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At least 73 records · Page 4

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NASA NTRS1972

Some remarks on elastic crack-tip stress fields.

It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly determined. The result is closely related to Bueckner's (1970) weight function, through which the stress intensity factor is expressed as a sum of work-like products between applied forces and values of the weight function at their points of application. An example of the method is given wherein the solution for a crack in a remotely uniform stress field is used to generate the expression for the stress intensity factor due to an arbitrary traction distribution on the faces of a crack. A corresponding theory is developed in an appendix for three-dimensional crack problems, although this appears to be directly useful chiefly for problems in which there is axial symmetry.

Rice, J. R.↗

NASA NTRS1974

The magnetosphere of Jupiter as observed with Pioneer 10. I - Instrument and principal findings

Description of the first in situ observations of energetic electrons of energy greater than 0.06 MeV in the magnetosphere of Jupiter during November-December 1973. The outer magnetosphere has the form of a thin disklike quasi-trapping region extending from about 20 to over 100 Jovian radii. This magnetodisk is confined near the magnetic equatorial plane and has approximate axial symmetry about the magnetic axis of the planet. The observations inside a radial distance of 12 Jovian radii are well organized by a centered dipolar model of the planet's magnetic field with a tilt of 9.5 plus or minus 0.5 deg to the rotational axis and with pole at a system III longitude of 230 plus or minus 3 deg. Absolute omnidirectional intensities of electrons within the stable trapping region inside 20 Jovian radii are given for five energy ranges greater than 0.06, 0.55, 5.0, 21, and 31 MeV.

Van Allen, J. A.↗

NASA NTRS1975

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Shih, Tso-Shin↗

NASA NTRS1975

Evolution of rotating interstellar clouds. I - Numerical techniques

A method is described for the numerical calculation of the hydrodynamic evolution of a self-gravitating configuration in two space dimensions with assumed axial symmetry. The calculation is formulated in cylindrical coordinates with respect to a moving Eulerian grid and is solved using explicit hydrodynamics combined with implicit radiative transfer. The physics included is appropriate for calculation of the collapse of a rotating protostellar cloud. The gravitational field is obtained by means of an alternating-direction iterative technique. Numerical tests to demonstrate the correctness of the method are presented for special cases.

Black, D. C.↗

NASA NTRS1977

A normalized view of Venus

A few Mariner 10 images of Venus have been 'normalized' to a standard scattering geometry using the exact solution by Chandrasekhar (1950) involving his H functions. The most striking feature of the normalized images is the bright polar ring or cap beyond about 50 deg latitude circle and a narrower brightness frequency distribution. The brightness variation along a meridian shows substantial axial symmetry on a large scale, and small-scale brightness variations over the planet are no more than about 10%. Inferences regarding the polar cloud tops in light of available evidence are discussed. The variation of mean brightness and of the ratio of mean square deviation of brightness to average brightness is comparable to the performance limits of the vidicon camera for the image sequence lasting about a day, so that the variation in distribution of dark and bright features over the planet and the UV albedo of the planet over about a day is small.

Limaye, S.↗

NASA NTRS1978

The structure of vortex breakdown

The term 'vortex breakdown', as used in the reported investigation, refers to a disturbance characterized by the formation of an internal stagnation point on the vortex axis, followed by reversed flow in a region of limited axial extent. Two forms of vortex breakdown, which predominate, are shown in photographs. One form is called 'near-axisymmetric' (sometimes 'axisymmetric'), and the other is called 'spiral'. A survey is presented of work published since the 1972 review by Hall. Most experimental data taken since Hall's review have been in tubes, and the survey deals primarily with such cases. It is found that the assumption of axial-symmetry has produced useful results. The classification of flows as supercritical or subcritical, a step that assumes symmetry, has proved universally useful. Experiments show that vortex breakdown is always preceded by an upstream supercritical flow and followed by a subcritical wake. However, a comparison between experiments and attempts at prediction is less than encouraging. For a satisfactory understanding of the structure of vortex breakdown it is apparently necessary to take into account also aspects of asymmetry.

Leibovich, S.↗

NASA NTRS1980

Collapse and equilibrium of rotating, adiabatic clouds

A numerical hydrodynamics computer code analysis of the collapse and establishment of equilibrium of adiabatic gas clouds restricted to axial symmetry found that the clouds are originally uniform in density and rotation. The method can compare the dynamic collapse and approach to equilibrium with the data on incompressible uniformly rotating equilibrium clouds and on equilibrium structures of differentially rotating polytropes. It is concluded that the stellar formation theory indicates that the low alpha fragments produced at the termination of the dynamic isothermal collapse phase of interstellar clouds may undergo significant dynamic collapse in an adiabatic regime leading to transitory ring formation and additional fragmentation on a smaller scale.

Boss, A. P.↗

NASA NTRS1981

Solar wind flow about the terrestrial planets. I - Modeling bow shock position and shape

A three-parameter method for modeling the position and shape of planetary bow waves was chosen to model the near portion of the Venus, earth and Mars bow shocks, and its results were compared with those of models using one to six free variables. It was found that the relative effective shapes of the near Martian, Cytherean, and terrestrial bow shocks are ellipsoidal, paraboloidal, and hyperboloidal, respectively, in response to the increasing bluntness of the obstacles that the planets present to the solar wind. No significant deviations from axial symmetry were found when the near bow waves of the earth and Venus were mapped into the aberrated terminator plane, in agreement with gas dynamic theory predictions neglecting the effects of the IMF because of their minuteness.

Slavin, J. A.↗

NASA NTRS1981

Acoustic transmission in lined flow ducts - A finite element eigenvalue problem

The problem of acoustical transmission in lined ducts with subsonic mean flow is of considerable practical interest in the context of fan noise attenuation in the ducted inlet regions of turbofan aircraft engines. If nonaxisymmetric liners are present, a loss of axial symmetry results, and the study of acoustic transmission involves the solution of a full two-dimensional eigenvalue problem. The reported investigation is concerned with such an eigenvalue problem. The employed method of solution is effectively a two-dimensional analog of an approach considered by Astley and Eversman (1979). The approach makes use of a Galerkin Finite Element Method whereby the weighting and basis functions are generated automatically by the discretization.

Astley, R. J.↗

NASA NTRS1981

Flame structure in a swirl stabilized combustor inferred by radiant emission measurements

Results of measurements of time-averaged chemiluminescent emissions from CH, OH, and CO2 and of Na tracer emissions along lateral lines-of-sight through a cylindrical premixed, swirl-stabilized combustor are reported. Assuming axial symmetry and small optical depth, raw data are inverted to obtain local emission levels from these species as a function of radius. The chemiluminescent emissions are interpreted as signatures of chemical reaction and used in determining the regions of reactions and heat release in the combustor. The data are compared with composition and velocity data obtained in the combustor for identical operating conditions. The results demonstrate that reaction occurs in a relatively narrow, turbulent flame-like combustion zone which begins upstream of the time-averaged location of the swirl-induced recirculation zone and propagates around and laterally away from the recirculation zone into the unburned gas.

Beyler, C. L.↗

NASA NTRS1983

The Gravitational Potential Due to Uniform Disks and Rings

The gravitational potential of bodies possessing axial symmetry can be expressed as a power series in distance, with the Legendre polynomials as coefficients. Such series, however, converge so slowly in the neighborhood of thin, uniform disks and rings that too many series terms must be summed in order to obtain an accurate field measure. A gravitational potential expression is presently obtained in closed form, in terms of complete elliptic integrals.

Lass, H.↗

NASA NTRS1986

Magnetic nonequilibrium and current sheet formation

This paper investigates the equilibrium of a cluster of long, straight, twisted magnetic flux tubes extending in the z-direction in a highly conducting fluid, subject to the boundary condition that the cluster is surrounded by a uniform pressure P. It is shown that there is equilibrium only for axial symmetry, i.e., only for a single twisted flux tube. Any more complicated cluster of twisted tubes is subject to nonequilibrium reconnection of the transverse component of the field. The example provides another perspective on the general absence of equilibrium, and consequent rapid dissipation, of any magnetic field subject to random small-scale internal strains, such as the fields extending outward from the convective zones of stars.

Vainshtein, S. I.↗

NASA NTRS1987

Magnetospheric environments of outer planet rings - Influence of Saturn's axially symmetric magnetic field

Saturn's main rings exist within a zone of negligible magnetospheric losses and surface alteration effects, substantially due to the solid-body absorption of inwardly diffusing magnetospheric particles. This process is presently shown to be especially efficient in the inner magnetosphere of Saturn, due to the near-axial symmetry of the planetary magnetic field relative to the equatorial rotation plane; under the assumption of comparable diffusion rates, the inward magnetospheric particle transport is far more inhibited in the inner Saturnian magnetosphere than in the same regions of Jupiter and Uranus, even when only rings of comparable widths and depths are considered. In light of this, ring particle surface exposure to the ion fluxes of the radiation belt remains a prepossessing rationale for low Uranian ring albedos.

Hood, L. L.↗

NASA NTRS1989

Simplified calculation of solar flux distribution on the side wall of cylindrical cavity solar receivers

A simple solar flux calculation algorithm for a cylindrical cavity type solar receiver has been developed and implemented on an IBM PC-AT. Using cone optics, the contour error method is utilized to handle the slope error of a paraboloidal concentrator. The flux distribution on the side wall is calculated by integration of the energy incident from cones emanating from all the differential elements on the concentrator. The calculations are done for any set of dimensions and properties of the receiver and the concentrator, and account for any spillover on the aperture plate. The results of this algorithm compared excellently with those predicted by more complicated programs. Because of the utilization of axial symmetry and overall simplification, it is extremely fast. It can be esily extended to other axisymmetric receiver geometries.

Bhandari, P.↗

NASA NTRS1990

Idealized tip-to-tail waverider model

The flow field of an idealized cone-derived waverider is axisymmetric. This forebody feature is preserved for the rest of the vehicle, including the inlet, cowl, combustor, and nozzle. There is thus an inviscid, tip-to-tail model in which both the external and internal flows are axisymmetric. The assumption of axial symmetry provides a major simplification for the analysis and allows for a systematic integration of the propulsion unit with the aerodynamics. The code is an initial formulation that provides only the most basic engineering data, such as lift, thrust, drag, and fuel consumption for a point-designed vehicle that may be cruising at a low hypersonic Mach number. The user may specify flight altitude and Mach number, a multiple shock configuration for the inlet, a few basic geometric parameter, H2 or CH4 as fuel, the fuel/air ratio, etc. A new design concept is used for the nozzle that avoids shock waves, minimizes the nozzle length, and may maximize its thrust. A general description of the model is provided with emphasis on the design of the nozzle and fins. Preliminary results are presented that compare the cruise flight range using H2 or CH4 as the fuel.

Emanuel, G.↗

NASA NTRS1991

Continuum modeling of catastrophic collisions

A two dimensional hydrocode based on 2-D SALE was modified to include strength effects and fragmentation equations for fracture resulting from tensile stress in one dimension. Output from this code includes a complete fragmentation summary for each cell of the modeled object: fragment size (mass) distribution, vector velocities of particles, peak values of pressure and tensile stress, and peak strain rates associated with fragmentation. Contour plots showing pressure and temperature at given times within the object are also produced. By invoking axial symmetry, three dimensional events can be modeled such as zero impact parameter collisions between asteroids. The code was tested against the one dimensional model and the analytical solution for a linearly increasing tensile stress under constant strain rate.

Ryan, Eileen V.↗

NASA NTRS1992

The density profile of the elliptical planetary nebula NGC 3242

We present the three-dimensional density structure of the elliptical planetary nebula NGC 3242, deconvolved from its H-alpha image. Using the simplistic assumptions that each mass element preserves its original velocity, which is radial and depends only on latitude, we deduce from this density profile the variation of mass-loss rate from the progenitor of NGC 3242 with latitude and time. The resulting somewhat qualitative mass-loss geometry and history are used to constrain models for the formation of the elliptical structure of NGC 3242. We argue that a triple system, with a very close brown dwarf companion and a more massive distant tertiary star, is compatible with the morphology of NGC 3242. In this model the brown dwarf, of about 0.01 solar mass, shared a common envelope with the progenitor star, and spun up the envelope through deposition of angular momentum. The oblate rotating envelope blew an axisymmetrical wind. We suggest that the presence of a third star, with a mass of about 1 solar mass and an orbital period of about 4000 years, could have caused the large scale deviation from axial symmetry seen in the density structure.

Soker, Noam↗

NASA NTRS1992

Properties of the gravity fields of terrestrial planets

The properties of the gravity fields of the earth, Mars, and Venus, as expressed by spherical harmonic coefficients, are examined, using the harmonic expansions of the respective planetary topographies reported by Balmino et al. (1973), Bills and Ferrari (1978), and Bills and Kobrick (1985). The items examined include the spectral magnitudes and slopes of the gravity coefficients; the correlations between gravity and topography; and the correlations among different gravity harmonics, expressed by axiality and angularity. It was found that Venus differs from the other two planets in its great apparent depths of compensation, indicating a tectonics dominated by a stiff upper mantle. In addition, Venus has less activity deep in the mantle than do earth or Mars. Mars is marked by large gravity irregularities, as well as by their axial symmetry on a global scale. Although earth is probably the most peculiar planet, spherical harmonics do not bring out its varied characteristics. It is clearly a more active planet than Venus, with activity deep in the mantle. The lower magnitude of its higher harmonics is considered to be due to water recycled to the upper mantle.

Kaula, William M.↗