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NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗

NASA NTRS2005

Fabrication of Spherical Reflectors in Outer Space

A process is proposed for fabrication of lightweight spherical reflectors in outer space for telescopes, radio antennas, and light collectors that would be operated there. The process would obviate the relatively massive substrates and frames needed to support such reflectors in normal Earth gravitation. According to the proposal, fabrication of a reflector would begin with blowing of a bubble to the specified reflector radius. Taking advantage of the outer-space vacuum as a suitable environment for evaporative deposition of metal, a metal-evaporation source would be turned on and moved around the bubble to deposit a reflective metal film over the specified reflector area to a thickness of several microns. Then the source would be moved and aimed to deposit more metal around the edge of the reflector area, increasing the thickness there to approximately equal to 100 micron to form a frame. Then the bubble would be deflated and peeled off the metal, leaving a thin-film spherical mirror having an integral frame. The mirror would then be mounted for use. The feasibility of this technology has been proved by fabricating a prototype at JPL. As shown in the figure, a 2-in. (.5-cm) diameter hemispherical prototype reflector was made from a polymer bubble coated with silver, forming a very smooth surface.

Wang, Yu↗

NASA NTRS1974

A method for the measurement and the statistical analysis of atmospheric turbulence

The instantaneous values of output voltages representing the wind velocity vector and the temperature at different elevations of the 250-foot meteorological tower located at NASA Wallops Flight Center are provided with the three dimensional split-film TSI Model 1080 anemometer system. The output voltages are sampled at a rate of one every 5 milliseconds, digitized and stored on digital magnetic tapes for a time period of approximately 40 minutes, with the use of a specially designed data acqusition system. A new calibration procedure permits the conversion of the digital voltages to the respective values of the temperature and the velocity components in a Cartesian coordinate system connected with the TSI probe with considerable accuracy. Power, cross, coincidence and quadrature spectra of the wind components and the temperature are obtained with the use of the fast Fourier transform. The cosine taper data window and ensemble and frequency smoothing techniques are used to provide smooth estimates of the spectral functions.

Tieleman, H. W.↗

NASA NTRS1987

Morphologic contrasts between Nirgal and Auqakuh Valles, Mars: Evidence of different crustal properties

Photoclinometric measurements were made of sidewall slopes in Nirgal and Auqakuh Valles and these results were interpreted in terms of the geologic setting and a simple geomorphic model to provide insights into the physical properties of crustal materials in these areas. Nirgal was interpreted to be a runoff channel and Auqakuh to be a fretted channel. Geomorphologic arguments for the sapping origin of Nirgal and Auqakuh Valles were presented. The morphologies of the channels, however, differ greatly: the tributaries of Nirgal end abruptly in theater-headed canyons, whereas the heads of tributaries of Auqakuh shallow gradually. The plateau surface surrounding both channels appears to be covered by smooth materials, presumably lava flows; they are continuous and uneroded in the Nirgal area, but at Auqakuh they are largely eroded and several layers are exposed that total about 200 m in thickness. For Nirgal Valles, the measurements show that sidewalls in the ralatively shallow upper reaches of the channel have average slopes near 30 degrees and, in the lower reaches, sidewall slopes exceed 50 degrees. Auqakuh, on the other hand, has maximum sidewall slopes of 14 degrees and an approximate maximum depth of 1000 m. Faint, horizontal layering in portions of the lower reaches of Nirgal may indicate inhomogeneity in either composition or topography.

Mackinnon, David J.↗

NASA NTRS1988

Collisional stripping of Mercury's mantle

A three-dimensional smoothed-particle hydrocode is the basis of the present numerical simulations of conditions under which a giant collision between a proto-Mercury and a planet one-sixth its size would lead to the loss of most of the silicate mantle of Mercury and thereby account for its anomalously high density. A head-on collision at 20 km/sec, and an off-axis impact parameter of half the radius of the proto-Mercury at 35 km/sec, are approximately equal in damage yielded; both will yield a remnant whose characteristics are those of the present Mercury.

Benz, Willy↗

NASA NTRS1982

Automatic evaluation of interferograms

A system for the evaluation of interference patterns was developed. For digitizing and processing of the interferograms from classical and holographic interferometers a picture analysis system based upon a computer with a television digitizer was installed. Depending on the quality of the interferograms, four different picture enhancement operations may be used: Signal averaging; spatial smoothing, subtraction of the overlayed intensity function and the removal of distortion-patterns using a spatial filtering technique in the frequency spectrum of the interferograms. The extraction of fringe loci from the digitized interferograms is performed by a foating-threshold method. The fringes are numbered using a special scheme after the removal of any fringe disconnections which appeared if there was insufficient contrast in the holograms. The reconstruction of the object function from the fringe field uses least squares approximation with spline fit. Applications are given.

Becker, F.↗

NASA NTRS1994

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Coirier, William John↗

NASA NTRS2002

Heat Transfer in a Complex Trailing Edge Passage for a High Pressure Turbine Blade: Simulation Results - Part 2:

A combined experimental and numerical study to investigate the heat transfer distribution in a complex blade trailing edge passage was conducted. The geometry consists of a two pass serpentine passage with taper toward the trailing edge, as well as from hub to tip. The upflow channel has an average aspect ratio of roughly 14:1, while the exit passage aspect ratio is about 5:1. The upflow channel is split in an interrupted way and is smooth on the trailing edge side of the split and turbulated on the other side. A turning vane is placed near the tip of the upflow channel. Reynolds numbers in the range of 31,000 to 61,000, based on inlet conditions, were simulated numerically. The simulation was performed using the Glenn-HT code, a full three-dimensional Navier-Stokes solver using the Wilcox k-omega turbulence model. A structured multi-block grid is used with approximately 4.5 million cells and average y+ values on the order of unity. Pressure and heat transfer distributions are presented with comparison to the experimental data. While there are some regions with discrepancies, in general the agreement is very good for both pressure and heat transfer.

Rigby, David L.↗

NASA NTRS2019

Wrinkle Ridges on Mercury and the Moon Within and Outside of Mascons

Found on all terrestrial planets, wrinkle ridges are anticlines formed by thrust faulting and folding resulting from crustal shortening. The MErcury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER) spacecraft's orbital phase returned high resolution images and topographic data of the previously unimaged northern high latitudes of Mercury where there are large expanses of smooth plains deformed by wrinkle ridges. Concurrently, the Lunar Reconnaissance Orbiter (LRO) is obtaining high resolution images and topographic data covering lunar mare wrinkle ridges. These data allow quantitative comparison of the scale of wrinkle ridges in smooth plains volcanic units on Mercury with mare wrinkle ridges. We evaluate the topographic relief of 300 wrinkle ridges within and outside of mascon basins on the Moon and Mercury. Measured wrinkle ridges range from ~112 to 776 m in relief with a mean of ~350 m (median = ~340 m, n = 150) on Mercury and from ~47 to 678 m in relief with a mean of ~198 m (median = ~168 m, n = 150) on the Moon. Wrinkle ridges on Mercury thus are approximately twice as large in mean relief compared to their counterparts on the Moon. The larger scale of Mercury's wrinkle ridges suggests that their formation can be attributed, in part, to global contraction. As global contraction on the Moon is estimated to be an order of magnitude smaller than on Mercury, the smaller scale of lunar wrinkle ridges suggests they most likely form primarily by load induced subsidence of the mare basalt. Wrinkle ridges located in lunar mascon basins and in the Caloris mascon on Mercury are not statistically significantly different in relief than ridges in non-mascon regions, suggesting comparable levels of contractional strain. The fact that mascon basins do not host wrinkle ridges with greater structural relief relative to non-mascon units may indicate the critical role lithospheric thickness plays in controlling subsidence and contraction of thick volcanic sequences on the Moon and Mercury.

Global contraction↗

NASA NTRS1988

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.

Burkholder, R. J.↗

NASA NTRS1999

Cloud 3D Effects Evidenced in Landsat Power Spectra and Autocorrelation Functions

An analysis of nadir reflectivity Fourier spatial power spectra and autocorrelation functions at solar wavelengths and for cloudy conditions has been carried out. The data come from Landsat Thematic Mapper (TM) observations, while Monte Carlo (MC) simulations are used to aid the interpretation of the Landsat results. We show that radiative processes produce consistent signatures on power spectra and autocorrelation functions. The former take a variety of forms not shown or explained in previous observational studies. We demonstrate that the TM spectra can potentially be affected by both radiative "roughening" at intermediate scales (approx. 1 -5 km), being more prevalent at large solar zenith angles, and the already documented radiative "smoothing" at small scales (less than 1 km). These processes are wavelength dependent, as shown by systematic differences between conservative (for cloud droplets) TM band 4 (approx. 0.8 microns) and absorbing band 7 (approx. 2.2 microns): band 7 exhibits more roughening and less smoothing. This is confirmed quantitatively by comparing least-squared fitted power spectral slopes for the two bands. It is also corroborated by a slower decrease with distance of autocorrelation function values for band 4 compared to band 7. The appearance of roughening at large solar zenith angles is a result of side illumination and shadowing and adds an additional complexity to the power spectra. MC spectra are useful in illustrating that scale invariant optical depth fields can produce complex power spectra that take a variety of shapes under different conditions. We show that radiative roughening increases with the decrease of single scattering albedo and with the increase of solar zenith angle (as in the observations). For high Sun there is also a clear shift of the radiative smoothing scale to smaller values as droplet absorption increases. The shape of the power spectrum is sensitive to the magnitude and type of cloud top height variability, with the spectral signatures of decorrelation between reflectance and optical depth at large scales becoming stronger as the magnitude of cloud top variations increase. Finally, the usefulness of power spectral analysis in evaluating the skill of novel optical depth retrieval techniques in removing 3D radiative effects is demonstrated. New techniques using inverse Non-local Independent Pixel Approximation (NIPA) and Normalized Difference of Nadir Reflectivity (NDNR) yield optical depth fields which better match the scale-by-scale variability of the true optical depth field.

Oreopoulos, Lazaros↗

NASA NTRS2004

Vestibular and Non-vestibular Contributions to Eye Movements that Compensate for Head Rotations during Viewing of Near Targets

We studied horizontal eye movements induced by en-bloc yaw rotation, over a frequency range 0.2 - 2.8 Hz, in 10 normal human subjects as th ey monocularly viewed a target located at their near point of focus. We measured gain and phase relationships between eye-in-head velocity and head velocity when the near target was either earth-fixed or head-fixed. During viewing of the earth-fixed near target,median gain was 1.49 (range 1.24 - 1.87) at 0.2 Hz for the group of subjects, but decl ined at higher frequencies, so that at 2.8 Hz median gain was 1.08 (r ange 0.68 - 1.67). During viewing of the head-fixed near target, median gain was 0.03 (range 0.01 - 0.10) at 0.2 Hz for the group of subjec ts, but increased at higher frequencies, so that at 2.8 Hz median gai n was 0.71 (range 0.28 - 0.94). We estimated the vestibular contribution to these responses (vestibulo-ocular reflex gain, Gvor) by applyin g transient head perturbations (peak acceleration> 1,000 deg's(exp 2) ) during sinusoidal rotation under the two viewing conditions. Median Gvor, estimated < 70m after the onset of head perturbation, was 0.98 (range 0.39 - 1.42) while viewing the earth-fixed near target, and 0. 97 (range 0.37 - 1.33) while viewing the head-fixed near target. For the group of subjects, 9 out of 10 subjects showed no sigificant diff erence of Gvor between the two viewing conditions ( p > 0.053 ) at all test frequencies. Since Gvor accounted for only approximately 73% of the overall response gain during viewing of the earth-fixed target, we investigated the relative contributions of non-vestibular factors. When subjects viewed the earth-fixed target under strobe illumination , to eliminate retinal image slip information, the gain of compensato ry eye movements declined compared with viewing in ambient room light . During sum-of-sine head rotations, while viewing the earth-fixed target, to minimize contributions from predictive mechanisms, gain also declined Nonetheless, simple superposition of smooth-pursuit tracking of sinusoidal target motion could not fully account for the overall r esponse at higher frequencies, suggesting other non-vestibular contributions. During binocular viewing conditions when vergence angle was s ignificantly greater than monocular viewing (p < 0.001), this gain of compensatory eye movements did not show proportional change; indeed, gain could not be correlated with vergence angle during monocular or binocular viewing. We conclude that several separate factors contribute to generate eye rotations during sinusoidal yaw head rotations whi le viewing a near target; these include the VOR, visual-tracking eye movements that utilize retinal image motion, predictive eye movements and, possibly, other unidentified nonvestibular factors. For these experiments, vergence was not an important determinant of response gain .

Han, Yanning H.↗

NASA NTRS1987

An embedded function approach for turbulent flow prediction

In conventional prediction methods for turbulent flow influence on surface properties, very small mesh sizes and considerable computational effort is required to adequately resolve the intense velocity and temperature profile variations that occur in the wall-layer region. In this study, an approach is described wherein an outer region numerical solution is smoothly matched to a set of embedded analytic profile functions in the near-wall region; these wall-layer profile functions having been derived through consideration of the coherent structure of the time-dependent near-wall flow provide analytic expressions for the mean velocity and enthalpy profiles in the wall layer. The concept is demonstrated through example applications to turbulent boundary-layer flows in two dimensions. The technique is shown to be very efficient and it is demonstrated that a reduction of approximately half the mesh points across the 2-D layer may be realized (as compared to conventional methods) with no degradation in accuracy.

Walker, J. D. A.↗

NASA NTRS1991

Inverse problems in diffraction

A two-dimensional problem of diffraction of a plane electromagnetic wave on a smooth 2 pi-periodic surface is considered. A numerical algorithm solving this problem is developed. An inverse problem of determination of the shape of 2 pi-periodic surface using the performance data of reverse scattering is considered. The inverse problem was solved by means of minimization of the residual functional with the help of the gradient descent method. The initial data were calculated with the help of the numerical method. On each step of the iterative method of minimization, the residual functional was calculated approximately with the help of the small slope method. The examples of the shape determination are considered.

Mikheev, Andrew G.↗

NASA NTRS1952

Hydrodynamic Impact of a System with a Single Elastic Mode II : Comparison of Experimental Force and Response with Theory

Hydrodynamic impact tests were made on an elastic model approximating a two-mass spring system to determine experimentally the effects of structural flexibility on the hydrodynamic loads encountered during seaplane landing impacts and to correlate the results with theory. A flexible seaplane was represented by a two-mass spring system consisting of a rigid prismatic float connected to a rigid upper mass by an elastic structure. The model had a ratio of sprung mass to hull mass of 0.6 and a natural frequency of 3.0 cycles per second. The tests were conducted in smooth water at fixed trims and included both high and low flight-path angles and a range of velocity. Theoretical and experimental comparisons indicated that the theoretical results agreed well with the experimental results.

Miller, Robert W↗

NASA NTRS1994

Comparison of large-scale structures and velocities in the local universe

Comparison of the large-scale density and velocity fields in the local universe shows detailed agreement, strengthening the standard paradigm of the gravitational origin of these structures. Quantitative analysis can determine the cosmological density parameter, Omega, and biasing factor, b; there is virtually no sensitivity in any local analyses to the cosmologial constant, lambda. Comparison of the dipole anisotropy of the cosmic microwave background with the acceleration due to the Infrared Astronomy Satellite (IRAS) galaxies puts the linear growth factor in the range beta approximately equals Omega (exp 0.6)/b = 0.6(+0.7/-0.3) (95% confidence). A direct comparison of the density and velocity fields of nearby galaxies gives beta = 1.3 (+0.7/-0.6), and from nonlinear analysis the weaker limit (Omega greater than 0.45 for b greater than 0.5 (again 95% confidence). A tighter limit (Omega greater than 0.3 (4-6 sigma)), is obtained by a reconstruction of the probability distribution function of the initial fluctuations from which the structures observed today arose. The last two methods depend critically on the smooth velocity field determined from the observed velocities of nearby galaxies by the POTENT method. A new analysis of these velocities, with more than three times the data used to obtain the above quoted results, is now underway and promises to tighten the uncertainties considerably, as well as reduce systematic bias.

Yahil, Amos↗

NASA NTRS2015

A Numerical and Experimental Study of Coflow Laminar Diffusion Flames: Effects of Gravity and Inlet Velocity

In this work, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting behavior of laminar coflow methane-air diffusion flames was investigated both computationally and experimentally. A series of flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) was assessed numerically under microgravity and normal gravity conditions with the fuel stream CH4 mole fraction ranging from 0.4 to 1.0. Computationally, the MC-Smooth vorticity-velocity formulation of the governing equations was employed to describe the reactive gaseous mixture; the soot evolution process was considered as a classical aerosol dynamics problem and was represented by the sectional aerosol equations. Since each flame is axisymmetric, a two-dimensional computational domain was employed, where the grid on the axisymmetric domain was a nonuniform tensor product mesh. The governing equations and boundary conditions were discretized on the mesh by a nine-point finite difference stencil, with the convective terms approximated by a monotonic upwind scheme and all other derivatives approximated by centered differences. The resulting set of fully coupled, strongly nonlinear equations was solved simultaneously using a damped, modified Newton's method and a nested Bi-CGSTAB linear algebra solver. Experimentally, the flame shape, size, lift-off height, and soot temperature were determined by flame emission images recorded by a digital camera, and the soot volume fraction was quantified through an absolute light calibration using a thermocouple. For a broad spectrum of flames in microgravity and normal gravity, the computed and measured flame quantities (e.g., temperature profile, flame shape, lift-off height, and soot volume fraction) were first compared to assess the accuracy of the numerical model. After its validity was established, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting tendency of laminar coflow methane-air diffusion flames was explored further by examining quantities derived from the computational results.

microgravity↗

NASA NTRS1985

Algebraic grid generation using tensor product B-splines

Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.

Saunders, B. V.↗