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At least 523 records · Page 29

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NASA NTRS1984

Optical matrix-matrix multiplication method demonstrated by the use of a multifocus hololens

A method of optical matrix-matrix multiplication is presented. The feasibility of the method is also experimentally demonstrated by the use of a dichromated-gelatin multifocus holographic lens (hololens). With the specific values of matrices chosen, the average percentage error between the theoretical and experimental data of the elements of the output matrix of the multiplication of some specific pairs of 3 x 3 matrices is 0.4 percent, which corresponds to an 8-bit accuracy.

Liu, H. K.↗

NASA NTRS1985

Reciprocating Magnetic Refrigerator

Unit cools to 4 K by adiabatic demagnetization. Two porous matrices of paramagnetic material gadolinium/gallium/garnet held in long piston called displacer, machined out of Micarta (phenol formaldehyde polymer). Holes in side of displacer allow heat-exchange fluid to flow to and through matrices within. Piston seals on displacer prevent substantial mixing of fluid in two loops. Magnetic refrigerator provides continuous rather than "one-shot" cooling.

Johnson, D. L.↗

NASA NTRS1984

Hydrodynamic impeller stiffness, damping, and inertia in the rotordynamics of centrifugal flow pumps

The lateral hydrodynamic forces experienced by a centrifugal pump impeller performing circular whirl motions within several volute geometries were measured. The lateral forces were decomposed into: (1) time averaged lateral forces and (2) hydrodynamic force matrices representing the variation of the lateral forces with position of the impeller center. It is found that these force matrices essentially consist of equal diagonal terms and skew symmetric off diagonal terms. One consequence of this is that during its whirl motion the impeller experiences forces acting normal and tangential to the locus of whirl. Data on these normal and tangential forces are presented; it is shown that there exists a region of positive reduced whirl frequencies, within which the hydrodynamic forces can be destablizing with respect to whirl.

Jery, S.↗

NASA NTRS1985

Polymer, metal and ceramic matrix composites for advanced aircraft engine applications

Advanced aircraft engine research within NASA Lewis is being focused on propulsion systems for subsonic, supersonic, and hypersonic aircraft. Each of these flight regimes requires different types of engines, but all require advanced materials to meet their goals of performance, thrust-to-weight ratio, and fuel efficiency. The high strength/weight and stiffness/weight properties of resin, metal, and ceramic matrix composites will play an increasingly key role in meeting these performance requirements. At NASA Lewis, research is ongoing to apply graphite/polyimide composites to engine components and to develop polymer matrices with higher operating temperature capabilities. Metal matrix composites, using magnesium, aluminum, titanium, and superalloy matrices, are being developed for application to static and rotating engine components, as well as for space applications, over a broad temperature range. Ceramic matrix composites are also being examined to increase the toughness and reliability of ceramics for application to high-temperature engine structures and components.

Mcdanels, D. L.↗

NASA NTRS1985

Dynamic Modeling of Structures from Measured Complex Modes

A technique is presented to use a set of identified complex modes together with an analytical mathematical model of a structure under test to compute improved mass, stiffness and damping matrices. A set of identified normal modes, computed from the measured complex modes, is used in the mass orthogonality equation to compute an improved mass matrix. This eliminates possible errors that may result from using approximated complex modes as normal modes. The improved mass matrix, the measured complex modes and the higher analytical modes are then used to compute the improved stiffness and damping matrices. The number of degrees-of-freedom of the improved model is limited to equal the number of elements in the measured modal vectors. A simulated experiment shows considerable improvements, in the system's analytical dynamic model, over the frequency range of the given measured modal information.

Ibrahim, S. R.↗

NASA NTRS1985

Multiprocessor sparse L/U decomposition with controlled fill-in

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Alaghband, G.↗

NASA NTRS1986

The effects of various implicit operators on a flux vector splitting method

Three different implicit operators in a numerical method for solving the two-dimensional steady Euler equations using flux vector splitting are investigated. These include the implementation of the true Jacobian matrices in the implicit part, the use of their splitting approximate form, and a modification of the implicit part of the scheme that uses the scalar form of the implicit part based on the spectral radii of the split Jacobian matrices. The three versions of the basic algorithm are compared with the results given by two common numerical methods using several two-dimensional test cases. Special attention is paid to the quality of results as well as computational efficiency and convergence properties.

Von Lavante, E.↗

NASA NTRS1986

Implicit hybrid schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Implicit hybrid algorithms employing symmetric planar Gauss-Seidel (SPGS) relaxation and either block-tridiagonally structured coefficient matrices (AF-SPGS) or block-triangular coefficient matrices (LU-SPGS) are derived to solve the flux-difference-split Navier-Stokes equations for three-dimensional incompressible flow in an upwind scheme. The physical basis of the approach is discussed, and results for problems involving vortex flow around a thin delta wing at Reynolds numbers 900,000 and 10,000 are presented graphically. It is found that AF-SPGS converges faster on vector computers which depend on long vector lengths to achieve optimum performance, whereas LU-SPGS is preferable on sequentially operating machines and vector computers using shorter vector lengths.

Hartwich, P.-M.↗

NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

NASA NTRS1986

Analysis of the SOR iteration for the 9-point Laplacian

The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. A theory for determining omega was given by Young (1950) for consistently ordered matrices. Here the optimal omega is determined for the 9-point stencil for the model problem of Laplace's equation on a square. Several orderings of the equations are considered, including the natural rowwise and multicolor orderings, all of which lead to non-consistently ordered matrices, and two equivalence classes of orderings are found with different convergence behavior and optimal omega's. The results for the natural rowwise ordering are compared to those of Garabedian (1956) and it is explained why both results are, in a sense, correct, even though they differ. Also analyzed is a pseudo SOR method for the model problem and it is shown that it is not as effective as the SOR methods. Finally, the point SOR methods are compared to known results for line SOR methods for this problem.

Loyce M. Adams↗

NASA NTRS1986

Optimization of aircraft interior panels

Eight different graphite composite panels were fabricated using four different resin matrices. The resin matrices included Hercules 71775, a blend of vinylpolystyrpyridine and bismaleimide, H795, a bismaleimide, Cycom 6162, a phenolic, and PSP 6022M, a polystyrylpyridine. Graphite panels were fabricated using fabric or unidirectional tape. This report describes the processes for preparing these panels and some of their mechanical, thermal and flammability properties. Panel properties are compared with state-of-the-art epoxy fiberglass composite panels.

Kourtides, Demetrius A.↗

NASA NTRS1987

Projection filters for modal parameter estimate for flexible structures

Single-mode projection filters are developed for eigensystem parameter estimates from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllability and observability matrices in general use. A global minimum optimization algorithm is developed to update the filter parameters by using interval analysis method. Modal parameters can be attracted and updated in the global sense within a specific region by passing the experimental data through the projection filters. For illustration of this method, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate model frequencies and dampings.

Huang, Jen-Kuang↗

NASA NTRS1986

Investigation of scene identification algorithms for radiation budget measurements

The computation of Earth radiation budget from satellite measurements requires the identification of the scene in order to select spectral factors and bidirectional models. A scene identification procedure is developed for AVHRR SW and LW data by using two radiative transfer models. These AVHRR GAC pixels are then attached to corresponding ERBE pixels and the results are sorted into scene identification probability matrices. These scene intercomparisons show that there generally is a higher tendency for underestimation of cloudiness over ocean at high cloud amounts, e.g., mostly cloudy instead of overcast, partly cloudy instead of mostly cloudy, for the ERBE relative to the AVHRR results. Reasons for this are explained. Preliminary estimates of the errors of exitances due to scene misidentification demonstrates the high dependency on the probability matrices. While the longwave error can generally be neglected the shortwave deviations have reached maximum values of more than 12% of the respective exitances.

Diekmann, F. J.↗

NASA NTRS1987

Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.

Liou, J.↗

NASA NTRS1986

Laser induced fluorescence and phosphorescence of matrix isolated glyoxal - Evidence for exciplex formation in the A 1Au and a 3Au states

Laser-induced fluorescence and phosphorescence as well as infrared and visible absorption spectra of glyoxal in Ar, N2, and CO matrices are presented and analyzed. Glyoxal in its first excited electronic state is shown to form an exciplex with its nearest neighbors in all three matrices, and transitions normally forbidden dominate the emission spectra. The spectral characteristics of these complexes are similar to those of the Ar-glyoxal complex found in supersonic beam experiments. Due to the matrix cage effect, no vibrational predissociation is observed. The phosphorescence lifetime is determined and an upper limit is given for the fluorescence lifetime. This, in combination with the relative intensities of fluorescence and phosphorescence, can be used to place limits on the quantum yields of the various relaxation processes.

Van Ijzendoorn, L. J.↗

NASA NTRS1985

Systematic estimation of forecast and observation error covariances in four-dimensional data assimilation

A two-part algorithm is presented for reliably computing weather forecast model and observational error covariances during data assimilation. Data errors arise from instrumental inaccuracies and sub-grid scale variability, whereas forecast errors occur because of modeling errors and the propagation of previous analysis errors. A Kalman filter is defined as the primary algorithm for estimating the forecast and analysis error convariance matrices. A second algorithm is described for quantifying the noise covariance matrices of any degree to obtain accurate values for the observational error covariances. Numerical results are provided from a linearized one-dimensional shallow-water model. The results cover observational noise covariances, initial instrumental errors and erroneous model values.

Dee, D. P.↗

NASA NTRS1986

Polymer, metal, and ceramic matrix composites for advanced aircraft engine applications

Mcdanels, D. L.↗

NASA NTRS1987

Single-mode projection filters for identification and state estimation of flexible structures

Single-mode projection filters are developed for eigensystem parameter identification and state estimation from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllabilty and observability matrices in the general sense. A global minimum optimization algorithm is developed to update the filter parameters by using the interval analysis method. Modal parameters can be identified and updated in the global sense within a specified region of parameters by passing the experimental data through the projection filters. For illustration of this new approach, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate modal frequencies and damping.

Huang, Jen-Kuang↗