Curvature after-effects as a function of the magnitude of curvature of the inspected material
Human observations of curvature after-effects as function of magnitude of curvature of inspected material
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Low-cost fabrication and direct bond installation of flat, single-curvature and compound-curvature ablative heat shield panels
Procedures for low cost fabrication and direct bond installation of flat, single curved, and compound curvature ablative heat shields on a DC-3 aircraft are discussed. The panel sizes and attachment locations are identified. In addition to the bonding of the four contoured panels, two flat panels were bonded to the nearly flat, lower surface of the center wing section. The detailed requirements and objectives of the investigation are described.
Norwood, L. B.↗
Curvature of the wind profile in the troposphere versus regions of CAT and non-CAT in the stratosphere
A discussion of the theoretical importance of the curvature of the wind profile to the amplitude of mountain waves is presented. Mechanisms favorable for clear air turbulence (CAT) are discussed in relation to such wave motions. It is shown that CAT encountered by the XB-70 aircraft in the stratosphere during expected mountain-wave conditions is related to the vertical gradient of curvature of the wind profile in the troposphere. Results indicate that 89% of the turbulent regions in the stratosphere occurred in expected mountain-wave areas and that 79% were located where the vertical gradient of curvature was positive in the 10-30,000 ft layer below. For the nonturbulent regions, 74% were outside expected mountain-wave areas and 98% of these occurred where the vertical gradient of curvature was negative. All the nonturbulent regions within expected mountain-wave areas occurred where the vertical gradient of curvature was negative.
Possiel, N.↗
Free-streaming radiation in cosmological models with spatial curvature
The effects of spatial curvature on radiation anisotropy are examined for the standard Friedmann-Robertson-Walker model universes. The effect of curvature is found to be very important when considering fluctuations with wavelengths comparable to the horizon. It is concluded that the behavior of radiation fluctuations in models with spatial curvature is quite different from that in spatially flat models, and that models with negative curvature are most strikingly different. It is therefore necessary to take the curvature into account in careful studies of the anisotropy of the microwave background.
Wilson, M. L.↗
Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades
The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.
Kvaternik, R. G.↗
NASTRAN modifications for recovering strains and curvatures
NASTRAN, NASA's general-purpose finite-element structural analysis program, has been modified to allow recovery of surface strains, reference plane strains, and local curvatures at nodes of general plane elements. NASTRAN routines that operate on element stress/strain/temperature relationships and strain/temperature relationships have been modified to incorporate generation and return of strains and curvatures in lieu of stresses. Strains and curvatures are then transformed to material axes and interpolated to generate corresponding strains and curvatures at nodes of element. This interpolation is accomplished using special surface-mapping function.
Chamis, C. C.↗
The crack problem in a specially orthotropic shell with double curvature
The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.
Delale, F.↗
Gravitropic basis of leaf blade nastic curvatures
The curvatures produced in leaf blades by auxin treatment have been described as nastic curvatures because the initial differential growth is always enhanced on the lower side, regardless of the side of application. It is now known, however, that blades can show differential growth of either the upper or the lower side depending on the conditions of treatment. The dorsiventrality of the blade therefore influences but does not limit the direction of curvature. The dorsiventral directionality of response to growth regulators and the response to changes in the orientation to gravity are seen as indicating that blade curvatures are analogous to negative or positive gravitropism. It is noted that neither blade hyponasty or epinasty can be accounted for by ethylene alone. Petiole responses, however, are not directional, and the leaf angle changes induced by rotation or auxin treatment can be accounted for by ethylene production.
Hayes, A. B.↗
The crack problem in a specially orthotropic shell with double curvature
The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip. Previously announced in STAR as N83-16782
Delale, F.↗
Convex curvature effects on the heated turbulent boundary layer
A convexly curved and isothermally heated wall with a 45-cm radius of curvature is subjected to turbulent boundary layer flow measurements in order to determine wall heat transfer rates and mean velocity and temperature profiles. Significant curvature effects are noted, with Stanton number and skin friction coefficient reductions of 35-40 percent by comparison with flat plate values for the same momentum or enthalpy thickness Reynolds numbers. Profiles of mean velocity and temperature show a more rapid growth of the wake regions, and a shortening of the log-linear region, as a result of curvature. Turbulent Prandtl numbers deduced from the mean temperature profiles under the assumption of a wall thermal law were found to be increased by 40-50 percent by this strong convex curvature.
Simon, T. W.↗
A mixing-length model for the prediction of convex curvature effects on turbulent boundary layers
A mixing-length model is developed for the prediction of turbulent boundary layers with convex streamwise curvature. For large layer thickness ratio, delta/R greater than 0.05, the model scales mixing length on the wall radius of curvature, R. For small delta/R, ordinary flat wall modeling is used for the mixing-length profile with curvature corrections, following the recommendations of Eide and Johnston (1976). Effects of streamwise change of curvature are considered; a strong lag from equilibrium is required when R increases downstream. Fifteen separate data sets were compared, including both hydrodynamic and heat transfer results. Six of these computations are presented and compared to experiment.
Adams, E. W.↗
Measurements of turbulent correlations in supersonic flows with longitudinal surface curvature
The effect of longitudinal surface curvature on the turbulent correlations of a supersonic turbulent boundary layer was studied experimentally in an axisymmetric channel. Upstream of the interaction, the nominal freestream Mach number was 3.78, the Reynolds number based on boundary layer momentum thickness was 5778, and the boundary layer thickness was 0.9 cm. For the flow with the longitudinal surface curvature, the overall turning angle was approximately 10.2 degrees, and maximum delta-j/kappa approximately 0.09. The shear stresses, measured by a hot wire anemometry, reached the peak values quite rapidly for the flow with surface curvature as compared to the corresponding flow without surface curvature.
Chou, J. H.↗
Stability of the cylindrical shell of variable curvature
This report is a first attempt to devise a calculation method for representing the buckling behavior of cylindrical shells of variable curvature. The problem occurs, for instance, in dimensioning wing noses, the stability of which is decisively influenced by the variability of curvature. The calculation is made possible by simplifying the stability equations (permissible for the shell of small curvature) and by assuming that the curvature 1/R as a function of the arc lengths can be represented by a very few Fourier terms. The formulas for the special case of an ellipse-like half oval with an axis ratio 1/3 ?= e ?= 1 under compression in longitudinal direction,shear, and a combination of shear and compression were evaluated. However, the results can also be applied approximately to an unsymmetrical oval-shell segment under compression, shear, and bending so that the numerical values contained in the diagrams 10 to 12 represent directly dimensioning data for the wing nose.
LOADS AND STRESSES, STRUCTURAL - BENDING↗
The importance of the curvature of the wind profile in determining regions of CAT and non-CAT
An investigation is conducted regarding the relationship between CAT and the curvature of the wind profile, taking into account cases of CAT encountered by the XB-70 in the stratosphere over the mountainous terrain of the western U.S. The results of the investigation show that the curvature of the wind profile is an important tropospheric variable in the determination of stratospheric CAT regions. These CAT regions are likely to occur in cases in which the curvature increases with height in the troposphere in areas when mountain waves are expected.
Possiel, N.↗
Relationships between the curvatures of tooth surfaces in three-dimensional gear systems
A three-dimensional gear system between crossing and intersecting axes is considered under the assumption that the first derivative of the transmission ratio is zero in the vicinity of the point of contact. The following are obtained; (1) an equation that relates the normal curvatures of the tooth surfaces in the section that passes through the vector of relative velocity; (2) a relation between the principal curvatures and principal directions of the two tooth surfaces; and (3) new formulas for determining the reduced curvatures of the surfaces.
Litvin, F. L.↗
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.↗
An experimental study of surface curvature effects on a supersonic turbulent boundary layer
The mean flow results of an experimental study of compressible turbulent boundary layers in an adverse pressure gradient with and without surface curvature effects are presented. The test was conducted in an axisymmetric flow facility. The upstream Reynolds number based on boundary layer momentum thickness was 5884 and the boundary layer thickness was 0.90 cm. The curvature effects were examined by studying two flows with essentially identical adverse pressure gradients. One flow was along a concave compression surface test section, while the other was along a straight-walled test section. Mean flow measurements included wall static pressure distributions, wall temperatures, pitot pressure profiles and total temperature profiles. The mean flow results indicated that the surface curvature resulted in a definite increase of turbulent mixing in the boundary layer.
Chou, J. H.↗
The effect of a short region of concave curvature on a supersonic turbulent boundary layer
Mean flow measurements have been made in a supersonic turbulent boundary layer experiencing a short region of concave curvature and an adverse pressure gradient. The incoming boundary layer had a Mach number of 2.87 and a unit Reynolds number of 6.3 x 10 to the 7th/m. Flow over constant radii curvatures of delta (0)/R = 0.10 and 0.02 with a fixed turning angle of 8 deg were investigated. Results indicate that both flows remain two-dimensional; length scales increase over their equilibrium values; the mean flow behaves similarly to subsonic flows experiencing concave curvature and lateral divergence; and boundary layer behavior is strongly similar to a corresponding 8 deg ramp flow.
Smits, A. J.↗