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At least 145 records · Page 8

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NASA NTRS1981

A three-dimensional turbulent compressible subsonic duct flow analysis for use with constructed coordinate systems

An approximate analysis is presented which is applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline. The primary flow direction is taken to coincide with the local direction of the duct centerline and is hence normal to transverse coordinate planes. The formulation utilizes vector components (velocity, vorticity, transport equations) defined in terms of local Cartesian directions aligned with the centerline tangent, although the governing equations themselves are expressed in general nonorthogonal coordinates. For curved centerlines, these vector quantities are redefined in new local Cartesian directions at each streamwise location. The use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation, and this provides for the aforementioned ease in using constructed coordinates.

Levy, R.↗

NASA NTRS1987

An Exponential Finite Difference Technique for Solving Partial Differential Equations

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.↗

NASA NTRS1988

Applications of an exponential finite difference technique

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Handschuh, Robert F.↗

NASA NTRS1991

Choice of velocity variables for complex flow computation

The issue of adopting the velocity components as dependent velocity variables for the Navier-Stokes flow computations is investigated. The viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form. With the use of Cartesian velocity vector, the momentum equations in curvilinear coordinates can retain the full conservation-law form and satisfy the physical conservation laws. With the curvilinear velocity components, source terms appear in differential equations and hence the full conservation law form can not be retained. In discrete expressions, algorithms based on the Cartesian components can satisfy the geometric conservation-law form for convection terms but not for viscous terms; those based on the curvilinear components, on the other hand, cannot satisfy the geometric conservation-law form for either convection or viscous terms. Several flow solutions for domain with 90 and 360 degree turnings are presented to illustrate the issues of using the Cartesian velocity components and the staggered grid arrangement.

Shyy, W.↗

NASA NTRS1992

Recognizing Patterns In Log-Polar Coordinates

Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.

Weiman, Carl F. R.↗

NASA NTRS1990

Dynamic model and cooperative control of a serially linked manipulator system

The use of a redundant manipulator to execute multiple tasks specified at different points on the manipulator is demonstrated. This is accomplished by decomposing a redundant arm at an intermediate arm location called the 'elbow' into two nonredundant local arms referred as the 'basearm' and the 'forearm'. This decomposition transforms a redundant arm into a serially linked dual-arm system, where the cooperation between the basearm and the forearm is carried out through the task distribution and the elbow control. The kinematics of a decomposed redundant manipulator are discussed, and a Cartesian space dynamic model and dynamic equation of a decomposed redundant manipulator are presented. The capability of generating Cartesian force, the local efficiency of generating Cartesian acceleration, and dynamic task distribution are discussed.

Lee, Sukhan↗

NASA NTRS1990

The Jet Propulsion Laboratory shared control architecture and implementation

A hardware and software environment for shared control of telerobot task execution has been implemented. Modes of task execution range from fully teleoperated to fully autonomous as well as shared where hand controller inputs from the human operator are mixed with autonomous system inputs in real time. The objective of the shared control environment is to aid the telerobot operator during task execution by merging real-time operator control from hand controllers with autonomous control to simplify task execution for the operator. The operator is the principal command source and can assign as much autonomy for a task as desired. The shared control hardware environment consists of two PUMA 560 robots, two 6-axis force reflecting hand controllers, Universal Motor Controllers for each of the robots and hand controllers, a SUN4 computer, and VME chassis containing 68020 processors and input/output boards. The operator interface for shared control, the User Macro Interface (UMI), is a menu driven interface to design a task and assign the levels of teleoperated and autonomous control. The operator also sets up the system monitor which checks safety limits during task execution. Cartesian-space degrees of freedom for teleoperated and/or autonomous control inputs are selected within UMI as well as the weightings for the teleoperation and autonmous inputs. These are then used during task execution to determine the mix of teleoperation and autonomous inputs. Some of the autonomous control primitives available to the user are Joint-Guarded-Move, Cartesian-Guarded-Move, Move-To-Touch, Pin-Insertion/Removal, Door/Crank-Turn, Bolt-Turn, and Slide. The operator can execute a task using pure teleoperation or mix control execution from the autonomous primitives with teleoperated inputs. Presently the shared control environment supports single arm task execution. Work is presently underway to provide the shared control environment for dual arm control. Teleoperation during shared control is only Cartesian space control and no force-reflection is provided. Force-reflecting teleoperation and joint space operator inputs are planned extensions to the environment.

Backes, Paul G.↗

NASA NTRS1994

On automating domain connectivity for overset grids

An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximated body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian Systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems.

Chiu, Ing-Tsau↗

NASA NTRS1995

On automating domain connectivity for overset grids

An alternative method for domain connectivity among systems of overset grids is presented. Reference uniform Cartesian systems of points are used to achieve highly efficient domain connectivity, and form the basis for a future fully automated system. The Cartesian systems are used to approximate body surfaces and to map the computational space of component grids. By exploiting the characteristics of Cartesian systems, Chimera type hole-cutting and identification of donor elements for intergrid boundary points can be carried out very efficiently. The method is tested for a range of geometrically complex multiple-body overset grid systems. A dynamic hole expansion/contraction algorithm is also implemented to obtain optimum domain connectivity; however, it is tested only for geometry of generic shapes.

Chiu, Ing-Tsau↗

NASA NTRS1996

The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations

A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.

Ku, Hwar-Ching↗

NASA NTRS1998

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable on-board computer resources.

Simpson, David G.↗

NASA NTRS1999

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

Simpson, David G.↗

NASA NTRS2012

Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis

An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant.

Ghrist, Richard W.↗

NASA NTRSDate not supplied

Advances in Automation of Overset Structured Volume Mesh Generation and Domain Connectivity

Automation of overset structured surface mesh generation has recently been accomplished by the creation of face, edge, and node meshes based on Boundary Representation solids as the geometry input. The current work continues the automation effort in overset volume mesh generation and domain connectivity based on the auto-generated surface meshes. All near-body curvilinear volume meshes are automatically generated using hyperbolic methods. Automation of this step is enabled by appropriate surface grid point distribution, and selection of boundary-splay and smoothing parameters based on concave and convex surface features. The off-body domain is covered by two automatically generated grid systems. The first contains a single Cartesian mesh with a uniform core enclosing all near-body volume meshes and stretched layers that extend to the far field, while the second consists of a set of small stretched Cartesian grids covering pockets of off-body orphan points. With high quality mesh overlap mostly guaranteed by the surface meshing scheme, orphan points that need to be covered by the second Cartesian mesh system are located away from the fine grid spacing region near the wall. Using line-segment and ray-pierce tests against the surface grids, hole-cutting is accomplished on both near and off-body volume grids resulting in appropriate clearances from the wall. The complete mesh generation automation process is demonstrated on five test cases where flow solutions are also computed and compared with solutions obtained using other methods.

TTT↗

NASA NTRS1944

A Solution of the Direct and Inverse Potential Problems for Arbitrary Cascades of Airfoils

Methods are given of determining the potential flow plast an arbitrary cascade of airfoils and the inverse problem of determining an airfoil having a prescribed velocity distribution in cascade. Results indicated that Cartesian mapping function method may be satisfactorily extended to include cascades. Numerical calculation for computing cascades by Cartesian mapping function method is considerably greater than for single airfoils but much less than hitherto required for cascades. Detailed results are presented graphically.

PRESSURE DISTRIBUTION - AIRFOILS↗

DOE OSTI2025

A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. In conclusion, we present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1971

Applications of laser ranging and VLBI observations for selenodetic control

The observation equations necessary to utilize lunar laser ranging and very long baseline interferometry measurements were developed for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The observation equations derived are based on a general model in which the unknown parameters included: the selenodetic Cartesian coordinates, the geocentric coordinates of earth stations, parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system, the parameters of the orientation of the average terrestrial coordinate system with respect to a fixed celestial coordinate system, and the geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris.

Fajemirokun, F. A.↗