattern, the FSS subreflector's transmitted/reflected field variation as functions of the polarization and incident angles with respect to the local coordinates was taken into account. An FSS transmission/reflection coefficient table is computed for TE and TM polarizations at various incident angles based on the planar FSS model. Next, the hybrid Geometric Optics (GO) and Physical Optics (PO) technique is implemented with linearly interpolating the FSS table to efficiently determine the FSS effects in a dual reflector antenna.

Wu, Te-Kao↗

NASA NTRS1993

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Cowsar, Lawrence C.↗

NASA NTRS1993

Numerical investigation of multi-element airfoils

The flow over multi-element airfoils with flat-plate lift-enhancing tabs was numerically investigated. Tabs ranging in height from 0.25 percent to 1.25 percent of the reference airfoil chord were studied near the trailing edge of the main-element. This two-dimensional numerical simulation employed an incompressible Navier-Stokes solver on a structured, embedded grid topology. New grid refinements were used to improve the accuracy of the solution near the overlapping grid boundaries. The effects of various tabs were studied at a constant Reynolds number on a two-element airfoil with a slotted flap. Both computed and measured results indicated that a tab in the main-element cove improved the maximum lift and lift-to-drag ratio relative to the baseline airfoil without a tab. Computed streamlines revealed that the additional turning caused by the tab may reduce the amount of separated flow on the flap. A three-element airfoil was also studied over a range of Reynolds numbers. For the optimized flap rigging, the computed and measured Reynolds number effects were similar. When the flap was moved from the optimum position, numerical results indicated that a tab may help to reoptimize the airfoil to within 1 percent of the optimum flap case.

Cummings, Russell M.↗

NASA NTRS1994

Scattering Cross Section of Sound Waves by the Modal Element Method

#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.

Baumeister, Kenneth J.↗

NASA NTRS1993

Comparison of symbolic and numerical integration methods for an assumed-stress hybrid shell element

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom and the significant time savings achieved is demonstrated through an example.

Rengarajan, Govind↗

NASA NTRS1994

Thermal analysis of a functionally graded material subject to a thermal gradient using the boundary element method

The boundary element method is utilized in this study to conduct thermal analysis of functionally graded composites, materials in which the internal microstructure or properties are explicitly tailored in order to obtain an optimal response, on the micromechanical (constituent) scale. A unique feature of the boundary element formulations used here is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one dimensional integrations. Using the computer code BEST-CMS, the through the thickness temperature profiles are computed for a representative material with varying numbers of fibers and fiber spacing in the thickness direction. The computed temperature profiles are compared to those obtained using an alternate analytical theory which explicitly couples the heterogeneous microstructure to the global analysis. The boundary element results compared favorably to the analytical calculations, with discrepancies that are explainable based on the boundary element formulation. The results serve both to demonstrate the ability of the boundary element method to analyze these types of materials, and to verify the accuracy of the analytical theory.

Goldberg, Robert K.↗

NASA NTRS1994

Collection requirements for trace-element analyses of extraterrestrial samples

Trace-element abundances have proven important in understanding the evolution of and interrelationships between different meteorites. Preliminary investigations of the trace-element contents of interplanetary dust particles indicate that trace-element abundances will prove equally important in distinguishing between micrometeorites of different types, comparing the interplanetary dust to the meteorites, and assessing the degree of thermal alteration experienced either on the parent body or during the collection process. Sample collection, delivery, and curation must be accomplished in a manner to avoid contamination with even trace amounts of the elements to be analyzed. The present SXRF sensitivity for micrometeorite analysis is of order 1 femtogram, but anticipated improvements in sensitivity will require sample contamination substantially below this level. Sample collection and handling equipment should be constructed from materials selected for ultrahigh purity, and serious consideration should be given in selecting the particular set of elements from which the collection apparatus is composed so as not to compromise useful information.

Flynn, George J.↗

NASA NTRS1994

Alkali element depletion by core formation and vaporization on the early Earth

The depletion of Na, K, Rb, and Cs in the Earth's upper mantle and crust relative to their abundances in chondrites is a long standing problem in geochemistry. Here we consider two commonly invoked mechanisms, namely core formation, and vaporization, for producing the observed depletions. Our models predict that a significant percentage of the Earth's bulk alkali element inventory is in the core (30 percent for Na, 52 percent for K, 74 percent for Rb, and 92 percent for Cs). These predictions agree with independent estimates from nebular volatility trends and (for K) from terrestrial heat flow data. Our models also predict that vaporization and thermal escape during planetary accretion are unlikely to produce the observed alkali element depletion pattern. However, loss during the putative giant impact which formed the Moon cannot be ruled out. Experimental, observational, and theoretical tests of our predictions are also described. Alkali element partitioning into the Earth's core was modeled by assuming that alkali element partitioning during core formation on the aubrite parent body (APB) is analogous to that on the early Earth. The analogy is reasonable for three reasons. First, the enstatite meteorites are the only known meteorites with the same oxygen isotope systematics as the Earth-Moon system. Second, the large core size of the Earth and the V depletion in the mantle requires accretion from planetesimals as reduced as the enstatite chondrites. Third, experimental studies of K partitioning between silicate and metal plus sulfide show that more K goes into the metal plus sulfide at higher pressures than at one atmosphere pressure. Thus partitioning in the relatively low pressure natural laboratory of the APB is a good guide to alkali elemental partitioning during the growth of the Earth.

Lodders, K.↗

NASA NTRS1992

Higher order finite element analysis of thick composite laminates

A higher order, sub-parametric, laminated, 3D solid finite element was used for the analysis of very thick laminated composite plates. The geometry of this element is defined by four nodes in the X-Y plane which define a prism of material through the thickness of the laminate. There are twenty-four degrees of freedom at each node; translations at the upper and lower surfaces of the laminate in each of the three coordinate directions, and the derivatives of these translations with respect to each coordinate. This choice of degrees of freedom leads to displacement and strain compatibility at the corners. Stacking sequence effects are accounted for by explicitly integrating the strain energy density through the thickness of the element. The laminated solid element was combined with a gap-contact element to analyze thick laminated composite lugs loaded through flexible pins. The resulting model accounts for pin bending effects that produce non-uniform bearing stresses through the thickness of the lug. A thick composite lug experimental test program was performed, and provided data that was used to validate the analytical model. Two lug geometries and three stacking sequences were tested.

Goering, J.↗

NASA NTRS1994

A Two Element Laminar Flow Airfoil Optimized for Cruise

Numerical and experimental results are presented for a new two-element, fixed-geometry natural laminar flow airfoil optimized for cruise Reynolds numbers on the order of three million. The airfoil design consists of a primary element and an independent secondary element with a primary to secondary chord ratio of three to one. The airfoil was designed to improve the cruise lift-to-drag ratio while maintaining an appropriate landing capability when compared to conventional airfoils. The airfoil was numerically developed utilizing the NASA Langley Multi-Component Airfoil Analysis computer code running on a personal computer. Numerical results show a nearly 11.75 percent decrease in overall wing drag with no increase in stall speed at sailplane cruise conditions when compared to a wing based on an efficient single element airfoil. Section surface pressure, wake survey, transition location, and flow visualization results were obtained in the Texas A&M University Low Speed Wind Tunnel. Comparisons between the numerical and experimental data, the effects of the relative position and angle of the two elements, and Reynolds number variations from 8 x 10(exp 5) to 3 x 10(exp 6) for the optimum geometry case are presented.

Steen, Gregory Glen↗

NASA NTRS1991

The individual element test revisited

The subject of the patch test for finite elements retains several unsettled aspects. In particular, the issue of one-element versus multielement tests needs clarification. Following a brief historical review, we present the individual element test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B, and C of the patch test and to the single element test are clarified.

Militello, Carmelo↗

NASA NTRS1994

Effects of heavy-element settling on solar neutrino fluxes and interior structure

We consider the effects of gravitational settling of both He and heavier elements on the predicted solar neutrino fluxes and interior sound speed and density profiles. We find that while the structural changes that result from the inclusion of both He and heavy-element settling are only slightly larger than the changes resulting from the inclusion of He settling alone, the additional increases in expected neutrino fluxes are of comparable size. Our preferred model with both He and heavy-element settling has neutrino count rates of 9.0 SNU for Cl-37 detectors and 137 SNU for Ga-71 detectors, as compared to 7.1 and 127 SNU for a comparable model without any diffusive separation, or 8.0 and 132 SNU for a model that includes He settling alone. We suggest that the correction factors by which the predicted neutrino fluxes of solar models calculated without including the effects of diffusion should be multiplied are 1.25 +/- 0.08 for Cl detectors, 1.07 +/- 0.02 for Ga detectors, and 1.28 +/- 0.09 for the B-8 flux (1 sigma errors). Comparison of internal sound speed and density profiles strongly suggests that the additional changes in calculated p-mode oscillation frequencies due to the inclusion of heavy-element settling will be small compared to the changes that result from He settling alone, especially for the higher degree modes. All models with diffusive separation give much better agreement with the observed depth of the convection zone than do nondiffusive models. The model that includes both He and heavy-element settling requires an initial He mass fraction Y = 0.280 and has a surface He abundance of Y = 0.251 at the solar age.

Proffitt, Charles R.↗

NASA NTRS1994

The evolution of magnetic network elements in the quiet Sun

Using the 155-h coordinated magnetograph data of Huairou and Big Bear Solar Observatories, we have studied the evolution and lifetime of magnetic network elements in an enhanced network region. Both statistical and counting methods give a mean lifetime of network elements of 50h. The network elements are divided into two categories according to their evolution: 'breakup' and 'merging'. They have similar average lifetimes. We also find that the number of the elements that disappear by merging is about twice that by breakup. This may indicate that the creation and disappearance of magnetic network elements are balanced.

Liu, Y.↗

NASA NTRS1995

Spectroscopic measurements of element abundances in the solar corona: Variations on the FIP theme

Solar wind and solar energetic particle (SEP) data yield systematic differences between elemental abundances in the corona and in the photosphere related to the first ionization potential (FIP) of the elements: low-FIP elements are preferentially enhanced relative to high-FIP elements by about a factor of four. Spectroscopic studies of the inner corona show that such a pattern may apply on average but not in detail for coronal loops: substantial abundance differences occur between different types of coronal structures, and variations have been found from flare to flare, from one active region to another, and over time in the same region; further, in some flares, anomalies such as enhanced Ne:O ratios, distinctly at odds with the FIP pattern, show that a competing element selection mechanism sometimes operates. Details of the observed abundance variability -- such as the magnitude of the variations, the relevant temporal and spatial scales, and correlations with other properties of the given coronal structure -- may give important clues to the processes which supply and heat the corona, or they may reflect the changing physical conditions or locations where those processes take place. However, many such details remain to be established definitively. At present, abundance variability is primarily a major complication to data analysis and interpretation. However, once it is better understood, it may provide a new diagnostic tool for probing the lower layers of the solar atmosphere.

Saba, J. L. R.↗

NASA NTRS1996

Verification of Orthogrid Finite Element Modeling Techniques

The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.

Steeve, B. E.↗