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NASA NTRS1981

Nonlinear dynamic phenomena in the space shuttle thermal protection system

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Housner, J. M.↗

NASA NTRS1985

Electromagnetic ion beam instabilities - Hot beams at interplanetary shocks

This paper considers Vlasov instabilities driven by a very hot ion beam streaming parallel to a magnetic field. The linear theory of electromagnetic instabilities driven by such a beam in a homogeneous, collisionless, nonrelativistic plasma is used. Numerical solutions of the full linear dispersion equation for bi-Maxwellian distribution functions are presented. If the thermal speed of the beam is greater than its drift speed, the two dominant modes are the right-hand and left-hand resonant ion beam instabilities. The parametric dependencies of the threshold drift speeds and growth rates for both modes are presented. In particular, the thresholds are shown to be sensitive functions of the beam temperature anisotropies. Arguments are presented that these two modes are driven by the suprathermal ion component at interplanetary shocks, and that the growth of these modes is sufficient to account for the amplitudes of MHD-like waves observed at such shocks.

Gary, S. P.↗

NASA NTRS1986

Parametric analytical study of instability-related delamination growth

The effect of various parameters on instability-related delamination growth was studied analytially. The configuration studied consisted of a thick composite laminate with a single through-width delamination located near one surface. Both mechanical and thermal loads were considered. All conclusions were based on the assumption that GI and GII govern delamination growth. An approximate superposition stress analysis was developed which gives closed form expressions for GI and GII. The simplicity of the analysis permitted examination of numerous configurations. Both GI and GII were found to be very sensitive to delamination length and location through the thickness. The magnitude of GI was also very sensitive to initial imperfections, which might be the results of an inclusion of finite thickness in the delamination. Critical loads for delamination growth were calculated based on three growth criteria. Large differences in the predictions highlight the need for a verified mixed-mode delamination growth criterion.

Whitcomb, J. D.↗

NASA NTRS1987

A new interpretation of plasma-line overshoot phenomena

The temporal evolution of Langmuir waves excited by high-power, high-frequency (HF) radio waves in the ionosphere is studied theoretically. This study is motivated by past observations made with the 450 MHz radar at Arecibo Observatory in Puerto Rico. Two kinds of nonlinear damping to the parametric decay instability are considered in the derivation of the rate equation for the spectral intensity of enhanced Langmuir waves. They are Langmuir wave cascading caused by nonlinear Landau damping and cross-field electron diffusion. The first damping process leads to the saturation of individual unstable Langmuir wave. The second process, which results from the incoherent scattering of electron orbits by the total excited Langmuir waves, yields anomalous damping that applies to each Langmuir wave. Consequently, Langmuir waves with smaller growth rates will be suppressed by those with larger growth rates. Such a mode competition process may cause the overshoot of the HF-enhanced plasma line observed with the Arecibo 430 MHz radar. Favorable agreement is obtained between theory and the Arecibo observations.

Kuo, S. P.↗

NASA NTRS1989

Parametric excitation of whistler waves by HF heater

Possible generation of whistler waves by Tromso HF heater is investigated. It is shown that the HF heater wave can parametrically decay into a whistler wave and a Langmuir wave. Since whistler waves may have a broad range of frequency, the simultaneously excited Langmuir waves can have a much broader frequency bandwidth than those excited by the parametric decay instability.

Kuo, S. P.↗

NASA NTRS1991

The dissipation of magnetohydrodynamic turbulence responsible for interstellar scintillation and the heating of the interstellar medium

The present reexamination of the problem of ISM heating via the damping of plasma irregularities responsible for interstellar scintillations of radio sources gives attention to the effects of recent observational results on the hot plasma of the irregularities and on developments of in the theory of MHD waves. The damping mechanisms considered are linear Landau damping, ion-neutral collisional damping, nonlinear steepening of wave packets, a parametric decay instability, and nonlinear Landau damping. The heat input from all damping mechanisms can be accommodated by the 'fluctifer' region containing the irregularities, if it has features similar to the extended H II envelopes.

Spangler, Steven R.↗

NASA NTRS1990

Investigation of nonlinear E.M. phenomena in the tethered magnetospheric cloud

Nonlinear effects of parametric and of heating type, produced in a plasma under the action of an electric field E(sub 0)(e exp i(omega)t), are considered in this work in connection with the Tethered Magnetospheric Cloud (TMC) accompanying the Tether Satellite System (TSS). The theoretical results show that these phenomena should appear in the ionosphere at high altitudes Z greater than or = (150-200) km, particularly, at Z approximately = 300 km of the TSS system orbit. Therefore, it is of a special interest to search these phenomena by such a unique experiment as the forthcoming first TSS-I and by the future, perhaps modified TSS missions. Because of the parametric decay instability, new branches of wave may be excited both around the electron and ion Lengmuir frequencies Omega (sub 0) = 2(pi)f(sub 0) and Omega (sub 0) = 2(pi)f(sub 0) under the influence of high frequency (HF), (f less than or = 10(exp 6) to few 10(exp 6) Hz), strong electric waves. The heating of all the kinds of particles is growing up very quickly in the ionosphere with altitude in the extra low and very low frequency ranges, F approximately = (1 to 10(exp 4) Hz, discussed below. The temperatures (energies), for example, of the electrons accelerated by the electric field become larger than the ionization potential in this frequency range already at altitudes Z greater than or = (150 - 200) km when the amplitude of the electric field is the absolute value of E(sub 0) approximately = (1-2) mV/m. The sources of these electric fields may be in the TSS-I mission, that so called Phantom Loop (PL) - the Tethered Electrodynamic Tail (TET), and the different kind of electromagnetic oscillations produced by different kinds of instabilities in the TMC plasma. The growth rates of these instabilities will become very high in the TSS surrounding magnetoplasma. However, in the future TSS missions, special artificial sources (generators) of electric fields should be used for these investigations.

Alpert, Yakov L.↗

NASA NTRS1995

Low-frequency waves associated with Langmuir waves in solar wind

The Ulysses spacecraft has detected several events of low-frequency electromagnetic waves in association with Langmuir waves in the solar wind. The high time resolution observations show that the Langmuir waves are very intense and occur as broad peaks superposed by collapsing millisecond spikes. The low-frequency waves are identified as electromagnetic lower hybrid waves. The observed energy densities of these waves often exceed the strong turbulence thresholds. It is shown that none of the parametric decay instabilities involving Langmuir and low-frequency waves are energetically favorable to explain the present observations. The low-frequency waves are proposed to arise from currents associated with gradients in the electron beam originating at sites where Langmuir waves scatter the beam electrons.

Thejappa, G.↗

NASA NTRSDate not supplied

Surface Instability of Liquid Propellants in Microgravity During Pulsed Settling Operations

Pulsing reaction control system (RCS) thrusters, vent valves, or other propulsion devices can preserve propellant resources in space, but this operation also effectively introduces a vibration to the vehicle. When the vibration is perpendicular to the liquid propellant surface, Faraday waves may be generated at the liquid-vapor interface. These Faraday instabilities can perturb or break up the liquid surface of cryogenic tanks, leading to inefficiencies in thermal management or even ullage collapse. Drawing from theory and experiments, an engineering model defining the allowable design regions for pulsed settling in microgravity was assembled and verified with computational fluid dynamics (CFD) simulations. A traditional settling metric, the Bond number, was also overlaid in the model to indicate which duty cycles were insufficient to overcome surface tension and aggregate propellant. Mission planners and engineers can consult the tool to rapidly evaluate the stability of a liquid-vapor interface given the pulse frequency and the excitation acceleration. Expressions developed for Faraday waves induced by a sinusoidal forcing input at standard gravity were found to provide excellent predictive capabilities for pulsed, or rectangular, waveforms in the absence of a consistent gravitational acceleration. This study extends the usage of these equations to an alternative forcing function and microgravity environments for the purpose of estimating natural frequencies, surface mode shapes, surface wave amplitudes, and the onset of droplet ejection. CFD simulations with the Loci/STREAM-VoF (Volume of Fluid) solver were initially validated against experimental results in standard gravity. Discrete points on the design map were then investigated with CFD and confirmed that the engineering model reliably indicates surface stability and most Faraday wave characteristics without requiring higher-fidelity tools. The engineering model is highly extensible and can be adapted for various propellant fill fractions, fluid properties, and tank sizes.

Faraday Waves↗

NASA NTRSDate not supplied

Surface Instability of Liquid Propellants in Microgravity During Pulsed Settling Operations

Faraday Waves↗

NASA NTRS1998

Constraints on Nonlinear and Stochastic Growth Theories for Type 3 Solar Radio Bursts from the Corona to 1 AU

Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.

Cairns, Iver H.↗

NASA NTRS2001

Three-Dimensional Aerodynamic Instabilities In Multi-Stage Axial Compressors

This thesis presents the conceptualization and development of a computational model for describing three-dimensional non-linear disturbances associated with instability and inlet distortion in multistage compressors. Specifically, the model is aimed at simulating the non-linear aspects of short wavelength stall inception, part span stall cells, and compressor response to three-dimensional inlet distortions. The computed results demonstrated the first-of-a-kind capability for simulating short wavelength stall inception in multistage compressors. The adequacy of the model is demonstrated by its application to reproduce the following phenomena: (1) response of a compressor to a square-wave total pressure inlet distortion; (2) behavior of long wavelength small amplitude disturbances in compressors; (3) short wavelength stall inception in a multistage compressor and the occurrence of rotating stall inception on the negatively sloped portion of the compressor characteristic; (4) progressive stalling behavior in the first stage in a mismatched multistage compressor; (5) change of stall inception type (from modal to spike and vice versa) due to IGV stagger angle variation, and "unique rotor tip incidence" at these points where the compressor stalls through short wavelength disturbances. The model has been applied to determine the parametric dependence of instability inception behavior in terms of amplitude and spatial distribution of initial disturbance, and intra-blade-row gaps. It is found that reducing the inter-blade row gaps suppresses the growth of short wavelength disturbances. It is also concluded from these parametric investigations that each local component group (rotor and its two adjacent stators) has its own instability point (i.e. conditions at which disturbances are sustained) for short wavelength disturbances, with the instability point for the compressor set by the most unstable component group. For completeness, the methodology has been extended to describe finite amplitude disturbances in high-speed compressors. Results are presented for the response of a transonic compressor subjected to inlet distortions.

Tan, Choon S.↗

NASA NTRS1993

Instability of rectangular jets

The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a center mode with maximum fluctuations concentrated in the central portion of the jet flow. The center mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the center mode would emerge as the dominant instability of the jet.

Tam, Christopher K. W.↗

NASA NTRS1988

The influence of and the identification of nonlinearity in flexible structures

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Zavodney, Lawrence D.↗

NASA NTRS1988

Filamentation instability of large-amplitude Alfven waves

An instability that leads to the filamentation of large-amplitude Alfven waves and gives rise to purely growing density and magnetic field fluctuations is studied. The dispersion relation of the instability is derived, from which the threshold conditions and the growth rates of the instability are analyzed quantitatively for applications to the solar wind plasma. Their dependence on the filamentation spectrum, the plasma beta, and the pump frequency and intensity was examined for both right-hand and left-hand circularly polarized Alfven waves. The excitation of filamentation instability for certain cases of interest is discussed and compared with that of the parametric decay and modulation instability. The relevance of the proposed instability to some observations is discussed.

Kuo, S. P.↗

NASA NTRS1991

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. David↗

NASA NTRS1991

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharamonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. D.↗

NASA NTRS1981

Finite element analysis of instability-related delamination growth

A parametric study of postbuckled through-width delaminations in laminated coupons was performed. A finite element analysis was developed to analyze the coupons as a combination of linear and geometrically nonlinear components. Because most of the coupon configuration studied behaves linearly, the mixed linear and nonlinear analysis greatly reduced computational costs. The analysis was verified by comparing numerical with exact solutions for simple hypothetical problems. In addition, measured lateral deflections of postbuckled through-width delaminations in laminated coupons were compared with predicted deflections. In the parametric study, stress distributions and strain-energy release rates were calculated for various delamination lengths, delamination depths, applied loads, and lateral deflections. Also, a small number of coupons with through-width delaminations were fatigue tested to obtain delamination growth data. Calculated strain-energy release rates were compared with the observed growth rates to determine the relative importance of the Mode 1 and Mode 2 components of energy release. Growth process was dominated by G sub I.

Whitcomb, J. D.↗