Search NASA⌕ Search

SEARCH · Search NASA

Results for “FOURIER SERIES”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

A new numerical method for the simulation of three-dimensional flow in a pipe

A new numerical technique for simulating three dimensional, unsteady, incompressible pipe flows is presented and its utility and accuracy is shown. Each vector function in the expansion of the velocity field is divergence free and satisfies the boundary conditions for viscous flow. Some of the benefits of the expansion technique are that pressure is eliminated from the dynamics, only two unknowns per mesh point are required, implicit treatment of the viscous terms is provided at no extra computational cost, and no fractional time steps are required. The method uses spectral expansions: Fourier series in the azimuthal and streamwise directions, and Jacobi polynominals in the radial direction. Previously announced in STAR as N82-31644

Leonard, A.↗
NASA NTRS1984

Spectral multigrid methods for elliptic equations II

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Zang, T. A.↗
NASA NTRS1984

On the control canonical structure of a class of scalar input systems

A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated. Previously announced in STAR as N83-28925

Teglas, R. G.↗
NASA NTRS1985

Application of two-dimensional unsteady aerodynamic to a free-tip rotor response analysis

The free-tip rotor utilizes a rotor blade tip which is structurally decoupled from the blade inboard section. The tip is free to pitch about its own pitch axis to respond to the local flow angularity changes. The tip also experiences the heaving motion due to the flapping of the rotor blade. For an airfoil in any pitching and heaving motion which can be expanded into a Fourier series, the lift and moment calculated by Theodoren's theory is simply the linear combination of the lift and moment calculated for each harmonic. These lift and moment are then used to determine the response of the free-tip rotor. A parametric study is performed to determine the effect of mechanical damping, mechanical spring, sweep, friction, and a constant control moment on the free-tip rotor response characteristics and the resulting azimuthal lift distributions. The results showed that the free-tip has the capability to suppress the oscillatory lift distribution around the azimuth and to eliminate a significant negative life peak on the advancing tip. This result agrees with the result of the previous analysis based on the steady aerodynamics.

Yates, L.↗
NASA NTRS1984

Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform

A technique for applying discrete Fourier series to infinite domains is presented. The technique uses mappings designed to minimize truncation error and can be applied to solve mixed initial boundary value problems among others. The method is alias-free and yields consistent differentiation and integration operators. The mapping-induced truncation error is explicitly expressible and small in nearly all cases of interest. The method is illustrated for three problems involving convection, diffusion, and vortex interaction.

Cain, A. B.↗
NASA NTRS1985

Conformational properties, torsional potential, and vibrational force field for methacryloyl fluoride - An ab initio investigation

The structure, torsional potentials, vibrational spectra, and harmonic force fields for s-cis and s-trans isomers of methacryloyl fluoride are examined to understand the conformational properties of the molecules and their relationship to macroscopic polymer properties. The structure is found to be in good agreement with experiment. It is shown by calculations that the energy difference between the cis and the transisomers is less than 1 kcal/mol at both the split valence and the split valence polarized levels, with the trans form favored. Analysis of the torsional potentials indicates that a rigid rotor model provides a reasonable description of the motion of the COF group in the molecule. The torsional barrier to interconvert the s-trans to the s-cis form is found to be 7.0 kcal/mol. A fit of the data to a three-term Fourier series shows that it is possible to reproduce the experimentally derived barrier, even though a direct determination indicates that the barrier is higher.

Laskowski, B. C.↗
NASA NTRS1985

Disturbance-accommodating tracking maneuvers of flexible spacecraft

In this paper the problem of maneuvering a flexible spacecraft through a large angle is considered, where the disturbance-accommodating feedback control tracks a desired output state. The desired output state is provided from an open-loop solution for the linear system model. The components of the disturbance vector are assumed to be represented in terms of Fourier series. Closed-form solutions are provided for the Ricati, prefilter, state trajectory, and residual state trajectory equations which define the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index for frequency-shaping, in order to smooth both the open- and closed-loop control commands.

Turner, J. D.↗
NASA NTRS1986

Vortex conception of rotor and mutual effect of screw/propellers

A vortex theory of screw/propellers with variable circulation according to the blade and its azimuth is proposed, the problem is formulated and circulation is expanded in a Fourier series. Equations are given for inductive velocities in space for crews, including those with an infinitely large number of blades and expansion of the inductive velocity by blade azimuth of a second screw. Multiparameter improper integrals are given as a combination of elliptical integrals and elementary functions, and it is shown how to reduce elliptical integrals of the third kind with a complex parameter to integrals with a real parameter.

Lepilkin, A. M.↗
NASA NTRS1986

Interaction of the equatorial midnight pressure bulge and thermospheric zonal winds

The zonal component of the thermospheric neutral wind in the equatorial region is found to flow eastward all night, having a minimum near midnight. The data, obtained by Spencer et al. on the Dynamics Explorer-2 (DE-2) satellite, and reported more recently by Wharton et al., indicate that the minimum feature is significant. The minimum is illustrated by a 4th order Fourier series fit to the data points reported by Wharton et al. A table gives the amplitudes and phases of the four harmonic components used with the estimated error for each amplitude. It is asked whether this behavior is due to the local passage of the equatorial midnight pressure bulge associated with the midnight temperature anomaly. If so, it is to be expected that other data characterizing the midnight temperature anomaly should show consistency with this observation, especially in view of the large changes observed in the zonal velocity in the midnight sector. Consistency in momentum conservation may be checked using available data from previous independent experiments. Such data, taken under similar conditions of solar activity, was substituted into the momentum equation and found to be consistent using a priori estimates of the effect of viscosity.

Herrero, F. A.↗
NASA NTRS1986

On crossover adjustment in satellite altimetry and its oceanographic implications

It is argued that, to remove the satellite orbital errors, the crossover adjustment method that represents orbital errors in terms of Fourier series is preferable to the conventional bias-and-tilt crossover adjustment method. However, no matter what technique is used in the crossover adjustment, orbital errors will introduce a geographically dependent error (mostly a large-scale slope, which, in terms of spherical harmonics, is represented by the degree 1 terms) into the derived sea surface topography. This is because the responsible orbital errors have left no traces in crossover differences and therefore can never be removed. However, it is possible to reduce this fundamental uncertainty substantially if the record length is long enough; its implications on observing the basin-scale ocean circulation by satellite altimetry are discussed. New methods for observing the large-scale oceanic variability are also proposed (the conventional approach being limited to observing the mesoscale variability).

Tai, C.-K.↗
NASA NTRS1986

The nonlinear development of Gortler vortices in growing boundary layers

The development of Gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion whilst the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflection character as the flow moves downstream. The latter result suggests that the major effect of Gortler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗
NASA NTRS1987

Development of improved gravity field estimates using existing altimeter data

The formulation of a Fourier series and geographic representation expressions for orbit error were reported. Addition activities include the study of undulation errors in the Lagrangian formulation, and the development and testing of all the necessary software for the above expression. Additionally, the matrix formulations that led to the formation of observed equations and covariance propagation were developed.

Source record↗
NASA NTRS1986

Time-dependent fracture strength of oriented polymers

A statistical consideration based upon a theory of microscopic molecular kinetics is developed to describe the time-dependent fracture process for oriented polymers. The interrelation between the macroscopic fracture strength and the microscopic behaviors is formulated with the aid of a double Fourier series expansion. The microscopic behavior in the vicinity of a point is expressed in the form of a spherical function which can be expanded into a series of symmetric tensorial terms. Subsequently, the fracture strength of polymers is evaluated in terms of both time and molecular orientation. By taking account of the individual values of the directional fraction of integrity, the time to fracture and the most probable direction of fracture within any volume element in a medium are predicted.

Mun, M. S.↗
NASA NTRS1986

The Nimbus 7 LIMS map archival tape

The development of the Langley Map Archival Tape (LAMAT) is described. The role of the Nimbus 7 orbit characteristics in the analysis and interpretation of LAMAT data is discussed. The pressure ranges and heights for the LAMAT components are given and the synoptic fields for each pressure and latitude were modeled as Fourier series in longitude with time-dependent coefficients. Examples of LAMAT temperature fields are presented and the accuracies of the LAMAT fields are evaluated. The fit between the Langley inverted profile archival tape (LAIPAT) and LAMAT is examined by comparing averaged zonal mean fields and standard deviations. Consideration is given to diurnal variations of LAIPAT data, and the time and spatial smoothing of the data.

Haggard, K. V.↗
NASA NTRS1987

Vibration suppression using a constrained rate-feedback Threshold control strategy

Quasi-closed form solutions are derived for the finite time, minimum force rate-feedback threshold controller to bring a system with or without known external disturbances back into an 'allowable' state manifold in finite time. The disturbances are assumed to be expandable in terms of Fourier series. The quasi-closed form solutions replace the solution of the two-point boundary value problem and definite integral constraints with the solution of algebraic equations and the calculation of matrix exponentials. Examples demonstrate the threshold control technique and compare the quasi-closed form solutions with MACSYMA generated exact solutions (for small system order) and with the numerical solution of the two-point boundary value problem.

Zimmerman, D. C.↗
NASA NTRS1987

Numerical modeling of troposphere-induced gravity wave propagation

Sources of internal gravity waves (IGW) in the upper atmosphere are assumed to be meteorological processes in the troposphere. These sources are vertically and horizontally inhomogeneous and time dependent. In order to describe the IGW propagation from such sources, a numerical solution of a system of hydrodynamical equations is required. In addition, it is necessary to take into account the influence of the altitude latitude inhomogeneity of the temperature and wind fields on the IGW propagation as well as the processes of dissipation. An algorithm is proposed for numerical modelling of the IGW propagation over a limited area from tropospheric local sources to the upper atmosphere. The algorithm takes into account all the above features. A spectral grid method is used with the expansion of wave fields into the Fourier series over longitude. The upper limit conditions were obtained from the requirement of a limited energy dissipation rate in an atmospheric column. The no slip (zero velocity) condition was used at the Earth's surface.

Gavrilov, N. M.↗
NASA NTRS1988

Analytical approximation of a distorted reflector surface defined by a discrete set of points

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Acosta, Roberto J.↗