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NASA NTRS1983

Eigenmode analysis of unsteady one-dimensional Euler equations

The initial boundary value problem describing the evolution of unsteady linearized perturbations of a steady, uniform subsonic flow is analyzed. The eigenmodes and eigenfrequencies of the system are derived and several examples are presented to illustrate the effect of different boundary conditions on the exponential decay rate of the eigenmodes. The resultant implications for the stability and convergence rates of finite difference computations are discussed.

Giles, M.↗

NASA NTRS1998

Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

Darmofal, David L.↗

NASA NTRS1983

Hall current effect on tearing mode instability

From a linear 2-D eigenmode analysis, it is found that the Hall current effect on collisional tearing mode instability becomes important for the thin magnetic reversal layer whose width is comparable to the ion inertia length; Hall currents produce a three-dimensional field structure and increase the reconnection (growth) rate. Since the magnetaic reversal layer widths both in the magnetopause and in the magnetotail are reported to become as thin as the ion inertial length (several hundred km) when the reconnection process is supposed to occur, the Hall current effect may explain the appearance of the dawn-dusk component of the magnetic field in the magnetotail reconnection region.

Terasawa, T.↗

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 NTRS1993

Linear theory of fast reconnection at an X-type neutral point

A complete analytic theory of dynamic linear reconnection at an X-type neutral point is developed. An eigenmode analysis, using cylindrical coordinates centered on the neutral point, extends the work of Craig & McClymont (1991) to include nonazimuthally symmetric perturbations on the flux function. It is demonstrated that all physically significant disturbances, both reconnective and nonreconnective, decay resistively on a 'fast' time scale. The significance of the linear theory is discussed within the general context of steady state and dynamic reconnection studies. Disturbances can be expected to focus explosively in the vicinity of the neutral point. This suggests the formation of a 'flux pile-up' current layer in which the bulk of the magnetic energy is released as heat rather than kinetic energy of mass motion.

Craig, I. J. D.↗

NASA NTRS1994

Gradient drift eigenmodes in the equatorial electrojet

The problem of kilometer-scale irregularities in the daytime equatorial electrojet is revisited by means of an eigenmode analysis of the gradient drift instability. Realistic physical parameters are used, including the modeled altitude variations of ion and electron collision frequencies and mobilities. The full fourth-order system of two coupled differential equations (each of second order) for the denisty and electrostatic potential perturbations is solved numerically by a relaxation technique. Under some approximations, the fourth-order system can be shown to reduce to a second-order differential equation for the perturbed potential or density. The latter is solved using a shooting technique and provides initial guesses for numerical solutions to the full problem. It is shown that the linear growth rate peaks for kilometer-scale waves, contrary to the findings of recent initial-value studies. This occurs because the equilibrium velocity shear is much more effective as a damping mechanism for short-wavelength modes than it is for the longer, kilometer-scale modes. These results provide a natural qualitative explanation for the observed dominance of kilometer-scale structures in the daytime electrojet spectrum.

Wang, X.-H.↗

NASA NTRS1993

Mode Profiles in Waveguide-Coupled Resonators

Surface acoustic wave (SAW) waveguide-coupled resonators are of considerable interest for narrow-band filter applications, though to date there has been very little published on the acoustic details of their operation. As in any resonator, one must fully understand its mode structure and herein we study the SAW mode profiles in these devices. Transverse mode profiles in the resonant cavity of the device were measured at various frequencies of interest using a knife-edge laser probe. In addition we predict the mode profiles for the device structure by two independent methods. One is a stack-matrix approach adapted from integrated optics and the other is a conventional analytical eigenmode analysis of the Helmholtz equation. Both modeling techniques are in good agreement with the measured results.

Hunt, William D.↗

NASA NTRS1984

Dynamic analysis of evolutive conservative systems. Discussion of eigenmode crossings

After an analysis of the close connection between the symmetries of a dynamical system and the multiplicity of its vibrational natural frequencies, it is proved by variational arguments that for a system of invariable symmetry the eigenfrequencies associated with the eigenmodes of a given symmetry type do not cross, in general, during the evolution of this system. The theory is implemented by some numerical calculations applied to the analysis of the evolution of the axisymmetric hydroelastic modes of the Ariane launch vehicle during burning of the first stage.

Morand, H. J. P.↗

NASA NTRS1979

Accuracy of an approximate static structural analysis technique based on stiffness matrix eigenmodes

Use of the stiffness matrix eigenmodes, instead of the vibration eigenmodes, as generalized coordinates is proposed for condensation of static load deflection equations in finite element stiffness method. The modes are selected by strain energy criteria and the resulting fast, approximate analysis technique is evaluated by applications to idealized built-up wings and a fuselage segment. The best results obtained are a two-order of magnitude reduction of the number of degrees of freedom in a high aspect ratio wing associated with less than one percent error in prediction of the largest displacement.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1988

An investigation of the relationship between sub-Saharan rainfall and global sea surface temperatures

The relationship between SST and rainfall index anomalies over sub-Saharan Africa for the 1970-1984 period is investigated. Results of an empirical orthogonal function analysis indicate that the most dominant eigenmode, EOF1, is characterized by warming over the central eastern Pacific, cooling over the eastern midlatitude Pacific, and warming over the entire Atlantic and Indian ocean basins. EOF1 is found to have statistically signifiant monthly correlations for the Sahel and Soudan regions, with the warm El Nino-like phases of SST EOF1 corresponding to drought conditions. These results suggest that the large-scale SST anomalies may be responsible for a large component of the observed vacillation of sub-Saharan rainfall.

Semazzi, F. H. M.↗

NASA NTRS1987

Near-symmetric instability for general Prandtl number

An analysis of the stability of a simple baroclinic flow to perturbations whose horizontal wave vector lies in and near the vertical plane containing the density gradient has been performed. The Ekman number (E) and 'azimuthal' wavenumber (alpha) were both assumed much less than 1, and expansions about these quantities were performed for the eigenmodes and Richardson number (R). Agreement with the previous analysis of Busse and Chen (1981) that the correction to the critical R was O(alpha) for Prandtl number (P) away from unity was obtained. An expression for the correction to the critical R for arbitrary P, and an approximate expression for P = 1 were obtained as new results. The correction for P = 1 has the same sign as that for P less than 1, and is O(alpha E exp 2/3). This result compares well with the numerical results of Miller and Antar (1986) for small E.

Reynolds, Nathaniel D.↗

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 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 NTRS1995

A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets

We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component B(sub n) normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Omega(sub n) is comparable to the Harris neutral sheet growth rate. A cross-tail B(sub y) component has little effect on the growth rate for B(sub y) approximately = B(sub n). Even in the limit B(sub y) much greater than B(sub n), the mode is strongly stabilized by B(sub n). We report than random pitch angle scattering can overcome the stabilizing effect of B(sub n) and drive the growth rate up toward the Harris neutral sheet (B(sub n) = 0) value when the pitch angle diffusion rate is comparable to Omega(sub n).

Brittnacher, M.↗

NASA NTRS1995

Spectroscopy of infrared-active phonons in high-temperature superconductors

For a large variety of superconducting materials both experimental and theoretical lattice dynamical studies have been performed to date. The assignment of the observed infrared- and Raman-active phonon modes to the particular lattice eigenmodes is generally accepted. We will concentrate here upon the analysis of the changes of the infrared-phonon parameters (frequency and linewidth) upon entering the superconducting state which, as will be shown, may provide information on the magnitude of the superconductivity-related gap and its dependence on the superconducting transition temperature Tc.

Litvinchuk, A. P.↗

NASA NTRS2014

Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

Flexible inhibitors are generally used in solid rocket motors (SRMs) as a means to control the burning of propellant. Vortices generated by the flow of propellant around the flexible inhibitors have been identified as a driving source of instabilities that can lead to thrust oscillations in launch vehicles. Potential coupling between the SRM thrust oscillations and structural vibration modes is an important risk factor in launch vehicle design. As a means to predict and better understand these phenomena, a multidisciplinary simulation capability that couples the NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This capability is crucial to the development of NASA's new space launch system (SLS). This paper summarizes the efforts in applying the coupled software to demonstrate and investigate fluid-structure interaction (FSI) phenomena between pressure waves and flexible inhibitors inside reusable solid rocket motors (RSRMs). The features of the fluid and structural solvers are described in detail, and the coupling methodology and interfacial continuity requirements are then presented in a general Eulerian-Lagrangian framework. The simulations presented herein utilize production level CFD with hybrid RANS/LES turbulence modeling and grid resolution in excess of 80 million cells. The fluid domain in the SRM is discretized using a general mixed polyhedral unstructured mesh, while full 3D shell elements are utilized in the structural domain for the flexible inhibitors. Verifications against analytical solutions for a structural model under a steady uniform pressure condition and under dynamic modal analysis show excellent agreement in terms of displacement distribution and eigenmode frequencies. The preliminary coupled results indicate that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor. This insight could have profound implications for SRM and flexible inhibitor designs for current and future launch vehicles including SLS.

Yang, H. Q.↗

NASA NTRS1985

Subseasonal and interannual variations of tropical convection and the El Nino/Southern Oscillation

It was found that during the northern winter, fluctuation in tropical convection is dominated by eastware propagating cloud clusters from the Indian Ocean. Most of these clusters reach as far as the central Pacific. Longitude time sections of outgoing longwave radiation (OLR) anomaly along the equator show that there are about 3 to 4 such episodes each winter. Also, simultaneous OLR anomalies over the equatorial central Pacific (ECP) and the maritime continent (MC) are negatively correlated and their variations are dominated by a 40 to 60 day period, suggesting the presence of a standing wave phenomenon. Such combination of propagating and standing phenomena can be captured by the extended empirical orthogonal function (EEOF) analysis. The EEOF method combines the temporal as well as the spatial correlation information to produce eigenmodes which have space time dependence. A 5 day and a 10 day lag in addition to the simultaneous spatial correlation is used.

Lau, K. M.↗

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.↗