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NASA NTRS2016

Investigation of Unsteady Pressure-Sensitive Paint (uPSP) and a Dynamic Loads Balance to Predict Launch Vehicle Buffet Environments

This NESC assessment examined the accuracy of estimating buffet loads on in-line launch vehicles without booster attachments using sparse unsteady pressure measurements. The buffet loads computed using sparse sensor data were compared with estimates derived using measurements with much higher spatial resolution. The current method for estimating launch vehicle buffet loads is through wind tunnel testing of models with approximately 400 unsteady pressure transducers. Even with this relatively large number of sensors, the coverage can be insufficient to provide reliable integrated unsteady loads on vehicles. In general, sparse sensor spacing requires the use of coherence-length-based corrections in the azimuthal and axial directions to integrate the unsteady pressures and obtain reasonable estimates of the buffet loads. Coherence corrections have been used to estimate buffet loads for a variety of launch vehicles with the assumption methodology results in reasonably conservative loads. For the Space Launch System (SLS), the first estimates of buffet loads exceeded the limits of the vehicle structure, so additional tests with higher sensor density were conducted to better define the buffet loads and possibly avoid expensive modifications to the vehicle design. Without the additional tests and improvements to the coherence-length analysis methods, there would have been significant impacts to the vehicle weight, cost, and schedule. If the load estimates turn out to be too low, there is significant risk of structural failure of the vehicle. This assessment used a combination of unsteady pressure-sensitive paint (uPSP), unsteady pressure transducers, and a dynamic force and moment balance to investigate the integration schemes used with limited unsteady pressure data by comparing them with direct integration of extremely dense fluctuating pressure measurements. An outfall of the assessment was to evaluate the potential of using the emerging uPSP technique in a production test environment for future launch vehicles. The results show that modifications to the current technique can improve the accuracy of buffet estimates. More importantly, the uPSP worked remarkably well and, with improvements to the frequency response, sensitivity, and productivity, will provide an enhanced method for measuring wind tunnel buffet forcing functions (BFFs).

Schuster, David M.↗

NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗

NASA NTRS2007

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Memarsadeghi, Nargess↗

NASA NTRS2008

Vibration Analysis of the Space Shuttle External Tank Cable Tray Flight Data with and without PAL Ramp

External Tank Cable Tray vibration data for three successive Space Shuttle flights were analyzed to assess response to buffet and the effect of removal of the Protuberance Air Loads (PAL) ramp. Waveform integration, spectral analysis, cross-correlation analysis and wavelet analysis were employed to estimate vibration modes and temporal development of vibration motion from a sparse array of accelerometers and an on-board system that acquired 16 channels of data for approximately the first two minutes of each flight. The flight data indicated that PAL ramp removal had minimal effect on the fluctuating loads on the cable tray. The measured vibration frequencies and modes agreed well with predicted structural response.

Walker, B. E.↗

NASA NTRS2008

Vibration Analysis of the Space Shuttle External Tank Cable Tray Flight Data With and Without PAL Ramp

External Tank Cable Tray vibration data for three successive Space Shuttle flights were analyzed to assess response to buffet and the effect of removal of the Protuberance Air Loads (PAL) ramp. Waveform integration, spectral analysis, cross-correlation analysis and wavelet analysis were employed to estimate vibration modes and temporal development of vibration motion from a sparse array of accelerometers and an on-board system that acquired 16 channels of data for approximately the first 2 min of each flight. The flight data indicated that PAL ramp removal had minimal effect on the fluctuating loads on the cable tray. The measured vibration frequencies and modes agreed well with predicted structural response.

Walker, Bruce E.↗

NASA NTRS2018

An Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. II: Approach Based on the Dyson and Bethe-Salpeter Equations

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scattering expansion of the total field, we derive the Dyson equation for the coherent field and the ladder approximated Bethe–Salpeter equation for the dyadic correlation function. Then, under the far-field assumption for sparsely distributed particles, the Dyson equation is reduced to the Foldy integral equation for the coherent field, while the iterated solution of the Bethe–Salpeter equation ultimately yields the vector radiative transfer equation.

Electromagnetic scattering↗

NASA NTRS1983

Some constraints on the color-magnitude diagram of giants in the galactic spheroid

The color-magnitude diagram of giants in the Galactic spheroid is shown to be important in determining the number-color histogram of stars brighter than B = 19 mag. This result is demonstrated by comparing a standard Galaxy model with observations of 391 stars in a field in the direction of Aquarius (l = 36.5 deg, b = -51.1 deg). More than 80 percent of the spheroid stars and 40 percent of all stars in this magnitude range and direction are predicted to be giants. At most, a few percent of the spheroid stars in the current sample can lie on the main sequence bluer than the turn-off onto the giant branch near B - V approximately 0.4. The available observations suggest that the blue tip of the horizontal branch of the spheroid must be sparsely populated about a factor of 10 less than would be expected if the color-magnitude diagram of the spheroid were the same as diagrams for any of the globular clusters M3, M13, or M92. The total dispersion in colors (measurement errors and intrinsic dispersion) has a standard deviation in B - V color that is less than 0.2 mag.

Bahcall, J. N.↗

NASA NTRS1981

Electromagnetic backscattering from a sparse distribution of lossy dielectric scatterers

Electromagnetic backscattering from a sparse distribution of lossy dielectric particles having random orientation and position is studied. The paper begins by using the Foldy approximation to find an equation for the mean field. From this equation, an effective permittivity for the scattering medium is obtained. The correlation of the scattered field is found by employing the distorted Born approximation, i.e., particles embedded in the effective medium are assumed to be single scatterers. The above method is then used to find the backscattering coefficients from a leaf canopy. The leaf canopy is modeled by a half space of dielectric discs that are small in comparison to a wavelength. Numerical results show that the depolarized cross section is a sensitive function of leaf inclination angle statistics.

Lang, R. H.↗

NASA NTRS1990

A review of reduced Navier-Stokes computations for compressible viscous flows

A reduced form of the Navier-Stokes equations, defined by a single composite of the Euler, boundary layer, and triple deck approximations, is considered for the computation of viscous interacting flows. Global pressure or pseudopotential relaxation methods are integrated with coupled sparse matrix direct solvers or coupled strongly implicit ILU algorithms to efficiently capture sharp shocks and regions of recirculation. Solutions are obtained for a variety of 2D and 3D geometries and for Mach numbers (M) spanning the range from incompressible (M = 0) to supersonic (M = 6) flow.

Rubin, S. G.↗

NASA NTRS2004

Saturn's Rings, the Yarkovsky Effects, and the Ring of Fire

The dimensions of Saturn's A and B rings may be determined by the seasonal Yarkovsky effect and the Yarkovsky-Schach effect; the two effects confine the rings between approximately 1.68 and approximately 2.23 Saturn radii, in reasonable agreement with the observed values of 1.525 and 2.267. The C ring may be sparsely populated because its particles are transients on their way to Saturn; the infall may create a luminous Ring of Fire around Saturn's equator. The ring system may be young: in the past heat flow from Saturn's interior much above its present value would not permit rings to exist.

Rubincam, David Parry↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. II: The Coherent Field

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of the so-called zeroth-order fields without a special treatment of the boundary regions. In this setting, we calculate the coherent fields reflected and transmitted by the layer, and the coherent field inside the layer. We found that these fields are analytically equivalent to plane electromagnetic waves, and investigated the fulfillment of the boundary conditions for the electric fields at the layer interfaces. The results are then particularized to the cases of normal incidence and a semi-infinite discrete random medium. For sparsely distributed particles, we present a self-consistent derivation of the coherent field and discuss the Twersky and Foldy approximations.

Adrian Doicu↗

NASA NTRS2012

G-LiHT: Goddard's LiDAR, Hyperspectral and Thermal Airborne Imager

Scientists at NASA's Goddard Space Flight Center have developed an ultra-portable, low-cost, multi-sensor remote sensing system for studying the form and function of terrestrial ecosystems. G-LiHT integrates two LIDARs, a 905 nanometer single beam profiler and 1550 nm scanner, with a narrowband (1.5 nanometers) VNIR imaging spectrometer and a broadband (8-14 micrometers) thermal imager. The small footprint (approximately 12 centimeters) LIDAR data and approximately 1 meter ground resolution imagery are advantageous for high resolution applications such as the delineation of canopy crowns, characterization of canopy gaps, and the identification of sparse, low-stature vegetation, which is difficult to detect from space-based instruments and large-footprint LiDAR. The hyperspectral and thermal imagery can be used to characterize species composition, variations in biophysical variables (e.g., photosynthetic pigments), surface temperature, and responses to environmental stressors (e.g., heat, moisture loss). Additionally, the combination of LIDAR optical, and thermal data from G-LiHT is being used to assess forest health by sensing differences in foliage density, photosynthetic pigments, and transpiration. Low operating costs (approximately $1 ha) have allowed us to evaluate seasonal differences in LiDAR, passive optical and thermal data, which provides insight into year-round observations from space. Canopy characteristics and tree allometry (e.g., crown height:width, canopy:ground reflectance) derived from G-LiHT data are being used to generate realistic scenes for radiative transfer models, which in turn are being used to improve instrument design and ensure continuity between LiDAR instruments. G-LiHT has been installed and tested in aircraft with fuselage viewports and in a custom wing-mounted pod that allows G-LiHT to be flown on any Cessna 206, a common aircraft in use throughout the world. G-LiHT is currently being used for forest biomass and growth estimation in the CONUS and Mexico in support of NASA's Carbon Monitoring System (CMS) and AMIGA-Carb (AMerican Icesat Glas Assessment of Carbon). For NASA's CMS, wall-to-wall G-LiHT data have been acquired over intensive study sites with historic LiDAR datasets, dense inventory data, stem maps and flux tower observations. For AMIGA-Carb, G-LiHT transects have been acquired over ICESat tracks and USDA-FS inventory plots throughout the CONUS, and similar data will be acquired in Mexico during 2013. This talk will highlight recent science results from continental-scale transects landscape-scale deployments of G-LiHT, as well as seasonal forest dynamics from repeat pass G-LiHT acquisitions.

Cook, Bruce↗

NASA NTRS2012

Can Asian Dust Trigger Phytoplankton Blooms in the Oligotrophic Northern South China Sea?

Satellite data estimate a high dust deposition flux (approximately 18 g m(exp-2 a(exp-1) into the northern South China Sea (SCS). However, observational evidence concerning any biological response to dust fertilization is sparse. In this study, we combined long-term aerosol and chlorophyll-a (Chl-a) measurements from satellite sensors (MODIS and SeaWiFS) with a 16-year record of dust events from surface PM10 observations to investigate dust transport, flux, and the changes in Chl-a concentration over the northern SCS. Our result revealed that readily identifiable strong dust events over this region, although relatively rare (6 cases since 1994) and accounting for only a small proportion of the total dust deposition (approximately 0.28 g m(exp-2 a(exp-1), do occur and could significantly enhance phytoplankton blooms. Following such events, the Chl-a concentration increased up to 4-fold, and generally doubled the springtime background value (0.15 mg m(exp-3). We suggest these heavy dust events contain readily bioavailable iron and enhance the phytoplankton growth in the oligotrophic northern SCS.

northern South China sea↗

NASA NTRS1983

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗

NASA NTRS1986

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗

NASA NTRS1994

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗

NASA NTRS1995

Validation of Global Climatologies of Trace Gases Using NASA Global Tropospheric Experiment (GTE) Data

Methane is an important trace gas because it is a greenhouse gas that affects the oxidative capacity of the atmosphere. It is produced from biological and anthropogenic sources, and is increasing globally at a rate of approximately 0.6% per year [Climate Change 1992, IPCC]. By using National Oceanic and Atmospheric Administration/Climate Monitoring and Diagnostics Laboratory (NOAA/CMDL) ground station data, a global climatology of methane values was produced. Unfortunately, because the NOAA/CMDL ground stations are so sparse, the global climatology is low resolution. In order to compensate for this low resolution data, it was compared to in-situ flight data obtained from the NASA Global Tropospheric Experiment (GTE). The smoothed ground station data correlated well with the flight data. Thus, for the first time it is shown that the smoothing process used to make global contours of methane using the ground stations is a plausible way to approximate global atmospheric concentrations of the gas. These verified climatologies can be used for testing large-scale models of chemical production, destruction, and transport. This project develops the groundwork for further research in building global climatologies from sparse ground station data and studying the transport and distribution of trace gases.

Courchaine, Brian↗

NASA NTRS1983

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

Baker, A. J.↗