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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Coordinate systems for the space shuttle program

A minimal set of well defined coordinate systems necessary for the interchange of data within the space shuttle program is presented. The document format consists of four parts: (1) a list of the subscripts identifying the coordinate systems, (2) a glossary explaning the terms used within the coordinate system definitions, (3) figures defining, both graphically and verbally, each coordinate system, and (4) an appendix (published separately) showing the relationships (transformations) between similar systems.

Davis, L. D.↗
DOE OSTI2026

Constructing field-aligned coordinate systems for gyrokinetic simulations of tokamaks in X-point geometries

Structures in tokamak plasmas are elongated along the direction of the magnetic field and short in the directions perpendicular to the magnetic field. Many tokamak simulation codes take advantage of this by using a field-aligned coordinate system. However, field-aligned coordinate systems have a coordinate singularity at magnetic X-points where the poloidal magnetic field vanishes, which makes it difficult to use field-aligned coordinate systems when simulating the core and scrape-off layer simultaneously. Here, we present an algorithm for grid generation and computing geometric quantities in a standard field-aligned coordinate system that avoids the singularity and allows one to conduct two-dimensional gyrokinetic axisymmetric simulations in X-point geometries. Convergence tests of advection, boundary value problems and geometric quantities all show greater than first-order convergence even in the vicinity of the X-point. We also demonstrate the geometric consistency of our algorithm with an example simulation of the spherical tokamak for energy production, which shows machine-precision particle conservation.

fusion plasma↗
NASA NTRS1980

A three-dimensional body-fitted coordinate system for flow field calculations on asymmetric nosetips

A three dimensional body-fitted coordinate system developed for use in the calculation of inviscid flows over ablated, asymmetric reentry vehicle nosetips is described. Because of the potential geometric asymmetries, no standard coordinate system (e.g., spherical, axisymmetric reference surface-normal) is capable of being closely aligned with the nosetip surface. To generate a 3-D, body-fitted coordinate system an analytic mapping procedure is applied that is conformal within each meridional plane of the nosetip; these transformations are then coupled circumferentially to yield a three dimensional coordinate system. The mappings used are defined in terms of hinge points, which are points selected to approximate the body contours in each meridional plane. The selection of appropriate hinge points was automated to facilitate the use of the resulting nosetip flow field code.

Hall, D. W.↗
NASA NTRS1976

Space telescope coordinate systems, symbols, and nomenclature definitions

The major coordinate systems as well as the transformations and transformation angles between them, for the Space Telescope are defined. The coordinate systems were primarily developed for use in pointing and control system analysis and simulation. Additional useful information (on nomenclature, symbols, quaternion operations, etc.) is also contained.

Kennel, H. F.↗
NASA NTRS1988

Reference coordinate systems: An update. Supplement 11

A common requirement for all geodetic investigations is a well-defined coordinate system attached to the earth in some prescribed way, as well as a well-defined inertial coordinate system in which the motions of the terrestrial frame can be monitored. The paper deals with the problems encountered when establishing such coordinate systems and the transformations between them. In addition, problems related to the modeling of the deformable earth are discussed. This paper is an updated version of the earlier work, Reference Coordinate Systems for Earth Dynamics: A Preview, by the author.

Mueller, Ivan I.↗
NASA NTRS1975

Nature of the requirements for reference coordinate systems /Review paper/

The current need for more precisely defined reference coordinate systems arises for geodynamics because the earth can certainly not be treated as a rigid body when measurement uncertainties reach the few-centimeter scale or its angular equivalent. At least two coordinate systems seem to be required. The first is a system defined in space relative to appropriate astronomical objects, suitable for ultimately expressing the dynamical equations of motion for the earth. The second coordinate system must be associated with the nonrigid earth in some well defined way so that the rotational motions of the whole earth are represented by the transformation parameters relating the earth system to the space-inertial system. The earth system should be defined so that the dynamical equations for relative motions of the various internal mechanical components of the earth and accurate measurements of these motions are conveniently expressed in this system.

Lundquist, C. A.↗
NASA NTRS1982

Error induced by coordinate systems

It is pointed out that the choice of a curvilinear coordinate system can have a substantial effect on the error in the numerical solution of a partial differential equation. The truncation error is dependent not only on the higher order derivatives of the solution and the local grid spacing, but also on the rate-of-change of the grid spacing and on the departure of the grid from orthogonality. In connection with the present investigation, an analysis is conducted of the local truncation error in the approximation of first and second order derivatives on a curvilinear grid. Attention is given to a number of examples which illustrate the two fundamental sources of truncation error in the numerical solution of partial differential equations on curvilinear coordinate systems. The first is the grid spacing and changes in grid spacing which is measured by the first and second order derivatives of the functions defining the coordinate system. The second source is the higher order derivatives of the solution itself.

Mastin, C. W.↗
NASA NTRS1974

Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies

A method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected region containing any number of arbitrarily shaped bodies is presented. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system. Numerical solutions for the lifting and nonlifting potential flow about Joukowski and Karman-Trefftz airfoils using this coordinate system generation show excellent comparison with the analytic solutions. The application to fields with multiple bodies is illustrated by a potential flow solution for multiple airfoils.

Thompson, J. F.↗
NASA NTRS2018

Applying the SOFIA Coordinate System to the HIRMES Instrument

The High-resolution Mid-infrared Spectrometer (HIRMES) will be in-flight aboard the Stratospheric Observatory for Infrared Astronomy (SOFIA) in late 2019, which will allow for observations of the structure and evolution of protoplanetary disks. SOFIA has a different coordinate system from the system being used to build HIRMES and needs to be defined and applied to HIRMES. This is necessary because the first mirror, which is aiming the incoming light onto the slit wheel by allowing for tip and tilt adjustments, cannot rotate. Thus, the SOFIA coordinate system allows for this additional degree of freedom and allows for the slit wheel to be in line with the telescope. Using a laser radar, multiple measurements around the instrument were taken of tooling balls, which quantified an uncertainty with the measurements. Also, a laser radar was used to scan the entirety of the instrument. The center of the front flange was determined using the measurements and scans of the instrument, which was used to determine the origin of the SOFIA coordinate system and its uncertainty. By knowing the center of the front flange, an off-center, rotated coordinate system was created, matching the mechanics' schematics for the system. Going forward, this coordinate system will allow for continued alignment of the instrument in preparation for flight and for accurate measurements when aboard SOFIA.

Wraback, Elizabeth↗
NASA NTRS1982

General curvilinear coordinate systems

The basic ideas of the construction and use of numerically-generated boundary-fitted coordinate systems for the numerical solution of partial differential equations are discussed. With such coordinate systems, all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries. A number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given. The material of this paper is applicable to all types of coordinate system generation.

Thompson, J. P.↗
NASA NTRS1977

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

Thompson, J. F.↗
NASA NTRS1980

Generation of orthogonal boundary-fitted coordinate systems

A method is presented for computing orthogonal boundary fitted coordinate systems for geometries with coordinate distributions specified on all boundaries. The system which has found most extensive use in generating boundary fitted grids is made up of Poisson equations, of which the functions P and Q provide a means for controlling the spacing and density of grid lines in the coordinate system. While questions remain concerning the existence and uniqueness of orthogonal systems, the generating method presented adds to the available, useful techniques for constructing these systems.

Coleman, R. M.↗
NASA NTRS1994

Propagation of experimental uncertainties from the tunnel to the body coordinate system in 3-D LDV flow field studies

An analysis of experimental laser Doppler velocimetry (LDV) data uncertainties that propagate from measurements in the tunnel coordinate system to results in the model system are provided. Calculations of uncertainties as functions of the variables that comprise the final result requires assessment of the contribution each variable makes. Such an analysis enables and necessitates the experimentalists to identify and address the contributing error sources in the experimental measurement system. This provides an opportunity to improve the quality of data derived from experimental systems. This is especially important in experiments where small changes in test conditions are expected to produce small, detectable changes in results. In addition, the need for high-quality experimental data for CFD method validation demands a thorough assessment of experimental uncertainty. Transforming from one Cartesian coordinate system to another by three sequential rotations, equations were developed to transform the variables initially obtained in the original coordinates into variables in the final coordinate system. Based on the transformation equations, propagation equations for errors in the experimentally-derived flow quantities were derived for a model at angle of attack. Experimental uncertainties were then propagated from the tunnel coordinate system into the model system.

Neuhart, Dan H.↗
NASA NTRS1977

A generalized orthogonal coordinate system for describing families of axisymmetric and two-dimensional bodies

A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.

Gnoffo, P. A.↗
NASA NTRS1973

Transformation between orbital parameters in different coordinate systems of the general relativistic Schwarzschild problem.

The relationships between the osculating orbital elements for a family of solutions of the general relativistic Schwarzschild problems are developed. These relationships provide a method for evaluating orbital elements in different Schwarzschild coordinate systems without the necessity of fitting to real data every time the system of coordinates is changed. The objectivity of different coordinate systems is discussed. Considerations of orbital motions favor the standard Schwarzschild metric, but the propagation of light signals is more objective in the metric of Painleve. Because the orbital motions usually dominate the representation of data, the standard Schwarzschild coordinates are the best objective choice for most applications.

Georgevic, R. M.↗
NASA NTRS1976

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Avis, L. M.↗
NASA NTRS1982

Reference coordinate systems for Earth dynamics: A preview

Geodynamics is the subject of intensive international research during last decade. A common requirement for all investigations is the necessity of a well defined coordinate system attached to the Earth in some prescribed way. In addition, a well defined inertial coordinate system is also needed in which the motions of the terrestrial system can be monitored. The problems encountered when establishing such coordinate systems and the transformations between them are presented. In addition, problems related to the modeling of the deformable Earth are discussed. Finally, action items are listed which are necessary to assure that the reference system issue is resolved early and that uniformity is assured by means of international agreements.

Mueller, I. I.↗