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Results for “AXIAL SYMMETRY”

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At least 145 records · Page 8
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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.↗
NASA NTRS1951

Supersonic flow around circular cones at angles of attack

The properties of conical flow without axial symmetry are analyzed. The flow around cones of circular cross section at small angles of attack is determined by correctly considering the effect of the entropy gradients in the flow.

Ferri, Antonio↗
NASA NTRS1952

Method of analysis for compressible flow through mixed-flow centrifugal impellers of arbitrary design

A method is presented for analysis of the compressible flow between the hub and the shroud of mixed-flow impellers of arbitrary design. Axial symmetry was assumed, but the forces in the meridional (hub to shroud) plane, which are derived from tangential pressure gradients, were taken into account. The method was applied to an experimental mixed-flow impeller. The analysis of the flow in the meridional plane of the impeller showed that the rotational forces, the blade curvature, and the hub-shroud profile can introduce severe velocity gradients along the hub and the shroud surfaces. Choked flow at the impeller inlet as determined by the analysis was verified by experimental results.

Hamrick, Joseph T↗
NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem

We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.

Shu, Frank H.↗
NASA NTRS1996

Nonlinear Analysis and Modeling of Tires

The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.

Noor, Ahmed K.↗
NASA NTRS1996

Ground Based Studies of Thermocapillary Flows in Levitated Drops

Ground-based experiments together with analytical studies are presently being conducted for levitated drops. Both acoustic and electrostatic techniques are being employed to achieve levitation of drops in a gaseous environment. The scientific effort is principally on the thermal and the fluid phenomena associated with the local heating of levitated drops, both at 1-g and at low-g. In particular, the thermocapillary flow associated with local spot heating is being studied. Fairly stable acoustic levitation of drops has been achieved with some exceptions when random rotational motion of the drop persists. The flow visualization has been carried out by light scattering from smoke particles for the exterior flow and fluorescent tracer particles in the drop. The results indicate a lack of axial symmetry in the internal flow even though the apparatus and the heating are symmetric. The theoretical studies for the past year have included fundamental analyses of acoustically levitated spherical drops. The flow associated with a particle near the velocity antinode is being investigated by the singular perturbation technique. As a first step towards understanding the effect of the particle displacement from the antinode, the flow field about the node has been calculated for the first time. The effect of the acoustic field on the interior of a liquid drop has also been investigated. The results predict that the internal flow field is very weak.

Sadhal, Satwindar Singh↗
NASA NTRS1960

The Numerical Calculation of Flow Past Conical Bodies Supporting Elliptic Conical Shock Waves at Finite Angles of Incidence

The inverse method, with the shock wave prescribed to be an elliptic cone at a finite angle of incidence, is applied to calculate numerically the supersonic perfect-gas flow past conical bodies not having axial symmetry. Two formulations of the problem are employed, one using a pair of stream functions and the other involving entropy and components of velocity. A number of solutions are presented, illustrating the numerical methods employed, and showing the effects of moderate variation of the initial parameters.

Briggs, Benjamin R.↗