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NASA NTRS1992

Diskoseismology - Signatures of black hole accretion disks

General relativity requires the existence of a spectrum of oscillations which are trapped near the inner edge of accretion disks around black holes. We have developed a general formalism for analyzing the normal modes of such acoustic perturbations of arbitrary thin disk models, approximating the dominant relativistic effects via a modified Newtonian potential (these modes do not exist in Newtonian gravity). The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall in to two main classes, which are analogous to the p-modes and g-modes in the sun. In this work, we compute the eigenfunctions and eigenfrequencies of isothermal disks. The (relatively small) rates of growth or damping of these oscillations due to gravitational radiation and parameterized models of viscosity are also computed.

Nowak, Michael↗

NASA NTRS1992

Eigenvalue error analysis of viscously damped structures using a Ritz reduction method

The efficient solution of the eigenvalue problem that results from inserting passive dampers with variable stiffness and damping coefficients into a structure is addressed. Eigenanalysis of reduced models obtained by retaining a number of normal modes augmented with Ritz vectors corresponding to the static solutions resulting from the load patterns introduced by the dampers has been empirically shown to yield excellent approximations to the full eigenvalue problem. An analysis of this technique in the case of a single damper is presented. A priori and a posteriori error estimates are generated and tested on numerical examples. Comparison theorems with modally truncated models and a Markov parameter matching reduced-order model are derived. These theorems corroborate the heuristic that residual flexibility methods improve low-frequency approximation of the system. The analysis leads to other techniques for eigenvalue approximation. Approximate closed-form solutions are derived that include a refinement to eigenvalue derivative methods for approximation. An efficient Newton scheme is also developed. A numerical example is presented demonstrating the effectiveness of each of these methods.

Chu, Cheng-Chih↗

NASA NTRS1993

Vibration localization in mono- and bi-coupled bladed disks - A transfer matrix approach

A transfer matrix approach to the analysis of the dynamics of mistuned bladed disks is presented. The study focuses on mono-coupled systems, in which each blade is coupled to its two neighboring blades, and bi-coupled systems, where each blade is coupled to its four nearest neighbors. Transfer matrices yield the free dynamics, both the characteristic free wave and the normal modes - in closed form for the tuned assemblies. Mistuned assemblies are represented by random transfer matrices and an examination of the effect of mistuning on harmonic wave propagation yields the localization factor - the average rate of spatial wave amplitude decay per blade - in the mono-coupled assembly. Based on a comparison of the wave propagation characteristics of the mono- and bi-coupled assemblies, important conclusions are drawn about the effect of the additional coupling coordinate on the sensitivity to mistuning and the strength of mode localization predicted by a mono-coupled analysis.

Ottarsson, Gisli↗

NASA NTRS1993

Radiative properties of a plasma moving across a magnetic field. I - Theoretical analysis. II - Numerical results

The early-time evolution of plasmas moving across a background magnetic field is addressed with a 2D model in which a plasma cloud is assumed to have formed instantaneously with a velocity across a uniform background magnetic field and with a Gaussian density profile in the two dimensions perpendicular to the direction of motion. This model treats both the dynamics associated with the formation of a polarization field and the generation and propagation of electromagnetic waves. In general, the results indicate that, to zeroth order, the plasma cloud behaves like a large dipole antenna oriented in the direction of the polarization field which oscillates at frequencies defined by the normal mode of the system. Radiation damping is shown to play an important role in defining the plasma cloud evolution, causing a rapid decay of the polarizaiton field and a loss of plasma kinetic energy and momentum on time scales comprable to several ion gyroperiods. Scaling laws are derived for the plasma momentum and energy loss rates, and predictions for the braking time, the amplitude and spectrum of the radiation field, and the total radiated power are presented for conditions relevant to the recent Combined Release and Radiation Effects Satellite experiments.

Roussel-Dupre, Robert↗

NASA NTRS1993

A preliminary study of the impact of the ERS 1 C band scatterometer wind data on the European Centre for Medium-Range Weather Forecasts global data assimilation system

A preliminary assessment of the impact of the ERS 1 scatterometer wind data on the current European Centre for Medium-Range Weather Forecasts analysis and forecast system has been carried out. Although the scatterometer data results in changes to the analyses and forecasts, there is no consistent improvement or degradation. Our results are based on comparing analyses and forecasts from assimilation cycles. The two sets of analyses are very similar except for the low level wind fields over the ocean. Impacts on the analyzed wind fields are greater over the southern ocean, where other data are scarce. For the most part the mass field increments are too small to balance the wind increments. The effect of the nonlinear normal mode initialization on the analysis differences is quite small, but we observe that the differences tend to wash out in the subsequent 6-hour forecast. In the Northern Hemisphere, analysis differences are very small, except directly at the scatterometer locations. Forecast comparisons reveal large differences in the Southern Hemisphere after 72 hours. Notable differences in the Northern Hemisphere do not appear until late in the forecast. Overall, however, the Southern Hemisphere impacts are neutral. The experiments described are preliminary in several respects. We expect these data to ultimately prove useful for global data assimilation.

Hoffman, Ross N.↗

NASA NTRS1993

A bi-directional two-phase/two-phase heat exchanger

This paper describes the design and test of a heat exchanger that transfers heat from one two-phase thermal loop to another with very small drops in temperature and pressure. The heat exchanger condenses the vapor in one loop while evaporating the liquid in the other without mixing of the condensing and evaporating fluids. The heat exchanger is bidirectional in that it can transfer heat in reverse, condensing on the normally evaporating side and vice versa. It is fully compatible with capillary pumped loops and mechanically pumped loops. Test results verified that performance of the heat exchanger met the design requirements. It demonstrated a heat transfer rate of 6800 watts in the normal mode of operation and 1000 watts in the reverse mode with temperature drops of less than 5 C between two thermal loops.

Ku, Jentung↗

NASA NTRS1993

Molecular-beam spectrum of the 970/cm Fermi triad of CF3CH3

A tunable MW-sideband CO2 laser is used with an electric-resonance optothermal spectrometer to investigate the IR spectrum of CF3CH3 near 970/cm. A Fermi-coupled triad of states is observed, resulting from the interactions of 2nu6+nu11 and nu5+nu12 with the fundamental vibration, nu10, which is assumed to carry the oscillator strength in this region. The high resolution (about 3 MHz) of the spectrometer allows the observation of tunneling splittings associated with the nu6 torsional vibration. These splittings are used to identify the torsional character of the states observed. At the normal-mode level the nu10 and nu5+nu12 states are found to be nearly degenerate and interacting by an anharmonic matrix element of about 3/cm. The present investigation illustrates the utility of using resolved torsional splittings to unravel complex vibrational couplings in molecules.

Fraser, G. T.↗

NASA NTRS1993

Are the 1986-1988 changes in solar free-oscillation frequency splitting significant?

The solar normal-mode splitting coefficients deduced from Big Bear Solar Observatory (BBSO) data differ between 1986 and 1988; inversions for equatorial rotation are slower at depth and faster near the surface in 1988 than in 1986. The significance of the change has been disputed. The data sets overlap for five splitting coefficients (a(j))super 5 sub j = 1 associated with 710 multiplets. On the assumption that rotation rate varies smoothly with radius, both data sets are satisfied by the same rotation model at all colatitudes except near 30-40 deg and near 70 deg (and at their southern hemisphere reflections 140-150 deg and 110 deg). The evidence for equatorial change is weak. Nonparametric tests show a significant offset in the magnitudes of a(1), a(2), and a(4), and of linear combinations sensitive to rotation at colatitudes of 60-80 deg (and 120 deg). Nonparametric tests show significant radial trends in the changes to a(2), a(4), and (less significantly) a(5). There is strong anticorrelation between a(2) and a(4), a(1) and a(3), and a(3) and a(5), suggesting that the estimates are not independent. Individual coefficients a(j) show more evidence for change than do 'physical' linear combinations, adding weight to this hypothesis. Some of the changes in splitting might be related to solar activity, which changed most near colatitude 70 deg from 1986 to 1988.

Gough, Douglas↗

NASA NTRS1988

Stiffnesses of a solid-rocket motor from an ambient vibration survey

Experience with many spacecraft configurations boosted by a variety of launch vehicles indicates that the maximum loads experienced throughout most of the structure are inertial in origin. These loads arise from the dynamic elastic response of the flight vehicle to the transient disturbances of launch and flight, and are highly dependent on the dynamic characteristics of both the spacecraft and the launch vehicle. It has proved to be most advantageous, in the analysis of this critical dependency of loads upon vehicle dynamic properties, to establish a mathematical model in terms of normal mode characteristics. In this way, the vibration behavior of an elastomechanical structure (or substructure) can be described by means of the so-called modal or natural degrees of freedom. The conduct of a mode survey test and the use of a suitably test-verified model in loads analyses is essential to the flight worthiness certification process of space systems. The desirability of such tests is confirmed by the fact that, almost invariably, significant deficiencies in the analytical models are revealed by the results. Therefore, this experimental program was undertaken to determine those properties of a solid-propellant rocket motor (SRM) which are required to characterize a dynamic model. Random ambient-excited accelerations were measured at a series of stations along the motor for the purpose of identifying the motor beam-like stiffnesses in bending, shear, and torsion. From a system identification point of view, it is significant that stiffness properties of a subsystem (the motor) are determined from modes of the full system (motor/stand configuration) using mode shape data of the subsystem only. This contrasts with traditional system identification approaches which rely upon complete system mode shapes.

Rubin, S.↗

NASA NTRS1940

Damping formulas and experimental values of damping in flutter models

The problem of determining values of structural damping for use in flutter calculations is discussed. The concept of equivalent viscous damping is reviewed and its relation to the structural damping coefficient g introduced in NACA Technical Report No. 685 is shown. The theory of normal modes is reviewed and a number of methods are described for separating the motions associated with different modes. Equations are developed for use in evaluating the damping parameters from experimental data. Experimental results of measurements of damping in several flutter models are presented.

Coleman, Robert P↗

NASA NTRS1990

Expert system for multidisciplinary analysis and optimization using ASTROS

This paper discusses the framework of a Knowledge Based Expert System (KBES) environment to design aerospace structures under structural and aerodynamic constraints using ASTROS (Automated Structural Optimization program). ASTROS is a synthesis tool built around the NASTRAN finite element program. The knowledge base capabilities are discussed for synthesizing in statics, normal mode, steady and unsteady aerodynamic disciplines. A description of the two ASTROS advisor modules the Editor/Bulk Data generator and Post-processor is included. Experiences and issues involved in hierarchical representation of knowledge as menu options at different levels of abstraction are presented. A brief overview of Knowledge Based Systems and the shell CLIPS (C Language Integrated Production System) used to develop the ASTROS Advisor are discussed. Illustrative examples of the advisor in designing airframe structures are also included.

Sarma, Hari K.↗

NASA NTRS1993

Evolution of disturbances in stagnation point flow

The evolution of three-dimensional disturbances in an incompressible three-dimensional stagnation-point flow in an inviscid fluid is investigated. Since it is not possible to apply classical normal mode analysis to the disturbance equations for the fully three-dimensional stagnation-point flow to obtain solutions, an initial-value problem is solved instead. The evolution of the disturbances provide the necessary information to determine stability and indeed the complete transient as well. It is found that when considering the disturbance energy, the planar stagnation-point flow, which is independent of one of the transverse coordinates, represents a neutrally stable flow whereas the fully three-dimensional flow is either stable or unstable, depending on whether the flow is away from or towards the stagnation point in the transverse direction that is neglected in the planar stagnation point.

Criminale, William O.↗

NASA NTRS1992

Linear stability theory and three-dimensional boundary layer transition

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

Spall, Robert E.↗

NASA NTRS1994

Modal decomposition of Hamiltonian variational equations

Over any finite arc of trajectory, the variational equations of a Hamiltonian system can be separated into 'normal' modes. This transformation is canonical, and the Lyapunov exponents over the trajectory arc occur as positive/negative pairs for conjugate modes, while the modal vectors remain unit vectors. This decomposition effectively solves the variational equations for any canonical, linear-dependent system. As an example, we study the Voyager I trajectory. In an interplanetary flyby, some of the modal variables increase by very large multiplicative factors, but this means that their conjugate modal variables decrease by those same very large multiplicative vectors. Maneuver strategies for this case are explored, and the minimum delta upsilon maneuver is found.

Wiesel, William E.↗

NASA NTRS1994

Towards enhancing and delaying disturbances in free shear flows

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Criminale, W. O.↗

NASA NTRS1993

An observing system simulation experiment for the Laser Atmospheric Wind Sounder (LAWS)

The present observing system-simulation experiments evaluate the potential of a Laser Atmospheric Wind Sounder (LAWS) instrument for 5-day forecasting, using a primitive-equation multilevel spectral global circulation model. A 55-deg-inclined and a 98-deg sun-synchronous orbit are examined, by adding LAWS wind profiles into a global 4D data-assimilation system, and comparing both the analyses and forecasts to a control experiment. The 4D data-assimilation system consists of a multivariate optimum interpolation analysis and a nonlinear, normal-mode intialization, using the aforementioned global circulation model.

Rohaly, G. D.↗

NASA NTRS1993

Long-pulse-length 2-micron diode-pumped YLiF4 laser

A diode-pumped Ho:Tm:YLiF4 laser at room temperature has achieved an optical efficiency of 5.9 percent under normal-mode operation. Long pulse lengths, of the order of 1 microsec, have been obtained by use of 4-m ring resonator, with laser energy output of 15 mJ in single Q-switched pulses for an input energy of 2.078 J.

Jani, Mahendra G.↗

NASA NTRS1992

Dynamic testing and analysis of extension-twist-coupled composite tubular spars

The results from a study aimed at improving the dynamic and aerodynamic characteristics of composite rotor blades through the use of extension-twist elastic coupling are presented. A set of extension-twist-coupled composite tubular spars, representative of the primary load carrying structure within a helicopter rotor blade, was manufactured using four plies of woven graphite/epoxy cloth 'prepreg.' These spars were non-circular in cross section design and were therefore subject to warping deformations. Three cross-sectional geometries were developed: square, D-shape, and flattened ellipse. Results from free-free vibration tests of the spars were compared with results from normal modes and frequency analyses of companion shell-finite-element models developed in MSC/NASTRAN. Five global or 'non-shell' modes were identified within the 0-2000 Hz range for each spar. The frequencies and associated mode shapes for the D-shape spar were correlated with analytical results, showing agreement within 13.8 percent. Frequencies corresponding to the five global mode shapes for the square spar agreed within 9.5 percent of the analytical results. Five global modes were similarly identified for the elliptical spar and agreed within 4.9 percent of the respective analytical results.

Lake, Renee C.↗