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NASA NTRS1989

The perception of geometrical structure from congruence

The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.

Lappin, Joseph S.↗

NASA NTRS2003

Numerical and Experimental Determination of the Geometric Far Field for Round Jets

To reduce ambiguity in the reporting of far field jet noise, three round jets operating at subsonic conditions have recently been studied at the NASA Glenn Research Center. The goal of the investigation was to determine the location of the geometric far field both numerically and experimentally. The combination of the WIND Reynolds-Averaged Navier-Stokes solver and the MGBK jet noise prediction code was used for the computations, and the experimental data was collected in the Aeroacoustic Propulsion Laboratory. While noise sources are distributed throughout the jet plume, at great distances from the nozzle the noise will appear to be emanating from a point source and the assumption of linear propagation is valid. Closer to the jet, nonlinear propagation may be a problem, along with the known geometric issues. By comparing sound spectra at different distances from the jet, both from computational methods that assume linear propagation, and from experiments, the contributions of geometry and nonlinearity can be separately ascertained and the required measurement distance for valid experiments can be established. It is found that while the shortest arc considered here (approx. 8D) was already in the geometric far field for the high frequency sound (St greater than 2.0), the low frequency noise due to its extended source distribution reached the geometric far field at or about 50D. It is also found that sound spectra at far downstream angles does not strictly scale on Strouhal number, an observation that current modeling does not capture.

Koch, L. Danielle↗

NASA NTRS2006

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Hrinda, Glenn A.↗

NASA NTRS2006

CAPRI: A Geometric Foundation for Computational Analysis and Design

CAPRI is a software building tool-kit that refers to two ideas; (1) A simplified, object-oriented, hierarchical view of a solid part integrating both geometry and topology definitions, and (2) programming access to this part or assembly and any attached data. A complete definition of the geometry and application programming interface can be found in the document CAPRI: Computational Analysis PRogramming Interface appended to this report. In summary the interface is subdivided into the following functional components: 1. Utility routines -- These routines include the initialization of CAPRI, loading CAD parts and querying the operational status as well as closing the system down. 2. Geometry data-base queries -- This group of functions allow all top level applications to figure out and get detailed information on any geometric component in the Volume definition. 3. Point queries -- These calls allow grid generators, or solvers doing node adaptation, to snap points directly onto geometric entities. 4. Calculated or geometrically derived queries -- These entry points calculate data from the geometry to aid in grid generation. 5. Boundary data routines -- This part of CAPRI allows general data to be attached to Boundaries so that the boundary conditions can be specified and stored within CAPRI s data-base. 6. Tag based routines -- This part of the API allows the specification of properties associated with either the Volume (material properties) or Boundary (surface properties) entities. 7. Geometry based interpolation routines -- This part of the API facilitates Multi-disciplinary coupling and allows zooming through Boundary Attachments. 8. Geometric creation and manipulation -- These calls facilitate constructing simple solid entities and perform the Boolean solid operations. Geometry constructed in this manner has the advantage that if the data is kept consistent with the CAD package, therefore a new design can be incorporated directly and is manufacturable. 9. Master Model access This addition to the API allows for the querying of the parameters and dimensions of the model. The feature tree is also exposed so it is easy to see where the parameters are applied. Calls exist to allow for the modification of the parameters and the suppression/unsuppression of nodes in the tree. Part regeneration is performed by a single API call and a new part becomes available within CAPRI (if the regeneration was successful). This is described in a separate document. Components 1-7 are considered the CAPRI base level reader.

Haimes, Robert↗

NASA NTRS2012

NPP VIIRS Early On-Orbit Geometric Performance

The NASA/NOAA Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the Suomi National Polar-orbiting Partnership (NPP) satellite was launched in October, 2011. The instrument geometric performance includes sensor spatial response, band-to-band co-registration (BBR), and geolocation accuracy and precision. The geometric performance is an important aspect of sensor data record (SDR) calibration and validation. In this paper we will discuss geometric performance parameter characterization using the first seven-month of VIIRS' earth and lunar data, and compare with the at-launch performance using ground testing data and analysis of numerical modeling results as the first step in on-orbit geometric calibration and validation.

Wolfe, Robert E.↗

NASA NTRSDate not supplied

Modeling and Sensitivity Analysis of Sandwich Composite Cylinders with Geometric Imperfections

It is well known that real shell structures can have significantly lower buckling loads and even different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The realistic buckling response can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.

Structural Modeling↗

NASA NTRSDate not supplied

Modeling and Sensitivity Analysis of Sandwich Composite Cylinders with Geometric Imperfections

It is well known that manufactured shell structures can have significantly lower buckling loads and different mode shapes than the theoretical predictions for perfect structures. Much of this difference can be attributed to geometric and loading imperfections, and geometrically nonlinear effects. The buckling response of cylindrical structures can be investigated using geometrically nonlinear finite element analyses and including radial imperfections. Such analyses are used in the NASA Engineering and Safety Center Shell Buckling Knockdown Factor Project, which has the goal of developing new analysis-based buckling design recommendations for select classes of cylindrical shell structures under uniaxial compressive load. The approach for modeling several sandwich composite cylinders with two-dimensional general-purpose shell elements and the influence of the element type selection and element size on the buckling load is discussed. The influence of geometric imperfections of various magnitudes on buckling behavior of a sandwich composite cylinder was also investigated.

Structural Modeling↗

NASA NTRSDate not supplied

: Modeling and Sensitivity Analysis of Sandwich Composite Cylinders with Geometric Imperfections

Structural Modeling↗

NASA NTRSDate not supplied

Experimental Characterization of Surface Roughness and Geometric Evaluations of Thin-Wall Laser Powder Directed Energy Deposition

Additive Manufacturing (AM) has offered many new design and manufacturing opportunities for components across various industries. As AM evolves there is a need to better understand outputs of the process including geometric limitations and surface roughness based on specific application requirements. One possible application area of AM are components using thin-wall (<2 mm) microchannel heat exchangers for subsystems across aerospace, and industrial applications. AM offers the opportunity to significantly reduce the cost and lead time associated with fabricating these complex parts with internal features such as an array of cooling channels. Laser Powder Bed Fusion (L-PBF) has been continuously demonstrated as a technique to fabricate heat exchangers with internal geometric complexities. However, L-PBF is limited in the scale at which parts can be fabricated. Laser Powder Directed Energy Deposition (LP-DED) has been demonstrated as an AM technology to significantly increase the scale of which thin-wall microchannel heat exchangers could be manufactured. Successful deployment of the LP-DED technology requires critical understanding of the resulting features from the build process. Surface roughness is one of the critical areas that effects the friction factor and pressure drop within a heat exchanger and must be well understood. This presentation will provide an overview of the characterization work completed to understand the LP-DED process for thin-walls representative of hydrogen resistant alloy NASA HR-1 that would be used in a Hydrogen-environment application. An overview of the experiments conducted with varying LP-DED parameters, evaluation of various geometric channel and geometric build features and resulting surface finish will be provided along with a summary of conclusions from these experiments. Results indicate that powder size is a major contributor and surface roughness varies between closed channel shapes and external surfaces.

Directed Energy Deposition↗

NASA NTRSDate not supplied

NASA HECC Geometry and Performance Review Part 2: Geometric Differences Between the as-Manufactured and Design-Intent Impeller Geometry and Their Effects on the Vaneless Diffuser Configuration Performance

An investigation of the NASA High Efficiency Centrifugal Compressor (HECC) vaneless diffuser configuration was performed. This multipart investigation focused on validating the computational model against experimental data. The validated model was then used to explore the effects of observed geometric differences between the as-manufactured and design-intent impellers. Lastly, the validated model was used for comparison against an experimental tip clearance study. Details regarding each of the parts are detailed below: This second part of a multipart investigation of the NASA HECC vaneless diffuser configuration focused on the comparison of the as-manufactured HECC vaneless computational model validated in Part I against a new model that used the same grid and solver settings but replaced the impeller section data with the design-intent sections from NASA/CR-2014-218114/Rev1. The 1D performance values showed that the as-manufactured impeller underperformed compared to the design-intent for all four speedlines that were simulated. Further investigation of radial profiles, loading and contours showed consistent underperformance of the as-manufactured. An investigation into the source of the difference led to the discovery of several geometric differences in the two impellers of magnitudes that could not be explained outside of manufacturing. The differences that were observed can be summarized into four categories: fillets, TE exit radius differences, splitter LE differences and main blade thickness differences. The investigation then shifted to attempting to isolate the geometric differences as best as possible and to understand their contribution to the observed underperformance. The investigation showed that out of the four geometric differences that were explored, the differences in the splitter blade had the largest effect.

centrifugal compressor↗

NASA NTRS2000

In-flight Geometric Calibration Plan

This MISR in-flight Geometric Calibration (IGC) Plan describes the concept, development strategy and operational design to be used for geometric calibration of the instrument and for producing the Geometric Calibration Dataset (GCD) which is required as an input to the L1B2 standard processing.

geometric in-flight calibration plan↗

NASA NTRS1971

The geometric factor of a cylindrical plate electrostatic analyzer

A method for calculating the geometric factor of cylindrical plate electrostatic energy analyzers with various detector geometries is described. The effects of the fringe-field are estimated. For a special simple case an exact geometric factor is calculated enabling an estimate of the inaccuracies of the approximations used in other cases. The results of some calculations are presented and a simple approximate expression for the geometric factor is deduced.

Johnstone, A. D.↗

NASA NTRS1972

The geometric factor of a cylindrical plate electrostatic analyzer.

A method for calculating the geometric factor of cylindrical plate electrostatic energy analyzers with various detector geometries is described. The effects of the fringe field are estimated. For a special simple case an exact geometric factor is calculated, enabling an estimate to be made of the inaccuracies of the approximations used in other cases. The results of some calculations are presented, and a simple approximate expression for the geometric factor is deduced.

Johnstone, A. D.↗

NASA NTRS1972

On the geometric analysis and adjustment of optical satellite observations

Satellite geodesy methods were catagorized into three divisions: geometric, dynamic, and mixed. These catagories furnish the basis for distinction between geometric and dynamic satellite geodesy. The dual adjustment, geometric analysis, and Cartesian coodinate determination are examined for two observing stations. Similar illustrations are given when more than two observing stations are used.

Tsimis, E.↗

NASA NTRS1974

Geometric distortions of autocollimation type scanners

One criterion of image quality is its geometric similarity to the control test. The ability of television, phototelevision, phototelegraphic, and other systems to transmit geometrically similar images is characterized by the geometric distortion coefficient. Linear distortions result from the inaccuracy of scanning mechanism element assembly, and distortions can be minimized during adjustment operations or may be easily compensated during image reception. Brief descriptions are given of the possible sources of nonlinear distortions which arise in these devices due to the scanning mechanism, objective distortion, or the nodding mirror.

Narayeva, M. K.↗

NASA NTRS1974

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures of slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.

Pathak, P. H.↗

NASA NTRS1975

Geometrical procedures for the analysis of spacecraft attitude and bias determinability

Geometrical procedures are presented for predicting the determinability of spacecraft attitude and bias parameters. An analysis is presented on three common attitude measurements: sun angle, nadir angle, and sun-to-earth mid-scan rotation angle. First, the geometry of these measurements is considered for an arbitrary fixed location of the spacecraft; then the effect of orbital motion is analyzed. The results are summarized in a set of simple geometrical rules. The application of these rules to the Synchronous Meteorological Satellite-2 (SMS-2) is discussed. As a result of this geometrical analysis, modifications were made to the SMS-2 bias determination schedule which substantially enhanced the determinability of attitude sensor biases.

Wertz, J. R.↗

NASA NTRS1979

Simplified and refined finite element approaches for determining stresses and internal forces in geometrically nonlinear structural analysis

Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.

Robinson, J. C.↗