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At least 55 records · Page 3

Gratings Fabricated on Flat Surfaces and Reproduced on Non-Flat Substrates

A method has been developed for fabricating gratings on flat substrates, and then reproducing the groove pattern on a curved (concave or convex) substrate and a corresponding grating device. First, surface relief diffraction grating grooves are formed on flat substrates. For example, they may be fabricated using photolithography and reactive ion etching, maskless lithography, holography, or mechanical ruling. Then, an imprint of the grating is made on a deformable substrate, such as plastic, polymer, or other materials using thermoforming, hot or cold embossing, or other methods. Interim stamps using electroforming, or other methods, may be produced for the imprinting process or if the same polarity of the grating image is required. The imprinted, deformable substrate is then attached to a curved, rigid substrate using epoxy or other suitable adhesives. The imprinted surface is facing away from the curved rigid substrate. As an alternative fabrication method, after grating is imprinted on the deformable substrate as described above, the grating may be coated with thin conformal conductive layer (for example, using vacuum deposition of gold). Then the membrane may be mounted over an opening in a pressured vessel in a manner of a membrane on a drum, grating side out. The pressure inside of the vessel may be changed with respect to the ambient pressure to produce concave or convex membrane surface. The shape of the opening may control the type of the surface curvature (for example, a circular opening would create spherical surface, oval opening would create toroidal surface, etc.). After that, well-known electroforming methods may be used to create a replica of the grating on the concave or convex membrane. For example, the pressure vessel assembly may be submerged into an electro-forming solution and negative electric potential applied to the metal coated membrane using an insulated wire. Positive electric potential may be then applied to a nickel or other metal plate submerged into the same solution. Metal ions would transfer from the plate through the solution into the membrane, producing high fidelity metal replica of the grating on the membrane. In one variation, an adhesive may be deposited on the deformable substrate, and then cured without touching the rigid, curved substrate. Edges of the deformable substrate may be attached to the rigid substrate to ensure uniform deformation of the deformable substrate. The assembly may be performed in vacuum, and then taken out to atmospheric pressure conditions to ensure that no air is trapped between the deformable and rigid substrates. Alternatively, a rigid surface with complementary curvature to the rigid substrate may be used to ensure uniform adhesion of the deformable substrate to the rigid substrate. Liquid may be applied to the surface of the deformable substrate to uniformly distribute pressure across its surface during the curing or hardening of the adhesive, or the film may be pressed into the surface using a deformable object or surface. After the attachment is complete, the grooves may be coated with reflective or dielectric layers to improve diffraction efficiency.

Content, David↗

Stresses and deformations in elliptical contacts

Topics presented deal with defining conformal and nonconformal surfaces, curvature sum and difference, and surface and subsurface stresses in elliptical contacts. Load-deflection relationships for nonconformal contacts are developed. The deformation within the contact is, among other things, a function of the ellipticity parameter and elliptic integrals of the first and second kinds. Simplified expressions that allow quick calculations of the deformation to be made simply from a knowledge of the applied load, the material properties, and the geometry of the contacting elements are presented.

Hamrock, B. J.↗

The Mean Curvature of the Influence Surface of Wave Equation With Sources on a Moving Surface

The mean curvature of the influence surface of the space-time point (x, t) appears in linear supersonic propeller noise theory and in the Kirchhoff formula for a supersonic surface. Both these problems are governed by the linear wave equation with sources on a moving surface. The influence surface is also called the Sigma - surface in the aeroacoustic literature. This surface is the locus, in a frame fixed to the quiescent medium, of all the points of a radiating surface f(x, t) = 0 whose acoustic signals arrive simultaneously to an observer at position x and at the time t. Mathematically, the Sigma- surface is produced by the intersection of the characteristic conoid of the space-time point (x, t) and the moving surface. In this paper, we derive the expression for the local mean curvature of the Sigma - space of the space-time point for a moving rigid or deformable surface f(x, t) = 0. This expression is a complicated function of the geometric and kinematic parameters of the surface f(x, t) = 0. Using the results of this paper, the solution of the governing wave equation of high speed propeller noise radiation as well as the Kirchhoff formula for a supersonic surface can be written as very compact analytic expression.

Farassat, F.↗

Spline-Based Smoothing of Airfoil Curvatures

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.↗

High-Fidelity Simulation of Turbulent Flow Past a Gaussian Bump

A spanwise-periodic computation of a turbulent flow past a Gaussian bump is performed in the form of a hybrid direct numerical simulation and wall-resolved large-eddy simulation. A fourth-order spatially-accurate flow solver is employed to perform the simulation, using 10.2 billion grid points for a Reynolds number of 170000 based on the bump height. The key findings from the simulation are reported in the acceleration and deceleration flow regions associated with the bump shape. Significant anisotropy in the normal Reynolds stresses, along both the wall-normal and streamwise directions, is observed within the acceleration region. The ratio between the Reynolds shear stress and turbulent kinetic energy in that region also experiences significant deviations from the norms of a zero pressure gradient turbulent boundary layer. The chosen Reynolds number generates strong flow separation in the adverse pressure gradient region, which is in contrast with a previous simulation at half the Reynolds number that only indicated incipient separation. An internal layer generated in the acceleration region evolves into a free shear layer that develops in the deceleration region and separates. Proper modeling of this inner layer appears crucial to predict the flow separation. Surface curvature effects on the attached flow development are also discussed.

Turbulent Boundary Layer↗

Direct Numerical Simulation of Flow Past a Gaussian Bump at a High Reynolds Number

We present the results from a direct numerical simulation of a spanwise-periodic turbulent flow past a Gaussian bump. The problem setup is designed to investigate the interaction of an incoming turbulent boundary layer with the strong favorable and adverse pressure gradients generated by the Gaussian bump as the flow passes over it at a Reynolds number of 340000 based on the bump height, or 4 million based on the bump length. The statistical results from the present simulation are compared against our earlier results at a Reynolds number of 2 million. An internal layer, which forms beneath the strongly accelerated boundary layer over the windward side of the bump, is found to generate its near-wall turbulence stress peaks in closer proximity of the wall in the higher Reynolds-number case. Furthermore, the logarithmic layer of the higher Reynolds-number boundary layer appears more resistant to changes induced by strong acceleration and surface curvature effects over the same region. Despite a nearly identical flow separation point in the two flows, the detached shear layer grows at a faster rate and subsequently reattaches at an earlier point in the higher Reynolds-number flow. The surface pressure and skin-friction distributions over the attached flow region compare well against the corresponding experimental data for both flows. However, some differences appear in the separated flow region, which are attributed to the three-dimensionality of the experimental model setup that is not included in the simulation owing to the spanwise periodic assumption. Comparisons with the stereoscopic particle image velocimetry measurements on the central plane of the experimental model over the windward side of the bump show reasonable overall agreement in the mean velocity components, but the turbulence stress components do not agree well at some streamwise locations. Comparisons over the leeward side of the bump show that the mean separated shear layer in the simulation is tilted significantly more toward the wall than the experimental shear layer on the central plane. This mismatch in the mean shear layer orientation is due to the experimental model three-dimensionality and tunnel end-wall effects, which are not modeled in the present spanwise-periodic simulation.

Favorable and Adverse Pressure Gradients↗

A Dynamic Nonlinear Subgrid-Scale Model for Large-Eddy Simulation of Complex Turbulent Flows

We present a new dynamic nonlinear subgrid-scale (SGS) model for large-eddy simulations (LES) and apply it to compute a flow involving pressure gradients, surface curvature and separation, for which data from a direct numerical simulation are available for comparison. The model, inspired by the triple model idea of Bardina et al. (“Improved Turbulence Models Based on Large Eddy Simulation of Homogeneous, Incompressible, Turbulent Flows,” Report No. TF-19, Thermosciences Division, Department of Mechanical Engineering, Stanford University, 1983), includes a Galilean-invariant term called the modified Leonard stress tensor, and two nonlinear terms comprised of the products of the strain-rate and rotation-rate tensors for an improved representation of the subgrid-scale dissipation, backscatter and anisotropy effects. The model does not employ any ad hoc averaging or clipping procedures, and does not require the specification of a characteristic length scale; hence, it naturally avoids the ambiguities associated with defining a proper length scale for anisotropic grids. Results from the wall-resolved LES of flow past a Gaussian bump using the new model demonstrate improved prediction of skin-friction, flow separation, mean flow profiles and turbulent quantities when compared to implicit LES as well as explicit LES using the Vreman SGS model on the same grid.

Turbulence↗

The prediction of the noise of supersonic propellers in time domain - New theoretical results

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Farassat, F.↗

Direct simulations of premixed turbulent flames with nonunity Lewis numbers

A principal effect of turbulence on premixed flames in the flamelet regime is to wrinkle the flame fronts. For nonunity Lewis numbers, Le is not equal to 1, the local flame structure is altered in curved regions. This effect is examined using direct numerical simulations of 3D isotropic turbulence with constant density, single-step Arrhenius kinetics chemistry. Simulations of Lewis numbers 0.8, 1.0, and 1.2 are compared. At the local level, curvature effects dominated changes to the flame structure while strain effects were insignificant. A strong Lewis-number-dependent correlation was found between surface curvature and the local flame speed. The correlation was positive for Le less than 1 and negative for Le greater than 1. At the global level, strain-related effects were more significant than curvature effects. The turbulent flame speed changed significantly with Lewis number, increasing as Le decreased. This was found to be due to strain effects that have a nonzero mean over the flame surface, rather than to curvature effects that have a nearly zero mean. The mean product temperature was also found to vary with Lewis number, being higher for Le greater than 1 and lower for Le less than 1.

Rutland, C. J.↗

Shear-Sensitive Liquid Crystal Coating Method: Surface-Inclination Effects on Shear Vector Measurements

The shear-sensitive liquid crystal coating (SSLCC) method is an image-based technique for both visualizing dynamic surface-flow phenomena, such as transition and separation, and for measuring the continuous shear-stress vector distribution acting on an aerodynamic surface. Under proper lighting and viewing conditions (discussed below), the coating changes color in response to an applied aerodynamic shear. This color-change response is continuous and reversible, with a response time of milliseconds, and is a function of both the shear magnitude and the shear vector orientation relative to the observer. The liquid crystal phase of matter is a weakly-ordered, viscous, non-Newtonian fluid state that exists between the nonuniform liquid phase and the ordered solid phase of certain organic compounds. Cholesteric liquid crystal compounds possess a helical molecular arrangement that selectively scatters white light, incident along the helical axis, as a three-dimensional spectrum. This property is linked to the helical pitch length, which is within the range of wavelengths in the visible spectrum. The pitch length, and hence the wavelength of the scattered light, is influenced by shear stress normal to the helical axis. This unique optical property produces a measurable color change in response to an applied shearing force. The full-surface shear stress vector measurement method, developed at NASA-Ames, is schematically illustrated. As with the visualization method, the coated test surface is illuminated from the normal direction with white light and the camera is positioned at an above-plane view angle of approximately 30 deg. Experiments have been initiated at NASA Ames to begin the process of quantifying surface-inclination (surface-curvature) effects on shear vector measurement accuracy. In preliminary experiments, surface-inclination angles theta(sub x), theta(sub y) of 0, +/-5, +/-10, and +/-15 deg were employed. In this arrangement, white-light illumination was positioned normal to the untilted test surface, and the camera above-plane view angle was set at 30 deg relative to the untilted test surface. As can be seen, vector-aligned lambda(sub d) values showed no dependence on theta(sub x) or theta(sub y) for absolute values of these tilt angles is less than or equal to 15 deg. Acquisition and analyses of full-surface color images are presently underway to definitively document the insensitivity limits of the shear vector measurement methodology to surface-slope variations.

Reda, Daniel C.↗

Effects of Periodic Unsteady Wake Flow and Pressure Gradient on Boundary Layer Transition Along the Concave Surface of a Curved Plate

Boundary layer transition and development on a turbomachinery blade is subjected to highly periodic unsteady turbulent flow, pressure gradient in longitudinal as well as lateral direction, and surface curvature. To study the effects of periodic unsteady wakes on the concave surface of a turbine blade, a curved plate was utilized. On the concave surface of this plate, detailed experimental investigations were carried out under zero and negative pressure gradient. The measurements were performed in an unsteady flow research facility using a rotating cascade of rods positioned upstream of the curved plate. Boundary layer measurements using a hot-wire probe were analyzed by the ensemble-averaging technique. The results presented in the temporal-spatial domain display the transition and further development of the boundary layer, specifically the ensemble-averaged velocity and turbulence intensity. As the results show, the turbulent patches generated by the wakes have different leading and trailing edge velocities and merge with the boundary layer resulting in a strong deformation and generation of a high turbulence intensity core. After the turbulent patch has totally penetrated into the boundary layer, pronounced becalmed regions were formed behind the turbulent patch and were extended far beyond the point they would occur in the corresponding undisturbed steady boundary layer.

Schobeiri, M. T.↗

Elliptic surface grid generation in three-dimensional space

A methodology for surface grid generation in three dimensional space is described. The method solves a Poisson equation for each coordinate on arbitrary surfaces using successive line over-relaxation. The complete surface curvature terms were discretized and retained within the nonhomogeneous term in order to preserve surface definition; there is no need for conventional surface splines. Control functions were formulated to permit control of grid orthogonality and spacing. A method for interpolation of control functions into the domain was devised which permits their specification not only at the surface boundaries but within the interior as well. An interactive surface generation code which makes use of this methodology is currently under development.

Kania, Lee↗

A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation

The problem of recognizing and positioning of objects in three-dimensional space is important for robotics and navigation applications. In recent years, digital range data, also referred to as range images or depth maps, have been available for the analysis of three-dimensional objects owing to the development of several active range finding techniques. The distinct advantage of range images is the explicitness of the surface information available. Many industrial and navigational robotics tasks will be more easily accomplished if such explicit information can be efficiently interpreted. In this research, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others. Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system. Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix. Finally, we have proposed one other new approach, which involves the formulation of a mapping between the explicit and implicit forms of representing quadric surfaces. This approach, when fully realized, will yield a three-dimensional discriminant, which will recognize quadric surfaces based upon their component surfaces patches. This approach is faster than prior approaches and at the same time is invariant to pose and orientation of the surfaces in three-dimensional space.

Alvertos, Nicolas↗

Turbulent boundary layers subjected to multiple curvatures and pressure gradients

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompaying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Gortler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

Bandyopadhyay, Promode R.↗

Software for Automated Generation of Cartesian Meshes

Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.

Aftosmis, Michael J.↗

A curvature-corrected Kirchhoff formulation for radar sea-return from the near vertical

A new theoretical treatment of the problem of electromagnetic wave scattering from a randomly rough surface is given. A high frequency correction to the Kirchhoff approximation is derived from a field integral equation for a perfectly conducting surface. The correction, which accounts for the effect of local surface curvature, is seen to be identical with an asymptotic form found by Fock (1945) for diffraction by a paraboloid. The corrected boundary values are substituted into the far field Stratton-Chu integral, and average backscattered powers are computed assuming the scattering surface is a homogeneous Gaussian process. Preliminary calculations for K(-4) ocean wave spectrum indicate a resonable modelling of polarization effects near the vertical, theta 45 deg. Correspondence with the results of small perturbation theory is shown.

Jackson, F. C.↗

Beyond the Kirchhoff approximation

The three most successful models for describing scattering from random rough surfaces are the Kirchhoff approximation (KA), the small-perturbation method (SPM), and the two-scale-roughness (or composite roughness) surface-scattering (TSR) models. In this paper it is shown how these three models can be derived rigorously from one perturbation expansion based on the extinction theorem for scalar waves scattering from perfectly rigid surface. It is also shown how corrections to the KA proportional to the surface curvature and higher-order derivatives may be obtained. Using these results, the scattering cross section is derived for various surface models.

Rodriguez, Ernesto↗

A continuum method for modeling surface tension

In the novel method presented for modeling the effects of surface tension on fluid motion, the interfaces between fluids with different, color-represented properties are finite-thickness transition regions across which the color varies continuously. A force density proportional to the surface curvature of constant color is defined at each point in the transition region; this force-density is normalized in such a way that the conventional description of surface tension on an interface is recovered when the ratio of local transition-reion thickness to local curvature radius approaches zero. The properties of the method are illustrated by computational results for 2D flows.

Brackbill, J. U.↗