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NASA NTRS1983

Scattering from randomly oriented circular discs with application to vegetation

A vegetation layer is modeled by a collection of randomly oriented circular discs over a half space. The backscattering coefficient from such a half space is computed using the radiative transfer theory. It is shown that significantly different results are obtained from this theory as compared with some earlier investigations using the same modeling approach but with restricted disc orientations. In particular, the backscattered cross-polarized returns cannot have a fast increasing angular trend which is inconsistent with measurements. By setting the appropriate angle of orientation to zero the theory reduces to previously published results. Comparisons are shown with measurements taken from milo, corn and wheat and good agreements are obtained for both polarized and cross-polarized returns.

Karam, M. A.↗

NASA NTRS1983

Green's function solution and applications for cracks emanating from a circular hole in an infinite sheet

Stress-intensity factors are obtained for point loaded equal length cracks emanating from a circular hole in an infinite plate. A series approach and the Muskhelishvili formulation in the two-dimensional theory of elasticity are used to derive the solution. The applicability of the solution is demonstrated by using it as a Green's function to obtain stress-intensity factors in the case of (1) biaxial tension and pure shear of an infinite plate and (2) tension and pin loading of a plate with cracks emanating from one hole in a row of holes.

Shivakumar, V.↗

NASA NTRS1985

Circularly-Polarized Microstrip Antenna

Microstrip construction compact for mobile applications. Circularly polarized microstrip antenna made of concentric cylindrical layers of conductive and dielectric materials. Coaxial cable feedlines connected to horizontal and vertical subelements from inside. Vertical subelement acts as ground for horizontal subelement.

Stanton, P. H.↗

NASA NTRS1983

Prediction of impact force and duration during low velocity impact on circular composite laminates

Two simple and improved models--energy-balance and spring-mass--were developed to calculate impact force and duration during low velocity impact of circular composite plates. Both models include the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations of the plate. The plate was transversely isotropic graphite/epoxy composite laminate and the impactor was a steel sphere. Calculated impact forces from the two analyses agreed with each other. The analyses were verified by comparing the results with reported test data.

Shivakumar, K. N.↗

NASA NTRS1984

An empirical method for predicting the mixing noise levels of subsonic circular and coaxial jets

An empirical method for predicting the static free field source noise levels of subsonic circular and coaxial jet flow streams is presented. The method was developed from an extensive data base of 817 jet tests obtained from five different government and industry sources in three nations. The prediction method defines the jet noise in terms of four components which are overall power level, power spectrum level, directivity index, and relative spectrum level. The values of these noise level components are defined on a grid consisting of seven frequency parameter values (Strouhal numbers) and seven directivity angles. The value of the noise level at each of these grid points is called a noise level coordinate and was defined as a function of five jet exhaust flow state parameters which are equivalent jet velocity, equivalent jet total temperature, the velocity ratio (outer stream to inner stream), temperature ratio, and area ratio. The functions were obtained by curve fitting in a least squares sense the noise level coordinates from the data base in a five dimensional flow state space using a third order Taylor series. The noise level coordinates define the component noise levels for all frequencies and directivities through a bicubic spline function.

Russell, J. W.↗

NASA NTRS1984

Steady viscous flow past a circular cylinder

Viscous flow past a circular cylinder becomes unstable around Reynolds number Re = 40. With a numerical technique based on Newton's method and made possible by the use of a supercomputer, steady (but unstable) solutions have been calculated up to Re = 400. It is found that the wake continues to grow in length approximately linearly with Re. However, in conflict with available asymptotic predictions, the width starts to increase very rapidly around Re = 300. All numerical calculations have been performed on the CDC CYBER 205 at the CDC Service Center in Arden Hills, Minnesota.

Fornberg, B.↗

NASA NTRS1984

Effect of a rotor wake on heat transfer from a circular cylinder

The effect of a rotor wake on heat transfer to a downstream stator was investigated. The rotor was modeled with a spoked wheel of 24 circular pins 1.59 mm in diameter. One of the stator pins was electrically heated in the midspan region and circumferentially averaged heat transfer coefficients were obtained. The experiment was run in an annular flow wind tunnel using air at ambient temperature and pressure. Reynolds numbers based on stator cylinder diameter ranged from .001 to .00001. Rotor blade passing frequencies ranged from zero to 2500 Hz. Stationary grids were used to vary the rotor inlet turbulence from one to four percent. The rotor-stator spacings were one and two stator pin diameters. In addition to the heat transfer coefficients, turbulence spectra and ensemble averaged wake profiles were measured. At the higher Reynolds numbers, which is the primary range of interest for turbulent heat transfer, the rotor wakes increased Nusselt number from 10 to 45 percent depending on conditions. At lower Reynolds numbers the effect was as much as a factor of two.

Simoneau, R. J.↗

NASA NTRS1984

Water-tunnel study of transition flow around circular cylinders

The recently reported phenomenon of asymmetric flow separation from a circular cylinder in the critical Reynolds number regime has been confirmed in a water-tunnel experiment. For the first time, an attempt was made to visualize the wake of the cylinder during the transition from subcritical to critical flow and to correlate the visualizations with lift and drag measurements. The occurrence of a dominant asymmetric-flow state was quite repeatable, both when increasing and decreasing the Reynolds number, resulting in a mean lift coefficient of C sub L approx 1.2 and a shift in the angle of the wake by about 12 deg. A distinctive step change in the drag and shedding frequency was also found to occur. A hysteresis was confirmed to exist in this region as the Reynolds number was cycled over the transition range. Both boundaries of the asymmetry appear to be supercritical bifurcations in the flow. The asymmetry was normally steady in the mean; however, there were instances when the direction of the asymmetry reversed and remained so for the duration of the Reynolds number sweep through this transition region. A second asymmetry was observed at a higher Reynolds number; however, the mean lift coefficient was much lower, and the direction of the asymmetry was not observed to reverse. Introducing a small local disturbance into the boundary layer was found to prevent the critical asymmetry from developing along the entire span of the cylinder.

Almosnino, D.↗

NASA NTRS1984

Investigation of the effects of pressure gradient, temperature and wall temperature ratio on the stagnation point heat transfer for circular cylinders and gas turbine vanes

Low and high pressure shock tubes were designed and constructed for the purpose of obtaining heat transfer data over a temperature range of 390 to 2500 K, pressures of 0.3 to 42 atm, and Mach numbers of 0.15 to 1.5 with and without pressure gradient. A square test section with adjustable top and bottom walls was constructed to produce the favorable and adverse pressure gradient over the flat plate with heat gages. A water cooled gas turbine nozzle cascade which is attached to the high pressure shock tube was obtained to measuse the heat flux over pressure and suction surfaces. Thin-film platinum heat gages with a response time of a few microseconds were developed and used to measure the heat flux for laminar, transition, and turbulent boundary layers. The laminar boundary heat flux on the shock tube wall agreed with Mirel's flat plate theory. Stagnation point heat transfer for circular cylinders at low temperature compared with the theoretical prediction, but for a gas temperature of 922 K the heat fluxes were higher than the predicted values. Preliminary flat plate heat transfer data were measured for laminar, transition, and turbulent boundary layers with and without pressure gradients for free-stream temperatures of 350 to 2575 K and flow Mach numbers of 0.11 to 1.9. The experimental heat flux data were correlated with the laminar and turbulent theories and the agreement was good at low temperatures which was not the case for higher temperatures.

Nagamatsu, H. T.↗

NASA NTRS1983

Turbulence and surface heat transfer near the stagnation point of a circular cylinder in turbulent flow

A turbulent boundary layer flow analysis of the momentum and thermal flow fields near the forward stagnation point due to a circular cylinder in turbulent cross flow is presented. Turbulence modeling length scale, anisotropic turbulence initial profiles and boundary conditions were identified as functions of the cross flow turbulence intensity and the boundary layer flow far field velocity. These parameters were used in a numerical computational procedure to calculate the mean velocity, mean temperature, and turbulence double correlation profiles within the flow field. The effects of the cross flow turbulence on the stagnation region momentum and thermal flow fields were investigated. This analysis predicted the existing measurements of the stagnation region mean velocity and surface heat transfer rate with cross flow Reynolds number and turbulence intensity less than 250,000 and 0.05, respectively.

Wang, C. R.↗

NASA NTRS1984

Large deflections of circular isotropic membranes subjected to arbitrary axisymmetric loading

Circular membranes with fixed peripheral edges, subjected to arbitrary axisymmetric loading are analyzed. A single governing differential equation in terms of radial stress is used. This nonlinear governing equation is solved using the finite difference method in conjunction with Newton-Raphson method. Three loading cases, namely (1) uniformly loaded membrane, (2) a membrane with uniform load over an inner portion, and (3) a membrane with ring load, are analyzed. Calculated central displacement and the central and edge radial stresses for uniformly loaded membrane, agree extremely well with the classical solution.

Kelkar, A.↗

NASA NTRS1984

Mass transfer from a circular cylinder: Effects of flow unsteadiness and slight nonuniformities

Experiments were performed to determine the effect of periodic variations in the angle of the flow incident to a turbine blade on its leading edge heat load. To model this situation, measurements were made on a circular cylinder oscillating rotationally in a uniform steady flow. A naphthalene mass transfer technique was developed and used in the experiments and heat transfer rates are inferred from the results. The investigation consisted of two parts. In the first, a stationary cylinder was used and the transfer rate was measured for Re = 75,000 to 110,000 and turbulence levels from .34 percent to 4.9 percent. Comparisons with both theory and the results of others demonstrate that the accuracy and repeatability of the developed mass transfer technique is about + or - 2 percent, a large improvement over similar methods. In the second part identical flow conditions were used but the cylinder was oscillated. A Strouhal number range from .0071 to .1406 was covered. Comparisons of the unsteady and steady results indicate that the magnitude of the effect of oscillation is small and dependent on the incident turbulence conditions.

Marziale, M. L.↗

NASA NTRS1984

Stress analysis of multilayered plates around circular holes

The elasticity problem for a thick plate consisting of two bonded dissimilar homogeneous layers is considered. It is assumed that the plate is infinite, contains a circular hole, and is subjected to axisymmetric external loads. A technique suitable to the formulation of three-dimensional boundary value problems is introduced and applied to the three-dimensional elasticity solution of an infinite plate with a hole. The effect of Poisson's ratio is studied in some detail, and the axisymmetric problem of a laminated plate is solved. The stresses at the interface are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singularity is presented and the stress intensity factors are computed. Some of the results are compared with those found from the finite element method. The agreement between the two sets with regard to trend and magnitude is found to be very satisfactory.

Delale, F.↗

NASA NTRS1984

Euler and Navier-Stokes solutions for supersonic shear flow past a circular cylinder

Euler and Navier-Stokes solutions of the supersonic shear flow past a circular cylinder are obtained. These solutions are used to study the basic flow structure around the cylinder. Both the inviscid and viscous calculations show the formation of a large recirculating flow region around the front stagnation point. The calculations further show that the overall size of the recirculating region is approximately the same for the Euler and Navier-Stokes solutions but the inside structure is quite different. The inviscid flow shows only one vortex whereas the viscous flow shows two vortices inside the recirculating flow region. The inner vortex in the Navier-Stokes solution is formed primarily due to the viscous effects near the body surface and its size depends upon the Reynolds number. It is found that with increasing Reynolds number, the inner vortex diminishes in size and the Navier-Stokes solution asymptotically approaches the Euler solution. These results indicate that the Euler equations may correctly predict certain high Reynolds number separation phenomenon in flows with natural inviscid vorticity source.

Kumar, A.↗

NASA NTRS1983

An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder

Attention is given to an experimental investigation of transport processes in the near wake of a circular cylinder, for a Reynolds number of 140,000, in which an X-array of hot wire probes mounted on a pair of whirling arms was used for flow measurement. Rotation of the arms in a uniform flow applies a wide range of relative flow angles to these X-arrays, making them inherently self-calibrating in pitch. A phase signal synchronized with the vortex-shedding process allowed a sorting of the velocity data into 16 populations, each having essentially constant phase. An ensemble average for each population yielded a sequence of pictures of the instantaneous mean flow field in which the vortices are frozen, as they would be on a photograph. The measurements also yield nonsteady mean data for velocity, intermittency, vorticity, stress, and turbulent energy production, as a function of phase. Emphasis is given in a discussion of study results to the nonsteady mean flow, which emerges as a pattern of centers and saddles in a frame of reference that moves with the eddies. The kinematics of the vortex formation process are described in terms of the formation and evolution of saddle points between vortices in the first few diameters of the near wake.

Cantwell, B.↗

NASA NTRS1983

The input mobility of an infinite circular cylindrical elastic shell filled with fluid

The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h/a = 0.05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.

Fuller, C. R.↗

NASA NTRS1984

A temperature correlation for the radiation resistance of a thick-walled circular duct exhausting a hot gas

It is often useful to know the radiation impedance of an unflanged but thick-walled circular duct exhausting a hot gas into relatively cold surroundings. The reactive component is shown to be insensitive to temperature, but the resistive component is shown to be temperature dependent. A temperature correlation is developed permitting prediction of the radiation resistance from a knowledge of the temperature difference between the ambient air and the gas flowing from the duct, and a physical basis for this correlation is presented.

Mahan, J. R.↗

NASA NTRS1984

Compression failure characteristics of + or - 45-deg-dominated laminates with a circular hole or impact damage

An investigation of the compression failure characteristics of + or - 45-deg-dominated laminates with a circular hole or impact damage was conducted. Graphite-epoxy laminates consisting of all + or - 45-deg plies and of + or - 45-deg and 90-deg plies were evaluated. Inplane shearing between the fibers and matrix (i.e., matrix shearing) was found to be the primary compression failure mechanism for an all + or - 45-deg laminate with a hole. The failure mechanism for the + or 45-deg-dominated laminates with a hole appeared to be a combination of delamination and matrix shearing. The compression failure stresses and strains for both the all + or - 45-deg laminate and the + or - 45-deg-dominated laminates were unaffected by impact damage at an energy level of 5.5 J when compared to results for undamaged control specimens. The failure stresses and strains for all laminates with impact damage at an energy level of 17.0 J or of 34.3 J were significantly lower than the corresponding data for the undamaged control specimens. The failure stresses and strains for these impact-damaged specimens were independent of the percentage of 90-deg plies in the laminate.

Shuart, M. J.↗