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At least 127 records · Page 7

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NASA NTRS1980

Optical phase distortion due to compressible flow over laser turrets

Analytical models for optical phase distortion due to compressible flow over a laser turret are developed. Phase distortion is calculated for both blunt and small perturbation turrets. For the blunt turret, the Janzen-Rayleigh technique is used to determine the flow field. Phase distortions of 2.2 wavelengths at 3.8 microns are calculated for the blunt turret. For small perturbation turrets, a versatile analytical model is developed for a turret on a fuselage with circular cross section. With a two dimensional Fourier series representation of the turret, any shape can be considered. Both subsonic and supersonic flows can be calculated. Phase distortions of 1.2 wavelengths at 3.8 microns are calculated for one turret at high subsonic Mach number. In addition to being of value for laser turrets, the methods are applicable to reconnaissance aircraft using photographic equipment and cruise missiles using celestial navigation.

Fuhs, A. E.↗

NASA NTRS1979

Amplitude effects on the dynamic performance of hydrostatic gas thrust bearings

A strip gas film bearing with inherently compensated inlets is analyzed to determine the effect of disturbance amplitude on its dynamic performance. The governing Reynolds' equation is solved using finite-difference techniques. The time dependent load capacity is represented by a Fourier series up to and including the third harmonics. For the range of amplitudes investigated the linear stiffness was independent of the amplitude, and the linear damping was inversely proportional to (1 - epsilon-squared) to the 1.5 power where epsilon is the amplitude relative to the film thickness.

Stiffler, A. K.↗

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 NTRS1980

Orthogonality of spherical harmonic coefficients

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

Mcleod, M. G.↗

NASA NTRS1981

Effect of load introduction on graphite epoxy compression specimens

Compression testing of modern composite materials is affected by the manner in which the compressive load is introduced. Two such effects are investigated: (1) the constrained edge effect which prevents transverse expansion and is common to all compression testing in which the specimen is gripped in the fixture; and (2) nonuniform gripping which induces bending into the specimen. An analytical model capable of quantifying these foregoing effects was developed which is based upon the principle of minimum complementary energy. For pure compression, the stresses are approximated by Fourier series. For pure bending, the stresses are approximated by Legendre polynomials.

Reiss, R.↗

NASA NTRS1981

Comparison of a barotropic blocking theory with observation

Hart (1979) showed that the truncated spectral equations obtained by Charney and Devore (1979) could be derived merely by assuming that the cross-stream scale of the topography was large compared to the downstream scale. Since actual topography does not have the large y scales postulated by Hart, his model was modified in the current investigation to obtain equations with arbitrary zonal variations of topography by projecting all variable functions onto the first topographic cross-stream mode. The topographic heights and streamfunctions are expanded as Fourier series in the cross-stream coordinate and the series are truncated after the first term. This accomplishes Hart's results but permits more realistic y variations in the topography. The present investigation is the first in a two-part series. The second part will deal with a two-layer baroclinic channel flow, again with arbitrary zonal variations of topography.

Charney, J. G.↗

NASA NTRS1981

Interaction of upstream flow distortions with high Mach number cascades

Features of the interaction of flow distortions, such as gusts and wakes with blade rows of advance type fans and compressors having high tip Mach numbers are modeled. A typical disturbance was assumed to have harmonic time dependence and was described, at a far upstream location, in three orthogonal spatial coordinates by a double Fourier series. It was convected at supersonic relative to a linear cascade described as an unrolled annulus. Conditions were selected so that the component of this velocity parallel to the axis of the turbomachine was subsonic, permitting interaction between blades through the upstream as well as downstream flow media. A strong, nearly normal shock was considered in the blade passages which was allowed curvature and displacement. The flows before and after the shock were linearized relative to uniform mean velocities in their respective regions. Solution of the descriptive equations was by adaption of the Wiener-Hopf technique, enabling a determination of distortion patterns through and downstream of the cascade as well as pressure distributions on the blade and surfaces. Details of interaction of the disturbance with the in-passage shock were discussed. Infuences of amplitude, wave length, and phase of the disturbance on lifts and moments of cascade configurations are presented. Numerical results are clarified by reference to an especially orderly pattern of upstream vertical motion in relation to the cascade parameters.

Englert, G. W.↗

NASA NTRS1981

The axisymmetric elasticity problem for a laminated plate containing a circular hole

The elasticity problem for a laminated thick plate which consists of two bonded dissimilar layers and which contains a circular hole is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface by using the Love strain function. Through the expansion of the boundary conditions into Fourier series the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented and the stress intensity factors are calculated.

Delale, F.↗

NASA NTRS1982

An exact plane-stress solution for a class of problems in orthotropic elasticity

An exact solution for the stress field within a rectangular slab of orthotropic material is found using a two dimensional Fourier series formulation. The material is required to be in plane stress, with general stress boundary conditions, and the principle axes of the material must be parallel to the sides of the rectangle. Two load cases similar to those encountered in materials testing are investigated using the solution. The solution method has potential uses in stress analysis of composite structures.

Erb, D. A.↗

NASA NTRS1982

Investigations of medium wavelength magnetic anomalies in the eastern Pacific using MAGSAT data

Efforts concerning spherical harmonic modeling of the Earth's magnetic field and the use of such models in removing core produced magnetic fields from magnetic fields of crustal origin are discussed. Results indicate that the terms of a spherical harmonic expansion do not uniquely determine a given wavelength of signal as the terms in a Fourier series do. Addition of terms of higher degree and order to a spherical harmonic expansion tend to fine tune the amplitude of the terms of lower degree and order. As a result, removal of such a model from a regional data set will not remove long wavelengths completely.

Harrison, C. G. A.↗

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.

Leonard, A.↗

NASA NTRS1981

LANDSAT-D MSS/TM tuned orbital jitter analysis model LDS900

The final LANDSAT-D orbital dynamic math model (LSD900), comprised of all test validated substructures, was used to evaluate the jitter response of the MSS/TM experiments. A dynamic forced response analysis was performed at both the MSS and TM locations on all structural modes considered (thru 200 Hz). The analysis determined the roll angular response of the MSS/TM experiments to improve excitation generated by component operation. Cross axis and cross experiment responses were also calculated. The excitations were analytically represented by seven and nine term Fourier series approximations, for the MSS and TM experiment respectively, which enabled linear harmonic solution techniques to be applied to response calculations. Single worst case jitter was estimated by variations of the eigenvalue spectrum of model LSD 900. The probability of any worst case mode occurrence was investigated.

Pollak, T. E.↗

NASA NTRS1983

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.

Teglas, R.↗

NASA NTRS1983

Spectral multigrid methods for elliptic equations 2

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 NTRS1983

The nonlocal theory of periodic density drift instabilities

The nonlocal theory of electrostatic density drift instabilities is developed for an arbitrary, periodic variation in plasma density. Linear Vlasov theory is applied to Fourier series representations of the plasma density, and the resulting equations are solved numerically. The growth rates of the universal drift instability are compared by using local and nonlocal theories. It is demonstrated that the local theory is inadequate if the nonlocal eigenfunctions of the electrostatic modes have significant amplitude over spatial regions wider than the regions of large plasma density gradients. Nonlocal effects can enhance wave-particle diffusion of a triangular-shaped variation and reduce wave-particle dissipation of a square-shaped irregularity.

Bernhardt, P. A.↗

NASA NTRS1984

LANDSAT-4 horizon scanner performance evaluation

Representative data spans covering a little more than a year since the LANDSAT-4 launch were analyzed to evaluate the flight performance of the satellite's horizon scanner. High frequency noise was filtered out by 128-point averaging. The effects of Earth oblateness and spacecraft altitude variations are modeled, and residual systematic errors are analyzed. A model for the predicted radiance effects is compared with the flight data and deficiencies in the radiance effects modeling are noted. Correction coefficients are provided for a finite Fourier series representation of the systematic errors in the data. Analysis of the seasonal dependence of the coefficients indicates the effects of some early mission problems with the reference attitudes which were computed by the onboard computer using star trackers and gyro data. The effects of sun and moon interference, unexplained anomalies in the data, and sensor noise characteristics and their power spectrum are described. The variability of full orbit data averages is shown. Plots of the sensor data for all the available data spans are included.

Bilanow, S.↗

NASA NTRS1984

Numerical simulation of boundary-layer transition

The transition to turbulence in boundary layers was investigated by direct numerical solution of the nonlinear, three-dimensional, incompressible Navier-Stokes equations in the half-infinite domain over a flat plate. Periodicity was imposed in the streamwise and spanwise directions. A body force was applied to approximate the effect of a nonparallel mean flow. The numerical method was spectra, based on Fourier series and Jacobi polynomials, and used divergence-free basis functions. Extremely rapid convergence was obtained when solving the linear Orr-Sommerfeld equation. The early nonlinear and three-dimensional stages of transition, in a boundary layer disturbed by a vibrating ribbon, were successfully simulated. Excellent qualitative agreement was observed with either experiments or weakly nonlinear theories. In particular, the breakdown pattern was staggered or nonstaggered depending on the disturbance amplitude.

Spalart, P. R.↗

NASA NTRS1983

Inlet flow distortion in turbomachinery - Comparison of theory and experiment in a transonic fan stage

Consideration is given to both velocity and temperature circumferential inlet distortions at upstream infinity (Seidel et al., 1980). The blade rows here are modeled as semiactuator disks, and losses and quasi-steady deviation angle correlations are included in the analysis. The governing equations are linearized, and the perturbations in stagnation pressure and stagnation temperature at upstream infinity are represented as Fourier series. The flow in the rotor is modeled as inviscid, one-dimensional, unsteady, and compressible. the flow is steady elsewhere. The deviation angles for the rotor and stator are taken to be functions of the relative inlet angle and Mach number, and use is made of the correlations contained in Johnson and Bullock (1965). It is assumed that the losses in relative stagnation pressure in the rotor and stator occur across the trailing edge. Boundary conditions applied at the various stations furnish the equations that make it possible to solve for the several quantities introduced in the linearization of the governing equations.

Seidel, B. S.↗