Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “bifurcation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33

An introduction to chaos theory in CFD

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Pulliam, Thomas H.↗

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Smyrlis, Yiorgos S.↗

Nondimensional parameters and equations for buckling of symmetrically laminated thin elastic shallow shells

A method of deriving nondimensional equations and identifying the fundamental parameters associated with bifurcation buckling of anisotropic shells subjected to combined loads is presented. The procedure and rationale used to obtain useful nondimensional forms of the transverse equilibrium and compatibility equations for buckling are presented. Fundamental parameters are identified that represent the importance of both membrane and bending orthotropy and anisotropy on the results.

Nemeth, Michael P.↗

A study of the response of nonlinear springs

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Hyer, M. W.↗

Effect of tabs on the evolution of an axisymmetric jet

The effect of vortex generators, in the form of small tabs at the nozzle exit, on the evolution of an axisymmetric jet was investigated experimentally over a jet Mach number range of 0.34 to 1.81. The effects of one, two, and four tabs were studied in comparison with the corresponding case without a tab. Each tab introduced an indentation in the shear layer, apparently through the action of streamwise vortices which appeared to be of the trailing vortex type originating from the tips of the tab rather that of the necklace vortex type originating from the base of the tab. The resultant effect of two tabs, placed at diametrically opposite locations, was to essentially bifurcate the jet. The influence of the tabs was essentially the same at subsonic and supersonic conditions indicating that compressibility has little to do with the effect.

Zaman, K. B. M. Q.↗

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 3: Advanced Fan Section Grid Generator Final Report and Computer Program User's Manual

A procedure is studied for generating three-dimensional grids for advanced turbofan engine fan section geometries. The procedure constructs a discrete mesh about engine sections containing the fan stage, an arbitrary number of axisymmetric radial flow splitters, a booster stage, and a bifurcated core/bypass flow duct with guide vanes. The mesh is an h-type grid system, the points being distributed with a transfinite interpolation scheme with axial and radial spacing being user specified. Elliptic smoothing of the grid in the meridional plane is a post-process option. The grid generation scheme is consistent with aerodynamic analyses utilizing the average-passage equation system developed by Dr. John Adamczyk of NASA Lewis. This flow solution scheme requires a series of blade specific grids each having a common axisymmetric mesh, but varying in the circumferential direction according to the geometry of the specific blade row.

Crook, Andrew J.↗

Chaos in driven Alfven systems

The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Hada, T.↗

Nonlinear behavior of solar gravity modes driven by He-3 in the core. II - Numerical simulations

The nonlinear behavior of gravity-mode oscillations driven by He-3-destroying reactions in the solar core has been examined by numerically integrating equations describing a very simplified model. The results of a previous bifurcation analysis, which suggest that such oscillations are unlikely to attain amplitudes sufficient to trigger core convection, are verified. These results are extended to models whose nuclear reaction rates and thermal stratification represent the core somewhat more accurately. Nonlinear processes give rise to a preference for the oscillations to develop as standing waves rather than traveling waves, thus breaking the degeneracy between these two types of motion which exists in linearized theory. Study of the large-amplitude behavior of the oscillations is hindered by a tendency for the model to become thermally unstable.

Merryfield, William J.↗

N-body models

The experimental discovery of an overstability in the central regions of galaxies is briefly discussed, and numerical methods for integrating orbits are briefly addressed. The overstability manifests itself as a growing amplitude in the orbit of a galaxy's nucleus about its mass centroid. This finding may complicate studies of the topological properties of orbits and studies of the bifurcation structure of orbits. A sample problem is used to illustrate the importance of a Liouville theorem in N-body calculations.

Miller, R. H.↗

An investigation of chaotic Kolmogorov flows

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Platt, N.↗

CO fundamental lines - Indicators for inhomogeneous atmospheres in cool stars

Carbon monoxide fundamental lines near 4.7 microns are employed to probe the thermal structure of the atmospheres of cool stars. A new non-LTE radiation transfer code is used to analyze high-resolution infrared CO line spectra and derive observation-based stellar atmosphere models. The main results are: (1) the CO-based models developed here deviate strongly from previously published models based on UV/visible observations; (2) varying degrees of agreement between the CO empirical models and predictions based on theoretical radiative-equilibrium atmosphere models are found; and (3) the parameter used to quantify this agreement is anticorrelated with the magnitude of chromospheric activity in the observed stars. These results suggest thermally bifurcated upper atmospheres as the standard case for cool stars.

Wiedemann, Guenter↗

Ultrastructural and cytochemical evidence for single impulse initiation zones in vestibular macular nerve fibers of rat

Cupric ion-ferricyanide labeling methods and related ferrocyanide-stained tissues were used to locate the characterize, at the ultrastructural level, presumptive impulse initiation zones in the three types of vestibular macular nerve fibers. Large-diameter, M-type vestibular nerve fibers terminate in a calyx at the heminode, and labeling is coextensive with the base of the calyx. Intermediate, M/U-type nerve fibers have short, unmyelinated preterminal segments that sometimes bifurcate intamacularly, and small-diameter, U-type nerve fibers have long, unmyelinated preterminal axons and up to three branches. Preterminals of these nerve fibers display ultrastructural heterogeneity that is correlated with labeling patterns for sodium channels and/or associated polyanionic sites. They have a nodelike ultrastructure and label heavily from near the heminode to the base of the macula. Their intramacular branches, less organized ultrastructurally, label only slightly. Results indicate that vestibular nerve fibers have one impulse initiation zone, located near the heminode, that varies in length according to nerve fiber type. Structural heterogeneity may favor impulse conduction in the central direction, and length of the impulse initiation zone could influence nerve discharge patterns.

Ross, Muriel D.↗

Nonlinear dynamics and predictability in the atmospheric sciences

Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.

Ghil, M.↗

Simulation of high-speed (orbital) releases of electron attachment materials in the ionosphere

The dynamics of ionospheric plasma irregularities produced by the release of electron attachment materials at orbital velocities across the geomagnetic field is studied. A two-dimensional electrostatic fluid model which includes electron attachment and mutual neutralization chemistry, self-consistent electric fields, and three-species transport is developed. Numerical simulations are performed to study the behavior at early and at late times after the release. At early times, of the order of or less than the attachment material neutral collision time, the negative ion cloud produced by the release may structure owing to the shear in the E x B velocity within the cloud. At high altitudes the cloud may bifurcate and form vortices on the back. At lower altitudes where ion-neutral collisional effects dominate, this structuring is suppressed. At late times, after a plasma depletion has formed due to neutralization chemistry, the cloud structures by the E x B interchange instability. Depending on the release altitude, the depletion structures by the collisional or inertial limit of this instability.

Scales, W. A.↗

Computation of Navier-Stokes equations for three-dimensional flow separation

Supersonic flows over a sharp and a flat-faced blunt fin mounted on a flat plate are simulated numerically. Several basic issues involved in the resultant three-dimensional steady flow separation are studied. Using the same number of grid points, different grid spacings are employed to investigate the effects of a grid resolution on the origin of the line of separation. Various shock strengths are used to study the so-called separation and unseparated boundary layer and to establish the existence or absence of secondary separation. The length of separation ahead of the flat-faced blunt fin, bifurcation of a horseshoe vortex, and the accessibility of a closed-type separation are investigated. The usual interpretation of the flow field from previous studies and new interpretations arising from the present simulation are discussed.

Hung, Ching-Mao↗

Early Archean (approximately 3.4 Ga) prokaryotic filaments from cherts of the apex basalt, Western Australia: The oldest cellularly preserved microfossils now known

In comparison with that known from later geologic time, the Archean fossil record is miniscule: although literally hundreds of Proterozoic formations, containing more that 2800 occurrences of bona fide microfossils are now known, fewer than 30 units containing some 43 categories of putative microfossils (the vast majority of which are of questionable authenticity) have been reported from the Archean. Among the oldest known fossils are Early Archean filaments reported from cherts of the Towers Formation and the Apex Basalt of the 3.3-3.6 Ga-old Warrawoona Group of Western Australia. The paleobiologic significance of the Towers Formation microstructures is open to question: thin aggregated filaments are properly regarded as dubiomicrofossils (perhaps biogenic, but perhaps not); therefore, they cannot be regarded as firm evidence of Archean life. Although authentic, filamentous microfossiles were reported from a second Towers Formation locality, because the precise layer containing the fossiliferous cherts was not relocated, this discovery can neither be reconfirmed by the original collector nor confirmed independently by other investigators. Discovery of microfossils in bedded cherts of the Apex Basalt, the stratigraphic unit immediately overlying the Towers Formation, obviates the difficulties stored above. The cellularly preserved filaments of the Apex Basalt meet all of the criteria required of a bona fide Archean microfossils. Recent studies indicate that the Apex assemblage includes at least six morphotypes of uniseriate filaments, composed of barrel-shaped, discoidal, or quadrate cells and exhibiting rounded or conical terminal cells and medial bifurcated and paired half-cells that reflect the occurrence of prokaryotic binary cell division. Interestingly, the majority of these morphotypes are morphologically more similar to extant cyanobacteria than to modern filamentous bacteria. Prokaryotes seem clearly to have been hypobradytelic, and the evidence suggests (but does not prove) that physiologically advanced oxygen-producing photosynthesizers may have been represented in the Early Archean biota.

Schopf, J. W.↗

Nonlinear rotordynamics analysis

Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.

Noah, Sherif T.↗

Structural performance of two aerobrake hexagonal heat shield panel concepts

Structural sizing and performance are presented for two structural concepts for an aerobrake hexagonal heat shield panel. One concept features a sandwich construction with an aluminum honeycomb core and thin quasi-isotropic graphite-epoxy face sheets. The other concept features a skin-rib isogrid construction with thin quasi-isotropic graphite-epoxy skins and graphite-epoxy ribs oriented at 0, +60, and -60 degs along the panel. Linear static, linear bifurcation buckling, and nonlinear static analyses were performed to compare the structural performance of the two panel concepts and assess their feasibility for a lunar transfer vehicle aerobrake application.

Dorsey, John T.↗