Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “CARTESIAN 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 199 records · Page 11

Interactive Scene Analysis Module - A sensor-database fusion system for telerobotic environments

Accomplishing a task with telerobotics typically involves a combination of operator control/supervision and a 'script' of preprogrammed commands. These commands usually assume that the location of various objects in the task space conform to some internal representation (database) of that task space. The ability to quickly and accurately verify the task environment against the internal database would improve the robustness of these preprogrammed commands. In addition, the on-line initialization and maintenance of a task space database is difficult for operators using Cartesian coordinates alone. This paper describes the Interactive Scene' Analysis Module (ISAM) developed to provide taskspace database initialization and verification utilizing 3-D graphic overlay modelling, video imaging, and laser radar based range imaging. Through the fusion of taskspace database information and image sensor data, a verifiable taskspace model is generated providing location and orientation data for objects in a task space. This paper also describes applications of the ISAM in the Intelligent Systems Research Laboratory (ISRL) at NASA Langley Research Center, and discusses its performance relative to representation accuracy and operator interface efficiency.

Cooper, Eric G.↗

Radiation heat transfer calculations using a control-angle, control-volume-based discrete ordinates method

A control-angle, control-volume-based discrete ordinates method (CA - CV DOM) is presented in this paper. A detailed formulation of the discretization equation is presented in two-dimensional Cartesian coordinate system. The procedure can be extended to curvilinear coordinate system with minor modifications. The step and modified-exponential schemes are used in this study. Present results converged to the grid independent solutions quickly and compared favorably against other published results for six test problems.

Chai, John C.↗

VLSI architectures for geometrical mapping problems in high-definition image processing

This paper explores a VLSI architecture for geometrical mapping address computation. The geometric transformation is discussed in the context of plane projective geometry, which invokes a set of basic transformations to be implemented for the general image processing. The homogeneous and 2-dimensional cartesian coordinates are employed to represent the transformations, each of which is implemented via an augmented CORDIC as a processing element. A specific scheme for a processor, which utilizes full-pipelining at the macro-level and parallel constant-factor-redundant arithmetic and full-pipelining at the micro-level, is assessed to produce a single VLSI chip for HDTV applications using state-of-art MOS technology.

Kim, K.↗

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 8: Cooling Flow/heat Transfer Analysis

The focus of this task was to validate the ADPAC code for heat transfer calculations. To accomplish this goal, the ADPAC code was modified to allow for a Cartesian coordinate system capability and to add boundary conditions to handle spanwise periodicity and transpiration boundaries. The primary validation case was the film cooled C3X vane. The cooling hole modeling included both a porous region and grid in each discrete hold. Predictions for these models as well as smooth wall compared well with the experimental data.

Hall, Edward J.↗

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 8: Cooling Flow/heat Transfer Analysis User's Manual

The focus of this task was to validate the ADPAC code for heat transfer calculations. To accomplish this goal, the ADPAC code was modified to allow for a Cartesian coordinate system capability and to add boundary conditions to handle spanwise periodicity and transpiration boundaries. This user's manual describes how to use the ADPAC code as developed in Task 5, NAS3-25270, including the modifications made to date in Tasks 7 and 8, NAS3-25270.

Hall, Edward J.↗

Implementation issues for a compact 6 degree of freedom force reflecting handcontroller with cueing of modes

Teleoperated control requires a master human interface device that can provide haptic input and output which reflect the responses of a slave robotic system. The effort reported in this paper addresses the design and prototyping of a six degree-of-freedom (DOF) Cartesian coordinate hand controller for this purpose. The device design recommended is an XYZ stage attached to a three-roll wrist which positions a flight-type handgrip. Six degrees of freedom are transduced and control brushless DC motor servo electronics similar in design to those used in computer controlled robotic manipulators. This general approach supports scaled force, velocity, and position feedback to aid an operator in achieving telepresence. The generality of the device and control system characteristics allow the use of inverse dynamics robotic control methodology to project slave robot system forces and inertias to the operator (in scaled form) and at the same time to reduce the apparent inertia of the robotic handcontroller itself. The current control design, which is not multiple fault tolerant, can be extended to make flight control or space use possible. The proposed handcontroller will have advantages in space-based applications where an operator must control several robot arms in a simultaneous and coordinated fashion. It will also have applications in intravehicular activities (within the Space Station) such as microgravity experiments in metallurgy and biological experiments that require isolation from the astronauts' environment. For ground applications, the handcontroller will be useful in underwater activities where the generality of the proposed handcontroller becomes an asset for operation of many different manipulator types. Also applications will emerge in the Military, Construction, and Maintenance/Manufacturing areas including ordnance handling, mine removal, NBC (Nuclear, Chemical, Biological) operations, control of vehicles, and operating strength and agility enhanced machines. Future avionics applications including advanced helicopter and aircraft control may also become important.

Jacobus, Heidi↗

A three-dimensional orthogonal laser velocimeter for the NASA Ames 7- by 10-foot wind tunnel

A three-component dual-beam laser-velocimeter system has been designed, fabricated, and implemented in the 7-by 10-Foot Wind Tunnel at NASA Ames Research Center. The instrument utilizes optical access from both sides and the top of the test section, and is configured for uncoupled orthogonal measurements of the three Cartesian coordinates of velocity. Bragg cell optics are used to provide fringe velocity bias. Modular system design provides great flexibility in the location of sending and receiving optics to adapt to specific experimental requirements. Near-focus Schmidt-Cassegrain optic modules may be positioned for collection of forward or backward scattered light over a large solid angle, and may be clustered to further increase collection solid angle. Multimode fiber optics transmit collected light to the photomultiplier tubes for processing. Counters are used to process the photomultiplier signals and transfer the processed data digitally via buffered interface controller to the host MS-DOS computer. Considerable data reduction and graphical display programming permit on-line control of data acquisition and evaluation of the incoming data. This paper describes this system in detail and presents sample data illustrating the system's capability.

Dunagan, Stephen E.↗

Galactic oscillator symmetry

Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.

Rosensteel, George↗

Nonlinear hydrodynamics of cosmological sheets. 1: Numerical techniques and tests

We present the numerical techniques and tests used to construct and validate a computer code designed to study the multidimensional nonlinear hydrodynamics of large-scale sheet structures in the universe, especially the fragmentation of such structures under various instabilities. This code is composed of two codes, the hydrodynamical code ZEUS-2D and a particle-mesh code. The ZEUS-2D code solves the hydrodynamical equations in two dimensions using explicit Eulerian finite-difference techniques, with modifications made to incorporate the expansion of the universe and the gas cooling due to Compton scattering, bremsstrahlung, and hydrogen and helium cooling. The particle-mesh code solves the equation of motion for the collisionless dark matter. The code uses two-dimensional Cartesian coordinates with a nonuniform grid in one direction to provide high resolution for the sheet structures. A series of one-dimensional and two-dimensional linear perturbation tests are presented which are designed to test the hydro solver and the Poisson solver with and without the expansion of the universe. We also present a radiative shock wave test which is designed to ensure the code's capability to handle radiative cooling properly. And finally a series of one-dimensional Zel'dovich pancake tests used to test the dark matter code and the hydro solver in the nonlinear regime are discussed and compared with the results of Bond et al. (1984) and Shapiro & Struck-Marcell (1985). Overall, the code is shown to produce accurate and stable results, which provide us a powerful tool to further our studies.

Anninos, Wenbo Y.↗

Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation

The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.

Adams, N. A.↗

A Velocity Distribution Model for Steady State Heat Transfer

Consider a box that is filled with an ideal gas and that is aligned along Cartesian coordinates (x, y, z) having until length in the 'y' direction and unspecified length in the 'x' and 'z' directions. Heat is applied uniformly over the 'hot' end of the box (y = 1) and is removed uniformly over the 'cold' end (y = O) at a constant rate such that the ends of the box are maintained at temperatures T(sub 0) at y = O and T(sub 1) at y = 1. Let U, V, and W denote the respective velocity components of a molecule inside the box selected at some random time and at some location (x, y, z). If T(sub 0) = T(sub 1), then U, Y, and W are mutually independent and Gaussian, each with mean zero and variance RT(sub 0), where R is the gas constant. When T(sub 0) does not equal T(sub 1) the velocity components are not independent and are not Gaussian. Our objective is to characterize the joint distribution of the velocity components U, Y, and W as a function of y, and, in particular, to characterize the distribution of V given y. It is hoped that this research will lead to an increased physical understanding of the nature of turbulence.

Hall, Eric B.↗

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Carpenter, J. Russell↗

Effects of Geometric Azimuthal Asymmetries of the PPM Stack on Electron Beam Characteristics

The effects of geometric azimuthally asymmetric properties of a periodic permanent magnet (PPM) focusing stack on electron beam characteristics obtained using a fully three dimensional (3D) particle-in-cell (PIC) code will be presented. The simulation model, using MAFIA (Solution of MAxwell's equations by the Finite-Integration-Algorithm), incorporates 3D behavior of the beam immersed in static fields calculated directly from the exact geometry and material properties of the 3D magnetic focusing structure. The Hughes 8916H, 18-40 GHz helical TWT for the millimeter-wave power module (MMPM) was used as a prototype. Firstly, the effects of C-magnets used at the input and output of the TWT to allow for coupling of the RF signal into and out of the tube are considered. The 8916H input and output C-magnets differ because coaxial couplers are used at the input and waveguide couplers are used at the output The repositioning of the beam from its central axis due to the inclusion of the output C-magnet was found to be most significant. The modeled output C-magnet and its orientation in the Cartesian coordinate system is shown, and a two-dimensional beam profile including the output C-magnet is also shown. A table presents the shift of the beam center off the central axis relative to the average radius of the beam at the longitudinal points A, B and C designated on an enclosed figure. Secondly, the addition of shunts, or rectangular iron pieces applied manually by a skilled technician in order to improve beam transmission, is considered. The shunts are applied to the top of the tube; thus, azimuthal symmetry of the focusing stack is interrupted. Although shunts are typically added during RF focusing, they are also typically added at the input section of the tube where RF forces are minimal, making an electron optics analysis meaningful. Because several shunts are usually applied to one pole piece, the simulations have been simplified by modeling a half washer with the same radius and longitudinal length as a shunt over the entire x, positive-y half of the transverse plane. A modeled pole piece and shunt as described are shown. Lastly, in order to study the effects of magnet misalignments, a magnet in the PPM stack was arbitrarily chosen and adjusted so that its central axis was shifted both 0.7 percent and 1.0 percent of the magnet outer diameter in the positive-y direction. In practice, positioning the magnets so that their central axis is accurately aligned with the central axis of the tube is challenging. Thus, it is a strong possibility that one or more magnets will be misaligned relative to the tube central axis.

Kory, Carol L.↗

Progress in a Study of Striations in the Dust Tail of Comet Hale-Bopp (C/1995 O1)

We report preliminary results of a massive investigation of the striation patterns observed in the dust tail of comet Hale-Bopp in March and April 1997. Our findings are based on 16 wide-field photographs taken with Schmidt cameras on March 2-20, with six more, from March 31-April 8, still waiting for analysis. Altogether approximately 700 individual striae were examined on the 16 images, which were scanned and computer processed to enhance the morphology. About 5300 stria points, or some 7-8 points per stria per image on the average, were measured and their astrometric positions determined and subsequently converted to a Cartesian coordinate system, aligned with the comet's projected radius vector and centered on the nucleus. The evolution of the striated tail has been studied using the Sekanina-Farrell fragmentation hypothesis (AJ 85, 1538, 1980), previously applied to other comets. This two-step model is characterized by the time of release from the nucleus of a parent object (or objects) whose motion is assumed to have been subjected to a constant repulsive acceleration beta(sub p) (presumably due to solar radiation pressure) until the time of fragmentation.

Sekanina, Z.↗

Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids

The efficient low dissipative high order schemes proposed by Yee et al. is formulated for 3-D curvilinear moving grids. These schemes consists of a high order base schemes combined with nonlinear characteristic filters. The amount of numerical dissipation is minimized by applying the schemes to the entropy splitting form of the inviscid flux derivatives. The analysis is given for a thermally perfect gas. The main difficulty in the extension of higher order schemes that were formulated in Cartesian coordinates to curvilinear moving grids is the higher order transformed metric evaluations. The higher order numerical evaluation of the transformed metric terms to insure freestream preservation is done in a coordinate invariant manner. The formulation is an improvement over existing formulation of high order scheme in curvilinear moving grids.

Vinokur, Marcel↗

Temporal Treatment of a Thermal Response for Defect Depth Estimation

Transient thermography, which employs pulse surface heating of an inspected component followed by acquisition of the thermal decay stage, is gaining wider acceptance as a result of its remoteness and rapidness. Flaws in the component s material may induce a thermal contrast in surface thermograms. An important issue in transient thermography is estimating the depth of a subsurface flaw from the thermal response. This improves the quantitative ability of the thermal evaluation: from one scan it is possible to locate regions of anomalies in thickness (caused by corrosion) and estimate the implications of the flaw on the integrity of the structure. Our research focuses on thick composite aircraft components. A long square heating pulse and several minutes observation period are required to receive an adequate thermal response from such a component. Application of various time-related informative parameters of the thermal response for depth estimation is discussed. A three-dimensional finite difference model of heat propagation in solids in Cartesian coordinates is used to simulate the thermographic process. Typical physical properties of polymer graphite composites are assumed for the model.

Plotnikov, Y. A.↗

Modeling of the Multiparameter Inverse Task of Transient Thermography

Transient thermography employs preheated surface temperature variations caused by delaminations, cracks, voids, corroded regions, etc. Often, it is enough to detect these changes to declare a defect in a workpiece. It is also desirable to obtain additional information about the defect from the thermal response. The planar size, depth, and thermal resistance of the detected defects are the parameters of interest. In this paper a digital image processing technique is applied to simulated thermal responses in order to obtain the geometry of the inclusion-type defects in a flat panel. A three-dimensional finite difference model in Cartesian coordinates is used for the numerical simulations. Typical physical properties of polymer graphite composites are assumed. Using different informative parameters of the thermal response for depth estimation is discussed.

Plotnikov, Y. A.↗