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NASA NTRS1994

Fabric geometry distortion during composites processing

Waviness and tow misalignment are often cited as possible causes of data scatter and lower compression stiffness and strength in textile composites. Strength differences of as much as 40 percent have been seen in composites that appear to have the same basic material and structural properties -- i.e., yarn orientation, yarn size, interlacing geometry. Fabric geometry distortion has been suggested as a possible reason for this discrepancy, but little quantitative data or substantial evidence exists. The focus of this research is to contribute to the present understanding of the causes and effects of geometric distortion in textile composites. The initial part of the study was an attempt to gather qualitative information on a variety of textile structures. Existing and new samples confirmed that structures with a significant direction presence would be more susceptible to distortion due to the compaction process. Thus, uniweaves (fiber vol frac: 54-72 percent) biaxial braids (vf: 34-58 percent) demonstrated very little fabric geometry distortion. In stitched panels, only slight buckling of z-direction stitches was observed, primarily near the surface. In contrast, for structures with high compaction ratios -- e.g., large cylindrical yarns (2.5:1) orpowder towpreg (4:1) -- there were visible distortions where previously smooth and periodic undulations were transformed to abrupt changes in direction. A controlled study of the effect of forming pressure on distortion was conducted on type 162 glass plain weave fabrics. Panels (6 x 6 in) were produced via a resin infusion type setup, but with an EPON 815 epoxy resin. Pressures ranging from hand layup to 200 psi were used (vf: 34-54 percent). Photomicrographs indicated that at pressures up to 50 psi, large changes in thickness were due primarily to resin squeeze out. At higher pressures, when intimate contact was made between the layers, there was some tow flattening and in-plane shifting to optimize nesting. However, even at 200 psi the period and amplitude of the tow undulation remained constant, suggesting that for this relatively fine fabric, distortions from compaction were not a problem. Because of the interest in using larger tows (to reduce cost) and more complex structures, tests were also run on 2D triaxial glass braid (113 yd/lb at 0, 225 yd/lb at +/- 45). Forming pressures of 20, 50, 200, and 500 psi were used, and short block compression tests were run. The 500 psi specimen had a 10 percent decrease in modulus and an almost 50 percent decrease in strength (vs. 20 psi). Because the total fiber wgt/panel was kept constant, the thickness varied from 0.32 to 0.22 in (49-70 percent vf). Yet, the strength value is clearly below what would be expected, even with the decrease in thickness. Photomicrographs of these samples will be taken to determine if more fabric distortion exists in the 500 psi specimens. Finally, because the ultimate goal is to be able to predict and control distortion in a variety of textile structures, a model compaction test was developed to directly measure the deformation of the tows during compaction. Layers of dry glass fabric were placed in a mold with a clear plexiglass window. The yarn amplitude and period was then calculated using image analysis of the videotaped deformation. Preliminary tests demonstrated the feasibility of this technique for simple fabrics with large tows.

Chen, Julie↗
NASA NTRS1995

Sensitivity analysis for large-deflection and postbuckling responses on distributed-memory computers

A computational strategy is presented for calculating sensitivity coefficients for the nonlinear large-deflection and postbuckling responses of laminated composite structures on distributed-memory parallel computers. The strategy is applicable to any message-passing distributed computational environment. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a parallel sparse equation solver based on a nested dissection (or multilevel substructuring) node ordering scheme; and (3) a multilevel parallel procedure for evaluating hierarchical sensitivity coefficients. The hierarchical sensitivity coefficients measure the sensitivity of the composite structure response to variations in three sets of interrelated parameters; namely, laminate, layer and micromechanical (fiber, matrix, and interface/interphase) parameters. The effectiveness of the strategy is assessed by performing hierarchical sensitivity analysis for the large-deflection and postbuckling responses of stiffened composite panels with cutouts on three distributed-memory computers. The panels are subjected to combined mechanical and thermal loads. The numerical studies presented demonstrate the advantages of the reduced basis technique for hierarchical sensitivity analysis on distributed-memory machines.

Watson, Brian C.↗
NASA NTRS1995

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Oh, K. S.↗
NASA NTRS1995

An efficiency study of the simultaneous analysis and design of structures

The efficiency of the Simultaneous Analysis and Design (SAND) approach in the minimum weight optimization of structural systems subject to strength and displacement constraints as well as size side constraints is investigated. SAND allows for an optimization to take place in one single operation as opposed to the more traditional and sequential Nested Analysis and Design (NAND) method, where analyses and optimizations alternate. Thus, SAND has the advantage that the stiffness matrix is never factored during the optimization retaining its original sparsity. One of SAND's disadvantages is the increase in the number of design variables and in the associated number of constraint gradient evaluations. If SAND is to be an acceptable player in the optimization field, it is essential to investigate the efficiency of the method and to present a possible cure for any inherent deficiencies.

Striz, Alfred G.↗
NASA NTRS1994

Three-dimensional hydrodynamic Bondi-Hoyle accretion. 1: Code validation and stationary accretors

We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle accretion. Totally absorbing stationary spheres of varying sizes (from 10.0 down to 0.02 Bondi radii) accrete matter from a homogeneous and slightly perturbed medium, which is taken to be an ideal gas (gamma = 5/3 or 1.2). To accommodate the long-range gravitational forces, the extent of the computational volume is typically a factor of 100 larger than the radius of the accretor. We compare the numerical mass accretion rates with the theoretical predictions of Bondi, to assess the validity of the code. The hydrodynamics is modeled by the piecewise parabolic method. No energy sources (nuclear burning) or sinks (radiation, conduction) are included. The resolution in the vicinity of the accretor is increased by multiply nesting several (6-8) grids around the stationary sphere, each finer grid being a factor of 2 smaller spatially than the next coarser grid. This allows us to include a coarse model for the surface of the accretor (vacuum sphere) on the finest grid while at the same time evolving the gas on the coarser grids. The accretion rates derived numerically are in in very good agreement (to about 10% over several orders of magnitude) with the values given by Bondi for a stationary accretor within a hydrodynamic medium. However, the equations have to be changed in order to include the finite size of the accretor (in some cases very large compared to the sonic point or even to the Bondi radius).

Ruffert, Maximilian↗
NASA NTRS1994

Three-dimensional hydrodynamic Bondi-Hoyle accretion. 2: Homogeneous medium at Mach 3 with gamma = 5/3

We investigate the hydrodynamics of three-dimensional classical Bondi-Hoyle accretion. Totally absorbing spheres of varying sizes (from 10 down to 0.01 accretion radii) move at Mach 3 relative to a homogeneous and slightly perturbed medium, which is taken to be an ideal gas (gamma = 5/3). To accommodate the long-range gravitational forces, the extent of the computational volume is 32(exp 3) accretion radii. We examine the influence of numerical procedure on physical behavior. The hydrodynamics is modeled by the 'piecewise parabolic method.' No energy sources (nuclear burning) or sinks (radiation, conduction) are included. The resolution in the vicinity of the accretor is increased by multiply nesting several (5-10) grids around the sphere, each finer grid being a factor of 2 smaller in zone dimension that the next coarser grid. The largest dynamic range (ratio of size of the largest grid to size of the finest zone) is 16,384. This allows us to include a coarse model for the surface of the accretor (vacuum sphere) on the finest grid, while at the same time evolving the gas on the coarser grids. Initially (at time t = 0-10), a shock front is set up, a Mach cone develops, and the accretion column is observable. Eventually the flow becomes unstable, destroying axisymmetry. This happens approximately when the mass accretion rate reaches the values (+/- 10%) predicted by the Bondi-Hoyle accretion formula (factor of 2 included). However, our three-dimensional models do not show the highly dynamic flip-flop flow so prominent in two-dimensional calculations performed by other authors. The flow, and thus the accretion rate of all quantities, shows quasi-periodic (P approximately equals 5) cycles between quiescent and active states. The interpolation formula proposed in an accompanying paper is found to follow the collected numerical data to within approximately 30%. The specific angular momentum accreted is of the same order of magnitude as the values previously found for two-dimensional flows.

Ruffert, Maximilian↗
NASA NTRS1994

Regional-scale flows in mountainous terrain. Part 1: A numerical and observational comparison

This study uses observed data and a numerical simulation to examine the generation of thermally driven flows across the Colorado mountain barrier on meso-beta to meso-alpha scales. The observations were collected from remote surface observing systems at exposed mountaintop locations throughout the state of Colorado, over the summers of 1984-88, as part of the Rocky Mountain Peaks Experiment (ROMPEX). The data show the development of a recurrent circulation system across the Colorado mountain barrier, operating on a diurnal timescale. From the observations, the basic structure of the flow system appears as a daytime inflow toward the highest terrain, and a nocturnal outflow away from it. However, when examined in detail, the flow system exhibits more unusual behavior, especially west of the barrier crest. Here, winds in the early evening are occasionally observed to onset abruptly from an easterly direction, generally counter to the upper-level winds. Observations from ROMPEX for 26 August 1985 are used to provide comparison data for a numerical simulation with the Regional Atmospheric Modeling System (RAMS). This three-dimensional case study experiment is initialized with data from the National Meteorological Center and incorporates two-way interactive grid nesting. From the observed data and case study simulation, four distinct phases of the regional-scale circulation system have been identified. In the development phase, a deep mountain-plains solenoid is generated through terrain heating along the Front Range. This circulation system transforms in the late afternoon transition phase into a westward-propagating density current (WPDC). The third phase, called the 'density-current propagation phase,' occurs as the WPDC moves westward across the mountains, leaving in its wake strong southeasterly flow at the mountaintop level. This current appears to be the cause of the peculiar easterly component winds found in the ROMPEX mountaintop observations along the western slope. In the final late-night adjustment phase, the WPDC dissipates near the western edge of the Colorado mountains and steady southerly flow evolves over the high mountain terrain. This southerly flow is the steady response to the differential heating that develops between the low-lying plains and the intermountain region.

Bossert, James E.↗
NASA NTRS1994

Asymptotic domination of cold relativistic MHD winds by kinetic energy flux

We study the conditions which lead to the conversion of most Poynting flux into kinetic energy flux in cold, relativistic hydromagnetic winds. It is shown that plasma acceleration along a precisely radial flow is extremely inefficient due to the near cancellation of the toroidal magnetic pressure and tension forces. However, if the flux tubes in a flow diverge even slightly faster than radially, the fast magnetosonic point moves inward from infinity to a few times the light cylinder radius. Once the flow becomes supermagnetosonic, further divergence of the flux tubes beyond the fast point can accelerate the flow via the 'magnetic nozzle' effect, thereby further converting Poynting flux to kinetic energy flux. We show that the Grad-Shafranov equation admits a generic family of kinetic energy-dominated asymptotic wind solutions with finite total magnetic flux. The Poynting flux in these solutions vanishes logarithmically with distance. The way in which the flux surfaces are nested within the flow depends only on the ratio of angular velocity to poliodal 4-velocity as a function of magnetic flux. Radial variations in flow structure can be expressed in terms of a pressure boundary condition on the outermost flux surface, provided that no external toriodal field surrounds the flow. For a special case, we show explicitly how the flux surfaces merge gradually to their asymptotes. For flows confined by an external medium of pressure decreasing to zero at infinity we show that, depending on how fast the ambient pressure declines, the final flow state could be either a collimated jet or a wind that fills the entire space. We discuss the astrophysical implications of our results for jets from active galactic nuclei and for free pulsar winds such as that believed to power the Crab Nebula.

Begelman, Mitchell C.↗
NASA NTRS1995

Flow downstream of the heliospheric terminal shock: Magnetic field line topology and solar cycle imprint

The topology of the magnetic field in the heliosheath is illustrated using plots of the field lines. It is shown that the Archimedean spiral inside the terminal shock is rotated back in the heliosheath into nested spirals that are advected in the direction of the interstellar wind. The 22-year solar magnetic cycle is imprinted onto these field lines in the form of unipolar magnetic envelopes surrounded by volumes of strongly mixed polarity. Each envelope is defined by the changing tilt of the heliospheric current sheet, which is in turn defined by the boundary of unipolar high-latitude regions on the Sun that shrink to the pole at solar maximum and expand to the equator at solar minimum. The detailed shape of the envelopes is regulated by the solar wind velocity structure in the heliosheath.

Nerney, Steven↗
NASA NTRS1995

The X-ray telescope on board ASCA

The Advanced Satellite for Cosmology and Astrophysics (ASCA) instrument uses identical conical foil X-ray mirrors for its four telescopes. One of the major advantages of ASCA's telescopes is the first time ever use of X-ray imaging over a broad energy band and high throughput for conducting astronomical spectroscopy. Nested thin foil reflectors make possible a large effective area up to 10 keV, even under the tight weight restriction of the ASCA spacecraft. The expected characteristics of the ASCA mirrors are summarized based on ray tracings and pre-flight calibrations. The total effective area of four telescopes at 1 and 7 keV are approximately 1200 and 600 sq cm, respectively. The image size (half power diameter: HPD) is about 3 min. The field of view is 24 min and 16 min full width at half maximum for 1 and 7 keV, respectively. Observations of several X-ray sources from space during the performance verification phase have confirmed those performances as well as the alignment of the optical systems.

Serlemitsos, Peter J.↗
NASA NTRS1994

Geology of the small Tharsis volcanoes: Jovis Tholus, Ulysses Patera, Biblis Patera, Mars

Jovis Tholus, Ulysses Patera, and Biblis Patera, three small volcanoes in the Tharsis area of Mars, provide important insight into the evolution of volcanism on Mars. All three are interpreted to be shield volcanoes, indicating that shield volcansim was present from the outset in Tharsis. Jovis Tholus is the least complex with simple repeated outpouring of lavas and caldera-forming events. Ulysses Patera is dominated by a giant caldera within which is a line of cinder cones or domes suggesting terminal stages of volcanism in which the magma had either significant volatiles or increased viscosity. Biblis Patera is characterized by nested calderas which have expanded by block faulting of the flank; it also exhibits lava flows erupted onto the flanks from events along concentric fractures. These shields are different from the younger Tharsis Montes shields only in terms of the volume of erupted material. The limited shield volume suggests that the magma source which fed the shields was rapidly depleted. The relatively large size ofthe calderas probably results from relatively large, shallow magma bodies rather than significant burial of the flanks by younger lavas. Eruption rates consistent with typical terrestrial basaltic eruptiuon rates suggest that these volcanoes were probably built over time spans of 10(exp 4) to 10(exp 5) years. Stratigraphic ages range from Early to Upper Hesperian; absolute ages range from 1.9 to 3.4 Ga.

Plescia, J. B.↗
NASA NTRS1993

Multi-resolution analysis for ENO schemes

Given a function u(x) which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. We apply this multi-resolution analysis to Essentially Non-oscillatory Schemes (ENO) schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one-dimensional case; this algorithm can be extended to the multi-dimensional case with cartesian grids.

Harten, Ami↗
NASA NTRS1994

Weightless bubble lattices: A case of froth wicking

In the absence of gravity drainage, froth wicking draws excess fluid onto a bubble lattice. Capillary forces only cause fluid transport; a moving front moves stably and without fluid fingering along a constant velocity bubble-fluid contact line. This percolation of fluid crawling up the lattice shows fluid coverage on lattice borders varies linearly with available surface area (proportional to lattice perimeter) and fluid accelerates through regions or nests of high bubble density (number of bubbles/sq cm). The development of nearly two-dimensional bubble lattices in variable gravity (step function between 0.01 and 1.8 times earthly gravity) are examined experimentally and a zeroth-order model for froth wetting is presented, which captures many of the principal observations. Possible applications for bubble lattices include adhesion casting of metals and separation of biological cells, bacteria, and particles.

Noever, David A.↗
NASA NTRS1995

Solar wind research with the Large Angle Spectroscopic Coronagraph (LASCO) experiment onboard the Solar and Heliospheric Observatory (SOHO) satellite

The ESA-NASA satellite, to be launched in October 1995, carries three nested coronagraphs, which will image the solar corona from 1.1 R(solar mass) to 30 R(solar mass). Super polished mirrors have been developed for the design of a mirror Lyot coronagraph which has a straylight level comparable with the coronal intensity from 1.1 R, to 30 R(solar mass) Coronal details can be imaged with a spatial resolution of 6 arc seconds. A Fabry Perot interferometer with a spectral resolution of 0.7 A at the wavelength of the green coronal emission line will allow the simultaneous construction of spectra over the entire field of view of 10(exp 6) pixels. The middle coronagraph (1.5 R(solar mass) - 6 R(solar mass)) and the outer coronagraph (3 R(solar mass) - 30 R(solar mass)) are externally occulted lens Lyot coronagraphs. Their straylight level 10(exp -11) B(solar mass) and 10(exp -12) B(solar mass) respectively is an order of magnitude smaller than the intensity of the corona. The sensitivity of LASCO to distinguish between different solar wind acceleration mechanisms will be discussed as well as its ability to discern different CME models.

Brueckner, G. E.↗
NASA NTRS1995

The Alignment Test System for AXAF-I's High Resolution Mirror Assembly

The AXAF-1 High Resolution Mirror Assembly (HRMA) consists of four nested mirror pairs of Wolter Type-1 grazing incidence optics. The HRMA assembly and alignment will take place in a vibration-isolated, cleanliness class 100, 18 meter high tower at an Eastman Kodak Company facility in Rochester, NY. Each mirror pair must be aligned such that its image is coma-free, and the four pairs must be aligned such that their images are coincident. In addition, both the HRMA optical axis and focal point must be precisely known with respect to physical references on the HRMA. The alignment of the HRMA mirrors is measured by the HRMA Alignment Test System (HATS), which is an integral part of the tower facility. The HATS is configured as a double-pass, autocollimating Hartmann test where each mirror aperture is scanned to determine the state of alignment. This paper will describe the design and operation of the HATS.

Waldman, Mark↗
NASA NTRS1996

Ion Thruster Support and Positioning System

A system for supporting and selectively positioning an ion thruster relative to a surface of a spacecraft includes three angularly spaced thruster support assemblies. Each thruster support assembly includes a frame which has a rotary actuator mounted thereon. The rotary actuator is connected to an actuator member which is rotatably connected to a thruster attachment member connected to a body of the thruster. A stabilizer member is rotatably mounted to the frame and to the thruster attachment member. The thruster is selectively movable in the pitch and yaw directions responsive to movement of the actuator members by the actuators on the thruster support assemblies. A failure of any one actuator on a thruster support assembly will generally still enable limited thruster positioning capability in two directions. In a retracted position the thruster attachment members are held in nested relation in saddles supported on the frames of the thruster support assemblies. The thruster is securely held in the retracted position during periods of high loading such as during launch of the spacecraft.

Haag, Thomas W.↗
NASA NTRS1996

Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems

Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.

Vanek, Petr↗
NASA NTRS1996

A Parallel Multilevel Spectral Element Scheme

A parallel multilevel strategy is developed using spectral (p) finite elements. Hierarchic bases are particularly well suited since the element matrices and vectors are nested and the multilevel projections easiliy performed. Since the basis degree is used to specify the multigrid level, an EBE strategy is natural br the multilevel technique. Results are presented for two candidate nonlinear elliptic transport problems: the augmented drift-diffusion equations of semiconductor device modeling and the stream function-vorticity equations of incompressible fluid dynamics.

Davis, M. B.↗