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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Analysis of the vibratory excitation of gear systems. II - Tooth error representations, approximations, and application

The second part of a theory for predicting the vibratory excitation of gear systems from fundamental descriptions of gear tooth elastic properties and deviations of tooth faces from perfect involute surfaces is presented. The first part of the theory provides expressions for the Fourier-series coefficients of the vibratory excitation, and this paper gives expressions for these Fourier-series coefficients in terms of easily interpreted gear tooth metrics that are readily evaluated from tooth-face measurements. Results are given for rectangular tooth-face contact regions using two-dimensional Legendre polynomial expansions of local tooth-pair stiffnesses and stiffness-weighted deviations of tooth faces from perfect involute surfaces. A rigorous transfer function approach is developed that permits separation of the effects of gear tooth errors and gear design parameters; the theory is applicable to helical and spur gears and is illustrated with measurements of tooth-spacing errors and tooth profiles obtained from a pair of spur gears.

Mark, W. D.↗
NASA NTRS1980

On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries

An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynomials expansions is given for this scheme. An example demonstrating the applicability of the method is given.

Moin, P.↗
NASA NTRS1981

Nonparametric identification of a class of nonlinear close-coupled dynamic systems

A nonparametric identification technique for the identification of close coupled dynamic systems with arbitrary memoryless nonlinearities is presented. The method utilizes noisy recorded data (acceleration, velocity and displacement) to identify the restoring forces in the system. The masses in the system are assumed to be known (or fairly well estimated from the design drawings). The restoring forces are expanded in a series of orthogonal polnomials and the coefficients of these polynomial expansions are obtained by using least square fit method. A particularly simple and computationally efficient method is proposed for dealing with separable restoring forces. The identified results are found to be relatively insensitive to measurement noise. An analysis of the effects of measurement noise on the quality of the estimates is given. The computations are shown to be relatively quick (when compared say to the Wiener identification method) and the core storage required relatively small, making the method suitable for onboard identification of large space structures.

Udwadia, F. E.↗
NASA NTRS1982

Line shape of the non-thermal 6300 A O/1D/ emission

The two-population model of Schmitt, Abreu and Hays (1981) is used to calculate the line shape of the atomic oxygen metastable state, nonthermal O(1D) 6300 A emission, in order to simulate observations made from a space platform at different zenith angles and altitudes. The Addition theorem, for spherical harmonics of a Legendre polynomial expansion of the nonthermal population distribution function, is used to obtain nonthermal line shapes observed at zenith angles other than the local vertical one.

Schmitt, G. A.↗
NASA NTRS1988

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗
NASA NTRS1988

Helioseismology from the South Pole: Comparison of 1987 and 1981 Results

Full disk images with 10 arc sec pixels and filtered to a 7 A pass band centered on the Ca II K line were obtained from the geographic South Pole in 1981 and 1987. In 1981, 50hr of essentially uninterrupted data were obtained. In 1987, three such runs were obtained over a period of 325 hours for a duty cycle of 47 percent. The 1987 observations are characterized by a much lower level of solar activity than 1981, a much improved CCD camera, considerably better image stability and a varying amount of instrumental scatter. The 1987 data have a substantially better signal-to-noise ratio than the 1981 data so that oscillations with degrees from 0 to 150 and frequencies from 2 to 7 mHz are well observed. The observations were reduced to spectra in l, m, and v. A comparison of p-mode frequencies measured in 1981 and 1987, and coefficients of Legendre polynomial expansions of frequency shifts caused by solar rotation are presented. The time behavior of systematic frequency shifts which depend upon m but which do not arise from rotation is described.

Jefferies, S. M.↗
NASA NTRS1989

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, J. M.↗
NASA NTRS1991

A spectral collocation method for compressible, non-similar boundary layers

An efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two-dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth-order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall-normal (spacelike) dimension. The spectral collocation algorithm is used to derive the nonsimilar mean velocity and temperature profiles in the boundary layer of a 'fuselage' (cylinder) in a high-speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.

Pruett, C. D.↗
NASA NTRS1992

Development of new flux splitting schemes

Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.

Liou, Meng-Sing↗
NASA NTRS1993

Solar activity and oscillation frequency splittings

Solar p-mode frequency splittings, parameterized by the coefficients through order N = 12 of a Legendre polynomial expansion of the mode frequencies as a function of m/L, were obtained from an analysis of helioseismology data taken at Big Bear Solar Observatory during the 4 years 1986 and 1988-1990 (approximately solar minimum to maximum). Inversion of the even-index splitting coefficients confirms that there is a significant contribution to the frequency splittings originating near the solar poles. The strength of the polar contribution is anti correlated with the overall level or solar activity in the active latitudes, suggesting a relation to polar faculae. From an analysis of the odd-index splitting coefficients we infer an uppor limit to changes in the solar equatorial near-surface rotatinal velocity of less than 1.9 m/s (3 sigma limit) between solar minimum and maximum.

Woodard, M. F.↗
NASA NTRS1992

Membrane triangles with corner drilling freedoms. I - The EFF element

The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.

Alvin, Ken↗
NASA NTRS1995

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Scott, James R.↗
NASA NTRS1996

Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations

This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.

Scott, James R.↗
NASA NTRS1994

Spectral Methods for Computational Fluid Dynamics

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral methods in numerical calculations stems from the attractive approximation properties of orthogonal polynomial expansions.

Zang, T. A.↗
NASA NTRS1999

Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.

Kousen, Kenneth A.↗
NASA NTRS1997

Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerenes and their Correlation with Three Geometric Parameters: Group Order, Aromaticity, and Size

Calculations were performed on the valence contribution to the static molecular third-order polarizabilities (gamma) of thirty carbon-cage fullerenes (C60, C70, five isomers of C78, and twenty-three isomers of C84). The molecular structures were obtained from B3LYP/STO-3G calculations. The values of the tensor elements and an associated numerical uncertainty were obtained using the finite-field approach and polynomial expansions of orders four to eighteen of polarization versus static electric field data. The latter information was obtained from semiempirical calculations using the AM1 hamiltonian.

Moore, Craig E.↗
NASA NTRS1999

What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations?

Recently, several linear scaling approaches have been introduced which replace the time dominating diagonalization step in semiempirical methods, enabling practical calculations to be performed, on very large molecules. This paper compares the accuracy and performance of pseudodiagonalization (PD), conjugate gradient density matrix search (CG-DMS), the Chebyshev polynomial expansion method (CEM), and purification of the density matrix (PDM) as linear scaling substitutions for diagonalization. The scaling, speed, and reliability of these methods are compared for AMI single point energy calculations on polyglycine chains (up to 20,000 atoms), water clusters (up to 12,300 atoms), and nucleic acids (up to 6300 atoms).

Daniels, Andrew D.↗
NASA NTRS2003

Genetic Algorithm Phase Retrieval for the Systematic Image-Based Optical Alignment Testbed

Phase retrieval requires calculation of the real-valued phase of the pupil fimction from the image intensity distribution and characteristics of an optical system. Genetic 'algorithms were used to solve two one-dimensional phase retrieval problem. A GA successfully estimated the coefficients of a polynomial expansion of the phase when the number of coefficients was correctly specified. A GA also successfully estimated the multiple p h e s of a segmented optical system analogous to the seven-mirror Systematic Image-Based Optical Alignment (SIBOA) testbed located at NASA s Marshall Space Flight Center. The SIBOA testbed was developed to investigate phase retrieval techniques. Tiphilt and piston motions of the mirrors accomplish phase corrections. A constant phase over each mirror can be achieved by an independent tip/tilt correction: the phase Conection term can then be factored out of the Discrete Fourier Tranform (DFT), greatly reducing computations.

Taylor, Jaime↗