Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “rectangular coordinates”

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 37 records · Page 2

Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft

This report compiles the various research activities conducted under the auspices of the NASA Grant NAG3-1026, "Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft" during the period of April 1989 to April 1994. The effort involved the development of multigrid based algorithms and computer programs for the calculation of the flow and temperature fields generated by Short Take-off and Vertical Landing (STOVL) aircraft, while hovering in ground proximity. Of particular importance has been the interaction of the exhaust jets with the head wind which gives rise to the hot gas ingestion process. The objective of new STOVL designs to reduce the temperature of the gases ingested into the engine. The present work describes a solution algorithm for the multi-dimensional elliptic partial-differential equations governing fluid flow and heat transfer in general curvilinear coordinates. The solution algorithm is based on the multigrid technique which obtains rapid convergence of the iterative numerical procedure for the discrete equations. Initial efforts were concerned with the solution of the Cartesian form of the equations. This algorithm was applied to a simulated STOVL configuration in rectangular coordinates. In the next phase of the work, a computer code for general curvilinear coordinates was constructed. This was applied to model STOVL geometries on curvilinear grids. The code was also validated in model problems. In all these efforts, the standard k-Epsilon model was used.

Vanka, S. P.↗

Radiation-detector optical-imaging device is of simplified construction

A simplified radiation detector was designed which employs an activated continuous front surface consisting of either the diffused or barrier type of semiconducting material with a grid structure on the nonactivated side of the detector. Its form may be either a rectangular coordinate or a polar coordinate system.

Source record↗

Computerized series solution of relativistic equations of motion.

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

Broucke, R.↗

The orbital mechanics of flight mechanics

A reference handbook on modern dynamic orbit theory is presented. Starting from the most basic inverse-square law, the law of gravity for a sphere is developed, and the motion of point masses under the influence of a sphere is considered. The reentry theory and the orbital theory are discussed along with the relative motion between two bodies in orbit about the same planet. Relative-motion equations, rectangular coordinates, and the mechanics of simple rigid bodies under the influence of a gravity gradient field are also discussed.

Dunning, R. S.↗

Study of ephemeris accuracy of the minor planets

The current state of minor planet ephemerides was assessed, and the means for providing and updating these emphemerides for use by both the mission planner and the astronomer were developed. A system of obtaining data for all the numbered minor planets was planned, and computer programs for its initial mechanization were developed. The computer based system furnishes the osculating elements for all of the numbered minor planets at an adopted date of October 10, 1972, and at every 400 day interval over the years of interest. It also furnishes the perturbations in the rectangular coordinates relative to the osculating elements at every 4 day interval. Another computer program was designed and developed to integrate the perturbed motion of a group of 50 minor planets simultaneously. Sampled data resulting from the operation of the computer based systems are presented.

Brooks, D. R.↗

Computer simulation of plasma and N-body problems

The following FORTRAN language computer codes are presented: (1) efficient two- and three-dimensional central force potential solvers; (2) a three-dimensional simulator of an isolated galaxy which incorporates the potential solver; (3) a two-dimensional particle-in-cell simulator of the Jeans instability in an infinite self-gravitating compressible gas; and (4) a two-dimensional particle-in-cell simulator of a rotating self-gravitating compressible gaseous system of which rectangular coordinate and superior polar coordinate versions were written.

Harries, W. L.↗

Expansion of the gravitational potential with computerized Poisson series

The paper describes a recursive formulation for the expansion of the gravitational potential valid for both the tesseral and zonal harmonics. The expansion is primarily in rectangular coordinates, but the classical orbit elements or equinoctial orbit elements can be easily substituted. The equations of motion for the zonal harmonics in both classical and equinoctial orbital elements are described in a form which will result in closed-form expressions for the first-order perturbations. In order to achieve this result, the true longitude or true anomaly have to be used as independent variables.

Broucke, R.↗

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Kozdoba, L. A.↗

Finite element concepts in computational aerodynamics

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Baker, A. J.↗

Coherent phasing of segmented mirrors

The technical issues associated with a coherently phased segmented mirror can be divided into two types. The first involves the issues of manufacturing the surface quality of the mirror segments themselves (coherent phasing of individual segments). The second involves assembly issues of initializing in 1 G and retaining in 0 G an aggregate segmented mirror (coherent phasing between individual segments). Using a rectangular coordinate system at the vertex of a mirror segment, the rigid body motions are the six translational and rotational degrees of freedom. A first cut primary mirror wavefront error budget is presented. For a minimum operational wavelength of 30 micrometers, the derived values from the budget are: segment surface quality (0.45 micrometers RMS), radius mismatch (50 PPM), segment piston error (1.3 micrometers, segment tip/tilt error (0.6 microrad). Either active or passive segmented mirrors can be addressed, but if the surface quality of the off-axis segment and the radius matching requirements can be passively met, then only segment alignment need be sensed and controlled during operation in orbit. For the active mirror case, dimensional stability of the mirror material during operation is a key factor in establishing the degree of active figure control required.

Jones, Peter A.↗

Propagation of high frequency jet noise using geometric acoustics

Spherical directivity of noise radiated from a convecting quadrupole source embedded in an arbitrary spreading jet is obtained by ray-tracing methods of geometrical acoustics. The six propagation equations are solved in their general form in a rectangular coordinate system. The noise directivity in the far field is calculated by applying an iteration scheme that finds the required radiation angles at the source resulting in propagation through a given observer point. Factors influencing the zone of silence are investigated. The caustics of geometrical acoustics and the exact locations where it forms is demonstrated by studying the variation in ray tube area obtained from transport equation. For a ring source convecting along the center-axis of an axisymmetric jet, the polar directivity of the radiated noise is obtained by an integration with respect to azimuthal directivity of compact quadrupole sources distributed on the ring. The Doppler factor is shown to vary slightly from point to point on the ring. Finally the scaling of the directivity pattern with power -3 of Doppler factor is investigated and compared with experimental data.

Khavaran, A.↗

Cape Photographic Durchmusterung, volume 2

The Cape Photographic Durchmusterung (CPD, Gill and Kapteyn 1895-1900) is a Photographic survey of southern stars in the declination range -18 to -90 degrees. This volume covers the declination range -53 through -89 degrees. Positions are given for 1875 equinox. The summary of the positional uncertainties quoted in the third volume of the published catalog gives +/- 0.28 sec (R.A.), +/- 0.044 arcmin (Dec.) for zones - 18 to -57 degrees, + 0.157 sec + 0.0764/cos(delta) sec (R.A.), +/- 0.056 arcmin (Dec.) for zones -58 to -85 degrees, +0.157 sec + 0.0353/cos (delta) sec (R.A.), + 0.0127 arcmin (Dec.) for the polar plate where, as explained in the introduction to the third volume, many positions were derived from rectangular coordinates (these are positions reported to 0.1 SCC (R.A.) and 0.001 arcmin (Dec.) in the -86 to -89 degree zones in the catalog). The probable error of a photographic magnitude, as determined by combining results for different magnitudes and weighting proportionately according to the numbers of stars in each class of magnitude, is given as +0.055 mag. From an analysis of the faint magnitude limits on the plates discussed in the third volume introduction, the catalog as a whole can be considered complete to photographic magnitude 9.2, but it is stated that it will be found practically complete, in or near the Milky Way, to magnitude 9.5.

Source record↗