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At least 703 records · Page 39

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NASA NTRS1990

Application of implicit numerical techniques to the solution of the three-dimensional diffusion equation

Implicit techniques for calculating three-dimensional, time-dependent heat diffusion in a cube are tested with emphasis on storage efficiency, accuracy, and speed of calculation. For this purpose, a tensor product technique with both Chebyshev collocation and finite differences and a generalized conjugate gradient technique with finite differences are used in conjunction with Crank-Nicolson discretization. An Euler explicit finite difference calculation is performed for use as a benchmark. The implicit techniques are found to be competitive with the Euler explicit method in terms of storage efficiency and speed of calculation and offer advantages both in accuracy and stability. Mesh stretching in the finite difference calculations is shown to markedly improve the accuracy of the solution.

Peltier, Leonard Joel↗

NASA NTRS1990

A Chebyshev matrix method for the spatial modes of the Orr-Sommerfeld equation

The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blasius boundary layer. The problems is linearized by the companion matrix technique for semiinfinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

Danabasoglu, Gokhan↗

NASA NTRS1991

Determining surface solar absorption from broadband satellite measurements for clear skies - Comparison with surface measurements

Using data from collocated satellite pixel measurements obtained during the Earth Radiation Budget Experiement and near-surface measurements carried out at the Boulder Atmospheric Observatory Tower, the shortwave (SW) surface radiation from broadband satellite measurements for clear-sky conditions was compared with surface measurements. Results demonstrate that the surface-SW absorption is a more meaningful quantity for climate studies than is surface insolation. It is also shown that a direct evaluation of the surface-SW absorption can be more accurately obtained from satellite measurements than can be surface insolation. An algorithm is presented for transferring satellite SW measurements to surface-SW absorption.

Cess, Robert D.↗

NASA NTRS1990

Dissipative compensators for flexible spacecraft control

The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.

Joshi, S. M.↗

NASA NTRS1990

Numerical simulation of transition in a rotating disk flow

An investigation of the laminar-turbulence transition process in a three-dimensional boundary layer on a rotating disk is initiated. Preliminary results from a direct numerical simulation using spectral collocation method are presented. The simulation results in the linear regime is tested against linear stability theory. Saturation of the primary disturbance energy suggests the importance of modal interaction in initiating transition.

Balachandar, S.↗

NASA NTRS1991

System identification and control of the JPL active structure

This paper describes recent advances in structural quieting technology as applied to active truss structures intended for high precision space based optics applications. Collocated active damping control loops are designed in order to impedance match piezoelectric active members to the structure. Noncollocated control loops are also studied in relation to controlling lightly damped structures.

Fanson, J. L.↗

NASA NTRS1991

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

Hanks, Brantley R.↗

NASA NTRS1991

Active vibration absorber for the CSI evolutionary model - Design and experimental results

The development of control of large flexible structures technology must include practical demonstrations to aid in the understanding and characterization of controlled structures in space. To support this effort, a testbed facility has been developed to study practical implementation of new control technologies under realistic conditions. The paper discusses the design of a second order, acceleration feedback controller which acts as an active vibration absorber. This controller provides guaranteed stability margins for collocated sensor/actuator pairs in the absence of sensor/actuator dynamics and computational time delay. Experimental results in the presence of these factors are presented and discussed. The robustness of this design under model uncertainty is demonstrated.

Bruner, Anne M.↗

NASA NTRS1991

Global precipitation estimates from satellite - Using difference fields of outgoing long-wave radiation

Global precipitation estimates using satellite data are derived using difference fields of outgoing long-wave radiation (OLR). The difference fields consist of clear OLR minus cloudy OLR, which is a measure of long-wave cloud radiative forcing at the top of the earth-atmosphere system; and clear daytime OLR minus clear night-time OLR, which is a measure of the diurnal variation of surface heating. All geophysical parameters used to compute OLR are derived from an analysis of the HIRS2/MSU sounding data. The derived global precipitation estimates show good agreement with collocated raingage data over land.

Wu, Man-Li↗

NASA NTRS1990

Using spatial coherence to retrieve cloud properties - ERBE experience and CERES applications

Cloud properties for individual ERBE scanner fields of view are obtained from simultaneous, collocated imagery data. The cloud properties are used to assess the performance of the ERBE maximum likelihood estimate of cloud conditions which ultimately influences estimates of the radiative fluxes at the top of the atmosphere. During EOS the analysis of MODIS observations within the fields of view of the CERES instruments promises to yield, in addition, estimates of surface radiative fluxes as well as the vertical distribution of radiative heating within the atmosphere.

Coakley, James A., Jr.↗

NASA NTRS1990

Quadrature imposition of compatibility conditions in Chebyshev methods

This paper handles a problem encountered in the solution by way of Chebyshev spectral collocation discretization of the Poisson equation with homogeneous Neumann boundary conditions. When pseudospectral Chebyshev methodology is utilized to discretize the partial differential equation these integrals have to be approximated by an appropriate quadrature formula. The correct quadrature formula is developed for these problems, taking into account the degree of the polynomials involved. It is shown that this formula leads to a well-conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

Gottlieb, D.↗

NASA NTRS1990

Improved operation of magnetic bearings for flywheel energy storage system

Analysis and operation of prototype 500-Wh flywheel at low speeds have shown that many factors affect the correct functioning of the magnetic bearings. An examination is made of a number of these, including magnetic bearing control system nonlinearities and displacement transducer positioning, and their effects upon the successful operation of the suspension system. It is observed that the bearing control system is extremely sensitive to actuator parameters such as coil inductance. As a consequence of the analysis of bearing relaxation oscillations, the bearing actuator design methodology which has previously been used, where coil parameter selection is based upon static considerations, has been revised. Displacement transducer sensors which overcome the collocation problem are discussed.

Zmood, R. B.↗

NASA NTRS1991

On the viscous modes of instability of a trailing line vortex

A viscous linear stability analysis of a trailing line (Batchelor) vortex is presented. Employing a staggered Chebyshev spectral collocation technique, very accurate results were obtained. The destabilizing role of viscous forces has been shown to produce two types of viscous instability modes. These viscous disturbances consist of an axisymmetric mode and an asymmetric mode. Both disturbances are long-wave instabilities with maximum growth rates which are orders of magnitude smaller than the inviscid modes which have been found by others. Comparison with experimental results and condensation trail observations are found to be in good qualitative agreement with the present study.

Khorrami, Mehdi R.↗

NASA NTRS1990

Second mode interactions in supersonic boundary layers

The nonlinear evolution of a two-dimensional second mode unstable wave in a Mach 4.5 wall-bounded flow is computed by solving the full time-dependent compressible Navier-Stokes equations. A highly accurate solution is obtained using spectral collocation methods. It is shown that departure from linearity first occurs in the critical layer due to the cubic nonlinearities in the momentum equation. This is a direct result of the large density perturbations in this regime. Time evolution studies of the growth rate as a function of normal distance from the plate suggests that the mode is evolving toward a nonlinear saturated state, and that this problem is possibly amenable to standard weakly nonlinear perturbation methods.

Erlebacher, Gordon↗

NASA NTRS1990

Enstrophy budget in decaying compressible turbulence

The interaction of vorticity and shock waves in decaying compressible turbulence is investigated by direct numerical simulation of the Navier-Stokes equation using a spectral method with 64-cubed collocation points. The Taylor microscale Reynolds number decreases from 36 to 17 and the rms Mach number from 0.8 to 0.4 during the decay. It is observed that vorticity is created inside curved shocks through baroclinic interaction and intensified by the compression of fluid elements. Vortex stretching is, on the other hand, dominant outside shocks and is responsible for enhancing the strength of vorticity. A dipole of vorticity is typically created at the vertex of curved shocks, the structure of which is explained in terms of jump relations of velocity derivatives across a curved shock.

Kida, Shigeo↗

NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗

NASA NTRS1991

Spectral methods for the Euler equations - The blunt body problem revisited

The present use of the Chebyshev spectral collocation method, in conjunction with shock-fitting, to solve the blunt-body problem gives attention to the boundary and the shock-acceleration equations. The crux of these procedures is the use of the characteristic compatibility relations to compute the body pressure and shock velocity. It is shown that converged solutions are obtainable without artificial smoothing, and that spectral accuracy is achieved.

Kopriva, David A.↗

NASA NTRS1991

Application of the Global Positioning System to crustal deformation measurement. II - The influence of errors in orbit determination networks

The errors introduced into GPS measurements of a geodetic network by means of adopting different sets of stations in central and southern California as fixed points (termed fiducial stations) were investigated. Solutions for a crustal deformation network spanning distances up to 350 km were computed with a variety of fiducial networks, using fiducial coordinates determined from VLBI. Results showed that three receivers collocated with VLBI sites provide a stable reference system at a few millimeter level in the horizontal components and at 10 mm in the vertical components, indicating that local survey errors between VLBI and GPS markers at fiducial sites do not severely affect the estimates of interstation vectors.

Larson, Kristine M.↗