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Results for “Convex geometry”

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NASA NTRS1974

Proton dose approximation in arbitrary convex geometry

An expansion is derived for the solution to the transport equation in two dimensions subject to boundary conditions given for an arbitrary convex region. Questions of high-energy transport are considered along with the properties of the dose response function. The expansion of the solution of the transport equation is presented in terms of a parameter which measures the lateral dispersion of an unidirectional beam. This parameter is usually small and the expansion is expected to converge rapidly. The dominant term in the expansion is related to fluence-to-dose conversion factors in a semiinfinite slab for normal incidence. A convenient parameterization of the conversion factors is provided along with numerical examples.

Wilson, J. W.↗

NASA NTRS1993

Automating spectral unmixing of AVIRIS data using convex geometry concepts

Spectral mixture analysis, or unmixing, has proven to be a useful tool in the semi-quantitative interpretation of AVIRIS data. Using a linear mixing model and a set of hypothesized endmember spectra, unmixing seeks to estimate the fractional abundance patterns of the various materials occurring within the imaged area. However, the validity and accuracy of the unmixing rest heavily on the 'user-supplied' set of endmember spectra. Current methods for emdmember determination are the weak link in the unmixing chain.

Boardman, Joseph W.↗

NASA NTRS1993

Determination of semi-arid landscape endmembers and seasonal trends using convex geometry spectral unmixing techniques

Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data were acquired during three consecutive growing seasons (26 September 1989, 22 March 1990, and 7 August 1990) over an area of the High Plains east of Greeley, Colorado (40 deg 20 min N and 104 deg 16 min W). A repeat visit to assess vegetation at its peak growth was flown on 6 June 1993. This region contains extensive eolian deposits in the form of stabilized dune complexes (small scale parabolic dunes superimposed on large scale longitudinal and parabolic dunes). Due to the dunes' large scale (2-10 km) and low relief (1-5 m), the scaling and morphological relationships that contribute to the evolution of this landscape are nearly impossible to understand without the use of remote sensing. Additionally, this area and regions similarly situated could be the first to experience the effects caused by global climate change. During the past 10,000 years there were at least four periods of extensive sand activity due to climate change, followed by periods of landscape stability, as shown in the stratigraphic record of this area.

Yuhas, Roberta H.↗

NASA NTRS2001

Laminarization of Turbulent Boundary Layer on Flexible and Rigid Surfaces

An investigation of the control of turbulent boundary layer flow over flexible and rigid surfaces downstream of a concave-convex geometry has been made. The concave-convex curvature induces centrifugal forces and a pressure gradient on the growth of the turbulent boundary layer. The favorable gradient is not sufficient to overcome the unfavorable; thus, the net effect is a destabilizing, of the flow into Gortler instabilities. This study shows that control of the turbulent boundary layer and structural loading can be successfully achieved by using localized surface heating because the subsequent cooling and geometrical shaping downstream over a favorable pressure gradient is effective in laminarization of the turbulence. Wires embedded in a thermally insulated substrate provide surface heating. The laminarized velocity profile adjusts to a lower Reynolds number, and the structure responds to a lower loading. In the laminarization, the turbulent energy is dissipated by molecular transport by both viscous and conductivity mechanisms. Laminarization reduces spanwise vorticity because of the longitudinal cooling gradient of the sublayer profile. The results demonstrate that the curvature-induced mean pressure gradient enhances the receptivity of the flow to localized surface heating, a potentially viable mechanism to laminarize turbulent boundary layer flow; thus, the flow reduces the response of the flexible structure and the resultant sound radiation.

Maestrello, Lucio↗

NASA NTRS2010

Modeling Neutral Densities Downstream of a Gridded Ion Thruster

The details of a model for determining the neutral density downstream of a gridded ion thruster are presented. An investigation of the possible sources of neutrals emanating from and surrounding a NEXT ion thruster determined that the most significant contributors to the downstream neutral density include discharge chamber neutrals escaping through the perforated grids, neutrals escaping from the neutralizer, and vacuum facility background neutrals. For the neutral flux through the grids, near- and far-field equations are presented for rigorously determining the neutral density downstream of a cylindrical aperture. These equations are integrated into a spherically-domed convex grid geometry with a hexagonal array of apertures for determining neutral densities downstream of the ion thruster grids. The neutrals escaping from an off-center neutralizer are also modeled assuming diffuse neutral emission from the neutralizer keeper orifice. Finally, the effect of the surrounding vacuum facility neutrals is included and assumed to be constant. The model is used to predict the neutral density downstream of a NEXT ion thruster with and without neutralizer flow and a vacuum facility background pressure. The impacts of past simplifying assumptions for predicting downstream neutral densities are also examined for a NEXT ion thruster.

Soulas, George C.↗

NASA NTRS1986

Transition mixing study

A computer model capable of analyzing the flow field in the transition liner of small gas turbine engines is developed. A FORTRAN code has been assembled from existing codes and physical submodels and used to predict the flow in several test geometries which contain characteristics similar to transition liners, and for which experimental data was available. Comparisons between the predictions and measurements indicate that the code produces qualitative results but that the turbulence models, both K-E and algebraic Reynolds Stress, underestimate the cross-stream diffusion. The code has also been used to perform a numerical experiment to examine the effect of a variety of parameters on the mixing process in transition liners. Comparisons illustrate that geometries with significant curvature show a drift of the jet trajectory toward the convex wall and weaker wake region vortices and decreased penetration for jets located on the convex wall of the liner, when compared to jets located on concave walls. Also shown were the approximate equivalency of angled slots and round holes and a technique by which jet mixing correlations developed for rectangular channels can be used for can geometries.

Reynolds, R.↗

NASA NTRS1993

IGES transformer and NURBS in grid generation

In the field of Grid Generation and the CAD/CAM, there are numerous geometry output formats which require the designer to spend a great deal of time manipulating geometrical entities in order to achieve a useful sculptured geometrical description for grid generation. Also in this process, there is a danger of losing fidelity of the geometry under consideration. This stresses the importance of a standard geometry definition for the communication link between varying CAD/CAM and grid system. The IGES (Initial Graphics Exchange Specification) file is a widely used communication between CAD/CAM and the analysis tools. The scientists at NASA Research Centers - including NASA Ames, NASA Langley, NASA Lewis, NASA Marshall - have recognized this importance and, therefore, in 1992 they formed the committee of the 'NASA-IGES' which is the subset of the standard IGES. This committee stresses the importance and encourages the CFD community to use the standard IGES file for the interface between the CAD/CAM and CFD analysis. Also, two of the IGES entities -- the NURBS Curve (Entity 126) and NURBS Surface (Entity 128) -- which have many useful geometric properties -- like the convex hull property, local control property and affine invariance, also widely utilized analytical geometries can be accurately represented using NURBS. This is important in today grid generation tools because of the emphasis of the interactive design. To satisfy the geometry transformation between the CAD/CAM system and Grid Generation field, the CAGI (Computer Aided Geometry Design) developed, which include the Geometry Transformation, Geometry Manipulation and Geometry Generation as well as the user interface. This paper will present the successful development IGES file transformer and application of NURBS definition in the grid generation.

Yu, Tzu-Yi↗

NASA NTRS2004

Geomorphology of Ma'adim Vallis, Mars,and Associated Paleolake Basins

Ma'adim Vallis, one of the largest valleys in the Martian highlands, appears to have originated by catastrophic overflow of a large paleola ke located south of the valley heads. Ma'adim Vallis debouched to Gus ev crater, 900 km to the north, the landing site for the Spirit Mars Exploration Rover. Support for the paleolake overflow hypothesis come s from the following characteristics: (I) With a channel width of 3 km at its head, Ma'adim Vallis originates at two (eastern and western) gaps incised into the divide of the approximately 1.1 M km(exp 2) enc losed Eridania head basin, which suggests a lake as the water source. (2) The sinuous course of Ma'adim Vallis is consistent with overland flow controlled by preexisting surface topography, and structural con trol is not evident or required to explain the valley course. (3) The nearly constant approximately 5 km width of the inner channel through crater rim breaches, the anastomosing course of the wide western tri butary, the migration of the inner channel to the outer margins of be nds in the valley's lower reach, a medial sedimentary bar approximate ly 200 m in height, and a step-pool" sequence are consistent with modeled flows of 1-5 x l0 (exp 6) m(exp 3)/s. Peak discharges were likely higher but are poorly constrained by the relict channel geometry. (4 ) Small direct tributary valleys to Ma'adim Vallis have convex-up lon gitudinal profiles, suggesting a hanging relationship to a valley that was incised quickly relative to the timescales of tributary developm ent. (5) The Eridania basin had adequate volume between the initial d ivide and the incised gap elevations to carve Ma'adim Vallis during a single flood. (6) The Eridania basin is composed of many overlapping , highly degraded and deeply buried impact craters. The floor materials of the six largest craters have an unusually high internal relief ( approximately 1 km) and slope (approximately 0.5-1.5 degrees) among d egraded Martian craters, which are usually flat-floored. Long-term, fluvial sediment transport appears to have been inhibited within these craters, and the topography is inconsistent with basaltic infilling. (7) Fluvial valleys do not dissect the slopes of these deeper crater floor depressions, unlike similar slopes that are dissected at higher levels in the watershed. These characteristics (6, 7) suggest that wa ter mantled at least the lower parts of the Eridania basin floor thro ughout the period of relatively intense erosion early in Martian hist ory. The lake level increased and an overflow occurred near the close of the Noachian (age determined using >5 km crater counts). Initially , the Eridania basin debouched northward at two locations into the in termediate basin, a highly degraded impact crater approximately 500 k m in diameter. As this intermediate basin was temporarily filled with water, erosion took place first along the lower (northern) reach of Ma'adim Vallis, debouching to Gusev crater. The western overflow point was later abandoned, and erosion of the intermediate basin interior was concentrated along the eastern pathway. Subsequent air fall depos ition, impact gardening, tectonism, and limited fluvial erosion modified the Eridania basin region, so evidence for a paleolake is restrict ed to larger landforms that could survive post-Noachian degradation p rocesses.

Irwin, Rossman, P., III↗

NASA NTRS2010

Streamwise Vortices on the Convex Surfaces of Circular Cylinders and Turbomachinery Blading

In assessing the results please recall that the Mach number regimes and model geometries differ considerably. Selection of the radius of curvature at the 10% chord location is consistent but arbitrary, although it does seem representative for most blades and gives a good fit for the results. Measured spanwise wavelengths of the periodic vortex arrays on blading are predicted well by the Kestin and Wood theory. If this behavior is at all common it could have implications for turbine aerodynamic and blade cooling design. The outcome is to establish that organized streamwise vorticity may occur more frequently on convex surfaces, such as turbine blade suction surfaces, than hitherto appreciated. Investigations and predictions of flow behavior should be extended to encompass that possibility.

Gostelow, Paul↗

NASA NTRS1988

Convex-profile inversion of asteroid lightcurves - Theory and applications

A theory for asteroid light curve interpretation is derived from the reformulation, extension, and calibration of Ostro and Connely's (1984) convex-profile inversion, and then used to constrain the shapes of selected asteroids. The ideal conditions for the estimation of an asteroid's main cross-section from a light curve are (1) that the viewing-illumination geometry be equatorial, (2) that the scattering be uniform and geometric, (3) that the asteroid surface contours parallel to the equatorial plane be convex, (4) and that the solar angle not equal zero. Results are presented from simulations calibrating the kind, severity, and predictability of systematic errors.

Ostro, Steven J.↗

NASA NTRS1980

Turbulent boundary layer on a convex, curved surface

The effects of strong convex curvature on boundary layer turbulence were investigated. The data gathered on the behavior of Reynolds stress suggested the formulation of a simple turbulence model. Three sets of data were taken on two separate facilities. Both rigs had flow from a flat surface, over a convex surface with 90 deg of turning, and then onto a flat recovery surface. The geometry was adjusted so that, for both rigs, the pressure gradient along the test surface was zero - thus avoiding any effects of streamwise acceleration on the wall layers. Results show that after a sudden introduction of curvature, the shear stress in the outer part of the boundary layer is sharply diminished and is even slightly negative near the edge. The wall shear also drops off quickly downstream. In contrast, when the surface suddenly becomes flat again, the wall shear and shear stress profiles recover very slowly towards flat wall conditions.

Gillis, J. C.↗

NASA NTRS1981

Experimental data and model for the turbulent boundary layer on a convex, curved surface

Experiments were performed to determine how boundary layer turbulence is affected by strong convex curvature. The data gathered on the behavior of the Reynolds stress suggested the formulation of a simple turbulence model. Data were taken on two separate facilities. Both rigs had flow from a flat surface, over a convex surface with 90 deg of turning and then onto a flat recovery surface. The geometry was adjusted so that, for both rigs, the pressure gradient along the test surface was zero. Two experiments were performed at delta/R approximately 0.10, and one at weaker curvature with delta/R approximately 0.05. Results show that after a sudden introduction of curvature the shear stress in the outer part of the boundary layer is sharply diminished and is even slightly negative near the edge. The wall shear also drops off quickly downstream. When the surface suddenly becomes flat again, the wall shear and shear stress profiles recover very slowly towards flat wall conditions. A simple turbulence model, which was based on the theory that the Prandtl mixing length in the outer layer should scale on the velocity gradient layer, was shown to account for the slow recovery.

Gillis, J. C.↗

NASA NTRS1987

Structural optimization of an alternate design for the space shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the shuttle solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in. diameter and 135 studs of 1 3/16 in. diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonliner displacement analysis. The minimum weight design has 135 studs of 1 3/16 in. diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, J.-F. M.↗

NASA NTRS1987

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, Jean-Francois M.↗

NASA NTRS2000

Computerized Generation and Simulation of Meshing and Contact of New Type of Novikov-Wildhaber Helical Gears

In this report, we propose a new geometry for low-noise, increased-strength helical gears of the Novikov-Wildhaber type. Contact stresses are reduced as a result of their convex-concave gear tooth surfaces. The gear tooth surfaces are crowned in the profile direction to localize bearing contact and in the longitudinal direction to obtain a parabolic function of transmission errors. Such a function results in the reduction of noise and vibrations. Methods for the generation of the proposed gear tooth surfaces by grinding and hobbing are considered, and a tooth contact analysis (TCA) computer program to simulate meshing and contact is applied. The report also investigates the influence of misalignment on transmission errors and shift of bearing contact. Numerical examples to illustrate the developed approaches are proposed. The proposed geometry was patented by Ford/UIC (Serial Number 09-340-824, pending) on June 28, 1999.

Litvin, Faydor L.↗

NASA NTRS1997

Low-leakage and low-instability labyrinth seal

Improved labyrinth seal designs are disclosed. The present invention relates to labyrinth seal systems with selected sealing surfaces and seal geometry to optimize flow deflection and produce maximum turbulent action. Optimum seal performance is generally accomplished by providing sealing surfaces and fluid cavities formed to dissipate fluid energy as a function of the geometry of the sealing surfaces along with the position and size of the fluid cavities formed between members of the labyrinth seal system. Improved convex surfaces, annular flow reversal grooves, flow deflection blocks and rough, machined surfaces cooperate to enhance the performance of the labyrinth seal systems. For some labyrinth seal systems a mid-cavity throttle and either rigid teeth or flexible spring teeth may be included.

Rhode, David L.↗

NASA NTRS1983

Research on non-planar wall geometries for turbulence control and skin-friction reduction

Eight turbulence-control/drag-reduction concepts under study at NASA Langley Research Center are discussed. These concepts include: slot injection, ion wind, large-eddy breakup devices, riblets, relaminarization, convex curvature, passive porous walls, and rigid wavy walls. Of these concepts, passive porous walls and small wavelength wavy walls are found to increase drag. Riblets, slot injection, and large-eddy breakup devices reduce net turbulent drag, at least for some conditions. The ion wind, relaminarization, and convex curvature studies are still in the early stages and require further work to evaluate their applicability for drag reduction.

Hefner, J. N.↗

NASA NTRS1990

Analytic Patch Configuration (APC) gateway version 1.0 user's guide

The Analytic Patch Configuration (APC) is an interactive software tool which translates aircraft configuration geometry files from one format into another. This initial release of the APC Gateway accommodates six formats: the four accepted APC formats (89f, 89fd, 89u, and 89ud), the PATRAN 2.x phase 1 neutral file format, and the Integrated Aerodynamic Analysis System (IAAS) General Geometry (GG) format. Written in ANSI FORTRAN 77 and completely self-contained, the APC Gateway is very portable and was already installed on CDC/NOS, VAX/VMS, SUN, SGI/IRIS, CONVEX, and GRAY hosts.

Bingel, Bradford D.↗