Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “phase velocity dispersion”

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 37 records · Page 2

Determination of plate wave velocities and diffuse field decay rates with braod-band acousto-ultrasonic signals

Lowest symmetric and lowest antisymmetric plate wave modes were excited and identified in broad-band acousto-ultrasonic (AU) signals collected from various high temperature composite materials. Group velocities have been determined for these nearly nondispersive modes. An algorithm has been developed and applied to determine phase velocities and hence dispersion curves for the frequency ranges of the broad-band pulses. It is demonstrated that these data are sensitive to changes in the various stiffness moduli of the materials, in agreement by analogy, with the theoretical and experimental results of Tang and Henneke on fiber reinforced polymers. Diffuse field decay rates have been determined in the same specimen geometries and AU configuration as for the plate wave measurements. These decay rates are of value in assessing degradation such as matrix cracking in ceramic matrix composites. In addition, we verify that diffuse field decay rates respond to fiber/matrix interfacial shear strength and density in ceramic matrix composites. This work shows that velocity/stiffness and decay rate measurements can be obtained in the same set of AU experiments for characterizing materials and in specimens with geometries useful for mechanical measurements.

Kautz, Harold E.↗

Stress waves in transversely isotropic media: The homogeneous problem

The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.

Marques, E. R. C.↗

Gas and drop behavior in reacting and non-reacting air-blast atomizer sprays

A detailed study of the two-phase flow produced by a gas-turbine air-blast atomizer is performed with the goal of identifying the interaction between the two phases for both nonreacting and reacting conditions. A two-component phase Doppler interferometry is utilized to characterize three flowfields produced by the atomizer: (1) the single-phase flow, (2) the two-phase nonreacting spray, and (3) the two-phase reacting spray. Measurements of the mean and fluctuating axial and azimuthal velocities for each phase are obtained. In addition, the droplet size distribution, volume flux, and concentration are measured. The results reveal the strong influence of the dispersed phase on the gas, and the influence of reaction on both the gas and the droplet field. The presence of the spray significantly alters the inlet condition of the atomizer. With this alteration quantified, it is possible to deduce that the inertia associated with the dispersed phase damps the fluctuating velocities of the gas. Reaction reduces the volume flux of the droplets, broadens the local volume distribution of the droplets in the region of the reaction zone, increases the axial velocities and radial spread of the gas, and increases the anisotropy in the region of the reaction zone.

Mcdonell, Vincent G.↗

Modified non-linear Burgers' equations and cosmic ray shocks

A reductive perturbation scheme is used to derive a generalized non-linear Burgers' equation, which includes the effects of dispersion, in the long wavelength regime for the two-fluid hydrodynamical model used to describe cosmic ray acceleration by the first-order Fermi process in astrophysical shocks. The generalized Burger's equation is derived for both relativistic and non-relativistic cosmic ray shocks, and describes the time evolution of weak shocks in the theory of diffusive shock acceleration. The inclusion of dispersive effects modifies the phase velocity of the shock obtained from the lower order non-linear Burger's equation through the introduction of higher order terms from the long wavelength dispersion equation. The travelling wave solution of the generalized Burgers' equation for a single shock shows that larger cosmic ray pressures result in broader shock transitions. The results for relativistic shocks show a steepening of the shock as the shock speed approaches the relativistic cosmic ray sound speed. The dependence of the shock speed on the cosmic ray pressure is also discussed.

Zank, G. P.↗

Ultrasonic investigation of the nematic-isotropic phase transition in MBBA.

Relaxation processes associated with the nematic-isotropic phase transition are investigated in liquid crystals of p-methoxybenzylidine-p-n-butylaniline. Sound velocity and absorption are measured at frequencies from 0.3 to 23 MHz at temperatures from 23 to 77 C in samples without preferred orientations. Particular attention is given to the region of transition at about 44 C. Sound absorption and velocity dispersion far from the phase transition region can be well described by a single relaxation process, while in the vicinity of the phase transition the acoustic properties are characteristic of a multiply relaxing fluid.

Eden, D.↗

Detection of the Orbital Modulation of Fe Kα Fluorescence Emission in Centaurus X-3 Using the High-resolution Spectrometer Resolve on board XRISM

Abstract The Fe K α fluorescence line emission in X-ray spectra is a powerful diagnostic tool for various astrophysical objects to reveal the distribution of cold matter around photoionizing sources. The advent of the X-ray microcalorimeter on board the XRISM satellite will bring new constraints on the emission line. We present one of the first such results for the high-mass X-ray binary Centaurus X-3, which is composed of an O-type star and a neutron star (NS). We conducted a 155 ks observation covering an entire binary orbit. A weak Fe K α line was detected in all orbital phases at an equivalent width (EW) of 10–20 eV. We found for the first time that its radial velocity (RV) is sinusoidally modulated by the orbital phase. The RV amplitude is 248 ± 13 km s −1 , which is significantly smaller than the value (391 km s −1 ) expected if the emission is from the NS surface, but is consistent if the emission takes place at the O star surface. We discuss several possibilities of the line production site, including the NS surface, O star surface, O star wind, and accretion stream from the O star to the NS. We ran radiative transfer calculation for some of them assuming spherically symmetric density and velocity profiles and an isotropic distribution of X-ray emission from the NS. None of them explains the observed EW and velocity dispersion dependence on the orbital phase, suggesting that more elaborated modeling is needed. In other words, the present observational results have the capability to constrain deviations from these assumptions.

High energy astrophysics↗

Waves in frazil and pancake ice and their detection in Seasat synthetic aperture radar imagery

Measurements of wavelength and direction derived from SAR imagery obtained from Seasat in October 1987 are compared with a theoretical model of waves propagating into an ice cover composed of frazil and pancake ice. The dispersion relation for phase and group velocities is derived, and the existence of an upper frequency limit for propagation into the ice is found. The wave radiation pressure exerted on the ice is derived from the reflection coefficient at the ice edge; it is found to cause a slick of frazil ice backed by thicker floes to become more dense or thick with increasing penetration. When the frazil ice becomes transformed into pancake ice, the raised edges of the pancakes cause the ice to appear bright despite the fact that there are no waves present at the Bragg wavelength. Directional wave number spectra are derived outside and inside the ice cover. The change of wavelength and angle of refraction of the dominant wave entering the ice field are both found to be characteristic of the dispersion relation derived theoretically.

Wadhams, Peter↗

Plate mode velocities in graphite/epoxy plates

Measurements of the velocities of the extensional and flexural plate modes were made along three directions of propagation in four graphite/epoxy composite plates. The acoustic signals were generated by simulated acoustic emission events (pencil lead breaks or Hsu-Neilson sources) and detected by by broadband ultrasonic transducers. The first arrival of the extensional plate mode, which is nondispersive at low frequencies, was measured at a number of different distances from the source along the propagation direction of interest. The velocity was determined by plotting the distance versus arrival time and computing its slope. Because of the large dispersion of the flexural mode, a Fourier phase velocity technique was used to characterize this mode. The velocity was measured up to a frequency of 160 kHz. Theoretical predictions of the velocities of these modes were also made and compared with experimental observations. Classical plate theory yields good agreement with the measured extensional velocities. For predictions of the dispersion of the flexural mode, Mindlin plates theory, which includes the effects of shear deformation and rotatory inertia was shown to give better agreement with the experimental measurements.

Prosser, W. H.↗

Imaging coherent phonons and precursor dynamics in LaFeAsO with 4D ultrafast electron microscopy

In this work, we used 4D ultrafast electron microscopy (UEM) to directly image femtosecond photoinduced structural dynamics in single-crystal LaFeAsO at initial temperatures of 300 and 100 K, above and below the known structural and magnetic phase-transition temperatures, respectively. With nanometer-picosecond resolution, we resolved an initial (precursor) sigmoidlike response arising from photothermal expansion and lattice reorientation that precedes the onset of propagating coherent acoustic phonons (CAPs). In the specific regions probed, the precursor response at 100 K is shorter than at 300 K ($t$ 0.5;100 K = 11.3ps vs $t$ 0.5;300 K = 17.8ps), and the CAP oscillation frequency is lowered with cooling (ƒ CAP;100 K = 12 GHz vs ƒ CAP;300 K = 21 GHz), correlated to known lattice softening due to the structural phase change. The transient CAP behaviors at 300 K are dispersive, displaying an exponentially decaying phase velocity over the first nanosecond. Further, the CAP symmetry at 300 K matches a first-order antisymmetric shear mode (A 1 ), while at 100 K it is best matched by a mostly nondispersive zero-order symmetric mode (S 0 ). These findings illustrate the sensitivity of UEM imaging to spatially heterogeneous dynamics in the Fe-pnictide materials and more broadly in other quantum materials.

36 MATERIALS SCIENCE↗

On the size of the cometary tail magnetic field

Ershkovich's (1978) criticism of previous arguments in favor of magnetic fields of approximately 100 gammas in cometary plasma tails are shown to be unjustified. It is argued that the folding velocity of tail streamers indicates a substantial tail magnetic field and that much of Ershkovich's disagreement stems from the choice of completely different models for a comet's plasma tail. It is concluded that the use of growth rates or phase-velocity information obtained from a dispersion relation to interpret large-amplitude disturbances, such as those in comet tails, is categorically incorrect.

Mendis, D. A.↗

Data–Driven Velocity Model Evaluation Using K–Means Clustering

In this work, we develop a data-driven clustering method to evaluate a velocity model using surface wave velocity dispersion. This is done by first computing theoretical dispersion curves for 1-D velocity profiles of all the grid locations and then splitting the resulting dispersion curves into a certain number of groups via the K-means clustering. The observed dispersion curves are also clustered following the same procedure and the velocity model is assessed by comparing the spatial patterns obtained for the observed and synthetic data sets. The method is applied to evaluate two community velocity models in southern California, CVM-S4.26 and CVM-H15.1, using phase velocity maps derived for 3–16 s Rayleigh waves. We found a good correlation in the spatial distribution of clusters between the result of CVM-S4.26 and that of the observed data, suggesting that the CVM-S4.26 fits the observed dispersion maps better than the CVM-H15.1 in terms of features extracted from the clustering analysis.

58 GEOSCIENCES↗

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗

Ultrasound propagation measurements and applications

This paper reviews three systems designed for accurately measuring the propagation of ultrasonic pulses. The three systems are presented in order of velocity-measuring precision: + or - 100 ns, + or - 1 ns, + or - 0.2 ns. Also included is a brief discussion of phase and group velocities, with reference to dispersive, highly attenuating materials. Measurement of attenuation by pulse-echo buffer rod techniques is described briefly. These techniques and instruments have been used to measure sound velocity and attenuation in a variety of materials and shapes, over a wide temperature range.

Lynnworth, L. C.↗

Characterization of a Multilayered Dielectric Transmissive Phase Modulator

We describe a multilayered dielectric stack configuration designed specifically for use as a transmissive phase modulator for broadband optical signals. Applications for this device range from full aperture wavefront correction to nonmechanical beam steering arrays for free space optical communication links. Our implementation employs alternating GaAs and AlAs layers of varying thickness on a GaAs substrate to create a bandpass region of high average transmission centered about the one micrometer wavelength. Within this transmission bandpass, the phase component of the complex transmission coefficient varies in a near-linear fashion with respect to wavelength. The transmission bandpass is designed to have a bandwidth of 21.0 nm (or 6.3THz frequency bandwidth) and to have an edge-to-edge phase change of greater than 47T radians. Modification of the stack materials' optical properties causes the transmission profile to shift spectrally, resulting in a phase modulation for bands of transmitted frequencies. Our broadband phase modulator imparts up to a full-cycle of phase modulation with low loss and low group velocity dispersion. We identify several methods for implementing the requisite modulation, including refractive index modulation through free carrier injection and optical path length modulation through variation in angle of incidence. At least one sample comprising 91 alternating layers has been fabricated to exhibit the bandpass properties required for optical signal phase modulation. We experimentally characterize the sample using an interferometer and spectrometer to measure the transmitted signal spectrum and relative phase modulation. We compare the experimental data to computational predictions and discuss the results.

Keys, Andrew S.↗

Mode properties of low-frequency waves: Kinetic theory versus Hall-MHD

In fluid theory, the ordering of low-frequency modes in a homogeneous plasma is based on the phase velocity, since modes do not intersect each other in dispersion diagrams as a function of wavenumber or other parameters. In linear kinetic theory, modes cross each other. Thus a consistent and useful classification should be based on the physical properties of the modes instead. This paper attempts such a classification by documeting the dispersion and general mode properties of the low-frequency waves (omega much less than (OMEGA(sub ci) OMEGA(sub ce) (exp 1/2)), where OMEGA(sub ci), OMEGA(sub ce) are the cyclotron frequencies of the ions and electrons, respectively) in kinetic theory, and by comparing them to the results of two-fluid theory. Kinetic theory gives a seperate Alfven/ion-cyclotron (A/IC) wave with phase speed Omega/k approximately = v(sub A) cos theta for omega much less than OMEGA(sub ci), where v(sub A) is the Alfven velocity and theta the angle of propagation between wave vector k and background magnetic field B(sub o). For a given wavenumber, the magnetosonic mode is a double-valued solution with a singular point in theta, beta parameter space, where beta is the ratio of thermal pressure to magnetic pressure. It is shown that a branch cut starting at the singular point theta approximately 30 deg, beta approximately 3 and leading to larger beta gives a practical and consitent seperation of this double-valued magnetosonic solution. Selection of this branch cut results in a moderately damped fast/magnetos onic and a heavily damped slow/sound wave. A comprehensive review of the polarization, compressibility and other mode properties is given and shown to be consistent with the selected branch cut. At small wavenumbers, the kinetic mode properties typically start to deviate significantly from their fluid counterparts at beta approximately 0.5. At larger beta, there is no longer a consistent correspondence between the fluid and kinetic modes. Kinetic theory also dictates the use of different mode properties to distinguish between them in observational data. For example, the phase between the density and magnetic field perturbation may become useless at high beta, whereas the direction of the magnetic field perturbations with respect to k and B(sub o) remains a useful characteristic. Two quantities based on this characteristic are suggested and are shown to be useful also to distinguish between the mirror mode and A/IC waves in a plasma with temperature anisotropy.

Krauss-Varban, D.↗

Material characterization of composite laminates using low-frequency plate wave dispersion data

A recently developed ultrasonic techique which has been successful in monitoring the integrity of advanced structures is described. The technique is based on a two-transducer contact type arrangement that can be used to determine the dispersion curves of guided waves generated within the specimen. The phase velocity of antisymmetric plate waves is determined through spectral analysis of signals recorded from a lead break source on the surface of graphite epoxy laminates. The influence of all five stiffness constants on the dispersion curves of both symmetric and antisymmetric plate waves is theoretically investigated for propagation at 0, 45, and 90 deg to the fibers. All but c12 were found to have a strong influence on the dispersion curves in this frequency range. The fit with the theoretically predicted dispersion curves was excellent for propagation parallel and perpendicular to the fibers in the unidirectional specimen and good for the other cases considered.

Mal, Ajit K.↗

Ion acoustic waves in a multi-ion plasma.

An exact treatment of the multispecies ion acoustic dispersion relation is given for an argon/helium plasma. Phase velocity and damping are obtained as a function of ion-electron temperature ratio and relative densities of the two species. There are two important modes in the plasma, with quite different phase velocities, which are referred to as principal heavy ion mode and principal light ion mode. Which of these is dominant depends on the relative densities of the two components, but, in general, the light ion mode becomes important for surprisingly small light ion contamination. Approximate analytic expressions are derived from damping rates and phase velocities and their domains of validity are investigated. Relevance of the results for the investigation of collisionless shocks is discussed.

Fried, B. D.↗