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At least 253 records · Page 14

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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.↗

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

Nonlinear problems in flight dynamics

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Chapman, G. T.↗

NASA NTRS1984

Tubing and cable cutting tool

A hand held hydraulic cutting tool was developed which is particularly useful in deactivating ejection seats in military aircraft rescue operations. The tool consists primarily of a hydraulic system composed of a fluid reservoir, a pumping piston, and an actuator piston. Mechanical cutting jaws are attached to the actuator piston rod. The hydraulic system is controlled by a pump handle. As the pump handle is operated the actuator piston rod is forced outward and thus the cutting jaws are forced together. The frame of the device is a flexible metal tubing which permits easy positioning of the tool cutting jaws in remote and normally inaccessible locations. Bifurcated cutting edges ensure removal of a section of the tubing or cable to thereby reduce the possibility of accidental reactivation of the tubing or cable being severed.

Mcsmith, D. D.↗

NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗

NASA NTRS1984

Numerical Investigation of unsteady inlet flow fields

The flow field within an unsteady, two-dimensional inlet is studied numerically, using a two dimensional Navier Stokes and a one-dimensional inviscid model. Unsteadiness is introduced by varying the outflow pressure boundary condition. The cases considered include outflow pressure variations which were a single pressure pulse, a rapid increase and a sine function. The amplitude of the imposed exit plane pressure disturbance varied between 1 percent and 20 percent of the mean exit pressure. At the higher levels of pressure fluctuation, the viscous flow field results bore little resemblance to the inviscid ones. The viscous solution included such phenomena as shock trains and bifurcating separation pockets. The induced velocity at the outflow plane predicted by the viscous model differs significantly from accoustical theory or small perturbation results.

Hsieh, T.↗

NASA NTRS1984

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗

NASA NTRS1984

A numerical analysis of contact and limit-point behavior in a class of problems of finite elastic deformation

Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.

Endo, T.↗

NASA NTRS1984

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 nonaxisymmeric 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. Previously announced in STAR as N84-10501

Hall, P.↗

NASA NTRS1984

Flow in a differentially rotated cylindrical drop at moderate Reynolds number

Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Re sub c. The slope of the locus of Re sub c for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio for exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.

Harriott, G. M.↗

NASA NTRS1984

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Hall, P.↗