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NASA NTRS1977

Measuring concave diffraction grating efficiencies at grazing incidence

The efficiency of a concave diffraction grating in a given order is obtained by measuring the intensities of the diffracted and incident beams and taking their ratio. A valid measurement requires that both the incident and diffracted beams be collected by the detector. At grazing incidence, however, the diffracted beam may spread beyond the detector due to aberrations. In addition, the diffracted beams of consecutive orders may overlap so that unambiguous efficiency measurements cannot be made. The effect of aberrations on efficiency measurements has been studied, using ray tracing, for the geometry of the measuring instrument in use at the Naval Research Laboratory. This instrument is attached to a VUV monochromator which furnishes a diverging beam. The main effect of aberrations for this instrument is a spread of the diffracted beam in the direction of dispersion. The width of the diffracted beam is wavelength dependent and is minimal at the horizontal focus, spreading to longer and shorter wavelengths. Reducing the divergence of the incident beam reduces the spread but, for small radius gratings, not always sufficiently so that the entire diffracted beam can be collected by the detector. The distance from the detector to the grating can also be adjusted to aid in collecting all the diffracted beam.

Hunter, W. R.↗

NASA NTRS1978

A numerical study of capillary stability in a circular cylindrical container with a concave spheroidal bottom

The paper describes a theoretical investigation of the stability under gravitational and surface forces of a liquid in a circular cylindrical container with a concave spheroidal bottom for the case in which the volume of the liquid is sufficiently small so that the bottom is not covered completely. The gravitational field is assumed to be directed along the symmetry axis of the container, and for a specific container shape the critical Bond number is calculated as a function of liquid volume for contact angles of gamma = 0, 1, 2, and 4 deg. For gamma = 0 deg, some critical equilibrium configurations and corresponding perturbation modes are presented.

Concus, P.↗

NASA NTRS1978

Heat transfer from a row of jets impinging on concave semi-cylindrical surface

Heat transfer from impinging jets has been analyzed. Based on similarities of the boundary conditions of the related flow fields, analogies between heat transfer from impinging jets at the stagnation point and in the wall jet region have been shown for several flow geometries. Calculation of heat transfer in the stagnation region and in the wall jet region, based on available theory and the parameters, obtained from direct measurements, have been carried out, for the single, round, impinging jets. It has been shown that heat transfer from a row of round jets impinging on flat and concave surfaces can be comprehensively described through analysis of impinging jets of simpler geometries. Finally, experimental results for the local and average heat transfer effects are presented and discussed. Comparisons are made with theory and results of other investigators, with fairly satisfactory agreement.

Hrycak, P.↗

NASA NTRS1983

An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface

Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.

Dagenhart, J. R↗

NASA NTRS1984

Aspheric concave grating spectrographs

The design of aspheric concave gratings for high-resolution spectroscopes is examined theoretically, using the requirements of the proposed Far-UV Spectroscopic Explorer (effective area 100 sq cm and lambda/delta lambda = 30,000 in the 90-120-nm range) as a concrete example and taking the limitations of current fabrication technology (straight grooves only and maximum density 6000 lines/mm) into account. The total-path function derived by Namioka (1961) for an ellipsoidal grating is subjected to aberration analysis to obtain the optical surface best suited to the design requirements; expressions for corrections to the conventional stigmatic Rowland-circle mount are obtained and shown to produce significant performance improvements; and the design advantages of coma-corrected non-Rowland geometries are explored. Ray tracings and deviation contours are provided.

Cash, W. C., Jr.↗

NASA NTRS1985

A study of laminar separation bubble in the concave region of an airfoil using laser velocimetry

Laser velocimetry (LV) was used to study the nature of laminar separation bubbles in the concave region of a 1.83-meter airfoil model which was tested in the NASA Langley Low Turbulence Pressure Tunnel. Three component, coincident data from LV measurements including histograms of particle velocity, mean velocity profiles, turbulence intensity, and Reynolds stresses within the shear layer were used to determine the locations of laminar separation, transition, and turbulent reattachment. boundary-layer parameters determined from velocity profiles were used to compare the results with existing empirical relations for describing the laminar separation bubble.

Mangalam, S. M.↗

NASA NTRS1986

Stability and control of compressible flows over a surface with concave-conves curvature

The active control of spatially unstable disturbances in a laminar, two-dimensional, compressible boundary layer over a curved surface is numerically simulated. The control is effected by localized time-periodic surface heating. We consider two similar surfaces of different heights with concave-convex curvature. In one, the height is sufficiently large so that the favorable pressure gradient is sufficient to stabilize a particular disturbance. In the other case the pressure gradient induced by the curvature is destabilizing. It is shown that by using active control that the disturbance can be stabilized. The results demonstrate that the curvature induced mean pressure gradient significantly enhances the receptivity of the flow localized time-periodic surface heating and that this is a potentially viable mechanism in air.

Maestrello, L.↗

NASA NTRS1987

Filament-Winding Technique for Concave Parts

Dummy mold and vacuum bagging yield accurate part girth. Proposed method of filament winding facilitates accurate fabrication of fiber/matrix composite parts having closed sections with concave surfaces. Parts laid up by hand now wound with filaments; reducing time and cost of fabrication and improving quality of parts.

Carter, Donald↗

NASA NTRS1987

The response of a compressible turbulent boundary layer to short regions of concave surface curvature

An experimental investigation of the supersonic flow of a boundary layer over short regions of concave surface curvature, using radii of curvature equivalent to 10 and 50 (models I and II, respectively) initial boundary layer thicknesses and 8-deg turning angle, notes that the boundary layer experienced a strong adverse pressure gradient as the boundary layer passed through the curved region. Attention is given to the mean and turbulent field for each flow, with comparisons of results to those for an 8-deg ramp. In the ramp and model I, turbulence levels increased significantly, together with structural parameters; in model II, despite an increase in turbulence levels, structural parameters remained essentially unchanged. The former results suggest that the perturbation is rapid, and describable in terms of total rather than local strains.

Jayaram, Mohan↗

NASA NTRS1989

Simple proof of the concavity of the entropy power with respect to Gaussian noise

A very simple proof of M. H. Costa's result that the entropy power of Xt = X + N (O, tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new inequalities about Fisher information, or at least to exploit the existing ones in new ways.

Dembo, Amir↗

NASA NTRS1990

Concave-outward slow shocks in coronal mass ejections

Formation of slow shocks in a simplified model corona consisting of closed magnetic field lines near the coronal base with overlying open magnetic field lines is analyzed. An increase in the magnetic field strength in the closed region is utilized to drive the corona outward, generating slow shocks for a suitable selection of parameters. The study demonstrates that concave-upward slow shocks can be formed in a magnetic environment, and provides evidence that nonlinear manifestations of all three wave modes (slow, intermediate, and fast) can occur as the corona adjusts from ambient conditions to those produced by the driver. The results show the existence of nonlinear disturbances due to all three wave modes in the coronal response to the expanding driver magnetic fields.

Steinolfson, R. S.↗

NASA NTRS1991

Free-stream turbulence and concave curvature effects on heated, transitional boundary layers, volume 1

An experimental investigation of the transition process on flat-plate and concave curved-wall boundary layers for various free-streem turbulence levels was performed. Where possible, sampling according to the intermittency function was made. Such sampling allowed segregation of the signal into two types of behavior: laminar-like and turbulent-like. The results from the investigation are discussed. Documentation is presented in two volumes. Volume one contains the text of the report including figures and supporting appendices. Volume two contains data reduction program listings and tabulated data.

Kim, J.↗

NASA NTRS1935

Tank Tests of a Model of a Flying-boat Hull Having a Longitudinally Concave Planing Bottom

The NACA model 11-B, which has a longitudinally concave planing bottom forward of the step, was tested over a wide range of loading. The results of the tests are presented as curves of resistance and trimming moment plotted against speed for various trim angles and as curves of resistance coefficient at best trim angle, and trimming-moment coefficient. The characteristics of the form at the optimum trim are compared with those of NACA model 11-C which has the same form with the exception of a planing bottom longitudinally straight near the step. Photographs of the models being towed in the tank are included for a comparison of the spray patterns. At the best angles of trim in each case model 11-B has lower resistance at high speeds, a higher maximum positive trimming moment near the hump speed, and a more favorable spray pattern than of model 11-C.

Parkinson, J B↗

NASA NTRS1954

On the three-dimensional instability of laminar boundary layers on concave walls

A study is made of the stability of laminar boundary-layer profiles on slightly curved walls relative to small disturbances that result from vortices whose axes are parallel to the principal direction of flow. The result is an eigenvalue problem by which, for a given undisturbed flow at a prescribed wall, the amplification or decay is computed for each Reynolds number and each vortex thickness. For neutral disturbances (zero amplification) a critical Reynolds number is determined for each vortex distribution. The numerical calculation produces amplified disturbances on concave walls only.

FLOW, LAMINAR↗

NASA NTRS1994

Large-eddy simulation of a boundary layer with concave streamwise curvature

Turbulence modeling continues to be one of the most difficult problems in fluid mechanics. Existing prediction methods are well developed for certain classes of simple equilibrium flows, but are still not entirely satisfactory for a large category of complex non-equilibrium flows found in engineering practice. Direct and large-eddy simulation (LES) approaches have long been believed to have great potential for the accurate prediction of difficult turbulent flows, but the associated computational cost has been prohibitive for practical problems. This remains true for direct simulation but is no longer clear for large-eddy simulation. Advances in computer hardware, numerical methods, and subgrid-scale modeling have made it possible to conduct LES for flows or practical interest at Reynolds numbers in the range of laboratory experiments. The objective of this work is to apply ES and the dynamic subgrid-scale model to the flow of a boundary layer over a concave surface.

Lund, Thomas S.↗

NASA NTRS1958

Heat-Transfer Measurements on a 5.5- Inch-Diameter Hemispherical Concave Nose in Free Flight at Mach Numbers up to 6.6

The aerodynamic heat transfer to a hemispherical concave nose has been measured in free flight at Mach numbers from 3.5 to 6.6 with corresponding Reynolds numbers based on nose diameter from 7.4 x 10(exp 6) to 14 x 10(exp 6). Over the test Mach number range the heating on the cup nose, expressed as a ratio to the theoretical stagnation-point heating on a hemisphere nose of the same diameter, varied from 0.05 to 0.13 at the stagnation point of the cup, was approximately 0.1 at other locations within 40 deg of the stagnation point, and varied from 0.6 to 0.8 just inside the lip where the highest heating rates occurred. At a Mach number of 5 the total heat input integrated over the surface of the cup nose including the lip was 0.55 times the theoretical value for a hemisphere nose with laminar boundary layer and 0.76 times that for a flat face. The heating at the stagnation point was approximately 1/5 as great as steady-flow tunnel results. Extremely high heating rates at the stagnation point (on the order of 30 times the stagnation-point values of the present test), which have occurred in conjunction with unsteady oscillatory flow around cup noses in wind-tunnel tests at Mach and Reynolds numbers within the present test range, were not observed.

Levine, Jack↗

NASA NTRS2002

On the Numerical Convergence to Steady State of Hypersonic Flows Over Bodies with Concavities

Two recent numerical studies of hypersonic flows over bodies with concavities revealed problems with convergence to a steady state with an oft-used application of local-time-stepping. Both simulated flows showed a time-like, periodic shedding of vortices in a subsonic domain bounded by supersonic external flow although the simulations, using local-time-stepping, were not time accurate. Simple modifications to the numerical algorithm were implemented to enable implicit, first-order accurate in time simulations. Subsequent time-accurate simulations of the two test problems converged to a steady state. The baseline algorithm and modifications for temporal accuracy are described. The requirement for sub-iterations to achieve convergence is demonstrated. Failure to achieve convergence without time accuracy is conjectured to arise from temporal errors being continuously refocused into a subsonic domain.

Gnoffo, Peter A.↗

NASA NTRS1985

A Study of Laminar Separation Bubble in the Concave Region of an Airfoil Using Laser Velocimetry

Laser velocimetry (LV) was used to study the nature of laminar separation bubbles in the concave region of a 1.83-meter airfoil model which was tested in the NASA Langley Low Turbulence Pressure Tunnel. Three component, coincident data from LV measurements including histograms of particle velocity, mean velocity profiles, turbulence intensity, and Reynolds stresses within the shear layer were used to determine the locations of laminar separation, transition, and turbulent reattachment. Boundary-layer parameters determined from velocity profiles were used to compare the results with existing empirical relations for describing the laminar separation bubble.

Mangalam, Sivaramakrishnan↗