Effect of short regions of surface curvature on compressible turbulent boundary layers
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Degani, David↗
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The perception of three-dimensionality across continuous surfaces
The apparent three-dimensionality of a viewed surface presumably corresponds to several internal preceptual quantities, such as surface curvature, local surface orientation, and depth. These quantities are mathematically related for points within the silhouette bounds of a smooth, continuous surface. For instance, surface curvature is related to the rate of change of local surface orientation, and surface orientation is related to the local gradient of distance. It is not clear to what extent these 3D quantities are determined directly from image information rather than indirectly from mathematically related forms, by differentiation or by integration within boundary constraints. An open empirical question, for example, is to what extent surface curvature is perceived directly, and to what extent it is quantitative rather than qualitative. In addition to surface orientation and curvature, one derives an impression of depth, i.e., variations in apparent egocentric distance. A static orthographic image is essentially devoid of depth information, and any quantitative depth impression must be inferred from surface orientation and other sources. Such conversion of orientation to depth does appear to occur, and even to prevail over stereoscopic depth information under some circumstances.
Stevens, Kent A.↗
Principal normal curvature of surfaces
Certain principal normal curvatures of differential geometry were developed for use in curvature matrices associated with the asymptotic solution of electromagnetic diffraction problems. The effort is directed toward microwave antenna simulations and high speed digital computer analysis of radiometric instruments used to obtain soil moisture, sea state, salinity and temperature data. It is shown that the methods used to develop the principal normal curvatures for paraboloid, hyperboloid, ellipsoid, sphere, and cone can be applied to other radiometer geometries such as the parabolic torus, even though the surface parameterizations are different. It is concluded that deployable offset geometries, distorted by rotational forces and solar loads may be analyzed by similar means given a suitable surface description.
Schmidt, R. F.↗
Shape from Shading: An Assessment
Previous efforts to recover surface shape from image irradiance are reviewed in order to assess what can and cannot be accomplished. The informational requirements and restrictions of these approaches are considered. In dealing with the question of what surface parameters can be recovered locally from image shading, it is shown that, at most, shading determines relative surface curvature, i.e., the ratio of surface curvature measured in orthogonal image directions. The relationship between relative surface curvature and the second derivatives of image irradiance is independent of other scene parameters, but insufficient to determine surface shape. This result places in perspective the difficulty encountered in previous attempts to recover surface orientation from image shading.
Smith, G. B.↗
Self-Assembly of Anisotropic Particles on Curved Surfaces
The surface curvature of membranes, interfaces, and substrates plays a crucial role in shaping the self-assembly of particles adsorbed on these surfaces. However, little is known about the interplay between particle anisotropy and surface curvature and how they couple to alter the free energy landscape of particle assemblies. Using molecular dynamics simulations, we investigate the effect of prescribed curvatures on a quasi-2D assembly of anisotropic patchy particles. By varying curvature and surface coverage, we uncover a rich geometric phase diagram, with curvature inducing ordered structures entirely absent on planar surfaces. Large spatial domains of ordered structures can contain hidden microdomains of orientational textures imprinted by the surface on the assembly. The dynamical landscape is also reshaped by surface curvature, with a glass-like state emerging at modest densities and high curvature. Changes to the symmetry of the surface curvature are found to result in distinct structures, including phases with mesoscale ordering. In conclusion, our findings show that the coupling between surface curvature and particle geometry opens an unexplored space of morphologies and structures that can be exploited for material design.
Fluids↗
Generation of gear tooth surfaces by application of CNC machines
This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.
Litvin, F. L.↗
Geometric Acoustics for Aircraft Noise Scattering
This paper discusses aircraft noise scattering by geometric acoustics, which consists of the basic features of sound propagation and reflection in rays or ray tubes, diffraction by smooth geometry in terms of surface creeping waves, and diffraction by abrupt geometry features such as the wing trailing edges. Based on the classic theories of these features, prediction methodologies can be constructed for aircraft noise scattering. The methodologies, however, require important modifications and extensions to account for unique features in aircraft noise applications, for both current conventional aircraft and future unconventional designs. These modifications and extensions include the derivation of a general reflection coefficient that contains the effects of surface geometry curvature, surface impedance, and mean flow. Corrections to the basic formulation of diffraction, both smooth geometry and sharp edges, are formulated to account for the finite dimensions of practical applications. For smooth geometry diffraction, a second order correction is used to continuously transition from insolified to shadow zones and an approach is presented to compute the properties of the geodesic path of surface wave propagation. A model is developed to make use of the ray propagation formulation for incoherent and partially coherent propagation and scattering, which is an important phenomenon in aircraft noise. Mean flow effect is also included in the methodology for low Mach number flows. Examples of calculations based on these theoretical developments are presented to illustrate the unique features in aircraft noise applications.
Yueping Guo↗
Asymptotic behavior of curvature of surface elements in isotropic turbulence
The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.
Girimaji, S. S.↗
Curvature effects on the stability of three-dimensional laminar boundary layers
The linear stability equations for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The system of equations is solved using a finite difference scheme in order to study the effects of streamline and surface curvature and compressibility on the stability of the flow past a swept wing. It is known that convex surface curvature can have a stabilizing effect on the laminar boundary layer. Conversely, concave surface curvature can be destabilizing. The magnitude of these effects for swept wings is determined. Results indicate that amplification rates and hence, N-factors, for the flow over the convex upper surface of a swept wing can be reduced by about 15 to 45 percent when curvature effects are included in the linear stability analysis. The results of the calculations show that concave curvature destabilizes crossflow type disturbances with a significant increase in amplification rate. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface.
Collier, F. S., Jr.↗
Convex curvature concept of viscous drag reduction
Experiments have indicated that for certain convex aerodynamic surface curvature ratios, wall-shear stresses remain low over considerable streamwide distances even after curvature is removed. The research whose progress is presently evaluated was first suggested by Bushnell (1983), who proposed that the convex-surface curvature be used in axisymmetric bodies to ascertain whether the viscous component of total drag is reduced. Attention is given to the evolution of the concept's implementation in an axisymmetric nose-body combination for passive viscous drag reduction.
Bandyopadhyay, Promode R.↗
Curvilinear magnetic effects in helicoid nanotubes
We report the fabrication and characterization of ferromagnetic helicoid nanotubes with a tunable surface curvature and chirality. Through combining focused electron beam induced deposition and magnetron sputtering we realize these complex curvilinear magnetic architectures. Electron holography reveals two distinct states: a single domain remanent state, with a magnetic chirality governed by the geometric chirality, and a vortex-anti-vortex domain wall, preferentially forming at areas of lower curvature. Micromagnetic simulations reveal how the geometry, specifically pitch and local surface curvature, affects the stability and formation of magnetic domain walls. Furthermore, we show that the interplay between magnetic and geometric chirality has a strong impact on domain wall motion, whereby a right-handed geometric chirality leads to faster domain wall motion and a left-handed geometry hinders domain wall transport. The results shown here highlight the potential of 3D magnetic architectures in spintronic devices and offer insights into how geometry and curvature affect the magnetization, the distribution of magnetic solitons and the motion of domain walls.
3D Nanomagnetism↗
Mean flow in turbulent boundary layers disturbed to alter skin friction
A comparative evaluation is made of recent developments in methods for the reduction of boundary layer drag, encompassing longitudinal surface riblets, 'outer layer' devices, (OLDs) and longitudinal convex surface curvature. The boundary layer of a surface with a longitudinal concave curvature is also studied, to complement the convex case results. The net drag reductions achievable by both riblets and OLDs are noted to be a rather modest 10 percent. Boundary layers exhibit asymmetric response to streamwise surface curvatures, with the response being slower for the case of a concave than a convex curvature.
Bandyopadhyay, P. R.↗
Impurity Extraction by Droplets
The goals are to model and to measure the phase equilibrium properties of a finely divided fluid containing a large number of chemically similar species. The objective is to develop an accurate, usable model for such phenomena as pollutant extraction of rain clouds, industrial separation in spray towers, and separation in emulsions. The project was designed as a hierarchy of complementary theoretical and experimental steps. A theory was developed to describe the segregation of complex impurities at the interface of a solvent. This phenomenon is important in phase behavior when a large fraction of molecules in a material are near an interface, the situation in a finely divided material. The theory will be modified to account for the effect of surface curvature on the surface tension. The study of mixtures differs from pure fluids not only because of the surface effects but also because composition differences between the droplet and the surrounding vapor can stabilize a droplet with respect to a bulk phase.
Morrison, G.↗
Investigation of generic hub fairing and pylon shapes to reduce hub drag
Reported are investigations of fairing configurations pointed toward substantially reducing hub drag. Experimental investigations have shown the importance of hub-fairing camber, lower-surface curvature, and relative size of the drag. The significance of pylon and hub fairings in combination have also been shown. Model test data presented here documented these findings, and also showed the effect of gaps and hub-fairing inclination angle on drag. From a drag standpoint, the best hub fairing had a circular arc, upper-surface curvature, a flat bottom surface, and 8.75% camber.
Stroub, Robert H.↗
Investigation of generic hub fairing and pylon shapes to reduce hub drag
This paper reports investigations of fairing configurations pointed toward substantially reducing hub drag. Experimental investigations have shown the importance of hub-fairing camber,lower-surface curvature, and relative size on the drag. The significance of pylon and hub fairings in combination have also been shown. Model test data presented here documented these findings, and also showed the effect of gaps and hub-fairing inclination angle on drag. From a drag standpoint, the best hub fairing had a circular arc, upper-surface curvature, a flat bottom surface, and 8.75 percent camber.
Stroub, Robert H.↗
SurFE-XD (Surface curvature-driven Finite Elements model for Diffusion under eXtreme conditions)
SurFE-XD is a mesoscale finite element framework to model surface diffusion under mutliphysics environments. The code uses legacy C++ library dolphin wrapped with python in a FEniCS driven unified form language and just-in-time (JIT) compilation setting. The purpose of the release is to attract wide-ranging usage of the code along with publication supplementation to support reproducibility of scientific data. SurFE-XD has been originally conceived under the LDRD-DR funding for “High-Gradient (C-BAND) Breakdown tolerant accelerator materials project. Currently SrFE-XD support electrostatics and Thermo-elasticity driven surface diffusion kernels. Releasing the code will also enable to include contributions from other physical regimes e.g., plasticity and electrodynamics etc as well portability to GPU-based platforms.
Bagchi, Soumendu↗
Thin film deployable reflector model for ET gamma ray imaging telescope system (ET-GRITS)
The Marshall Space Flight Center is developing a thin film reflector for a Gamma Ray Imaging Telescope System (GRITS) using the Shuttle External Tank (ET). The concept is to install an inflatable reflector in the ET that could be transferred from the orbiter in orbit. This is a study of a scale model reflector for the ET GRITS application. The approach is to form 1/2 mil film into a spherical mirror mounted on a seven-foot diameter metal ring. The ring mount is sealed and slightly evacuated to pressurize the film into shape. Several different fabrication techniques were investigated using seamed gore designs to form the reflector. Also studied was casting a film into a seamless circular sheet. The goal for this model was to achieve a one milliradian (rms) surface curvature error over 90 percent of the reflector area. This curvature was measured by a laser scanning instrument. The results show how different reflector designs and fabrication techniques contribute to surface curvature and focusing errors.
Huegele, Vinson B.↗
Computational Analysis of the G-III Laminar Flow Glove
Under NASA's Environmentally Responsible Aviation Project, flight experiments are planned with the primary objective of demonstrating the Discrete Roughness Elements (DRE) technology for passive laminar flow control at chord Reynolds numbers relevant to transport aircraft. In this paper, we present a preliminary computational assessment of the Gulfstream-III (G-III) aircraft wing-glove designed to attain natural laminar flow for the leading-edge sweep angle of 34.6deg. Analysis for a flight Mach number of 0.75 shows that it should be possible to achieve natural laminar flow for twice the transition Reynolds number ever achieved at this sweep angle. However, the wing-glove needs to be redesigned to effectively demonstrate passive laminar flow control using DREs. As a by-product of the computational assessment, effect of surface curvature on stationary crossflow disturbances is found to be strongly stabilizing for the current design, and it is suggested that convex surface curvature could be used as a control parameter for natural laminar flow design, provided transition occurs via stationary crossflow disturbances.
Malik, Mujeeb R.↗