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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Radio-Frequency Tank Eigenmode Sensor for Propellant Quantity Gauging

Although there are several methods for determining liquid level in a tank, there are no proven methods to quickly gauge the amount of propellant in a tank while it is in low gravity or under low-settling thrust conditions where propellant sloshing is an issue. Having the ability to quickly and accurately gauge propellant tanks in low-gravity is an enabling technology that would allow a spacecraft crew or mission control to always know the amount of propellant onboard, thus increasing the chances for a successful mission. The Radio Frequency Mass Gauge (RFMG) technique measures the electromagnetic eigenmodes, or natural resonant frequencies, of a tank containing a dielectric fluid. The essential hardware components consist of an RF network analyzer that measures the reflected power from an antenna probe mounted internal to the tank. At a resonant frequency, there is a drop in the reflected power, and these inverted peaks in the reflected power spectrum are identified as the tank eigenmode frequencies using a peak-detection software algorithm. This information is passed to a pattern-matching algorithm, which compares the measured eigenmode frequencies with a database of simulated eigenmode frequencies at various fill levels. A best match between the simulated and measured frequency values occurs at some fill level, which is then reported as the gauged fill level. The database of simulated eigenmode frequencies is created by using RF simulation software to calculate the tank eigenmodes at various fill levels. The input to the simulations consists of a fairly high-fidelity tank model with proper dimensions and including internal tank hardware, the dielectric properties of the fluid, and a defined liquid/vapor interface. Because of small discrepancies between the model and actual hardware, the measured empty tank spectra and simulations are used to create a set of correction factors for each mode (typically in the range of 0.999 1.001), which effectively accounts for the small discrepancies. These correction factors are multiplied to the modes at all fill levels. By comparing several measured modes with the simulations, it is possible to accurately gauge the amount of propellant in the tank. An advantage of the RFMG approach of applying computer simulations and a pattern-matching algorithm is that the Although there are several methods for determining liquid level in a tank, there are no proven methods to quickly gauge the amount of propellant in a tank while it is in low gravity or under low-settling thrust conditions where propellant sloshing is an issue. Having the ability to quickly and accurately gauge propellant tanks in low-gravity is an enabling technology that would allow a spacecraft crew or mission control to always know the amount of propellant onboard, thus increasing the chances for a successful mission. The Radio Frequency Mass Gauge (RFMG) technique measures the electromagnetic eigenmodes, or natural resonant frequencies, of a tank containing a dielectric fluid. The essential hardware components consist of an RF network analyzer that measures the reflected power from an antenna probe mounted internal to the tank. At a resonant frequency, there is a drop in the reflected power, and these inverted peaks in the reflected power spectrum are identified as the tank eigenmode frequencies using a peak-detection software algorithm. This information is passed to a pattern-matching algorithm, which compares the measured eigenmode frequencies with a database of simulated eigenmode frequencies at various fill levels. A best match between the simulated and measured frequency values occurs at some fill level, which is then reported as the gauged fill level. The database of simulated eigenmode frequencies is created by using RF simulation software to calculate the tank eigenmodes at various fill levels. The input to the simulations consists of a fairly high-fidelity tank model with proper dimensions and including internal tank harare, the dielectric properties of the fluid, and a defined liquid/vapor interface. Because of small discrepancies between the model and actual hardware, the measured empty tank spectra and simulations are used to create a set of correction factors for each mode (typically in the range of 0.999 1.001), which effectively accounts for the small discrepancies. These correction factors are multiplied to the modes at all fill levels. By comparing several measured modes with the simulations, it is possible to accurately gauge the amount of propellant in the tank. An advantage of the RFMG approach of applying computer simulations and a pattern-matching algorithm is that the

Zimmerli, Gregory A.↗
NASA NTRS2013

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

Kinetic Eigenmode Spectra↗
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 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 NTRS1987

Computational procedures for evaluating the sensitivity derivatives of vibration frequencies and Eigenmodes of framed structures

Computational procedures are presented for evaluating the sensitivity derivatives of the vibration frequencies and eigenmodes of framed structures. Both a displacement and a mixed formulation are used. The two key elements of the computational procedure are: (a) Use of dynamic reduction techniques to substantially reduce the number of degrees of freedom; and (b) Application of iterative techniques to improve the accuracy of the derivatives of the eigenmodes. The two reduction techniques considered are the static condensation and a generalized dynamic reduction technique. Error norms are introduced to assess the accuracy of the eigenvalue and eigenvector derivatives obtained by the reduction techniques. The effectiveness of the methods presented is demonstrated by three numerical examples.

Fetterman, Timothy L.↗
NASA NTRS1993

Resonant behavior of MHD waves on magnetic flux tubes. IV - Total resonant absorption and MHD radiating eigenmodes

Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.

Goossens, Marcel↗
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 NTRS1987

Higher eigenmodes in the Blasius boundary-layer stability problem

The higher spatial-stability eigenmodes for the Blasius boundary layer are examined by using asymptotic theory, and an infinite number of modes are found. The asymptotic results are shown to be in close agreement with results from a direct numerical solution of the Orr-Sommerfeld problem. The asymptotic theory would therefore provide an efficient tool in exploratory searches for the eigenvalues.

Hultgren, Lennart S.↗
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 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 NTRS1975

Acoustic eigenmodes of corrugated ducts

Acoustic propagation in two-dimensional corrugated ducts is analyzed. A transform is made to a coordinate system that matches the duct walls. The resulting wave equation separates in space and time. The spatial differential equation is then solved by expanding in the eigenfunctions of a flat-walled duct. The prescription for this expansion is given by the appropriate application of time-independent perturbation theory. Calculations of first-order corrections for a periodic duct of both finite and infinite length are presented.

Succi, G. P.↗
NASA NTRS1999

Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed.

Kousen, Kenneth A.↗
NASA NTRS2010

Coherent Eigenmodes in Homogeneous MHD Turbulence

The statistical mechanics of Fourier models of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence is discussed, along with their relevance for dissipative magnetofluids. Although statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation, i.e., we have coherent structure. We use eigenanalysis of the modal covariance matrices in the probability density function to explain this phenomena in terms of `broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We provide examples from 2-D and 3-D magnetohydrodynamic simulations of homogeneous turbulence, and show new results from long-time simulations of MHD turbulence with and without a mean magnetic field

Shebalin, John V.↗
NASA NTRS2013

Radio frequency tank eigenmode sensor for propellant quantity gauging

A method for measuring the quantity of fluid in a tank may include the steps of selecting a match between a measured set of electromagnetic eigenfrequencies and a simulated plurality of sets of electromagnetic eigenfrequencies using a matching algorithm, wherein the match is one simulated set of electromagnetic eigenfrequencies from the simulated plurality of sets of electromagnetic eigenfrequencies, and determining the fill level of the tank based upon the match.

Zimmerli, Gregory A.↗
NASA NTRS1987

Spectral characteristics of hydromagnetic waves in the magnetosphere

The presence of discrete frequencies in the resonant response of the magnetosphere is considered. The eigenequation characterizing the eigenmodes of the hydromagnetic waves in a cylindrical model for the outer magnetosphere is shown to have two turning points along the radial axis. The turning point locations are related to the values of the eigenperiod and the associated east-west wavenumber of the eigenmode. It is also found that only the discrete set of the magnetospheric cavity eigenmodes can efficiently couple the perturbations excited on the boundary of the magnetosphere to the field-line resonant mode excited inside the turning point of the cavity eigenmode.

Kuo, S. P.↗
NASA NTRS1988

Streaming sausage, kink and tearing instabilities in a current sheet with applications to the earth's magnetotail

This paper investigates the growth rates and eigenmode structures of the streaming sausage, kink, and tearing instabilities in a current sheet with a super-Alfvenic flow. The growth rates and eigenmode structures are first considered in the ideal incompressible limit by using a four-layer model, as well as a more realistic case in which all plasma parameters and the magnetic field vary continuously along the direction perpendicular to the magnetic field and plasma flow. An initial-value method is applied to obtain the growth rate and eigenmode profiles of the fastest growing mode, which is either the sausage mode or kink mode. It is shown that, in the earth's magnetotail, where super-Alfvenic plasma flows are observed in the plasma sheet and the ratio between the plasma and magnetic pressures far away from the current layer is about 0.1-0.3 in the lobes, the streaming sausage and streaming tearing instabilities, but not kink modes, are likely to occur.

Lee, L. C.↗
NASA NTRS1994

A unifying comparison of nearly scatter free transport models

Gombosi et al. (1993) recently derived a modified telegrapher's equation for charged particle transport under the influence of isotropic scattering. This equation obeys causality and disallows upstream diffusion for particles with random velocities smaller than the bulk flow velocity. The acausal diffusion equation was obtained to lowest order in the expansion of smallness prameters. The paper by Gombosi et al. (1993) prompted responses from Pauls et al. (1993) and Earl (1993). This paper is written to explain the differences between the methods, assumptions, and results of Gombosi et al. (1993), Pauls et al. (1993), and Earl (1993) and presents a new method of obtaining approximate solutions. It is shown that the assumptions used by Gombosi et al. (1993) and Pauls et al. (1993) are physically equivalent. In our solution method, the solution of the modified telegrapher's equation is obtained as the casual limit of solutions accurate to second order in the smallness parameter expansion. In order to investigate the coherent velocity, we have also developed `wavenumber eigenfunctions' which account for all the pitch angle dependence in our Boltzmann equation. Using truncation, Earl (1993) obtains approximations for the wavenumber dependence of the lowest two frequency modes, which correspond to two of the wavenumber eigenmodes. We find that a consequence of including only two wavenumber eigenmodes is that one obtains solutions which disobey causality at sufficiently short times. Furthermore, the coherent velocity of the two eigenmodes is strongly dependent on wavenumber and approaches the particle velocity in the limit of large wavenumber for both isotropic and anisotropic scattering processes. We conclude that Earl's (1993) solutions and solutions obtained using the new solution method implicitly assume weak acausality and reasonable behavior in the temporal regime, t less than 4 tau. The solutions are not strictly consistent with the behavior of the lowest two frequency modes but have similar behavior in the regime of low wavenumber.

Schwadron, N. A.↗
NASA NTRS1973

Radiative damping of trapped gravity waves in the solar atmosphere.

The radiative damping of trapped gravity waves in an optically thin atmosphere is studied for a stratified Boussinesq fluid. The character of the atmospheric eigenmodes depends on the distribution of the Brunt-Vaisala frequency N and the radiative relaxation time tau. The calculations for simple layer models show that if N x tau is large over some finite fraction of the trapping region, then modes of long lifetime can exist. In order to suppress gravity waves entirely, it is necessary that N x tau be less than or equal to 1 over the entire trapping region. Qualitative application of the results to the solar atmosphere leads to the conclusion that gravity wave eigenmodes of the solar atmosphere, although damped, are by no means eliminated by radiative effects.

Clark, P. A.↗