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NASA NTRS2003

Combining Multiple Gyroscope Outputs for Increased Accuracy

A proposed method of processing the outputs of multiple gyroscopes to increase the accuracy of rate (that is, angular-velocity) readings has been developed theoretically and demonstrated by computer simulation. Although the method is applicable, in principle, to any gyroscopes, it is intended especially for application to gyroscopes that are parts of microelectromechanical systems (MEMS). The method is based on the concept that the collective performance of multiple, relatively inexpensive, nominally identical devices can be better than that of one of the devices considered by itself. The method would make it possible to synthesize the readings of a single, more accurate gyroscope (a virtual gyroscope) from the outputs of a large number of microscopic gyroscopes fabricated together on a single MEMS chip. The big advantage would be that the combination of the MEMS gyroscope array and the processing circuitry needed to implement the method would be smaller, lighter in weight, and less power-hungry, relative to a conventional gyroscope of equal accuracy. The method (see figure) is one of combining and filtering the digitized outputs of multiple gyroscopes to obtain minimum-variance estimates of rate. In the combining-and-filtering operations, measurement data from the gyroscopes would be weighted and smoothed with respect to each other according to the gain matrix of a minimum- variance filter. According to Kalman-filter theory, the gain matrix of the minimum-variance filter is uniquely specified by the filter covariance, which propagates according to a matrix Riccati equation. The present method incorporates an exact analytical solution of this equation.

Bayard, David S.↗

NASA NTRS2021

Patched Local Lunar Gravity Solutions using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into twelve regions and two polar caps, with a resolution of 0.15˚ x 0.15˚ (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Sander Goossens↗

NASA NTRS1999

Growth of Homoepitaxial ZnO Semiconducting Films

As a high temperature wide-band-gap (3.3 eV at room temperature) semiconductor, ZnO has been used for many applications such as wave-guides, solar cells, and surface acoustic wave devices, Since ZnO has a 60 meV excitonic binding energy that makes it possible to produce excitonic lasing at room temperature, a recent surge of interest is to synthesize ZnO films for UV/blue/green laser diodes. These applications require films with a smooth surface, good crystal quality, and low defect density. Thus, homoepitaxial film growth is the best choice. Homoepitaxial films have been studied in terms of morphology, crystal structure, and electrical and optical properties. ZnO single crystal substrates grown by the hydrothermal method are mechanically polished and annealed in air for four hours before the films are deposited. The annealing temperature-dependence on ZnO substrate morphology and electrical properties is investigated. Films are synthesized by off-axis reactive sputtering deposition. This produces films that have very smooth surfaces with roughness less than or equal to 5 nm on a 5 microns x 5 microns area. The full width at half maximum of film theta rocking curves measured by the x-ray diffraction is slightly larger than that of the crystal substrate. Films are also characterized by measuring resistivity, optical transmittance, and photoluminescence. The properties of ZnO films grown on (0001) ZnO and (0001) sapphire substrates will also be compared and discussed.

Zhu, Shen↗

NASA NTRS1986

An explicit finite-volume time-marching procedure for turbulent flow calculations

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite-volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is not required. Different time steps are used in the different governing equations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes (length/height - 1000). The method is compared with two test cases. Essentially incompressible turbulent boundary layer flow in an adverse pressure gradient is calculated and the computed distributions of mean velocity and shear are in good agreement with the measurements. Transonic viscous flow in a converging diverging nozzle is calculated; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good.

Nicholson, Stephen↗

NASA NTRS1987

An explicit finite-volume time-marching procedure for turbulent flow calculations

Nicholson, Stephen↗

NASA NTRS1997

Hypersonic Flow Computations on Unstructured Meshes

A method for computing inviscid hypersonic flow over complex configurations using unstructured meshes is presented. The unstructured grid solver uses an edge{based finite{volume formulation. Fluxes are computed using a flux vector splitting scheme that is capable of representing constant enthalpy solutions. Second{order accuracy in smooth flow regions is obtained by linearly reconstructing the solution, and stability near discontinuities is maintained by locally forcing the scheme to reduce to first-order accuracy. The implementation of the algorithm to parallel computers is described. Computations using the proposed method are presented for a sphere-cone configuration at Mach numbers of 5.25 and 10.6, and a complex hypersonic re-entry vehicle at Mach numbers of 4.5 and 9.8. Results are compared to experimental data and computations made with established structured grid methods. The use of the solver as a screening tool for rapid aerodynamic assessment of proposed vehicles is described.

Bibb, K. L.↗

NASA NTRS1971

Investigation of the fracture mechanics of boride composites

Fracture energies of WC-6Co, Boride 5 (ZrB2+SiC), Boride 8(ZrB2+SiC+C) and Boride 8-M2(ZrB2+SiC+C) were measured by slow bend and impact tests of notched charpy bars. Cobalt bonded tungsten carbide exhibited impact energies of 0.76 ft-lb or 73.9 in-lb/square inch. Boride 5 and the Boride 8 exhibit impact energies one third and one quarter of that observed for WC-6Co comparing favorably with measurements for SiC and Si3N4. Slow bend-notched bar-fracture energies for WC-6Co were near 2.6 in-lb/square inch or 1/20 the impact energies. Slow bend energies for Boride 8-M2, Boride 8 and Boride 5 were 58%, 42% and 25% of the value observed for WC-6Co. Fractograph showed differences for WC-6Co where slow bend testing resulted in smooth transgranular cleavage while samples broken by impact exhibited intergranular failures. By contrast the boride fractures showed no distinction based on testing method. Fabrication studies were conducted to effect alteration of the boride composites by alloying and introduction of graphite cloth.

Kaufman, L.↗

NASA NTRS1979

Comparison of atmospheric density data from mass spectrometers and atmospheric drag on the Aeros satellites

The comparison of perigee density data near 230 km for satellite Aeros-A has been extended to the complete mission time. The average ratio between orbital drag derived density and mass spectrometer measurements is very near to 1 with a large scatter reflected by a standard deviation of the order of 20%. A method of comparison was developed and tested which uses the observed rate of change of orbital period in comparison with the orbital decay computed from the actual mass spectrometer data measured at discrete positions along the orbit. This method proves that deviations from the average ratio of 1 between perigee densities from drag and mass spectrometers are due to the smoothing and poor resolution of the orbital drag technique.

Roemer, M.↗

NASA NTRS1981

Velocity-space synthesis of ISEE-1 measurements of the three dimensional electron distribution function

A computer package which produces contour plots of the three dimensional electron distribution function measured by an electron spectrometer aboard ISEE-1 is described. Examples of the contour plots and an explanation of how to use the program, including the necessary computer code for running the program on the GSFC 360/91 computer is presented. The method by which the discrete measurements of the distribution function, given by points on the four dimensional surface are synthesized into a smooth surface in a three dimensional space which can be contoured is described. The velocity components are parallel and perpendicular to the magnetic field, respectively, in the proper frame of the electrons.

Fitzenreiter, R. J.↗

NASA NTRS1983

A mathematical model for efficient estimation of aircraft motions

In the usual formulation of the aircraft state-estimation problem, motions along a flight trajectory are represented by a plant consisting of nonlinear state and measurement models. Problem solution using this formulation requires that both state- and measurement-dependent Jacobian matrices be evaluated along any trajectory. In this paper it is shown that a set of state variables can be chosen to realize a linear state model of very simple form, such that all nonlinearities appear in the measurement model. The potential advantage of the new formulation is computational: the Jacobian matrix corresponding to a linear state model is constant, a feature that should outweigh the fact that the measurement model is more complicated than in the conventinal formulation. To compare the modeling methods, aircraft motions from typical flight-test and accident data were estimated, using each formulation with the same off-line (smoothing) algorithm. The results of these experiments, reported in the paper, demonstrate clearly the computational superiority of the linear state-variable formulation. The procedure advocated here may be extended to other nonlinear estimation problems, including on-line (filtering) applications.

Bach, R. E., Jr.↗

NASA NTRS1985

Noniterative three-dimensional grid generation using parabolic partial differential equations

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

Edwards, T. A.↗

NASA NTRS1987

Measurement of the effect of manufacturing deviations on natural laminar flow for a single engine general aviation airplane

Renewed interest in natural laminar flow (NLF) had rekindled designer concern that manufacuring deviations may destroy the effectiveness of NLF for an operational aircraft. Experiments are summarized that attemtped to measure total drag changes associated with three different wing surface conditions on an aircraft typical of current general aviation high performance singles. The speed power technique was first used in an attempt to quantify the changes in total drag. Predicted and measured boundary layer transition locations for three different wing surface conditions were also compared, using two different forms of flow visualization. The three flight test phases included: assessment of an unpainted airframe, flight tests of the same aircraft after painstakingly filling and sanding the wings to design contours, and similar measurement after this aricraft was painted. In each flight phase, transition locations were monitored using with sublimating chemicals or pigmented oil. Two-dimensional drag coefficients were estimated using the Eppler-Somers code and measured with a wake rake in a method very similar to Jones' pitot traverse method. The net change in two-dimensional drag coefficient was approximately 20 counts between the unpainted aircraft and the hand-smoothed aircraft for typical cruise flight conditions.

Source record↗

NASA NTRS1987

Unsteady Euler solution of transonic helicopter rotor flow

A new time-accurate Euler method is presented for calculating the transonic flow over a lifting or nonlifting rotor blade in both hover and forward flight. The approach is to solve the conservative Euler equations in a rotor-fixed frame of reference using a finite-volume method. The discretized equations are solved by using a Runge-Kutta multistage scheme with a new higher-order implicit residual smoothing procedure. Preliminary results were compared with wind-tunnel data. In all the cases considered, good agreement was found with experimental data.

Chang, I-Chung↗

NASA NTRS1991

Grid generation strategies for turbomachinery configurations

Turbomachinery flow fields involve unique grid generation issues due to their geometrical and physical characteristics. Several strategic approaches are discussed to generate quality grids. The grid quality is further enhanced through blending and adapting. Grid blending smooths the grids locally through averaging and diffusion operators. Grid adaptation redistributes the grid points based on a grid quality assessment. These methods are demonstrated with several examples.

Lee, K. D.↗

NASA NTRS1991

A multi-block multigrid method for the solution of the Euler and Navier-Stokes equations for three-dimensional flows

A multi-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell-vertex method which employs central-difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques, and variable-coefficient numerical smoothing results in an efficient and robust scheme. The multi-block strategy places the block loop within the Runge-Kutta loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one- and two-block calculations in which the two-block grid is generated by splitting the one-block grid. Results are presented for both Euler and Navier-Stokes computations of wings and wing-fuselage combinations.

Atkins, H. L.↗

NASA NTRS1991

Heat transfer in the turbulent boundary layer with a step change in surface roughness

Measurements of Stanton numbers, velocity profiles, temperature profiles, and turbulence intensity profiles are reported for turbulent flat plate boundary layer flows with a step change in surface roughness. The first 0.9 m length of the test surface is roughened with 1.27 mm diameter hemispheres spaced 2 base diameters apart in a staggered array. The remaining 1.5 m length is smooth. The experiments show that the step change from a rough to a smooth surface has a dramatic effect on the convective heat transfer. In many cases, the Stanton number drops below the smooth-wall correlation immediately downstream of the change in roughness. The Stanton number measurements are compared with predictions using the discrete element method with excellent results.

Taylor, Robert P.↗

NASA NTRS1992

Percolation analysis of nonlinear structures in scale-free two-dimensional simulations

Results are presented of applying percolation analysis to several two-dimensional N-body models which simulate the formation of large-scale structure. Three parameters are estimated: total area (a(c)), total mass (M(C)), and percolation density (rho(c)) of the percolating structure at the percolation threshold for both unsmoothed and smoothed (with different scales L(s)) nonlinear with filamentary structures, confirming early speculations that this type of model has several features of filamentary-type distributions. Also, it is shown that, by properly applying smoothing techniques, many problems previously considered detrimental can be dealt with and overcome. Possible difficulties and prospects with the use of this method are discussed, specifically relating to techniques and methods already applied to CfA deep sky surveys. The success of this test in two dimensions and the potential for extrapolation to three dimensions is also discussed.

Dominik, Kurt G.↗

NASA NTRS2003

Calculation of Free-Free Opacities

Free-free absorption is an important contribution to the opacity for radiation transport through hot materials Temperatures can be as high as several keV, such that it becomes a computational challenge to solve the Schrodinger equation efficiently for rapidly oscillating continuum functions for high angular momenta. Several groups\footnots, including ours, have studied the phase amplitude solution (PAS) of the Schrodinger equation, in which one solves equations for the wave function amplitude and phase, which are: smooth functions of the electron energy. It is also important to have an accurate Schroudinger benchmark for the development of the PAS method. We present results for dipole matrix elements, Gaunt factors, and cross sections for the absorption of radiation at various energies for Cs XIX at temperature=100 eV and density=0.187 g/cc for our newly developed PAS and Schrodinger benchmark.

Bhatia, A. K.↗