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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 307 records · Page 17
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NASA NTRS1976

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.

Rubin, S. G.↗
NASA NTRS1975

Applications of satellite technology to gravity field determination

Various techniques for using satellite technology to determine the earth's gravity field are analyzed and compared. A high-low configuration satellite to satellite tracking mission is recommended for the determination of the long wavelength portion of the gravity field. Satellite altimetry and satellite gradiometry experiments are recommended for determination of the short wavelength portion of the gravity field. The recently developed least squares collocation method for estimating the gravity field from satellite derived data is analyzed and its equivalence to conventional methods is demonstrated.

Argentiero, P.↗
NASA NTRS1976

Crack-opening displacements in center-crack, compact, and crack-line wedge-loaded specimens

The theoretical crack-opening displacements for center-crack, compact, and crack-line wedge-loaded specimens (reported in the ASTM Proposed Recommended Practice for R-Curve Determination (1974)) disagree with experimental measurements in the literature. The disagreement is a result of using approximate specimen configurations and load representation to obtain the theoretical displacements. An improved method of boundary collocation is presented which was used to obtain the theoretical displacements in these three specimen types; the actual specimen configurations and more accurate load representation were used. In the analysis of crack-opening displacements in the compact and crack-line wedge-loaded specimens, the effects of the pin-loaded holes were also included. The theoretical calculations agree with the experimental measurements reported in the literature. Also examined are accurate polynomial expressions for crack-opening displacements in both compact and crack-line wedge-loaded specimens.

Newman, J. C., Jr.↗
NASA NTRS1976

Calculation of subsonic and supersonic steady and unsteady aerodynamic forces using velocity potential aerodynamic elements

Expressions for calculation of subsonic and supersonic, steady and unsteady aerodynamic forces are derived, using the concept of aerodynamic elements applied to the downwash velocity potential method. Aerodynamic elements can be of arbitrary out of plane polygon shape, although numerical calculations are restricted to rectangular elements, and to the steady state case in the supersonic examples. It is suggested that the use of conforming, in place of rectangular elements, would give better results. Agreement with results for subsonic oscillating T tails is fair, but results do not converge as the number of collocation points is increased. This appears to be due to the form of expression used in the calculations. The methods derived are expected to facilitate automated flutter analysis on the computer. In particular, the aerodynamic element concept is consistent with finite element methods already used for structural analysis. The method is universal for the complete Mach number range, and, finally, the calculations can be arranged so that they do not have to be repeated completely for every reduced frequency.

Haviland, J. K.↗
NASA NTRS1976

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗
NASA NTRS1976

A new method for solving problems of sound radiation from a duct for the case of low Mach number

A method for rapidly solving duct end-plane impedance problems is presented which is based on deriving a form of the Helmholtz integral formula expressing the normal derivative of the acoustic pressure at a boundary point. A set of integral expressions is obtained by satisfying the existing boundary conditions and then solved using a general collocation method. The results obtained for the Levine-Schwinger (1948) problem agree well with the exact values. In the case of a duct flow having a temperature mismatch with the surroundings, the results show an increase in the magnitude of the reflection coefficient for the case of a cold core, and a decrease in its value for the case of a hot core, as compared with the case of exhaust into a uniform medium. A phase change of between pi/2 and pi is nearly always achieved, which indicates the tendency towards maintaining a constant pressure at the exit plane. The method can easily be extended to arbitrary duct shapes as long as they are axisymmetric.

Wahbah, M. M.↗
NASA NTRS1976

Mode 1 stress intensity factors for round compact specimens

The mode 1 stress intensity factors were computed for round compact specimens by the boundary collocation method. Results are presented for ratios A sub T/R sub 0 in the range 0.3 to 0.8, where A sub t is the distance from the specimen center to the crack tip for a specimen of diameter 2R sub 0.

Gross, B.↗
NASA NTRS1977

AEMS implementation cost study for Boeing 727

Costs for airline operational implementation of a NASA-developed approach energy management system (AEMS) concept, as applied to the 727 airplane, were determined. Estimated costs are provided for airplane retrofit and for installation of the required DME ground stations. Operational costs and fuel cost savings are presented in a cost-of-ownership study. The potential return on the equipment investment is evaluated using a net present value method. Scheduled 727 traffic and existing VASI, ILS, and collocated DME ground station facilities are summarized for domestic airports used by 727 operators.

Allison, R. L.↗
NASA NTRS1977

Mode I analysis of a cracked circular disk subject to a couple and a force

Mode 1 stress intensity coefficients were obtained for an edge-cracked disk (round compact specimen). Results for this plane elastostatic problem, obtained by a boundary collocation analysis are presented for ratios 0.35 less than A/D less than 1, where A is the crack length and D is the disk diameter. The results presented are for two complementary types of loading. By superposition of these results the stress intensity factor K sub I for any practical load line location of a pin-loaded round compact specimen can be obtained.

Gross, B.↗
NASA NTRS1977

Displacement coefficients along the inner boundaries of radially cracked ring segments subject to forces and couples

Displacement results of plane boundary collocation analysis are given for various locations on the inner boundaries of radially cracked ring segments (C-shaped specimens) subject to two complementary types of loading. Results are presented for ratios of outer to inner radius R sub o/R sub i in the range of 1.1 to 2.5, and ratios a/W in the range 0.1 to 0.8 where a is the crack length for a specimen of wall thickness W. By combination of these results the resultant displacement coefficient delta or the corresponding influence coefficient, can be obtained for any practical load line location of a pin loaded specimen.

Gross, B.↗
NASA NTRS1977

Analysis of radially cracked ring segments subject to forces and couples

Results of planar boundary collocation analysis are given for ring segment (C-shaped) specimens with radial cracks, subjected to combined forces and couples. Mode I stress intensity factors and crack mouth opening displacements were determined for ratios of outer to inner radius in the range 1.1 to 2.5 and ratios of crack length to segment width in the range 0.1 to 0.8.

Gross, B.↗
NASA NTRS1977

Stress-intensity factors for a wedge-loaded edge crack in a semi-infinite strip

The problem of a semi infinite strip containing an edge crack is considered. It is assumed that the strip is loaded by a frictionless rigid wedge pressed into the crack. The resulting crack contact problem is formulated in terms of a system of singular integral equations. The behavior of the solution near the singular points is studied in detail. A series of numerical examples are given and the results are compared with those obtained by the method of boundary collocation and by the simple beam theory.

Erodogan, F.↗
NASA NTRS1977

Gravity model improvement using GEOS-3 (GEM 9 and 10)

The use of collocation permitted GEM 9 to be a larger field than previous derived satellite models, GEM 9 having harmonics complete to 20 x 20 with selected higher degree terms. The satellite data set has approximately 840,000 observations, of which 200,000 are laser ranges taken on 9 satellites equipped with retroreflectors. GEM 10 is complete to 22 x 22 with selected higher degree terms out to degree and order 30 amounting to a total of 592 coefficients. Comparisons with surface gravity and altimeter data indicate a substantial improvement in GEM 9 over previous satellite solutions; GEM 9 is in even closer agreement with surface data than the previously published GEM 6 solution which contained surface gravity. In particular the free air gravity anomalies calculated from GEM 9 and a surface gravity solution are in excellent agreement for the high degree terms.

Lerch, F. J.↗
NASA NTRS1977

The separated turbulent boundary layer over a wavy wall

A study and application of the fourth order spline collocation procedure, numerical solution of boundary layer like differential equations, is presented. A simple inversion algorithm for the simultaneous solution of the resulting difference equations is given. Particular attention is focused on the boundary condition representation for the spline second derivative approximations. Solutions using the spline procedure, as well as the three point finite difference method, are presented for several model problems in order to assess and improve the spline numerical scheme. Application of the resulting algorithm to the incompressible laminar self similar boundary layer equations is presented.

Polak, A.↗
NASA NTRS1978

Fault-tolerant software for aircraft control systems

Concepts for software to implement real time aircraft control systems on a centralized digital computer were discussed. A fault tolerant software structure employing functionally redundant routines with concurrent error detection was proposed for critical control functions involving safety of flight and landing. A degraded recovery block concept was devised to allow collocation of critical and noncritical software modules within the same control structure. The additional computer resources required to implement the proposed software structure for a representative set of aircraft control functions were discussed. It was estimated that approximately 30 percent more memory space is required to implement the total set of control functions. A reliability model for the fault tolerant software was described and parametric estimates of failure rate were made.

Source record↗
NASA NTRS1978

The prediction and mapping of geoidal undulations from GEOS-3 altimetry

From the adjusted altimeter data an approximation to the geoid height in ocean areas is obtained. Methods are developed to produce geoid maps in these areas. Geoid heights are obtained for grid points in the region to be mapped, and two of the parameters critical to the production of an accurate map are investigated. These are the spacing of the grid, which must be related to the half-wavelength of the altimeter signal whose amplitude is the desired accuracy of the contour; and the method adopted to predict the grid values. Least squares collocation was used to find geoid undulations on a 1 deg grid in the mapping area. Twenty maps, with their associated precisions, were produced and are included. These maps cover the Indian Ocean, Southwestern and Northeastern portions of the Pacific Ocean, and Southwest Atlantic and the U.S. Calibration Area.

Kearsley, W.↗
NASA NTRS1977

Mode I stress intensity factors for round compact specimens

Mode I stress intensity factors were computed for round compact specimens by the boundary collocation method. Results are presented for ratios At/R0 in the range 0.3 to 0.8, where At is the distance from the specimen center to the crack tip for a specimen of diameter 2R0.

Gross, B.↗
NASA NTRS1978

Displacement coefficients along the inner boundaries of radially cracked ring segments subject to forces and couples

Displacement results of plane boundary collocation analysis are given for various locations on the inner boundaries of radially cracked ring segments (C-shaped specimens) subject to two complementary types of loading. Results are presented for ratios of outer to inner radius in the range of 1.1 to 2.5 and ratios a/W in the range 0.1 to 0.8, where a is the crack length for a specimen of wall thickness W. By combination of these results the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load line location of a pin-loaded specimen.

Gross, B.↗