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NASA NTRS1981

Models for Jupiter's decametric arcs

Arc-shaped structures that dominate Jupiter's decametric emission are discussed in terms of a magnetic fine structure. The sequence of arcs manifest the occurence of widespread fine structures similar to the white ovals on Jupiter's visible surface. An arc concave toward increasing time occurs at the east limb passage, and an arc convex occurs at the west limb passage, which is consistent with the early source producing vertex early arcs, and the late source producing vertex late arcs. Due to the geometry of the Io plasma torus (IPT) which is arranged so that Io skims the northern surface of the IPT, for any connection between Io and Jupiter's surface that involves Alfven waves, the propagation time, the refraction and the directional defocusing of these waves must be strongly influenced by the amount of Alfven wave path length between the instantaneous position of Io and the surface of the IPT.

Warwick, J. W.↗

NASA NTRS2008

Jet Engine Fan Blade Containment Using an Alternate Geometry

With a goal of reducing jet engine weight, simulations of a fan blade containment system with an alternate geometry were tested and analyzed. A projectile simulating a fan blade was shot at two alternate geometry containment case configurations using a gas gun. The first configuration was a flat plate representing a standard case configuration. The second configuration was a flat plate with a radially convex curve section at the impact point. The curved surface was designed to force the blade to deform plastically, dissipating energy before the full impact of the blade is received by the plate. The curved case was able to tolerate a higher impact velocity before failure. The computational model was developed and correlated with the tests and a weight savings assessment was performed. For the particular test configuration used in this study the ballistic impact velocity of the curved plate was approximately 60 m/s (200 ft/s) greater than that of the flat plate. For the computational model to successfully duplicate the test, the very high strain rate behavior of the materials had to be incorporated.

Carney, K.S.↗

NASA NTRS1979

Axial jet mixing of ethanol in cylindrical containers during weightlessness

An experimental program was conducted to examine the liquid flow patterns that result from the axial jet mixing of ethanol in 10-centimeter-diameter cylindrical tanks in weightlessness. A convex hemispherically ended tank and two Centaur liquid-hydrogen-tank models were used for the study. Four distinct liquid flow patterns were observed to be a function of the tank geometry, the liquid-jet velocity, the volume of liquid in the tank, and the location of the tube from which the liquid jet exited.

Aydelott, J. C.↗

NASA NTRS1987

Asteroid lightcurve inversion

One of the most fundamental physical properties of any asteroid is its shape. Lightcurves provide the only source of shape information for most asteroids. Unfortunately, the functional form of a lightcurve is determined by the viewing/illumination geometry and the asteroid's light scattering characteristics as well as its shape, and in general it is impossible to determine an asteroid's shape from lightcurves. A technique called convex-profile inversion (CPI) that obtains a convex profile, P, from any lightcurve is introduced. If certain ideal conditions are satisfied, then P is an estimator for the asteroid's mean cross section, C, a convex set defined as the average of all cross sections C(z) cut by planes a distance z above the asteroids's equatorial plane. C is therefore a 2-D average of the asteroid's 3-D shape.

Ostro, Steven J.↗

NASA NTRS1980

Kinematic correction for roller skewing

A theory of kinematic stabilization of rolling cylinders is developed for high-speed cylindrical roller bearings. This stabilization requires race and roller crowning to product changes in the rolling geometry as the roller shifts axially. These changes put a reverse skew in the rolling elements by changing the rolling taper. Twelve basic possible bearing modifications are identified in this paper. Four have single transverse convex curvature in the rollers while eight have rollers with compound transverse curvature composed of a central cylindrical band of constant radius surrounded by symmetric bands with both slope and transverse curvature.

Savage, M.↗

NASA NTRS1980

Kinematic correction for roller skewing

A theory of kinematic stabilization of rolling cylinders is developed for high-speed cylindrical roller bearings. This stabilization requires race and roller crowning to produce changes in the rolling geometry as the roller shifts axially. These changes put a reverse skew in the rolling elements by changing the rolling taper. Twelve basic possible bearing modifications are identified in this paper. Four have single transverse convex curvature in the rollers while eight have rollers with compound transverse curvature composed of a central cylindrical band of constant radius surrounded by symmetric bands with both slope and transverse curvature.

Savage, M.↗

NASA NTRS1976

Roller bearing geometry design

A theory of kinematic stabilization of rolling cylinders is extended and applied to the design of cylindrical roller bearings. The kinematic stabilization mechanism puts a reverse skew into the rolling elements by changing the roller taper. Twelve basic bearing modification designs are identified amd modeled. Four have single transverse convex curvature in their rollers while eight have rollers which have compound transverse curvature made up of a central cylindrical band surrounded by symmetric bands with slope and transverse curvature. The bearing designs are modeled for restoring torque per unit axial displacement, contact stress capacity, and contact area including dynamic loading, misalignment sensitivity and roller proportion. Design programs are available which size the single transverse curvature roller designs for a series of roller slopes and load separations and which design the compound roller bearings for a series of slopes and transverse radii of curvature. The compound rollers are proportioned to have equal contact stresses and minimum size. Design examples are also given.

Savage, M.↗

NASA NTRS1984

A method for interface shape control during Bridgman type crystal growth of HgCdTe alloys

A method is described for interface shape control of Hg(1-x)Cd(x)Te alloys during Bridgman-type crystal growth. The authors have used this method for several years to obtain the flat or convex interface shapes required for simultaneously reducing radial compositional variations and crystal defects. The method turns to advantage the thick-walled, fused-silica ampules required for growing these alloys. A proper combination of furnace geometry (two isothermal zones separated by a thin barrier), upper- and lower-zone temperatures, and growth rate is required. Examples of results are reported.

Szofran, F. R.↗

NASA NTRS1996

T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review

We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanies by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.

Mischenko, Michael I.↗

NASA NTRS1993

Large eddy simulation of a boundary layer with concave streamwise curvature

One of the most exciting recent developments in the field of large eddy simulation (LES) is the dynamic subgrid-scale model. The dynamic model concept is a general procedure for evaluating model constants by sampling a band of the smallest scales actually resolved in the simulation. To date, the procedure has been used primarily in conjunction with the Smagorinsky model. The dynamic procedure has the advantage that the value of the model constant need not be specified a priori, but rather is calculated as a function of space and time as the simulation progresses. This feature makes the dynamic model especially attractive for flows in complex geometries where it is difficult or impossible to calibrate model constants. The dynamic model was highly successful in benchmark tests involving homogeneous and channel flows. Having demonstrated the potential of the dynamic model in these simple flows, the overall direction of the LES effort at CTR shifted toward an evaluation of the model in more complex situations. The current test cases are basic engineering-type flows for which Reynolds averaged approaches were unable to model the turbulence to within engineering accuracy. Flows currently under investigation include a backward-facing step, wake behind a circular cylinder, airfoil at high angles of attack, separated flow in a diffuser, and boundary layer over a concave surface. Preliminary results from the backward-facing step and cylinder wake simulations are encouraging. Progress on the LES of a boundary layer on a concave surface is discussed. Although the geometry of a concave wall is not very complex, the boundary layer that develops on its surface is difficult to model due to the presence of streamwise Taylor-Gortler vortices. These vortices arise as a result of a centrifugal instability associated with the convex curvature.

Lund, Thomas S.↗

NASA NTRS1974

A parametric study of effect of forebody shape on flow angularity at Mach 8

Flow angularity and static pressure measurements have been made on the lower surface of nine forebody models that simulate the bottom forward surface of a hypersonic aircraft. Measurements were made in an area of the forebody that represents the location of an inlet of a scramjet engine. A parametric variation of the forebody surface investigated the effect of: (1) spanwise curvature; (2) longitudinal curvature; and (3) planform shape on both flow angularity and static pressure distribution. Results of each of the three parametric variations of geometry were compared to those for the same flat delta forebody. Spanwise curvature results showed that a concave shape and the flat delta had the lowest flow angularity and lowest rate of increase in flow angularity with angle of attack. Longitudinal curvature results showed a convex surface to give the better flow at the higher angles of attack. The better of the two planform shapes tested was a convex elliptical shape. Limited flow field calculations were made at angles of attack using a three dimensional, method-of-characteristics program. In general, at all angles of attack there was agreement between data and theory.

Johnson, C. B.↗

NASA NTRS2004

Measurement of an Evaporating Drop on a Reflective Substrate

A figure depicts an apparatus that simultaneously records magnified ordinary top-view video images and laser shadowgraph video images of a sessile drop on a flat, horizontal substrate that can be opaque or translucent and is at least partially specularly reflective. The diameter, contact angle, and rate of evaporation of the drop as functions of time can be calculated from the apparent diameters of the drop in sequences of the images acquired at known time intervals, and the shadowgrams that contain flow patterns indicative of thermocapillary convection (if any) within the drop. These time-dependent parameters and flow patterns are important for understanding the physical processes involved in the spreading and evaporation of drops. The apparatus includes a source of white light and a laser (both omitted from the figure), which are used to form the ordinary image and the shadowgram, respectively. Charge-coupled-device (CCD) camera 1 (with zoom) acquires the ordinary video images, while CCD camera 2 acquires the shadowgrams. With respect to the portion of laser light specularly reflected from the substrate, the drop acts as a plano-convex lens, focusing the laser beam to a shadowgram on the projection screen in front of CCD camera 2. The equations for calculating the diameter, contact angle, and rate of evaporation of the drop are readily derived on the basis of Snell s law of refraction and the geometry of the optics.

Chao, David F.↗

NASA NTRS1991

A generalized scheme for three-dimensional hyperbolic grid generation

A hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification is generalized such that high quality three-dimensional grids can be obtained for a wide variety of geometries. The speed of the scheme is one to two orders of magnitude faster than typical elliptic grid generation methods. The robustness of the scheme is significantly enhanced by several new techniques. By using a spatially variable smoothing coefficient, orthogonality and smoothness of the grid are maintained around complex concave and convex surface topologies. A metric correction procedure is employed to guarantee that the grid marches out of a corner by bisecting the angles subtended by the neighboring points. Extra robustness at severe convex corners is achieved by special local treatments. Different extrapolation methods are used to provide smoothness at floating edges and axis regions. The versatility of the new hyperbolic grid generation scheme is demonstrated by three-dimensional grids generated for external components of the intergrated Space Shuttle vehicle and the SOFIA telescope.

Chan, William M.↗

NASA NTRS1992

The shape of asteroid 1917 Cuyo

Lightcurves obtained for 1917 Cuyo at solar phase angles near 54 degrees have an amplitude delta m = 0.44 mag. However, convex-profile inversion of the lightcurves yields an estimate of the asteroid's mean cross section (C, a 2-D average of the 3-D shape) that is only slightly noncircular, with an elongation approximately 1.15. The estimate of C undoubtedly contains systematic errors, the most severe of which could arise from non-equatorial viewing/illumination geometry. However, Cuyo's radar echo shows very little variation in bandwidth vs. rotation phase, supporting the hypothesis that this asteroid's elongation is rather modest.

Ostro, Steven J.↗

NASA NTRSDate not supplied

Rollable Corrugated Tubular Booms

A promising candidate for a new class of deployable composite boom is the COrrugated ROllable TUbular Boom (COROTUB), which is to be employed on future large space structures by the National Aeronautics and Space Administration (NASA). The COROTUB’s two corrugated thin shells form a closed section, which yields high bending and torsional stiffness, allowing for high dimensional stability. The corrugation geometry that dictates the boom cross-section shape was completely defined by closed-form analytical equations given a set of key design parameters. Parametric studies of two geometric variables were used to evaluate which parameters most influence the cross-section’s area moment of inertia and torsional constant. The number of corrugations, flattened height of the boom, and concave and convex corrugation radii were varied to study the complete boom design space. Deeper corrugations increased the local buckling (crimpling) loads of the thin-shell boom but reduced the area moment of inertia and therefore the global buckling load of the beam-column member, and thus a fine balance was sought. Finite element analyses of pure bending and compression load cases for short, 1.22-m-long fully-deployed booms ofeither the same size (flattened height) or similar inertia properties, were first carried out to efficiently study this design trade-off in detail.A second computational study evaluated the boom transition shape and the structural response of a 6-m-long partially-deployed boom, where the effects of partially bracing the root of the boom were also assessed. It was found that bracing length could greatly affect the strength and stiffness of this boom.Bracing type (as in the discrete number of clamps at the root) had no effect on stiffness, but particularly impacted strength for loading cases and boundary conditions that promoted the onset of local web buckling at the root. The corrugated designs were also found to improve, by as much as 20%, the boom bending and axial strength and boom transition length from flat to deployed when compared to a state-of-the-art boom alternative of the same size, for short bracing distances, such as those that would be required by small satellite applications. In addition, they showed a comparable structural response for longer bracing supports.

Booms↗

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 NTRSDate not supplied

Corrugated Rollable Tubular Booms

A promising candidate for a new class of deployable composite boom is the COrrugated ROllable TUbular Boom (COROTUB), which is to be employed on future large space structures by the National Aeronautics and Space Administration (NASA). This is due to its two corrugated thin-shells forming a closed-section,which yields high bending and torsion stiffness, allowing for high dimensional stability. The corrugation geometry that dictates the boom cross-section shape is completely defined by closed-form analytical equations given a set of key input parameters available to the designer. Parametric studies changing two geometric variables are used to evaluate which parameters most influence the cross-section’s area moment of inertia and torsional constant. The number of corrugations, flattened height of the boom, and concave and convex corrugation radii are varied to study the complete boom design space. Deeper corrugations increase the local buckling loads (crimpling) of the thin-shell boom but reduce the area moment of inertia and therefore the global Euler buckling load of the compressive member,and thus a fine balance is sought. Finite element analyses of pure bending and compression load cases for 1.22 m boom specimens were carried out to study this design trade-off in detail. Based on previous work, several thin-ply composite laminates have been selected for the different shells that form the cross-section. Feasible boom designs with a maximized stiffness and load-carrying capacity will be manufactured to study their rollability and for experimental characterization. Structural characterization tests and additional numerical analyses will provide guidelines towards future corrugated boom designs and adequate boundary conditions to maximize the boom bending strength.

Deployable Booms↗

NASA NTRS1976

Structural optimization via a design space hierarchy

Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.

Vanderplaats, G. N.↗