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NASA NTRS1989

Development of higher-order modal methods for transient thermal and structural analysis

A force-derivative method which produces higher-order modal solutions to transient problems is evaluated. These higher-order solutions converge to an accurate response using fewer degrees-of-freedom (eigenmodes) than lower-order methods such as the mode-displacement or mode-acceleration methods. Results are presented for non-proportionally damped structural problems as well as thermal problems modeled by finite elements.

Camarda, Charles J.↗

NASA NTRS1989

Structural damage assessment as an identification problem

Damage assessment of structural assemblies is treated as an identification problem. A brief review of identification methods is first presented with particular focus on the output error approach. The use of numerical optimization methods in identifying the location and extent of damage in structures is studied. The influence of damage on eigenmode shapes and static displacements is explored as a means of formulating a measure of damage in the structure. Preliminary results obtained in this study are presented and special attention is directed at the shortcomings associated with the nonlinear programming approach to solving the optimization problem.

Hajela, Prabhat↗

NASA NTRS1989

Higher order dispersion in the propagation of a gravity wave packet

To the first order of approximation, the complex amplitude of a wave packet in an anisotropic and dispersive medium is convected with the group of velocity. However, a gravity wave is a vector wave. Its wave packet must be formed by superposition of various wave numbers with corresponding frequencies, as is the case for scalar waves, and additionally by superposing many eigenmodes which also depend on the wave number. To represent the vector wave packet self-consistently, it is found that a gradient term must be included in the expansion. For a Guassian wave packet, this gradient term is shown to have important implications on the velocity vector as represented by its hodograph. Numerical results show that the hodograph is influenced by the location of the relative position of interest from the center of a Gaussian pulse. Higher order expansion shows that an initial Gaussian wave packet will retain its Gaussian shape as it propagates, but the pulse will spread in all directions with its major axis undergoing a rotation. Numerical results indicate that these higher order dispersive effects may be marginally observable in the atmosphere.

Yeh, K. C.↗

NASA NTRS1988

A new look at equatorial quasi-biennial oscillation models

Simplified quasi-biennial oscillation models are studied, taking bifurcation theory into account. It is found that the model has a trivial steady solution of no mean zonal flow when the two components of the wave forcing are symmetric. The steady solution becomes unstable with respect to an oscillatory eigenmode when the amplitude of the wave forcing exceeds a critical value. Periodic solutions branch off from the steady solution at this point because of Hopf bifurcation. If the two components are not symmetric, the model has a nontrivial steady solution with nonzero mean zonal flow. Hopf bifurcation takes place and periodic solutions which are not symmetric with respect to time appear. A two-level model is developed to analyze the quasi-biennial oscillation mechanism. It is shown that both vertical diffusion and the shielding effect are needed to obtain periodic solutions.

Yoden, Shigeo↗

NASA NTRS1988

Monolithic nonplanar ring lasers - Resistance to optical feedback

The sensitivity of a monolithic unidirectional nonplanar ring laser to optical feedback depends on the polarization eigenmodes of the resonator, which are complicated functions of the resonator geometry. Resonator geometries that increase the loss difference between the two directions of propagation around the ring improve the resistance of the lasers to optical feedback. Here, measurements on Nd:YAG nonplanar ring lasers having two different ring geometries are discussed. Currently, 1 percent optical feedback produces a 10 percent reduction in useful output power for the more feedback-resistant oscillator, a tenfold improvement over previous designs.

Nilsson, Alan C.↗

NASA NTRS1989

The stability of a compressible stratified shear layer

The stability of a shear layer under the effect of gravity is investigated using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent the curvature effects of the flow and magnetic field line geometry. A general eigenmode equation is derived for a two-dimensional MHD fluid, and an energy-principle analysis to explain the effect of compressibility on the critical Richardson number is presented. For the case of a hyperbolic tangent shear flow and exponential density profile, it was found that, in the Boussinesq approximation, the compressibility raises the critical Richardson number from 1/4 to as much as 1/2, with the exact value depending on the value of the magnetic field at infinity. Under approximation of a strong asymptotic magnetic field, without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. The long-wavelength stability boundary for the Richardson number J = 0 is characterized by a normalized phase velocity c =

Wang, Z.↗

NASA NTRS1989

Calculations of inlet distortion induced compressor flow field instability

Calculations of the onset of flow instability are carried out for low-speed multistage axial compressors operating with asymmetric inlet flow. The modeling of the fluid dynamic interaction between the spoiled and unspoiled sectors of the compressor is the most important feature of the calculation procedure. The calculations show that annulus average slope of the compressor pressure rise characteristic equal to zero is a useful approximate stability criterion for situations where the dynamics of the compressor flow field do not couple strongly to the compression system or the structure of the imposed distortion is not similar to that of the eigenmodes of the flow in the compressor annulus. This criterion is employed to investigate the relationship between the present model and the 'parallel compressor' model. Calculations are also presented for cases when compressor and compressor system are closely coupled, and situations in which the compressor is subjected to a rotating distortion. These first-of-a-kind computations, and the accompanying description of the physical mechanisms, show that the stability of the flow in the compressor can be adversely affected if the temporal or spatial structure of the distortion is such that resonant type responses can be evoked either from the compressor or from compressor/compression system interactions.

Chue, R.↗

NASA NTRS1990

Computation Of Flutter In Turbomachinery

"Direct" solution procedure supplants conventional eigenmode analysis. Iterative computational procedure yields critical mach number for onset of flutter and flutter angular frequency, of propfan, turbine with unshrouded blades, or other turbomachinery. Procedure applied to aeroelastic analysis of propfan, in which finite-element model of propfan structure combined with model of unsteady aerodynamics based on three-dimensional subsonic-lifting-surface theory. Particularly suitable for optimization in design because as optimal design evolves, flutter solution expected to change incrementally, so previous solution provides good estimates for start of current solution.

Murthy, Durbha V.↗

NASA NTRS1989

Laboratory and theoretical studies of baroclinic processes

An understanding is being developed for processes which may be important in the atmosphere, and the definition and analysis of baroclinic experiments utilizing the geophysical fluid flow cells (GFFC) apparatus in microgravity space flights. Included are studies using numerical codes, theoretical models, and terrestrial laboratory experiments. The numerical modeling is performed in three stages: calculation of steady axisymmetric flow, calculation of fastest-growing linear eigenmodes, and nonlinear effects (first, wave-mean flow interactions, then wave-wave interactions). The code can accommodate cylindrical, spherical, or channel geometry. It uses finite differences in the vertical and meridional directions, and is spectral in the azimuthal. The theoretical work was mostly in the area of effects of topography upon the baroclinic instability problem. The laboratory experiments are performed in a cylindrical annulus which has a temperture gradient imposed upon the lower surface and an approximately isothermal outer wall, with the upper and inner surfaces being nominally thermally insulating.

Miller, Timothy↗

NASA NTRS1989

Ballooning stability of axisymmetric plasmas with sheared equilibrium flows

A WKB theory is formulated for large-n ballooning modes in axisymmetric, toroidal plasmas with sheared equilibrium flows. The validity of the standard ballooning respresentation is severely restricted in the presence of sheared toroidal flow, despite the fact that to leading order in (1/n), where n is the azimuthal number, the eigenmode equation contains only derivatives along a field line. Necessary and sufficient conditions for stability are obtained in a high-beta ordering for rigid toroidal rotation as well as field-aligned flows.

Bhattacharjee, A.↗

NASA NTRS1990

Approximate Schumann resonance parameters for a two-scale-height ionosphere

An isotropic, spherically symmetric two-scale-height ionosphere's transverse magnetic mode eigenfrequencies, as well as the height and angular profiles of its electric and magnetic fields, are presently addressed by an approximate solution. The electromagnetic energy in the eigenmodes is equally partitioned between the electric and magnetic fields, allowing a simple expression of the relative degrees of dissipation within the radial and tangential dissipation layers. The results obtained may be relevant to interpretations of the temporal variations in the Schumann resonances.

Sentman, D. D.↗

NASA NTRS1990

Simulation studies of plasma waves in the electron foreshock - The generation of downshifted oscillations

The generation of waves with frequencies downshifted from the plasma frequency, as observed in the electron foreshock, is analyzed by particle simulation. Wave excitation differs fundamentally from the familiar excitation of the plasma eigenmodes by a gentle bump-on-tail electron distribution. Beam modes are destabilized by resonant interaction with bulk electrons, provided the beam velocity spread is very small. These modes are stabilized, starting with the higher frequencies, as the beam is broadened and slowed down by the interaction with the wave spectrum. Initially a very cold beam is also capable of exciting frequencies considerably above the plasma frequency, but such oscillations are quickly stabilized. Low-frequency modes persist for a long time, until the bump in the electron distribution is completely 'ironed' out. This diffusion process also is quite different from the familiar case of well-separated beam and bulk electrons. A quantitative analysis of these processes is carried out.

Dum, C. T.↗

NASA NTRS1991

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

Ukeiley, L.↗

NASA NTRS1991

What maintains the zonal circulation in planetary atmospheres?

The latest Voyager observations have shown large zonal velocities in Neptune's atmosphere, with some indication of alternating jets. Similar wind velocities have also been observed on Venus and are characteristic of planetary atmospheres in general, which is remarkable considering that the available solar or internal heating varies by more than a factor of 1000. A simplified model of the planetary circulation which provides some qualitative understanding is discussed. The basic assumption is that the source driving the circulation is also generating the dissipating eddies which are simulated by diffusion. Thus, the magnitude and structure of the zonal circulation are independent both of the source and the dissipation rate. The zonal velocities are related to the speed of sound and are of comparable magnitude in different atmospheres; although the available heating varies by a large factor, and the planetary parameters vary over a wide range. The alternating jets are described by a convective eigenmode which develops when energy transport out of the planetary interior is important, as is the case on Jupiter, Neptune, and Saturn.

Mayr, H. G.↗

NASA NTRS1991

Determination of Rotordynamic Coefficients for Labyrinth Seals and Application to Rotordynamic Design Calculations

In today's rotordynamic calculations, the input parameters for a finite element analysis (FEA) determine very much the reliability of eigenvalue and eigenmode predictions. While modeling of an elastic structure by means of beam elements etc. is relatively straightforward to perform and the input data for journal bearings are usually known exactly enough, the determination of stiffness and damping for labyrinth seals is still the subject of many investigations. Therefore, the rotordynamic influence of labyrinths is often not included in FEA for rotating machinery because of a lack of computer programs to calculate these parameters. This circumstance can give rise to severe vibration problems especially for high performance turbines or compressors, resulting in remarkable economic losses. The forces generated in labyrinths can be described for small motions around the seal center with a linearized force-motion relationship. Several years ago, we started with the development of computer codes for the determination of rotordynamic seal coefficients. Our different approaches to evaluate the dynamic fluid forces generated by turbulent, compressible seal flow are introduced.

Weiser, P.↗

NASA NTRS1992

Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature

Acoustic receptivity of a Blasius boundary layer in the presence of distributed surface irregularities is investigated analytically. It is shown that, out of the entire spatial spectrum of the surface irregularities, only a small band of Fourier components can lead to an efficient conversion of the acoustic input at any given frequency to an unstable eigenmode of the boundary layer flow. The location, and width, of this most receptive band of wavenumbers corresponds to a relative detuning of O(R sub l.b.(exp -3/8)) with respect to the lower-neutral instability wavenumber at the frequency under consideration, R sub l.b. being the Reynolds number based on a typical boundary-layer thickness at the lower branch of the neutral stability curve. Surface imperfections in the form of discrete mode waviness in this range of wavenumbers lead to initial instability amplitudes which are O(R sub l.b.(exp 3/8)) larger than those caused by a single, isolated roughness element. In contrast, irregularities with a continuous spatial spectrum produce much smaller instability amplitudes, even compared to the isolated case, since the increase due to the resonant nature of the response is more than that compensated for by the asymptotically small band-width of the receptivity process. Analytical expressions for the maximum possible instability amplitudes, as well as their expectation for an ensemble of statistically irregular surfaces with random phase distributions, are also presented.

Choudhari, Meelan↗

NASA NTRS1992

Nonlocal analysis of finite-beam-driven instabilities

The fully kinetic integral eigenmode equation in wave-number space is used to describe the nonlocal behavior of electrostatic waves in an electron-beam plasma, which are studied in the low-temperature-beam regime and the warm-beam regime. The case of strongly magnetized electrons and unmagnetized ions, which corresponds to the waves in a frequency range from the lower-hybrid to the electron plasma frequency, is examined. Three wave modes are found. The first group consists of modes that have dispersive properties similar to the uniform, infinite beam-plasma system. Depending on the beam width, the growth rates are strongly reduced. The second group, surface modes, are localized at the periphery of the beam region and are less unstable than the unstable modes of the first group. The third group represents natural oscillations of the background plasma. These modes are virtually unaffected by the beam.

Serizawa, Y.↗

NASA NTRS1992

Analysis of cyclotron harmonic emissions at the outer planets

The flyby missions of Voyagers 1 and 2 at Jupiter, Saturn and Uranus revealed intense waves above the electron gyrofrequency. Observation of waves at the upper hybrid frequency is often accompanied by power at adjacent electron Bernstein harmonics, and the relative power in these modes depends both on the density and temperature ratios of the cold background electron population and the hot magnetospheric electrons which drive the instability. A model of electron distributions which is consistent with observations is used for analysis of the excited waves, their dependence upon plasma parameters, and the time scales of the saturation processes. It is shown that in the presence of two-temperature electron distributions the linear excitation is due to a fluidlike coupling of two eigenmodes for perpendicular propagation and to kinetic destalization of oblique modes. The dependence of linear growth rates on propagation angle is presented, along with results from particle simulations. A quasi-linear diffusion time for relaxing the hot electron loss cone is calculated and compared with simulation results. This time scale is faster than for local saturation by heating the cold population, and also the convective amplification time scale, suggesting that the waves saturate at quasi-linear levels, while being convectively localized to the equatorial regions of the outer planetary magnetospheres.

Roth, I.↗