Search NASA⌕ Search

SEARCH · Search NASA

Results for “Cartesian”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Pressurized expulsion of nonisothermal single-phase cryogen

The performance of single-phase storage and expulsion systems as affected by temperature variations within the stored cryogen which are generated during heat transfer is discussed. Peculiar operating responses are indicated by spontaneous changes in fluid pressure which accompany g level changes, increased heater surface temperature, and durations of pressure cycles which differ considerably from that which is computed for an isothermal cryogen. The nonisothermal characteristics are predicted with a numerical model which includes the simultaneous solution of the time dependent conservation equations of mass, energy, and momentum in two space dimensions of Cartesian coordinates for boundary conditions which approximate those of the flight cryogenic system. The methodology of the numerical method and some comparisons between the predictions and the Apollo 12 flight data are included.

Forester, C. K.↗
NASA NTRS1971

A numerical solution of the Navier-Stokes equations for supercritical fluid thermodynamic analysis

An explicit numerical solution of the compressible Navier-Stokes equations is applied to the thermodynamic analysis of supercritical oxygen in the Apollo cryogenic storage system. The wave character is retained in the conservation equations which are written in the basic fluid variables for a two-dimensional Cartesian coordinate system. Control-volume cells are employed to simplify imposition of boundary conditions and to ensure strict observance of local and global conservation principles. Non-linear real-gas thermodynamic properties responsible for the pressure collapse phenomonon in supercritical fluids are represented by tabular and empirical functions relating pressure and temperature to density and internal energy. Wall boundary conditions are adjusted at one cell face to emit a prescribed mass flowrate. Scaling principles are invoked to achieve acceptable computer execution times for very low Mach number convection problems. Detailed simulations of thermal stratification and fluid mixing occurring under low acceleration in the Apollo 12 supercritical oxygen tank are presented which model the pressure decay associated with de-stratification induced by an ordinary vehicle maneuver and heater cycle operation.

Heinmiller, P. J.↗
NASA NTRS1972

Conjugate gradient optimization programs for shuttle reentry

Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems.

Powers, W. F.↗
NASA NTRS1973

Numerical interactive controller

Device allows interaction of operator with data in computer central processor in order to shift frame of data in Cartesian coordinates and slew desired data into view. ''Cursor generator program,'' in conjunction with device, provides light pen with sufficient resolving power to identify any particular set of coordinates with single-cell accuracy.

Brokl, S. S.↗
NASA NTRS1972

On the geometric analysis and adjustment of optical satellite observations

Satellite geodesy methods were catagorized into three divisions: geometric, dynamic, and mixed. These catagories furnish the basis for distinction between geometric and dynamic satellite geodesy. The dual adjustment, geometric analysis, and Cartesian coodinate determination are examined for two observing stations. Similar illustrations are given when more than two observing stations are used.

Tsimis, E.↗
NASA NTRS1972

Coordinate transformation by minimizing correlations between parameters

This investigation was to determine the transformation parameters (three rotations, three translations and a scale factor) between two Cartesian coordinate systems from sets of coordinates given in both systems. The objective was the determination of well separated transformation parameters with reduced correlations between each other, a problem especially relevant when the sets of coordinates are not well distributed. The above objective is achieved by preliminarily determining the three rotational parameters and the scale factor from the respective direction cosines and chord distances (these being independent of the translation parameters) between the common points, and then computing all the seven parameters from a solution in which the rotations and the scale factor are entered as weighted constraints according to their variances and covariances obtained in the preliminary solutions. Numerical tests involving two geodetic reference systems were performed to evaluate the effectiveness of this approach.

Kumar, M.↗
NASA NTRS1973

Robot computer problem solving system

A robot computer problem solving system which represents a robot exploration vehicle in a simulated Mars environment is described. The model exhibits changes and improvements made on a previously designed robot in a city environment. The Martian environment is modeled in Cartesian coordinates; objects are scattered about a plane; arbitrary restrictions on the robot's vision have been removed; and the robot's path contains arbitrary curves. New environmental features, particularly the visual occlusion of objects by other objects, were added to the model. Two different algorithms were developed for computing occlusion. Movement and vision capabilities of the robot were established in the Mars environment, using LISP/FORTRAN interface for computational efficiency. The graphical display program was redesigned to reflect the change to the Mars-like environment.

Merriam, E. W.↗
NASA NTRS1974

A rapid numerical solution to subsonic flow over planar and axisymmetric profiles at an angle of attack of 0 deg

A numerical solution is presented for the incompressible flow over thin planar and axisymmetric profiles at an angle of attack of 0 degrees. The method uses a finite-difference field solution to the governing equation with a Gauss-Seidel successive overrelaxation scheme. However, the use of a simple Cartesian grid system restricts this method to slender profiles. Results are presented for a cambered airfoil, airfoil in wall effect (two-dimensional flowthrough inlet), body of revolution, and flowthrough nacelle. A computer program is presented which can be used for any of the previously mentioned cases with simple input changes. Results for compressible flow are available with the use of the appropriate two-dimensional or axisymmetric compressibility corrections. Computational time for a typical field calculation of 3000 grid points and 200 cycles through the field is less than 1 minute with less than 50,000 octal storage on the Control Data Corporation 6600 computing system.

Mascitti, V. R.↗
NASA NTRS1972

Hydrodynamic water impact

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Kettleborough, C. F.↗
NASA NTRS1973

A Finite-Element Formulation for Subsonic Flows Around Complex Configurations

The problem of potential steady subsonic 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 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. This yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Morino, L.↗
NASA NTRS1973

Parabolic cylinder antennas

Some of the features of single and dual parabolic-cylinder reflector antenna systems are discussed in terms of wave conversions, field divergence, and wavefronts in Fresnel and Fraunhofer regions. Beam-squinting, by mechanical displacement and electrical phase gradient methods, is introduced together with the combination of these methods. In the case of dual parabolic cylinders there is also a discussion of surface-truncation, parametric representation of surface intersections, main-aperture blockage by the subsystem, and beam squinting. A few diffraction patterns are presented to illustrate the type of data available via a formulation equivalent to the complex-vector Kirchhoff-Kottler formulation. Main and cross-polarization components of the solution are available as they are inherently part of the field solution in the Cartesian coordinate system. A means of displaying main and cross-polarization components for arbitrary beam-scanning in space is outlined. Extensions to monopulse tracking with variable-beamwidth (zooming) capability are introduced.

Schmidt, R. F.↗
NASA NTRS1974

A method for the measurement and the statistical analysis of atmospheric turbulence

The instantaneous values of output voltages representing the wind velocity vector and the temperature at different elevations of the 250-foot meteorological tower located at NASA Wallops Flight Center are provided with the three dimensional split-film TSI Model 1080 anemometer system. The output voltages are sampled at a rate of one every 5 milliseconds, digitized and stored on digital magnetic tapes for a time period of approximately 40 minutes, with the use of a specially designed data acqusition system. A new calibration procedure permits the conversion of the digital voltages to the respective values of the temperature and the velocity components in a Cartesian coordinate system connected with the TSI probe with considerable accuracy. Power, cross, coincidence and quadrature spectra of the wind components and the temperature are obtained with the use of the fast Fourier transform. The cosine taper data window and ensemble and frequency smoothing techniques are used to provide smooth estimates of the spectral functions.

Tieleman, H. W.↗
NASA NTRS1973

Time-split finite-volume method for three-dimensional blunt-body flow

An efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented. It is a second-order-accurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form. These equations are written with respect to a Cartesian coordinate system in which an embedded mesh adjusts in time to the motion of the bow shock that is automatically captured as part of the weak solution. With such an adjusting mesh, oscillations in flow properties near the shock are shown to be virtually eliminated. The scheme uses a time-splitting concept that accelerates the convergence appreciably. Comparisons are made between computed and experimental results.

Rizzi, A. W.↗
NASA NTRS1973

Applications of the Kustaanheimo-Stieffel transformation of the perturbed two-body problem

The Newtonian differential equations of motion for the two-body problem can be transformed into four linear harmonic-oscillator equations by simultaneously applying the regularization step dt/ds = r and the Kustaanheimo-Stieffel (KS) transformation. The regularization step changes the independent variable from time to a new variable s, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. A derivation of a uniform, regular solution for the perturbed two-body problem in the four-dimensional space is presented. The variation-of-parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. This ten-element solution has mixed secular terms that degrade the long-term accuracy during numerical integration. Therefore, to eliminate these terms, the solution is modified by introducing two additional elements.

Bond, V. R.↗
NASA NTRS1974

Conservation equations of gasdynamics in curvilinear coordinate systems

Description of a new method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms. It is thus possible to readily apply difference schemes derived for Cartesian coordinates which conserve mass, momentum, and energy in the total flow field. The method is derived for orthogonal coordinates, and then extended to cover the most general class of coordinate transformations, using general tensor analysis. Several special features of the equations are discussed.

Vinokur, M.↗
NASA NTRS1974

Small parametric model of the precomputation of meteorological fields on the basis of complete equations and its energetic analogs

A small parametric, nonadiabatic model for precomputation of meteorological fields on the basis of complete equations, along with its energetic analogs is described. The model incorporates integral characteristics of the components of the wind speed and the analogous functions of the total fluxes of the ocean, and uses a Cartesian isobaric system of coordinates.

Borisenkov, Y. P.↗
NASA NTRS1974

Development of inverse inviscid transonic solution methods

A numerical method suitable for the analysis and/or design of supercritical transonic airfoils is reported. In order to achieve accuracy, the method utilizes the full inviscid potential flow equations; and in order to remain simple it solves the problem in a stretched Cartesian grid system. The resulting computer program has several advantages over others of its type -- its use in either the direct analysis mode in which the airfoil shape is prescribed and the flow field and surface pressures are determined, or in the inverse mode in which the surface pressures are given and the airfoil shape and flow field are computed. Other advantages of the program include its use in a design program, the rotated finite difference scheme and its determination of the airfoil shape simultaneously with the flow field relaxation solution.

Carlson, L. A.↗
NASA NTRS1974

A finite-element method for lifting surfaces in steady incompressible subsonic flow

The problem of potential steady subsonic flow for lifting surfaces is considered. This problem requires the solution of an integral equation relating the value of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface is divided into small (quadrilateral hyperboloidal) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each element and equal to their values at the centroids of the elements. This yields a set of linear algebraic equations. Numerical results are in good agreement with existing ones.

Morino, L.↗