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NASA NTRS1981

Topology of three-dimensional separated flows

Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.

Tobak, M.↗

NASA NTRS1981

Automated syringe sampler

A number of sampling services are disposed in a rack which slides into a housing. In response to a signal from an antenna, the circutry elements are activated which provide power individually, collectively, or selectively to a servomechanism thereby moving an actuator arm and the attached jawed bracket supporting an evaculated tube towards a stationary needle. One open end of the needle extends through the side wall of a conduit to the interior and the other open end is maintained within the protective sleeve, supported by a bifurcated bracket. A septum in punctured by the end of the needle within the sleeve and a sample of the fluid medium in the conduit flows through the needle and is transferred to a tube. The signal to the servo is then reversed and the actuator arm moves the tube back to its original position permitting the septum to expand and seal the hole made by the needle. The jawed bracket is attached by pivot to the actuator to facilitate tube replacement.

Purgold, G. C.↗

NASA NTRS1981

Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies

The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.

Broucke, R.↗

NASA NTRS1981

Static noise tests on modified augmentor wing jet STOL research aircraft

Noise measurements were made to determine if recent modifications made to the bifurcated jetpipe to increase engine thrust had at the same time reduced the noise level. The noise field was measured by a 6-microphone array positioned on a 30.5m (100 ft) sideline between 90 and 150 degrees from the left engine inlet. Noise levels were recorded at three flap angles over a range of engine thrust settings from flight idle to emergency power and plotted in one-third octave band spectra. Little attenuation was observed at maximum power, but significant attenuation was achieved at approach and cruise power levels.

Cook, G. R.↗

NASA NTRS1982

Coaxial prime focus feeds for paraboloidal reflectors

A TE11 - TM11 dual mode coaxial feed for use in prime focus paraboloidal antenna systems is investigated. The scattering matrix parameters of the internal bifurcation junction was determined by the residue calculus technique. The scattering parameters and radiation fields of the aperture were found from the Weinstein solution. The optimum modeing ratio for minimum cross-polarization was determined along with the corresponding optimum feed dimensions. A peak cross-polarization level of -58 dB is predicted. The frequency characteristics were also investigated and a bandwidth of 5% is predicted over which the cross-polarization remains below -30 dB, the input VSWR is below 1.15, and the phase error is less than 10 deg. Theoretical radiation patterns and efficiency curves for a paraboloidal reflector illuminated by this feed were computed. The predicted sidelobe level is below -30 dB and aperture efficiencies greater than 70% are possible. Experimental results are also presented that substantiates the theoretical results. In addition, experimental results for a 'short-cup' coaxial feed are given. The report includes extensive design data for the dual-mode feed along with performance curves showing cross-polarization as a function of feed parameters. The feed is useful for low-cost ground based receiving antennas for use in direct television satellite broadcasting service.

Collin, R. E.↗

NASA NTRS1982

Minimization versus homotopy algorithms

The relative merits and demerits of the minimization techniques are assessed using globally convergent quasi-Newton algorithms on the one hand and the homotopy algorithms on the other hand for the solution of problems of nonlinear structural analysis. Like the homotopy algorithms, the globally convergent quasi-Newton algorithms are equally suited for the solution of the nonlinear equations of structural analysis directly without having to pose the problem as an equivalent minimization problem. In the close neighborhood of the limit and bifurcation points quasi-Newton algorithms experience difficulties. Homotopy algorithms are robust for practically all types of nonlinear problems but are computationally not as cost effective since they provide an extremely accurate prediction of the response by calculating it as a large number of points. Globally convergent algorithms can perform well with very approximate Hessians, while homotopy algorithms require extremely accurate Hessians. While quasi-Newton algorithms can be very easily structured to exploit sparsity and symmetry, homotopy algorithms are not presently so structured and would require special modifications for exploitation of such features without sacrificing robustness and global convergence.

Kamat, M. P.↗

NASA NTRS1981

Chaotic behavior and fluid dynamics

It is shown that while fluids are very complicated systems having many degrees of freedom, the basic mechanism underlying the observed chaotic behavior of fluid turbulence may not require the consideration of many degrees of freedom. Simple dynamical systems display erratic and chaotic behavior reminiscent of turbulence, the key to which is the 'sensitivity to initial conditions' introduced by Ruelle (1978). Simple models which are sensitive to initial data and have permitted workers to study chaotic behavior are described, with attention to the Lorenz equations, Landau's idea of a continuous transition to turbulence via an infinite cascade of bifurcations, and one-dimensional maps.

Yorke, J. A.↗

NASA NTRS1982

On the coronae of rapidly rotating stars. III - An improved coronal rotation-activity relation in late type dwarfs

While it has previously been claimed that X-ray luminosity, or surface flux, varies as a power of the rotational velocity in G dwarfs, it is demonstrated that a single power law does not provide an acceptable fit to all the data. The data are describable by a power law, with a break in slope near a 12-day period which occurs at the same rotational period as the bifurcation in Vaughan and Preston's (1980) chromospheric study of G dwarfs. It is speculated that the two breaks are both related and due to a change in the stellar dynamo mode, which, at a rotation period of 12 days, corresponds to an age of one billion years for single G dwarfs.

Walter, F. M.↗

NASA NTRS1982

The condensational instability in the solar transition region and corona

The stability of plasmas at temperatures and densities typical of the solar transition region and corona is investigated using both a linear analysis and nonlinear time-dependent numerical simulations. Growth rates, decay rates, and oscillation frequencies of the perturbations determined from the linear analysis are in excellent agreement with the simulations. The nonlinear regime is characterized by a bifurcation of the plasma into a cool dense condensation surrounded by a hot tenuous corona. The condensation may then be accelerated by forces in the plasma such as those arising from gravity or differential heating. Finally, the results of the detailed simulation show that the transition region is a dynamically stable structure which is the result of the nonlinear evolution of the condensational instability.

Oran, E. S.↗

NASA NTRS1982

Analytical and experimental vibration and buckling characteristics of a pretensioned stayed column

Modal vibration tests to determine lateral modes of vibration of a stayed column and static axial compression tests to determine the column's buckling and postbuckling behavior have been performed. Effects of stay tension levels and vibration-load interaction are presented. Two finite element models are used to analyze the column, a three-dimensional frame using NASTRAN and an equivalent two-dimensional frame using an exact dynamic stiffness matrix. Both analyses correlated well with the linear vibration and buckling experimental data. Results indicate premature buckling of the column due to vibration-load interaction and nonlinear oscillations due to stay slackening. Postbuckling behavior of the column is unusual because of stay slackening and results in a postbuckling restoring force of less than the bifurcation buckling load. Guidelines for design of pretensioned structures are presented which consider buckling, postbuckling and vibration behavior.

Belvin, W. K.↗

NASA NTRS1981

A family of solution algorithms for nonlinear structural analysis based on relaxation equations

A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that it provides a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.

Park, K. C.↗

NASA NTRS1982

Transient phenomena of shock-induced turbulent separation for a spikebody and stalling airfoil at transonic and supersonic speeds

The time-dependent, compressible, Reynolds-averaged, full Navier-Stokes equations are applied to solve an axisymmetric flow around a forward-facing stepbody (spikebody) at supersonic speeds and a stalling airfoil at transonic speeds. Important transient and unsteady phenomena, not yet well understood, are examined, and significant new findings of the present solution to the phenomena are discussed. The phenomena described in detail are as follows: The evolution of the shock wave pressure built up by the impact of the pressure waves, one from the trailing edge; the separation of the flow as influenced by the shock wave; the location of the reversed flow, the separation point, and the reattachment point; and the transient (or unsteady) phenomena of the flow pulsation, oscillation, and stalling of the body and airfoil wake flow. The numerical results show that the transient flow instability is caused by a supersonic jet induced in the separation bubble by the shock-bifurcation (lambda shock) mechanism between the separation shock and the reflected shock. Pulsation and stall phenomena are caused by a sudden increase in the leading-edge pressure due to the jet and the separation bubble interacting along the stagnation point flow.

Yoshikawa, K. K.↗

NASA NTRS1982

Polar views of the earth's aurora with Dynamics Explorer

Preliminary examination of the first global auroral images gained with the vacuum-ultraviolet imaging photometer on board DE 1 reveals a remarkable spatial configuration of auroral luminosities. Frequently the northern auroral oval is bifurcated by a sun-aligned arc extending from the midday auroral zone to the nighttime sector of the oval. Simultaneous plasma measurements with the low-altitude DE-2 spacecraft are used to show that the character of plasmas above the polar arc is similar to those found over the poleward zones of the auroral oval. The spatial distribution of auroral luminosities is suggestive of a two-cell structure of current systems and convection electric fields over the earth's polar cap and a similar division of the corresponding lobe in the magnetotail.

Frank, L. A.↗

NASA NTRS1983

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

Noor, A. K.↗

NASA NTRS1983

Period doubling and chaos in partial differential equations for thermosolutal convection

Numerical experiments on two-dimensional thermosolutal convection reveal a transition from periodic oscillations to chaos through a sequence of period-doubling bifurcations. Within the chaotic region there are narrow periodic windows. This is the first example of period-doubling in solutions of partial differential equations. A truncated model indicates that this behavior is associated with heteroclinic explosions.

Moore, D. R.↗

NASA NTRS1983

On neutron star structure and the millisecond pulsar

The millisecond pulsar is the first observed example of a neutron star spinning rapidly enough to approach the Jacobi bifurcation point and thus affords the possibility of constraining neutron star physics. The pulsar must be rotating below the critical frequency at which its equilibrium configuration would become nonaxisymmetric, since the lifetime of this configuration against decay by gravitational radiation is very short. This critical frequency may be used to set a lower limit of 2 x 10 to the 14th g/cu cm on the density of the star. If the mass is 0.5-1.5 solar mass, several of the stiffer neutron star equations of state may be ruled out, and the radius should be less than 16 km. The condition for axisymmetry also imposes an upper limit on the rotation rate to which neutron stars may be spun up by accretion disks in binary systems.

Harding, A. K.↗

NASA NTRS1983

The evolution equations for Taylor vortices in the small gap limit

The centrifugal instability of the viscous fluid flow between concentric circular cylinders in the small gap limit is considered. The amplitude of the Taylor vortex is allowed to depend on a slow time variable, a slow axial variable, and the polar angle. It is shown that the amplitude of the vortex cannot in general be described by a single amplitude equation. However, if the axial variations are periodic a single amplitude equation can be derived. In the absence of any slow axial variations it is shown that a Taylor vortex remains stable to wavy vortex perturbations. Furthermore, in this situation, stable nonaxisymmetric modes can occur but do not bifurcate from the Taylor vortex state. The stability of these modes is shown to be governed by a modified form of the Eckhaus criterion.

Hall, P.↗

NASA NTRS1984

Mathematical modeling of the aerodynamic characteristics in flight dynamics

Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

Tobak, M.↗