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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Consistent boundary conditions for Reduced Navier-Stokes (RNS) scheme applied to 3-dimensional internal viscous flows

A consistent and efficient set of boundary conditions is developed for the multi-sweep space-marching pressure-elliptic Reduced Navier-Stokes (RNS) scheme as applied for 3-D internal viscous flow problems. No-slip boundary conditions are directly imposed on the solid walls. There is no iteration procedure required in the cross plane to ensure mass conservation across each marching plane. The finite difference equations forming the coefficient matrix are ordered such that the surface normal velocity is specified on all the solid walls; unlike external flows, a pressure boundary condition in the cross plane is not required. Since continuity is directly satisfied at all points in the flow domain, the first order momentum equations can be solved directly for the pressure without the need for a Poisson pressure correction equation. The procedure developed herein can also be applied with periodic boundary conditions. The analysis is given for general compressible flows. Incompressible flow solutions are obtained, for straight and curved ducts of square cross section, to validate the procedure. These solutions are used to demonstrate the applicability of the RNS scheme, with the improved boundary conditions for internal flows with strong interaction, as would be encountered in ducts and turbomachinery geometries.

Reddy, D. R.↗
NASA NTRS1987

Linear baroclinic instability in the presence of large scale topography

The effect of a planetary-scale, wavenumber 2 topography on baroclinically active disturbances is investigated for a channel domain in a two-layer, quasi-geostrophic context. When the lower-layer zonal velocity is nonzero, the topography influences the disturbances by forcing a stationary wave, and the topography and the forced wave influence the growth rates and the spatial structures of the time-dependent solutions. The case of zero zonal velocity in the lower layer was also investigated, for which no forced wave exists. Asymptotic forms of the equations, valid when the topographic effect (governed by the ratio of the nondimensional topographic height to the rotational Froude number) is small, are used to obtain both the stationary and time-dependent solutions. The latter are also obtained using a numerical approach, in which is determined the eigenvalues and eigenfunctions of a matrix representing the dynamical equations. Agreement is good between the two approaches. Recent laboratory experiments with a baroclinic annulus in which there is a false bottom with wavenumber 2 topography, are used to select governing parameters. The simultaneous presence of a stationary forced wave of wavenumber 2 and a time-dependent baroclinic wave of wavenumber 4, which has wavenumber 2 and 6 sidebands due to the topography, yields a flow field that exhibits some principal features of the laboratory experiments. The position of the forced wave and the location of an excursion in latitude of the storm track show qualitative resemblance to those features observed in the atmosphere.

Reynolds, Nathaniel Dunton↗
NASA NTRS1974

Ellipsometric measurements of epitaxial GaAs layers on a GaAs substrate

An extensive examination of ellipsometric equations for anisotropic surfaces and films is reported. It is shown that the reflection matrix can be calculated by writing Maxwell's equations in 6 x 6 matrix form and by applying appropriate boundary conditions at proper points in the development of the formalism, reducing the equation for the propagation of light to an eigenvalue problem using a 4 x 4 matrix.

Desmet, D. J.↗
NASA NTRS2004

Direct Measurements of Eddy Transport and Thermal Dispersion in a High Porosity Matrix

Thermal losses from the hot end to the cold end of a Stirling cycle regenerator due to thermal dispersion through the regenerator matrix may significantly degrade the performance of the machine. Because of poor access to the void spaces within the porous medium, no direct measurements of thermal dispersion have been made and dispersion models have been derived indirectly. This is done by measuring the overall thermal performance of the regenerator and subtracting off the energy transfer caused by molecular conduction and advected enthalpy flows computed from volume-averaged fluid velocity and temperature. In the current program, a large-scale porous matrix consisting of stacked wire screens with a porosity of 90% is installed in a flow rig which is operated in a Reynolds number range that represents Stirling engine regenerator flow. Experiments are conducted to measure turbulent transport of momentum at the exit phase using hot-wires. The relationship of such turbulent transport terms to the thermal dispersion term in the volumetric-averaged energy equation for the regenerator matrix is developed and the measurements are used to determine cross-stream thermal dispersion. A dispersion model based upon the measurements is proposed and compared with models documented in the literature.

Niu, Yi↗
NASA NTRS2001

Implementation of Fiber Substructuring Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were incorporated into a mechanics of materials based micromechanics method. In the current work, the micromechanics method is revised such that the composite unit cell is divided into a number of slices. Micromechanics equations are then developed for each slice, with laminate theory applied to determine the elastic properties, effective stresses and effective inelastic strains for the unit cell. Verification studies are conducted using two representative polymer matrix composites with a nonlinear, strain rate dependent deformation response. The computed results compare well to experimentally obtained values.

Goldberg, Robert K.↗
NASA NTRS1988

A general explicit solution of the central overlap problem

The matrix of the normal equations of a central overlapping-plate solution with general models for frame parameters and the star parameters is inverted explicitly in terms of the inverses of the matrices in the isolated systems for the frame and star parameters. This makes it possible to calculate from explicit formulas the numerical estimates of the star and frame parameters which would follow from a rigorous overlapping-plate solution. Also, the covariance matrix of the adjustment parameters are calculated.

Eichhorn, Heinrich↗
NASA NTRS1979

A computer program to generate equations of motion matrices, L217 (EOM). Volume 1: Engineering and usage

The equations of motion program L217 formulates the matrix coefficients for a set of second order linear differential equations that describe the motion of an airplane relative to its level equilibrium flight condition. Aerodynamic data from FLEXSTAB or Doublet Lattice (L216) programs can be used to derive the equations for quasi-steady or full unsteady aerodynamics. The data manipulation and the matrix coefficient formulation are described.

Kroll, R. I.↗
NASA NTRS1976

On the characteristic exponents of the general three-body problem

A description is given of some properties of the characteristic exponents of the general three-body problem. The variational equations on which the analysis is based are obtained by linearizing the Lagrangian equations of motion in the neighborhood of a given known solution. Attention is given to the fundamental matrix of solutions, the characteristic equation, the three trivial solutions of the variational equations of the three-body problem, symmetric periodic orbits, and the half-period properties of symmetric periodic orbits.

Broucke, R.↗
NASA NTRS2000

Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.

Goldberg, Robert K.↗
NASA NTRS1975

Ellipsometer measurements of epitaxial GaAs layers: A concept

Report discusses analysis involving Maxwell's equations formed in a 6-by-6 matrix. By applying boundary conditions at proper points in sample, equation for propagation of light through anisotropic medium is reduced to eigenvalue problem resulting in 4-by-4 matrix.

Desmet, D. J.↗
NASA NTRS2006

STRANAL-PMC Version 2.0

Version 2.0 of the Strain Rate Dependent Analysis of Polymer Matrix Composites (STRANAL-PMC) software has been released. A prior version was reported in Analyzing Loads and Strains in Polymer- Matrix Composites (LEW-17227), NASA Tech Briefs, Vol. 26, No. 11 (November 2002), page 36. To recapitulate: Modified versions of constitutive equations of viscoplasticity of metals are used to represent deformation of a polymeric matrix. The equations are applied in a micromechanical approach, proceeding upward from slices of unit cells, through the ply level, to the laminate level. The constitutive equations are integrated in time by a Runge- Kutta technique. To predict the ultimate strength of each composite ply, failure criteria are implemented within the micromechanics. The inputs to STRANAL-PMC are the laminate geometry, properties of the fiber and matrix materials, and applied stress or strain versus time. The outputs are time-dependent stresses and strains at the slice, ply, and laminate levels. The improvements in version 2.0 include more rigorous representation of hydrostatic- stress effects in the matrix, refinement and extension of ply failure models, and capabilities to analyze transverse shear stresses. Version 2.0 can be implemented as a material-model code within transient dynamic finite-element codes.

Goldberg, Robert↗
NASA NTRS1985

Postbuckling analysis using a general purpose code

A new capability for solving postbuckling problems in shell structures is described. The matrix theory to adapt Newton's method to nonlinear finite element shell analysis is outlined first. The matrix theory is directed at writing consistent linear algebratic equations for problems where the tangent stiffness matrix is singular or nearly singular. The matrix theory suggests a change of variables as part of the usual iterative procedure in Newton's method. The change of variables is shown to be feasible for introduction into the algorithm programmed in general purpose codes for finite element analysis of structures. Numerical results from a new option that has been programmed in an existing general purpose code are presented. The analysis of shell structures for collapse and for branching at bifurcation loads is illustrated by the numerical examples.

Thurston, G. A.↗
NASA NTRS2012

Efficient Implementation of the Invariant Imbedding T-Matrix Method and the Separation of Variables Method Applied to Large Nonspherical Inhomogeneous Particles

Three terms, ''Waterman's T-matrix method'', ''extended boundary condition method (EBCM)'', and ''null field method'', have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIMþSOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIMþSOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIMþSOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIMþSOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging.

Invariant imbedding method↗
NASA NTRS1991

Serial and parallel computation of Kane's equations for multibody dynamics

The analysis of the efficiency of algorithms resulting from Kane's Equation for serial and parallel computation of mass matrix is examined. The algorithms resulting from Kane's equation and Modified Kane's equations are detailed. An analysis was made of two classes of algorithms for computation of mass matrix: the Newton-Euler based algorithms and the Composite rigid body algorithms. An analysis was also made of the efficiency of different algorithms for serial and parallel computations. Conclusions are drawn and presented.

Fijany, Amir↗
NASA NTRS1993

METal matrix composite ANalyzer (METCAN): Theoretical manual

This manuscript is intended to be a companion volume to the 'METCAN User's Manual' and the 'METAN Demonstration Manual.' The primary purpose of the manual is to give details pertaining to micromechanics and macromechanics equations of high temperature metal matrix composites that are programmed in the METCAN computer code. The subroutines which contain the programmed equations are also mentioned in order to facilitate any future changes or modifications that the user may intend to incorporate in the code. Assumptions and derivations leading to the micromechanics equations are briefly mentioned.

Murthy, P. L. N.↗
NASA NTRS1977

FCAP - A new tool for the performance and structural analysis for complex flexible aircraft with active control

A very general formulation has been developed for the analysis of complex flexible-aircraft configurations in presence of active control. The formulation is incorporated into a computer program, Flight Control Analysis Program (FCAP), which is designed in a modular fashion to incorporate aircraft dynamics and aerodynamics for complex configurations, as well as sensor, actuator and control logic element dynamics. Formulation of the total aircraft dynamic system is accomplished in matrix form by casting equations in state vector format. The system stability and performance are determined in either the frequency or time domain using classical analysis techniques. Fully unsteady aerodynamics is used for the evaluation of the flutter characteristics as well as the gust response of the aircraft.

Morino, L.↗
NASA NTRS1980

Modal cost analysis for linear matrix-second-order systems

Reduced models and reduced controllers for systems governed by matrix-second-order differential equations are obtained by retaining those modes which make the largest contributions to quadratic control objectives. Such contributions, expressed in terms of modal data, used as mode truncation criteria, allow the statement of the specific control objectives to influence the early model reduction from very high order models which are available, for example, from finite element methods. The relative importance of damping, frequency, and eigenvector in the mode truncation decisions are made explicit for each of these control objectives: attitude control, vibration suppression and figure control. The paper also shows that using modal cost analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop modal coordinates which are most critical to the quadratic control performance criterion. In this way, the modes which should be controlled (and hence the modes which must be observable by choice of measurements), are deduced from truncations of the optimal controller.

Skelton, R. E.↗