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NASA NTRS2005

STEREO WAVES Capabilities for Studying Initiation and Early-time Dynamics of Solar Eruptions

In 2006, NASA will launch the twin STEREO spacecraft from Kennedy Space Center into a pair of heliocentric orbits near 1 AU such that the spacecraft will move away from Earth (ahead and behind) at about 22 degrees per year. The purposes of the STEREO Mission are to understand the causes and mechanisms of coronal mass ejection (CME) initiation and to follow the propagation of CMEs through the heliosphere. Additionally, STEREO will study the mechanisms and sites of solar energetic particle (SEP) acceleration and determine 3-D time-dependent traces of the magnetic topology, temperature, density and velocity of the solar wind between the sun and Earth. To accomplish these goals, each STEREO spacecraft will be equipped with set of optical and particles and fields instruments including the STEREO WAVES (SWAVES) instrument which will use radio waves to track the location of CME-driven shocks (via type I1 bursts) and the 3-D topology of open field lines along which energetic particles flow (via the ubiquitous type I11 bursts). Type 11 bursts very often commence with a series of special type 111 bursts (called SA or type 111-L bursts) that likely coincide with CME liftoff time, thus SWAVES should be able to determine this time to within 15 sec. It is also known that the occurrence of SEP events is usually accompanied by type I1 radio bursts at decametric wavelengths as well as strong type III bursts at all wavelengths. SWAVES will be able to determine the initiation of these bursts to within 15 sec, and from the simultaneous measurements from the two spacecraft, should be able to triangulate their source locations. The utility of radio observations and the capabilities of SWAVES will be illustrated by showing a number of examples using the similar Wind WAVES instrument in combination with SOH0 coronagraph and RHESSI high energy X-ray/gamma ray observations.

Kaiser, M. L.↗

NASA NTRS1988

A stereo triangulation system for structural identification: Analytical and experimental results

Identification of large space structures' distributed mass, stiffness, and energy dissipation characteristics poses formidable analytical, numerical, and implementation difficulties. Development of reliable on-orbit structural identification methods is important for implementing active vibration suppression concepts which are under widespread study in the large space structures community. Near the heart of the identification problem lies the necessity of making a large number of spatially distributed measurements of the structure's vibratory response and the associated force/moment inputs with sufficient spatial and frequency resolution. In the present paper, we discuss a method whereby tens of active or passive (retro-reflecting) targets on the structure are tracked simultaneously by the focal planes of two or more video cameras mounted on an adjacent platform. Triangulation (optical ray intersection) of the conjugate image centroids yield inertial trajectories of each target on the structure. Given the triangulated motion of the targets, we apply and extend methodology developed by Creamer, Junkins, and Juang to identify the frequencies, mode shapes, and updated estimates for the mass/stiffness/damping parameterization of the structure. The methodology is semi-automated, for example, the post experiment analysis of the video imagery to determine the inertial trajectories of the targets typically requires less than thirty minutes of real time. Using methodology discussed herein, the frequency response of a large number of points on the structure (where reflective targets are mounted) on the structure can be determined from optical measurements alone. For comparison purposes, we also utilize measurements from accelerometers and a calibrated impulse hammer. While our experimental work remains in a research stage of development, we have successfully tracked and stereo triangulated 20 targets (on a vibrating cantilevered grid structure) at a sample frequency of 200 HZ, and have established conclusively the feasibility and desirability of this approach. We discuss, in summary, recent advances in analog and digital video processing methodology, actuation methods, and bring them to bear on the structural identification problem. We include a brief discussion of our experimental hardware and some recent experimental results which support the practical feasibility of this structural vibration sensing approach.

Junkins, J. L.↗

NASA NTRSDate not supplied

Derivation of Effective Properties Based on Porous Scale Simulations Using Filtering Techniques

This study presents a method for derivation of effective properties at the interface and in-depth of porous materials. The method defines a Representative Elementary Volume (REV) and applies filtering techniques to computer effective properties such as porosity and flow quantities, such as velocity and pressure. The script, developed to process the data was tested on the VTK type files that contain the mesh information and the flow solution. The method allows to choose between two types of filters, such as cellular and top-hat and define the size of the REV and number of samples along the domain. Extraction of the REV from the domain is performed to exact boundaries requested for the user. This is done using a triangulation technique and cutting through the cells to comply to the requested boundaries of the volume. The method can be applied to both structured and unstructured meshes. Filtering the material porosity and flow quantities involves integration of the numerical data. The algorithm provides three integration methods, such as Riemann sum, Monte Carlo and Quadrature rule to perform the integration. The Monte-Carlo technique permits the use of either uniform or linearly spaced distribution of points. The Quadrature rule is currently applicable to tetrahedral element types. The Monte Carlo and Quadrature rule methods require interpolation of the flow quantities at the sample points. For interpolation, two methods were tested and are readily available, Gaussian interpolation and re-sampling. It has been shown that re-sampling method has better consistency and acceptable accuracy in interpolation of the data. The algorithm was written in Python language and uses a number of modules. The major module besides numpy is PyVista. It is used to process the computational domain, clip the REV and interpolate the data. Quadrature rule integration was performed using a quadpy module. ParaView software was used externally to convert the flow solution to the VTK (or more specifically VTU) format. Integration of ParaView in the same environment with PyVista encountered problems and could not be implemented in this work. The developed algorithm is expected to be applicable to unstructured meshes and more complex porous structures as soon as the data can be passed in VTK type format. With the report is provided Python script for filtering the solution and a Matlab script for simple generation and processing of 2-D and 3-D porous channel geometries. The two scripts don't communicate.

Alexsander Zibitsker↗

NASA NTRS1974

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

Saxena, N. K.↗

NASA NTRS1975

Effects of various experimental parameters on errors in triangulation solution of elongated object in space

The effects of various experimental parameters on the displacement errors in the triangulation solution of an elongated object in space due to pointing uncertainties in the lines of sight have been determined. These parameters were the number and location of observation stations, the object's location in latitude and longitude, and the spacing of the input data points on the azimuth-elevation image traces. The displacement errors due to uncertainties in the coordinates of a moving station have been determined as functions of the number and location of the stations. The effects of incorporating the input data from additional cameras at one of the stations were also investigated.

Long, S. A. T.↗

NASA NTRS2000

Preliminary Study of a Model Rotor in Descent

Within a program designed to develop experimental techniques for measuring the trajectory and structure of vortices trailing from the tips of rotor blades, the present preliminary study focuses on a method for quantifying the trajectory of the trailing vortex during descent flight conditions. This study also presents rotor loads and blade surface pressures for a range of tip-path plane angles and Mach numbers. Blade pressures near the leading edge and along the outer radius are compared with data obtained on the same model rotor, but in open jet facilities. A triangulation procedure based on two directable laser-light sheets, each containing an embedded reference, proved effective in defining the spatial coordinates of the trailing vortex. When interrogating a cross section of the flow that contains several trailing vortices, the greatest clarity was found to result when the flow is uniformly seeded. Surface pressure responses during blade-vortex interactions appeared equally sensitive near the leading edge and along the outer portion of the blade, but diminished rapidly as the distance along the blade chord increased. The pressure response was virtually independent of whether the tip-path plane angle was obtained through shaft tilt or cyclic pitch. Although the shape and frequency of the pressure perturbations on the advancing blade during blade-vortex interaction are similar to those obtained in open-jet facilities, the angle of the tip-path plane may need to be lower than the range covered in this study.

McAlister, K. W.↗

NASA NTRS1992

Adaptive remeshing for three-dimensional compressible flow computations

A practical solution algorithm for steady 3D Euler flows is presented. This algorithm employs coupling of a surface triangulator, an automatic tetrahedral mesh generator, an unstructured grid flow solver, and an error estimation procedure. The performance of the method is illustrated using a shock interaction problem in high Mach number flow over a swept circular cylinder.

Peraire, J.↗

NASA NTRS1999

Location and Geologic Setting for the Three U.S. Mars Landers

Super resolution of the horizon at both Viking landing sites has revealed "new" features we use for triangulation, similar to the approach used during the Mars Pathfinder Mission. We propose alternative landing site locations for both landers for which we believe the confidence is very high. Super resolution of VL-1 images also reveals some of the drift material at the site to consist of gravel-size deposits. Since our proposed location for VL-2 is NOT on the Mie ejecta blanket, the blocky surface around the lander may represent the meter-scale texture of "smooth palins" in the region. The Viking Lander panchromatic images typically offer more repeat coverage than does the IMP on Mars Pathfinder, due to the longer duration of these landed missions. Sub-pixel offsets, necessary for super resolution to work, appear to be attributable to thermal effects on the lander and settling of the lander over time. Due to the greater repeat coverage (particularly in the near and mid-fields) and all-panchromatic images, the gain in resolution by super resolution processing is better for Viking than it is with most IMP image sequences. This enhances the study of textural details near the lander and enables the identification rock and surface textures at greater distances from the lander. Discernment of stereo in super resolution im-ages is possible to great distances from the lander, but is limited by the non-rotating baseline between the two cameras and the shorter height of the cameras above the ground compared to IMP. With super resolution, details of horizon features, such as blockiness and crater rim shapes, may be better correlated with Orbiter images. A number of horizon features - craters and ridges - were identified at VL-1 during the misison, and a few hils and subtle ridges were identified at VL-2. We have added a few "new" horizon features for triangulation at the VL-2 landing site in Utopia Planitia. These features were used for independent triangulation with features visible in Viking Orbiter and MGS MOC images, though the actual location of VL-1 lies in a data dropout in the MOC image of the area. Additional information is contained in the original extended abstract.

Parker, T. J.↗

NASA NTRS1994

Incremental triangulation by way of edge swapping and local optimization

This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve(s), refine existing triangulations based on solution error measures, and partition meshes based on the Cuthill-McKee, spectral, and coordinate bisection strategies.

Wiltberger, N. Lyn↗

NASA NTRSDate not supplied

Considerations for Optimal Sensor Placement for Higher Accuracy Object Localization for Urban Air Mobility

Previous research into object localization has shown that sensor placement and alignment plays an important role in achieving higher accuracy levels of the estimated location of a tracked Urban Air Mobility Vehicle. In general, a near-orthogonal intersection between the ground node observation vectors results in the highest accuracy due to a smaller overlapping uncertainty region between both. This applies to triangulation by means of ground node camera angle observations as well as trilateration by means of ground node distance measurements. However, this simple concept is not easily fulfilled with a network of a limited number of static ground nodes and a moving object to be localized. This case study performs sensitivity analyses and explores practical ways on how to achieve higher estimate accuracy levels in this context.

sensor placement↗

NASA NTRS2025

Considerations for Optimal Sensor Placement for Higher Accuracy Object Localization for Urban Air Mobility

sensor placement↗

NASA NTRS1977

Contouring randomly spaced data

Computer program using triangulation contouring technique contours data points too numerous to fit into rectangular grid. Using random access procedures, program can handle up to 56,000 data points and provides up to 20 contour intervals for multiple number of parameters.

Kibler, J. F.↗

NASA NTRS1994

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Jorgenson, Philip C. E.↗

NASA NTRS1978

The control net of Mars - May 1977

The development of planet-wide control nets of Mars is reviewed, and the May 1977 update is described. This updated control net was computed by means of a large single-block analytical triangulation incorporating the new direction of the spin axis and the new rotation rate of Mars, as determined from radio tracking data provided by the Viking lander spacecraft. The analytical triangulation adjusts for planimetric control only (areocentric latitude and longitude) and for the camera orientation angles. Most of the areocentric radii at the control points were interpolated from radio occultation measurements, but a few were determined photogrammetically, and a substantial number were derived from elevation contours on the 1976 USGS topographic series of Mars maps. A value of V, measured from Mars' vernal equinox along the equator to the prime meridian (Airy-0) is presented.

Davies, M. E.↗

NASA NTRS1995

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗

NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

NASA NTRS2000

Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications

A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.

Marcum, David L.↗

NASA NTRS1978

Detection of horizontal crustal movements by photogrammetric methods

The photogrammetric methods can be applied only if the horizontal displacements of the ground are of the order of several centimeters, because the standard error of the points so determined cannot, at the present time, be smaller than two centimeters. The procedure to be adopted, which has already been applied with satisfactory results for the densification of geodetic nets, is the aerial analytical triangulation. The taking can be executed with wide-angle cameras (f = 15 cm), or normal-angle cameras (f = 30 cm) and format 23 x 23 cm. Since the average scale of photos must be chosen in relation with the desired accuracy and then is independent of the principal distance of the cameras, the number of photos is constant, whereas the flying height varies according to the focal length.

Solaini, L.↗