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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.

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At least 487 records · Page 27
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NASA NTRS1986

Thermohydrodynamic analysis for laminar lubricating films

A Galerkin-type analysis to include thermal effects in laminar lubricating films was performed. The lubricant properties were assumed constant except for a temperature-dependent Newtonian viscosity. The cross-film temperature profile is established by collocation at the film boundaries and two interior Lobatto points. The interior temperatures are determined by requiring that the zeroth and first moment of the energy equation be satisfied across the film. The fluidity is forced to conform to a third--degree polynomial appropriate to the Lobatto-point temperatures. Preliminary indications are that the use of just two such sampling points enables satisfactory prediction of bearing performance even in the presence of substantial viscosity variation.

Elrod, H. G.↗
NASA NTRS1986

Finite length effects in Taylor-Couette flow

Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cyclinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.

Streett, C. L.↗
NASA NTRS1987

Improving the geological interpretation of magnetic and gravity satellite anomalies

Quantitative analysis of the geologic component of observed satellite magnetic and gravity fields requires accurate isolation of the geologic component of the observations, theoretically sound and viable inversion techniques, and integration of collateral, constraining geologic and geophysical data. A number of significant contributions were made which make quantitative analysis more accurate. These include procedures for: screening and processing orbital data for lithospheric signals based on signal repeatability and wavelength analysis; producing accurate gridded anomaly values at constant elevations from the orbital data by three-dimensional least squares collocation; increasing the stability of equivalent point source inversion and criteria for the selection of the optimum damping parameter; enhancing inversion techniques through an iterative procedure based on the superposition theorem of potential fields; and modeling efficiently regional-scale lithospheric sources of satellite magnetic anomalies. In addition, these techniques were utilized to investigate regional anomaly sources of North and South America and India and to provide constraints to continental reconstruction. Since the inception of this research study, eleven papers were presented with associated published abstracts, three theses were completed, four papers were published or accepted for publication, and an additional manuscript was submitted for publication.

Hinze, William J.↗
NASA NTRS1986

Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

Bernardi, Christine↗
NASA NTRS1986

A practical assessment of spectral accuracy for hyperbolic problems with discontinuities

Physical and transform space filtering has been applied to the Fourier spectral collocation solution of the constant coefficient scalar wave equation with a discontinuous initial condition. High order accuracy can be extracted from the unfiltered solution. Smooth, high order Fourier space filtering gives expected polynomial order solutions away from the discontinuity. Spectral accuracy is observed with the physical space filter of Gottlieb and Tadmor.

Kopriva, David A.↗
NASA NTRS1987

Toward the large-eddy simulations of compressible turbulent flows

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model (in terms of Favre-filtered fields) is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The three dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96 to the third power grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. Future applications of these compressible subgrid-scale models to the large-eddy simulation of supersonic aerodynamic flows are discussed briefly.

Erlebacher, G.↗
NASA NTRS1987

A new approach for vibration control in large space structures

An approach for augmenting vibration damping characteristics in space structures with large panels is presented. It is based on generation of bending moments rather than forces. The moments are generated using bimetallic strips, suitably mounted at selected stations on both sides of the large panels, under the influence of differential solar heating, giving rise to thermal gradients and stresses. The collocated angular velocity sensors are utilized in conjunction with mini-servos to regulate the control moments by flipping the bimetallic strips. A simple computation of the rate of dissipation of vibrational energy is undertaken to assess the effectiveness of the proposed approach.

Kumar, K.↗
NASA NTRS1987

Error analysis for spectral approximation of the Korteweg-De Vries equation

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Maday, Y.↗
NASA NTRS1987

Spectral multigrid methods for the solution of homogeneous turbulence problems

New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

Erlebacher, G.↗
NASA NTRS1987

A new method of imposing boundary conditions for hyperbolic equations

A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

Funaro, D.↗
NASA NTRS1986

Plates and shells containing a surface crack under general loading conditions

The severity of the underlying assumptions of the line-spring model (LSM) are such that verification with three-dimensional solutions is necessary. Such comparisons show that the model is quite accurate, and therefore, its use in extensive parameter studies is justified. Investigations into the endpoint behavior of the line-spring model have led to important conclusions about the ability of the model to predict stresses in front of the crack tip. An important application of the LSM was to solve the contact plate bending problem. Here the flexibility of the model to allow for any crack shape is exploited. The use of displacement quantities as unknowns in the formulation of the problem leads to strongly singular integral equations, rather than singular integral equations which result from using displacement derivatives. The collocation method of solving the integral equations was found to be better and more convenient than the quadrature technique. Orthogonal polynomials should be used as fitting functions when using the LSM as opposed to simpler functions such as power series.

Joseph, Paul F.↗
NASA NTRS1987

Geoid undulation computations at laser tracking stations

Geoid undulation computations were performed at 29 laser stations distributed around the world using a combination of terrestrial gravity data within a cap of radius 2 deg and a potential coefficient set up to 180 deg. The traditional methods of Stokes' and Meissl's modification together with the Molodenskii method and the modified Sjoberg method were applied. Performing numerical tests based on global error assumptions regarding the terrestrial data and the geopotential set it was concluded that the modified Sjoberg method is the most accurate and promising technique for geoid undulation computations. The numerical computations for the geoid undulations using all the four methods resulted in agreement with the ellipsoidal minus orthometric value of the undulations on the order of 60 cm or better for most of the laser stations in the eastern United States, Australia, Japan, Bermuda, and Europe. A systematic discrepancy of about 2 meters for most of the western United States stations was detected and verified by using two relatively independent data sets. For oceanic laser stations in the western Atlantic and Pacific oceans that have no terrestrial data available, the adjusted GEOS-3 and SEASAT altimeter data were used for the computation of the geoid undulation in a collocation method.

Despotakis, Vasilios K.↗
NASA NTRS1986

Preconditioning matrices for Chebyshev derivative operators

The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.

Rothman, Ernest E.↗
NASA NTRS1986

Failure-accommodating control of large flexible spacecraft

This paper considers the problem of designing failure-accommodating controllers for large flexible spacecraft when there are sector-type nonlinearities in the loops. It is proved that an LQG-type controller can be made failure tolerant by inserting appropriate gains in the actuator paths and state estimator residual paths. For the state feedback case, when the actuators are saturating type, it is proved that there exists a finite region of attraction, which is invariant in the presence of these gains. Another class of controllers, which employs collocated sensors and actuators is presented, and is shown to have excellent failure-accommodation properties in addition to its robustness properties.

Joshi, S. M.↗
NASA NTRS1986

Conforming versus non-conforming boundary elements in three-dimensional elastostatics

A critical comparison of two basic formulations in three-dimensional elastostatics, using conforming and nonconforming boundary elements, is presented. The basic structure of the boundary element method is developed. The peculiarities that both types of boundary elements present in relation to the numerical implementation are discussed. Through selected examples, key issues such as the computational advantages and disadvantages of both formulations, mesh discretization and accuracy questions, and optimal location of the collocation nodes in the case of nonconforming elements are addressed. It is shown that conforming elements are able to produce more accurate results than nonconforming ones, with substantial economy in the final size of the system equations.

Manolis, G. D.↗
NASA NTRS1987

Calculation of stresses and forces between the skin and stiffener in composite panels

A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and on elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress function. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. The local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.

Hyer, M. W.↗
NASA NTRS1987

Spectral methods in fluid dynamics

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

Hussaini, M. Y.↗
NASA NTRS1986

Narrow- and broad-band satellite measurements of shortwave radiation - Conversion simulations with a general circulation model

The Oregon State University/Lawrence Livermore National Laboratory general circulation model has been employed as a vehicle for suggesting and exploring various means of converting narrow-band measurements of reflected solar radiation from the earth-atmosphere system to broad-band quantities. For purely illustrative purposes within the model's solar radiation routine, a narrow-band filter function consisting of a square-wave window extending from 0.5 to 0.9 microns is adopted. A limitation of the model, for this sort of endeavor, is that it does not include the wavelength dependence of surface albedos. Nevertheless, the model simulations tend to mimic the calibration of a narrow-band instrument, utilizing reflected solar radiation from the earth-atmosphere system as simultaneously measured by a collocated broad-band instrument; for the model, however, this is done in terms of fluxes, in contrast to instrument-measured radiances. The model results suggest that it might be preferable to perform narrow- to broad-band conversions in terms of planetary albedo (or an equivalent quantity), rather than in terms of reflected fluxes or radiances. Further improvement is achieved if, for instruments that can differentiate between clear and overcast conditions, separate clear and overcast calibrations are performed.

Cess, Robert D.↗