Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Normal modes”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Geometric analysis of wing sections

This paper describes a new geometric analysis procedure for wing sections. This procedure is based on the normal mode analysis for continuous functions. A set of special shape functions is introduced to represent the geometry of the wing section. The generators of the NACA 4-digit airfoils were included in this set of shape functions. It is found that the supercritical wing section, Korn airfoil, could be well represented by a set of ten shape functions. Preliminary results showed that the number of parameters to define a wing section could be greatly reduced to about ten. Hence, the present research clearly advances the airfoil design technology by reducing the number of design variables.

Chang, I.-CHUNG↗
NASA NTRS1994

Numerical simulation of baroclinic Jovian vortices

We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an f plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler two-dimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a beta plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.

Achterberg, Richard K.↗
NASA NTRS1994

Evolution of the Southern Hemisphere subpolar middle atmosphere during summer and autumn

The evolution of zonal wind and zonal wavenumber one (wave 1) in the Southern Hemisphere subpolar middle atmosphere is described for the period December 1978 - May 1979 using temperature and ozone measurements from the Limb Infrared Monitor of the Stratosphere (LIMS) experiment. In late December maximum zonal easterlies of approx. -70 m/s are observed at 0.1 mb, 60 deg S. A zonal flow reversal occurs during late February and westerlies subsequently increase to 60-70 m/s in the upper stratosphere by April - May. LIMS zonal winds are compared with rocketsonde measurements and nadir sounder (derived) winds for summer and autumn. Although quantitative agreement is found at stratospheric levels, substantial discrepancies are evident in the mesosphere, most likely a reflection of sampling and resolution differences in the respective datasets. Stationary and traveling wave 1 temperature disturbances (amplitudes approx. 1 - 2 K at 60 deg S) are observed by LIMS during summer. The stationary wave is confined to the lower stratosphere near the level of zero zonal- mean wind flow, whereas the traveling wave is prominent in the middle stratosphere moves west at a rate similar to the zonal-mean wind, and exhibits a vertical - meridional structure similar to a P(sub 4)(sup 1) normal mode Rossby wave. A substantial intensification of wave 1 activity occurs during autumn (amplitudes approx. 5 - 10 K), which is found to be associated with an upward-directed Eliasse - Palm flux near the subpolar tropopause level. Evidence relating wave 1 activity in the lower - middle stratosphere to the occurrence of zonal ozone perturbations of 10% - 20% amplitude is presented for summer and autumn.

Miles, T.↗
NASA NTRS1994

Quasi-biennial oscillation and tropical waves in total ozone

Westward and eastward propagating tropical waves in total ozone are investigated in 13 years (1979-1991) of version 6 total column ozone data from the Nimbus 7 total ozone mapping spectrometer (TOMS) satellite instrument. A clear synchronization between the stratospheric quasi-biennial osciallation (QBO) zonal winds and the fast (periods less than 15 days) propagating waves in tropical TOMS data is detailed. Largest total ozone wave amplitudes (about 3-6 Dobson units) occur when their phase propagation direction is primarily opposite the Singapore QBO lower-stratospheric winds. This effect is most apparent in meridionally symmetric components. Examination of specific episodes, including cross-spectral calculations with Singapore rawinsonde wind data (10-70 hPa), reveals signatures of tropically confined eastward propagating Kelvin waves of zonal wavenumbers 1-2 during the descending eastward QBO phase, consistent with acceleration of that QBO phase by Kelvin waves. The TOMS results are also consistent with possible forcing of the westward QBO wind phase by episodes of both meridionally symmetric and asymmetric westward waves. However, in contrast to the case of eastward (Kelvin) waves the strongest westward events appear to be filtered by, rather than forcing, the westward phase of the stratospheric QBO wind. These dominant westward episodes are interpreted as meridionally symmetric westward global normal modes and tropically confined equatorial-Rossby waves 2-6. The events exhibit phase and group speeds characteristic of wave dynamics rather than simple wind advection. These results underscore the utility of the long time series and excellent horizontal coverage of TOMS data for dynamical investigations in the relatively observation-poor tropical stratosphere.

Ziemke, J. R.↗
NASA NTRS1993

Reply to the comment by Y. Ricard, R. Sabadini, and G. Spada

We welcome this opportunity which Drs. Ricard, Sabadini and Spada (RSS) have offered us to elaborate on some points concerning the connection between convective circulations and rotational dynamics. The relationship of the linear viscoelastic normal-mode theory to other approaches, such as viscous and the non-linear viscoelastic treatments, can be found in Moser et al. (1993). We will address the issues raised by RSS by first going over the reference system. This will be followed by a discussion concerning long-term polar wander and relative angular momentum. We will also go over the issues concerning the off-diagonal terms in the total moment of inertia and polar wander.

Moser, Jiri↗
NASA NTRS1994

A singularity free approach to post glacial rebound calculations

Calculating the post glacial response of a viscoelastic Earth model using the exponential decay normal mode technique leads to intrinsic singularities if viscosity varies continuously as a function of radius. We develop a numerical implementation of the Complex Real Fourier transform (CRFT) method as an accurate and stable procedure to avoid these singularities. Using CRFT, we investigate the response of a set of Maxwell Earth models to surface loading. We find that the effect of expanding a layered viscosity structure into a continuously varying structure is to destroy the modes associated with the boundary between layers. Horizontal motion is more sensitive than vertical motion to the viscosity structure just below the lithosphere. Horizontal motion is less sensitive to the viscosity of the lower mantle than the vertical motion is. When the viscosity increases at 670 km depth by a factor of about 60, the response of the lower mantle is close to its elastic limit. Any further increase of the viscosity contrast at 670 km depth or further increase of viscosity as a continuous function of depth starting from 670 km depth is unlikely to be resolved.

Fang, Ming↗
NASA NTRS1994

Observations of the 5-day wave in the mesosphere and lower thermosphere

The 5-day planetary wave has been detected in the winds measured by the High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS) in the mesosphere and lower thermosphere (50-110 km). The appearances of the 5-day wave are transient, with a lifetime of 10-20 days in the two-year data set. The structures of selected 5-day wave events are in generally good agreement with the (1,1) Rossby normal mode for both zonal and meridional components. A climatology of the 5-day wave is presented for an altitude of 95 km and latitudes mainly between 40 deg S and 40 deg N.

Wu, D. L.↗
NASA NTRS1993

Stochastic dynamics of baroclinic waves

The maintenance of variance and attendant heat flux in linear, forced dissipative baroclinic shear flows subject to stochastic excitation is examined. The baroclinic problem, is intrinsically nonnormal and its stochastic dynamics is found to differ significantly from the more familiar stochastic dynamics of normal systems. When the shear is sufficiently great in comparison to dissipative effects, stochastic excitation supports highly enhanced variance levels in these nonnormal systems compared to variance levels supproted by the same forcing and dissipation in related normal systems. The eddy variance and associated heat flux are found to arise in response to transient amplification of a subset of forcing functions that obtain energy from the mean flow and project this energy on a distinct subset of response functions (EOFs) that are in turn distinct from the set of normal modes of the system. A method for obtaining the dominant forcing and response functions as well as the distribution of heat flux for a given flow is described.

Farrell, Brian F.↗
NASA NTRS1993

Parametric instabilities of parallel-propagating Alfven waves: Some analytical results

We consider the stability of a circularly polarized Alfven wave (the pump wave) which propagates parallel to the ambient magnetic field. Only parallel-propagating perturbations are considered, and we ignore dispersive effects due to the ion cyclotron frequency. The dissipationless MHD equations are used throughout; thus possibibly important effects arising from Landau and transit time damping are omitted. We derive a series of analytical approximations to the dispersion relation using A = (Delta B/B(sub O))(exp 2) as a small expansion parameter; Delta B is the pump amplitude, and B(sub O) is the ambient magnetic field strength. We find that the plasma beta (the square of the ratio of the sound speed to the Alfven speed) plays a crucial role in determining the behavior of the parametric instabilities of the pump. If 0 less than beta less than 1 we find the familiar result that the pump decays into a forward propagating sound wave and a backward propagating Alfven wave with maximum growth rate gamma(sub max) varies A(sup 1/2), but beta cannot be too close to 0 or to 1. If beta approx. 1, we find gamma(sub max) varies A(sup 3/4), if beta greater than 1, we find gamma(sub max) varies A(sup 3/2), while if beta approx. 0, we obtain gamma(sub max) varies A(sup 1/3); moreover, if beta approx. 0 there is a nearly purely growing instability. In constrast to the familiar decay instability, for which the backward propagating Alfven wave has lower frequency and wavenumber than the pump, we find that if beta greater than or approx. equal to 1 the instability is really a beat instability which is dominated by a transverse wave which is forward propagating and has frequency and wavenumber which are nearly twice the pump values. Only the decay instability for 0 less than beta less than 1 can be regarded as producing two recognizable normal modes, namely, a sound wave and an Alfven wave. We discuss how the different characteristics of the instabilities may affect the evolution of Alfven waves in the solar wind. However, for a solar wind in which beta approx. 1 the growth times of the instabilities are probably too long for these instabilities to have an appreciable effect inside 1 AU.

Jayanti, V.↗
NASA NTRS1993

Turbine blade forced response prediction using FREPS

This paper describes a software system called FREPS (Forced REsponse Prediction System) that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced response dynamic stresses in axial flow turbomachinery blades due to aerodynamic and mechanical excitations. A flutter analysis capability is also incorporated into the system. The FREPS system performs aeroelastic analysis by modeling the motion of the blade in terms of its normal modes. The structural dynamic analysis is performed by a finite element code such as MSC/NASTRAN. The steady aerodynamic analysis is based on nonlinear potential theory and the unsteady aerodynamic analyses is based on the linearization of the non-uniform potential flow mean. The program description and presentation of the capabilities are reported herein. The effectiveness of the FREPS package is demonstrated on the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine. Both flutter and forced response analyses are performed and typical results are illustrated.

Murthy, Durbha, V.↗
NASA NTRS1995

Acoustic wave propagation in the solar atmosphere 1. Rediscussion of the linearized theory including nonstationary solutions

The normal dispersion analysis for linear adiabatic wave propagation in stratified atmospheres adopts a real frequency and solves for the complex vertical wavenumber. We show that an exponentially stratified atmosphere does not have any spatially bounded normal modes for real frequencies. The usual treatment involves a representation where the imaginary part of the vertical wavenumber yields a rho(sup -1/2) dependence of the velocity amplitude which diverges as the absolute value of z approaches infinity. This solution includes a cutoff frequency below which acoustic modes cannot propagate. The standard dispersion analysis is a local representation of the wave behavior in both space and time but which is assumed to represent the motion throughout - infinity is less than t is less than infinity and 0 is less than infinity. However, any solution which has a purely sinusoidal time dependence extends through this full domain and is divergent due to the rho(sup -1/2) dependence. We show that a proper description is in terms of a near field of a boundary piston which is driven arbitrarily as a function of space and time. The atmosphere which responds to this piston is a semi-infinite layer which has an initially constant sound speed but which has the usual gravitational stratification. In a restricted domain of space and time above this boundary, the wavelike behavior of the medium may be described by frequencies and vertical wavenumbers which are both complex. When both parameters are allowed to have imaginary components, a new range of solutions is found for which there is virtually no cutoff frequency. We show that vertical energy propagation can take place through the solar atmosphere as a result of oscillations below the nominal cutoff frequency. Previously, the largest amplitude oscillations which generally have low frequencies were dropped from the calculation of energy flux becuase their frequencies are below the cutoff frequency. This new family of near-field waves permits these modes to carry energy vertically outward and raises the possibility that the largest amplitude 5 minute oscillations play a substantial role in the transport of acoustic energy to the chromosphere.

Wang, Zhengzhi↗
NASA NTRS1996

Fully-Coupled Fluid/Structure Vibration Analysis Using MSC/NASTRAN

MSC/NASTRAN's performance in the solution of fully-coupled fluid/structure problems is evaluated. NASTRAN is used to perform normal modes (SOL 103) and forced-response analyses (SOL 108, 111) on cylindrical and cubic fluid/structure models. Bulk data file cards unique to the specification of a fluid element are discussed and analytic partially-coupled solutions are derived for each type of problem. These solutions are used to evaluate NASTRAN's solutions for accuracy. Appendices to this work include NASTRAN data presented in fringe plot form, FORTRAN source code listings written in support of this work, and NASTRAN data file usage requirements for each analysis.

Fernholz, Christian M.↗
NASA NTRS1996

PROP3D: A Program for 3D Euler Unsteady Aerodynamic and Aeroelastic (Flutter and Forced Response) Analysis of Propellers. Version 1.0

This guide describes the input data required, for steady or unsteady aerodynamic and aeroelastic analysis of propellers and the output files generated, in using PROP3D. The aerodynamic forces are obtained by solving three dimensional unsteady, compressible Euler equations. A normal mode structural analysis is used to obtain the aeroelastic equations, which are solved using either time domain or frequency domain solution method. Sample input and output files are included in this guide for steady aerodynamic analysis of single and counter-rotation propellers, and aeroelastic analysis of single-rotation propeller.

Srivastava, R.↗
NASA NTRS1996

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

Reddy, T. S. R.↗
NASA NTRS1995

Diode-Pumped Long-Pulse-Length Ho:Tm:YLiF4 Laser at 10 Hz

An optical efficiency of 0.052 under normal mode operation for diode-pumped Ho:Tm:YLiF4 at a pulse repetition frequency of 10 Hz has been achieved. Laser output energy of 30 mJ in single Q-switched pulses with 600-ns pulse length were obtained for an input energy of 3 J. A diffusion-bonded birefringent laser rod consisting of Ho:Tm-doped and undoped pieces of YLF was utilized for 10-Hz operation.

Jani, Mahendra G.↗
NASA NTRS1993

Kinematic Dynamo In Turbulent Circumstellar Disks

Many circumstellar disks associated with objects ranging from protoplanetary nebulae, to accretion disks around compact stars allow for the generation of magnetic fields by an (alpha)omega dynamo. We have applied kinematic dynamo formalism to geometrically thin accretion disks. We calculate, in the framework of an adiabatic approximation, the normal mode solutions for dynamos operating in disks around compact stars. We then describe the criteria for a viable dynamo in protoplanetary nebulae, and discuss the particular features that make accretion disk dynamos different from planetary, stellar, and galactic dynamos.

Stepinski, T.↗
NASA NTRS1993

On Magnetic Dynamos in Thin Accretion Disks around Compact and Young Stars

A variety of geometrically thin accretion disks commonly associated with such astronomical objects as X-ray binaries, cataclysmic variables, and protostars are likely to be seats of MHD dynamo actions. Thin disk geometry and the particular physical environment make accretion disk dynamos different from stellar, planetary, or even galactic dynamos. We discuss those particular features of disk dynamos with emphasis on the difference between protoplanetary disk dynamos and those associated with compact stars. We then describe normal mode solutions for thin disk dynamos and discuss implications for the dynamical behavior of dynamo-magnetized accretion disks.

Stepinski, T. F.↗
NASA NTRS1997

User's Manual for DuctE3D: A Program for 3D Euler Unsteady Aerodynamic and Aeroelastic Analysis of Ducted Fans

The program DuctE3D is used for steady or unsteady aerodynamic and aeroelastic analysis of ducted fans. This guide describes the input data required and the output files generated, in using DuctE3D. The analysis solves three dimensional unsteady, compressible Euler equations to obtain the aerodynamic forces. A normal mode structural analysis is used to obtain the aeroelastic equations, which are solved using either the time domain or the frequency domain solution method. Sample input and output files are included in this guide for steady aerodynamic analysis and aeroelastic analysis of an isolated fan row.

Srivastava, R.↗