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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 NTRS1974

A finite element formulation for supersonic flows around complex configurations

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element are assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations whose coefficients are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Morino, L.↗
NASA NTRS1974

A finite-element analysis for steady and oscillatory subsonic flow around complex configurations

The problem of potential subsonic flow around complex configurations is considered. The solution is given of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element. The coefficients of the equation are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented. The results obtained with the above formulation are compared with existing analytical and experimental results.

Chen, L. T.↗
NASA NTRS1974

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

Morino, L.↗
NASA NTRS1974

Free geometric adjustment of the OSU/NGSP global network /solution WN-4/

The paper presents the results of the OSU WN 4 geometric adjustment for the coordinates of 152 satellite tracking stations. The results, when referred to the WN 4 ellipsoid of a = 6,378,127.8 m and 1/f = 298.25 produce geoid undulations consistent with dynamically determined ones. The average standard deviation in a Cartesian coordinate is plus or minus 4.0 m; in height, plus or minus 2.7 m. Comparisons with coordinates obtained from dynamic solutions show significant inconsistencies in the orientation of the coordinate systems.

Mueller, I. I.↗
NASA NTRS1975

Numerical solution of the Navier-Stokes equations with topography

A finite difference scheme for solving the equations of fluid motion in a generalized coordinate system has been constructed. The scheme conserves mass and all the first integral moments of the motion. The scheme also advectively 'almost conserves' second moments, in that the magnitude of implicit numerical smoothing is typically about an order smaller than explicit viscosity and diffusion. Calculations with the model support the theoretical conjecture that the difference scheme is stable whenever the analogous Cartesian scheme is stable. The scheme has been used to calculate dry atmospheric convection due to differential heating between top and bottom of mountainous terrain. The general small-scale characteristics of mountain up-slope winds have been simulated. In addition, the results have demonstrated the crucial role played by the eddy diffusivities and the environmental stability, in determining both the quantitative and the qualitative features of the circulation.

Gal-Chen, T.↗
NASA NTRS1975

The transformation of aerodynamic stability derivatives by symbolic mathematical computation

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Howard, J. C.↗
NASA NTRS1977

Thermal-radiation model

Central Cartesian coordinate system calculates thermal environment around rocket plume. Radiative heat exchange between surfaces is calculated by Monte Carlo method.

Claunch, W. C.↗
NASA NTRS1976

Conformal coordinates associated with uniformly accelerated motion

Specific problems in the theory of relativity are often simplified by an appropriate choice of the coordinate system. Restricted conformal coordinates provide an especially simple analysis of motion with uniform acceleration, known as hyperbolic motion. Conformal coordinates x', t' may be obtained from Cartesian coordinates x, t by the transformation x'+ct'=F(x+ct) and x'-ct'=G(x-ct), where c is the velocity of light. A variable motion of the x' system is determined by the choice of the functions F and G.

Jones, R. T.↗
NASA NTRS1976

Polyatomic molecule vibrations

Polyatomic molecule vibrations are analyzed as harmonic vibrations along normal coordinates. The energy eigenvalues are found for linear and nonlinear symmetric triatomic molecules for valence bond models of the potential function with arbitrary coupling coefficients; such models can usually be fitted to observed energy levels with reasonably good accuracy. Approximate normal coordinates for the H2O molecule are discussed. Degenerate vibrational modes such as occur in CO2 are analyzed and expressions for Fermi resonance between close-lying states of the same symmetry are developed. The bending modes of linear triatomic molecules are expressed in terms of Laguerre polynomials in cylindrical coordinates as well as in terms of Hermite polynomials in Cartesian coordinates. The effects of large-amplitude bending such as occur in the C3 molecule are analyzed, along with anharmonic effects, which split the usually degenerate bending mode energy levels. Finally, the vibrational frequencies, degeneracies, and symmetry properties of XY3, X2Y2, and XY4 type molecules are discussed.

Source record↗
NASA NTRS1975

On Similarity Transformation and Geodetic Network Distortions Based on Doppler Satellite Observations

Models used in geodesy to transform two sets of coordinates are studied and distortions in geodetic networks are investigated. Commonly used transformation models are first reviewed and most of them are interpreted. Differences between various models are discussed. Pitfalls in partial solutions are then considered. It is shown that only as many chords and/or directional elements can be used in the computation as are needed to completely determine the size or shape of the polyhedron implied in the set of Cartesian coordinates. Each additional element causes the normal matrix to be singular provided that all correlations between the chords are used. A number of tables and maps indicating distortions in the NAD 27, Precise Traverse M-R '72, AUS, and SAD 69 geodetic datums are also included. The residuals of the coordinates are scanned for systematic patterns after transforming each geodetic system to the NWL9D Doppler system. Also, an attempt is made to show scale distortions in the NAD 27.

Leick, Alfred↗
NASA NTRS1976

Biostereometric analysis of body form - The second manned Skylab mission

Results of biostereometric analyses of the body form of the Skylab 3 crew before and after flight. The Cartesian coordinates of numerous points on the body surface were derived by stereophotogrammetry, and mathematical analysis of the coordinate description allowed computation of the surface area and volume of the body, the volume of body segments, and the area and shape of cross sections. The weight loss in all three crew members was accompanied by a loss in volume distributed between the trunk and legs, with the legs showing the greatest proportional loss. The observed loss of volume apparently resulted from a combined loss of fluid in the abdomen and legs, of muscle in the legs and paraspinal region, and of fat in the abdomen and buttocks.

Whittle, M. W.↗
NASA NTRS1976

Inverse transonic airfoil design including viscous interaction

A numerical technique was developed for the analysis of specified transonic airfoils or for the design of airfoils having a prescribed pressure distribution, including the effect of weak viscous interaction. The method uses the full potential equation, a stretched Cartesian coordinate system, and the Nash-MacDonald turbulent boundary layer method. Comparisons with experimental data for typical transonic airfoils show excellent agreement. An example shows the application of the method to design a thick aft-cambered airfoil, and the effects of viscous interaction on its performance are discussed.

Carlson, L. A.↗
NASA NTRS1976

The theory of the gravitational potential applied to orbit prediction

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.

Kirkpatrick, J. C.↗
NASA NTRS1977

Interplanetary medium data book, appendix

Computer generated listings of hourly average interplanetary plasma and magnetic field parameters are given. Parameters include proton temperature, proton density, bulk speed, an identifier of the source of the plasma data for the hour, average magnetic field magnitude and cartesian components of the magnetic field. Also included are longitude and latitude angles of the vector made up of the average field components, a vector standard deviation, and an identifier of the source of magnetic field data.

King, J. H.↗
NASA NTRS1976

Crossed beam studies of ion-molecule reactions in methane and ammonia

A crossed-beam apparatus is used to measure the product ion velocity and angular distributions for the following ion-molecule reactions in the relative energy range from 2 to 9 eV: CH4(+) + NH3 yields NH4(+) + CH3; CH4(+) + NH3 yields CNH5(+) + H2; NH2(+) + CH4 yields CNH4(+) + H2 (or 2H); and CH3(+) + NH3 yields CNH4(+) + H2 (or 2H). These reactions are also studied by means of deuterium labeling as a further probe of the detailed reaction dynamics. Probability contour plots for the four reactions are constructed in Cartesian velocity space, and product peaks in the plots are discussed. Relative cross sections and Q values are computed for two of the reactions as well as for the corresponding deuterium-labelled reactions. The results show that the present ion-neutral condensation reactions are highly exothermic with a deep well for the internal complex, that little hydrogen scrambling occurs, and that the energy of the reactions is released mainly as internal energy, even to the extent of producing two hydrogen atoms in some cases rather than one hydrogen atom or molecule.

Smith, G. P. K.↗
NASA NTRS1977

Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.

Chiu, Y. T.↗
NASA NTRS1977

National Geodetic Satellite Program, Part II: Ohio State University

Data analysis was carried out to obtain an improved global network combining all participating tracking stations in a single worldwide coordinate system. Mathematical formulations were derived, programmed, and tested. Observational data were used to determine the relative positions of tracking stations in an arbitrary Cartesian coordinate system. The position of this coordinate system was estimated with respect to an absolute system. A primary network was established in which station positions were known to an internal consistency of 10 meters or better for the following purposes: (1) to establish the relative relationships between the various geodetic datums in use around the world; and (2) to connect isolated tracking stations, islands, navigational beacons, and other points of interest. Results are presented.

Mueller, I. I.↗
NASA NTRS1977

Improved ground truth geoid for the GEOS-3 calibration area

The purpose of this investigation is to develop methods and procedures are reported for computing a detailed geoid to be used as geodetic ground truth for the calibration and verification of GEOS-3 altimeter data. The technique developed is based on rectifying the best available detailed geoid so that the rectified geoid will have correct scale, orientation, shape and position with respect to the geocenter. The approach involved the development of a mathematical model based on a second degree polynomial, in rectangular Cartesian coordinates, describing the geoid undulations at the control stations. A generalized least squares solution was obtained for the polynomial which describes the variation of the undulation differences between the control stations geoid and the gravimetric geoid. Three rectified geoid were determined. These geoids correspond to three sets of tracking station data: (1) WFC/C-band data; (2) GSFC/C-band data; and (3) OSU-275 data. The absolute accuracy of these rectified geoids is linearly correlated with the uncertainties of the tracking station coordinates and, to a certain extent, with those of the detailed geoid being rectified.

Mourad, A. G.↗