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NASA NTRS1993

Nonlinear evolution of electromagnetic ion beam instabilities

A comparative study of the ion/ion right-hand resonant instability and the ion/ion nonresonant instability is carried out to investigate and contrast their properties. Linear analysis demonstrates that the nonresonant instability becomes resonant if the density of the ion beam is sufficiently high. Hybrid simulations show that both the resonant and nonresonant instabilities result in the formation of nonlinear pulses, called pulsations, but with distinct features. For example, the pulsations generated by the resonant instability have a positive correlation with the ion density, while those generated by the nonresonant instability are likely to have a relatively weak negative correlation. The waves generated by the nonresonant instability are subject to a parametric decay instability and tend to form a state of condensate where the turbulence becomes nearly monochromatic.

Akimoto, K.↗

NASA NTRS1999

Crack Growth Simulation and Residual Strength Prediction in Airplane Fuselages

This is the final report for the NASA funded project entitled "Crack Growth Prediction Methodology for Multi-Site Damage." The primary objective of the project was to create a capability to simulate curvilinear fatigue crack growth and ductile tearing in aircraft fuselages subjected to widespread fatigue damage. The second objective was to validate the capability by way of comparisons to experimental results. Both objectives have been achieved and the results are detailed herein. In the first part of the report, the crack tip opening angle (CTOA) fracture criterion, obtained and correlated from coupon tests to predict fracture behavior and residual strength of built-up aircraft fuselages, is discussed. Geometrically nonlinear, elastic-plastic, thin shell finite element analyses are used to simulate stable crack growth and to predict residual strength. Both measured and predicted results of laboratory flat panel tests and full-scale fuselage panel tests show substantial reduction of residual strength due to the occurrence of multi-site damage (MSD). Detailed comparisons of n stable crack growth history, and residual strength between the predicted and experimental results are used to assess the validity of the analysis methodology. In the second part of the report, issues related to crack trajectory prediction in thin shells; an evolving methodology uses the crack turning phenomenon to improve the structural integrity of aircraft structures are discussed, A directional criterion is developed based on the maximum tangential stress theory, but taking into account the effect of T-stress and fracture toughness orthotropy. Possible extensions of the current crack growth directional criterion to handle geometrically and materially nonlinear problems are discussed. The path independent contour integral method for T-stress evaluation is derived and its accuracy is assessed using a p- and hp-version adaptive finite element method. Curvilinear crack growth is simulated in coupon tests and in full-scale fuselage panel tests. Both T-stress and fracture toughness orthotropy are found to be essential to predict the observed crack paths. The analysis methodology and software program (FRANC3D/STAGS) developed herein allows engineers to maintain aging aircraft economically while insuring continuous airworthiness. Consequently, it will improve the technology to support the safe operation of the current aircraft fleet as well as the design of more damage-tolerant aircraft for the next generation fleet.

Chen, Chuin-Shan↗

NASA NTRS2004

On Nonlinear Combustion Instability in Liquid Propellant Rocket Motors

All liquid propellant rocket instability calculations in current use have limited value in the predictive sense and serve mainly as a correlating framework for the available data sets. The well-known n-t model first introduced by Crocco and Cheng in 1956 is still used as the primary analytical tool of this type. A multitude of attempts to establish practical analytical methods have achieved only limited success. These methods usually produce only stability boundary maps that are of little use in making critical design decisions in new motor development programs. Recent progress in understanding the mechanisms of combustion instability in solid propellant rockets"' provides a firm foundation for a new approach to prediction, diagnosis, and correction of the closely related problems in liquid motor instability. For predictive tools to be useful in the motor design process, they must have the capability to accurately determine: 1) time evolution of the pressure oscillations and limit amplitude, 2) critical triggering pulse amplitude, and 3) unsteady heat transfer rates at injector surfaces and chamber walls. The method described in this paper relates these critical motor characteristics directly to system design parameters. Inclusion of mechanisms such as wave steepening, vorticity production and transport, and unsteady detonation wave phenomena greatly enhance the representation of key features of motor chamber oscillatory behavior. The basic theoretical model is described and preliminary computations are compared to experimental data. A plan to develop the new predictive method into a comprehensive analysis tool is also described.

Sims, J. D.↗

NASA NTRS1982

Geometric and rediametric distortion in spaceborne SAR imagery

Distortions inherent on synthetic aperture radio (SAR) imagery and the development to date of unsupervised postprocessing rectification techniques are described. The geometric distortion can be divided into two categories: (1) distortion derived from the radar viewing geometry, this includes such effects as ground range nonlinearities, radar foreshortening and radar layover; (2) distortion introduced during the data processing, these distortions result from approximations made during the correlation such as in estimation of the target phase history, or compensation for the earth rotation. The processor induced distortions depends on the specific correlation algorithm used for image formation. The effects are addressed on the image product resulting from assumptions during the processing and it specifically considers distortions inherent in digital imagery produced by the digital image processor.

Curlander, J. C.↗

NASA NTRS1983

Constant-temperature hot-wire anemometer practice in supersonic flows. II - The inclined wire

The performance of a constant-temperature inclined hot-wire in a supersonic flow is critically examined. It is shown that calibration techniques applicable to subsonic flow, such as the cosine cooling law cannot be used when the flow is supersonic. Calibration and measurement procedures appropriate to supersonic flow are suggested, together with the possible limits on their validity. Experimental results for different wires indicate that the sensitivities do not seem to depend on flow direction according to any simple correlation. When the sensitivity exhibits a strong dependence on flow direction, the wire should be discarded to avoid errors due to nonlinear effects.

Smits, A. J.↗

NASA NTRS1983

Integrated optical circuits for numerical computation

The development of integrated optical circuits (IOC) for numerical-computation applications is reviewed, with a focus on the use of systolic architectures. The basic architecture criteria for optical processors are shown to be the same as those proposed by Kung (1982) for VLSI design, and the advantages of IOCs over bulk techniques are indicated. The operation and fabrication of electrooptic grating structures are outlined, and the application of IOCs of this type to an existing 32-bit, 32-Mbit/sec digital correlator, a proposed matrix multiplier, and a proposed pipeline processor for polynomial evaluation is discussed. The problems arising from the inherent nonlinearity of electrooptic gratings are considered. Diagrams and drawings of the application concepts are provided.

Verber, C. M.↗

NASA NTRS1986

On the structure of artificially generated water wave trains

The structure of an artificially generated sinusoidal water wave train of fixed frequency under the influence of wind is analyzed. Artificially generated waves of 1 Hz are studied at seven wind speeds in the range of 140-400 cm/s. It is observed that the water wave train deformed by wind consists of two components at both the fundamental mode and the harmonics. The amplitude and phase of the wave components are derived, and the dispersion relation and component phase speeds are examined. The data reveal that the amplitude of the forced and free-traveling second harmonics correlate with previous theories, and that the deviation of the measured phase speed from the linear theory is caused by the nonlinearity of the primary wave, the interaction between short gravity waves and the primary wave, and the advection effects of wind drift.

Papadimitrakis, Yiannis A.↗

NASA NTRS1993

Effect of Malmquist bias on correlation studies with IRAS data base

The relationships between galaxy properties in the sample of Trinchieri et al. (1989) are reexamined with corrections for Malmquist bias. The linear correlations are tested and linear regressions are fit for log-log plots of L(FIR), L(H-alpha), and L(B) as well as ratios of these quantities. The linear correlations for Malmquist bias are corrected using the method of Verter (1988), in which each galaxy observation is weighted by the inverse of its sampling volume. The linear regressions are corrected for Malmquist bias by a new method invented here in which each galaxy observation is weighted by its sampling volume. The results of correlation and regressions among the sample are significantly changed in the anticipated sense that the corrected correlation confidences are lower and the corrected slopes of the linear regressions are lower. The elimination of Malmquist bias eliminates the nonlinear rise in luminosity that has caused some authors to hypothesize additional components of FIR emission.

Verter, Frances↗

NASA NTRS1994

Acoustics of laminar boundary layers breakdown

Boundary layer flow transition has long been suggested as a potential noise source in both marine (sonar-dome self noise) and aeronautical (aircraft cabin noise) applications, owing to the highly transient nature of process. The design of effective noise control strategies relies upon a clear understanding of the source mechanisms associated with the unsteady flow dynamics during transition. Due to formidable mathematical difficulties, theoretical predictions either are limited to early linear and weakly nonlinear stages of transition, or employ acoustic analogy theories based on approximate source field data, often in the form of empirical correlation. In the present work, an approach which combines direct numerical simulation of the source field with the Lighthill acoustic analogy is utilized. This approach takes advantage of the recent advancement in computational capabilities to obtain detailed information about the flow-induced acoustic sources. The transitional boundary layer flow is computed by solving the incompressible Navier-Stokes equations without model assumptions, thus allowing a direct evaluation of the pseudosound as well as source functions, including the Lighthill stress tensor and the wall shear stress. The latter are used for calculating the radiated pressure field based on the Curle-Powell solution of the Lighthill equation. This procedure allows a quantitative assessment of noise source mechanisms and the associated radiation characteristics during transition from primary instability up to the laminar breakdown stage. In particular, one is interested in comparing the roles played by the fluctuating volume Reynolds stress and the wall-shear-stresses, and in identifying specific flow processes and structures that are effective noise generators.

Wang, Meng↗

NASA NTRS1997

Analysis of Particle Image Velocimetry (PIV) Data for Acoustic Velocity Measurements

Acoustic velocity measurements were taken using Particle Image Velocimetry (PIV) in a Normal Incidence Tube configuration at various frequency, phase, and amplitude levels. This report presents the results of the PIV analysis and data reduction portions of the test and details the processing that was done. Estimates of lower measurement sensitivity levels were determined based on PIV image quality, correlation, and noise level parameters used in the test. Comparison of measurements with linear acoustic theory are presented. The onset of nonlinear, harmonic frequency acoustic levels were also studied for various decibel and frequency levels ranging from 90 to 132 dB and 500 to 3000 Hz, respectively.

Blackshire, James L.↗

NASA NTRS2003

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Chang, Chau-Lyan↗

NASA NTRS1980

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Stephens, W. B.↗

NASA NTRS1962

BUCKLING AND POST-BUCKLING OF ELASTIC SHELLS

Some theoretical investigations of buckling of elastic shells are surveyed in this report. Only geometrically perfect shells are considered; initial dents and out-of-roundness are not taken into account. Several questions raised by the studies are: (a) Under what conditions is the infinitesimal theory of buckling of shells adequate? (b) How does the energy theory of buckling of shells correlate with the method based on equilibrium equations for bending moments, tensions, and shears in a buckled configuration? (c) How important are nonlinear terms in the tangential displacements u, v in the strain-displacement relations for buckling and post-buckling studies? (d) How important are the boundary conditions for u, v in affecting stability? (e) If a condition of snap-through is approached, how much external work is required to push the shell "over the hump" into the buckled configuration? (f) How reliable are mathematical approximations used previously in the infinitesimal theory of buckling of shells? Tentative and incomplete answers to some of these questions are suggested.

ELASTIC BUCKLING↗

NASA NTRS1989

Non-WKB evolution of solar wind fluctuations - A turbulence modeling approach

Recent observations indicate systematic changes in the interplanetary inertial range velocity-magnetic field correlation with increasing heliocentric distance. Here, a multiple length scale model for the evolution of the small scale fluctuations due to local nonlinear couplings as well as couplings to large scale gradients is outlined, which is similar to that used in turbulence modeling of inhomogeneous shear flows. A simple special case solution is given, indicating that couplings to large scale flow gradients can cause radial evolution of the type seen in observations. The strongest couplings of this type are linear and do not appear in the usual WKB orderings. The relationship of the present approach to WKB theory is not fully understood at present.

Ye, Zou↗

NASA NTRS1995

Evidence for chemical processing of precometary icy grains in circumstellar environments of pre-main-sequence stars

We report the detection of a broad absorption feature near 2166/cm in the spectrum of the Taurus cloud cource Elias 18. This pre-main-sequence source is the second in Taurus, the third in our survey, and the fifth known in the sky to show the broad 2166/cm absorption feature. Of equal importance, this feature is not seen toward several other embedded sources in our survey, nor is it seen toward the source Elias 16, located behind the Taurus cloud. Laboratory experiments with interstellar ice analogs show that such a feature is associated with a complex C triple bonded to N containing compound (called X(C triple bonded to N)) that results from high-energy processing (ultraviolet irradiation or ion bombardment) of simple ice components into more complex, organic components. We find a nonlinear anticorrelation between the abundance of X(C triple bonded to N) and frozen CO components in nonpolar lattices. We find no correlation between the abundance of X(C triple bonded to N) and frozen CO in polar lattices. Because the abundances of frozen CO and H2O are strongly correlated with each other and with visual extinction toward sources embedded in and located behind the Taurus molecular cloud, these ice components usually are associated with intracloud material. Our results indicate that X(C triple bonded to N) molecules result from chemical processing of dust grains dominated by nonpolar icy mantles in the local environments of pre-main-sequence stars. Such processing of icy grains in the early solar system may be an important source of organic compounds observed in minor solar system bodies. The delivery of these organic compounds to the surface of the primitive Earth through comet impacts may have provided the raw materials for prebiotic chemistry.

Tegler, Stephen C.↗

NASA NTRS1995

Turbulence in the solar wind: Kinetic effects

Although a casual look at the fluctuating magnetic and velocity fields in the solar wind may be reminiscent of a chaotic and disordered flow, there is, nonetheless. considerable organization and structure in the temporal and spatial evolution of those fluctuations. Much of that evolution is controlled by processes operating on rather large scales for example, in the inner heliosphere, the fluctuations in magnetic and velocity are highly correlated in the sense of outward propagating Alfven waves. This correlation can be destroyed both in time and distance by the velocity gradients present between fast and slow streams and by other nonlinear processes which stir the medium, producing a turbulent cascade of energy from large to small scales. Many aspects of this turbulent evolution can be described using fluid models; however, at some scale the fluid approximation breaks down and a more detailed paradigm is necessary. The breakdown is evident in the power spectrum of magnetic fluctuations at scales approaching the wavelength of ion cyclotron waves. At those scales, as evident in Mariner 10 and other magnetometer data, the spectrum bends over and the fluctuations damp, possibly heating the ambient plasma. Some evidence for heating of the solar wind is present in the Voyager data. Fluid models can be modified to some extent to incorporate aspects of a kinetic treatment. This is done by modifying the dissipation terms in the fluid equations and by including extra terms, such as the Hall term. As the scale lengths of phenomena shrink further and approach the spatial and temporal scales characteristic of electron phenomena, the fluid description must be abandoned altogether and a fully kinetic treatment is required. One example is the generation of Langmuir solitons produced by the electron beams that generate type 3 solar radio bursts.

Goldstein, M. L.↗

NASA NTRS1996

Optimal Signal Filtration in Optical Sensors with Natural Squeezing of Vacuum Noises

The structure of optimal receiver is discussed for optical sensor measuring a small displacement of probe mass. Due to nonlinear interaction of the field and the mirror, a reflected wave is in squeezed state (natural squeezing), two quadratures of which are correlated and therefore one can increase signal-to-noise ratio and overcome the SQL. A measurement procedure realizing such correlation processing of two quadratures is clarified. The required combination of quadratures can be produced via mixing of pump field reflected from the mirror with local oscillator phase modulated field in duel-detector homodyne scheme. Such measurement procedure could be useful not only for resonant bar gravitational detector but for laser longbase interferometric detectors as well.

Gusev, A. V.↗

NASA NTRS2000

Modal Survey Test of the SOTV 2X3 Meter Off-Axis Inflatable Concentrator

NASA's Marshall Space Flight Center has had several projects involving inflatable space structures. Projects in solar thermal propulsion have had the most involvement, primarily inflatable concentrators. A flight project called Shooting Star Experiment initiated the first detailed design, analysis and testing effort involving an inflatable concentrator that supported a Fresnel lens. The lens was to concentrate the sun's rays to provide an extremely large heat transfer for an experimental solar propulsion engine. Since the conclusion of this experiment, research and development activities for solar propulsion at Marshall Space Flight Center have continued both in the solar propulsion engine technology as well as inflatable space structures. Experience gained in conducting modal survey tests of inflatable structures for the Shooting Star Experiment has been used by dynamic test engineers at Marshall Space Flight Center to conduct a modal survey test on a Solar Orbital Transfer Vehicle (SOTV) off-axis inflatable concentrator. This paper describes how both previously learned test methods and new test methods that address the unique test requirements for inflatable structures were used. Effects of the inherent nonlinear response of the inflatable concentrator on test methods and test results are noted as well. Nine analytical mode shapes were successfully correlated to test mode shapes. The paper concludes with several "lessons learned" applicable to future dynamics testing and shows how Marshall Space Flight Center has utilized traditional and new methods for modal survey testing of inflatable space structures.

Engberg, Robert C.↗