Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

Generation and scattering of sound in vortical flow

We present solutions to scattering problems for unsteady disturbances to a mean swirling flow in an annular duct with a rigid 'splitter'. This situation has application to rotor-stator interaction noise in aeroengines, where the flow downstream of the fan is swirling and bifurcates into the by-pass duct and the engine core. We also consider the trailing edge extension of this problem. Inviscid mean flow in a cylindrical annulus is considered, with both axial and swirling (azimuthal) velocity components. The presence of vorticity in the mean flow couples the acoustic and vorticity modes of irrotational flow. Instead we have one combined spectrum of acoustic-vorticity waves in which the 'sonic' and 'nearly-convected' modes are fully coupled. In addition to the aeroacoustics application the results offer insight into the behaviour of these acoustic-vorticity waves, and the precise nature of the coupling between the two types of mode. Two regimes are discussed in which progress has been made, one for a specialised mean flow, uniform axial flow and rigid body swirl, and a second regime in which the frequency is assumed large, valid for any axisymmetric mean flow. The Wiener-Hopf technique is used to solve the scattering problems mathematically, and we present numerical evaluations of these solutions. Several new effects are seen to arise due to the mean vorticity, in particular the generation of sound at a trailing edge due to the scattering of a nearly convected disturbance, in contrast to the way a convected gust silently passes a trailing edge in uniform mean flow.

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, - ∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t), no more singular than h = Ο(x1/2) for x ↓ 0. A mode, incident from x < 0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = Ο(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z (ω) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ω → 0, the modulus fends to |R001| → (1 + M)/(1 -M) without and to 1 with Kutta condition, while the end correction tends to ∞ without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow.

The preparation, characterization and tribological properties of TA-C : H deposited using an electron cyclotron wave resonance plasma beam source

A compact electron cyclotron wave resonance (ECWR) source has been developed for the high rate deposition of hydrogenated tetrahedral amorphous carbon (ta-C:H). The ECWR provides growth rates of up to 900 Å/min over a 4″ diameter and an independent control of the deposition rate and ion energy. The ta-C:H was deposited using acetylene as the source gas and was characterized in terms of its sp3 content, mass density, intrinsic stress, hydrogen content, C-H bonding, Raman spectra, optical gap, surface roughness and friction coefficient. The results obtained indicated that the film properties were maximized at an ion energy of approximately 167 eV, corresponding to an energy per daughter carbon ion of 76 eV. The relationship between the incident ion energy and film densification was also explained in terms of the subsurface implantation of carbon ions into the growing film.

Hydrogen content estimation of hydrogenated amorphous carbon by visible Raman spectroscopy

In the present study, we report the hydrogen content estimation of the hydrogenated amorphous carbon (a-C:H) films using visible Raman spectroscopy in a fast and nondestructive way. Hydrogenated diamondlike carbon films were deposited by the plasma enhanced chemical vapor deposition, plasma beam source, and integrated distributed electron cyclotron resonance techniques. Methane and acetylene were used as source gases resulting in different hydrogen content and sp2/sp3 fraction. Ultraviolet-visible (UV-Vis) spectroscopic ellipsometry (1.5-5 eV) as well as UV-Vis spectroscopy were provided with the optical band gap (Tauc gap). The sp2/sp3 fraction and the hydrogen content were independently estimated by electron energy loss spectroscopy and elastic recoil detection analysis-Rutherford back scattering, respectively. The Raman spectra that were acquired in the visible region using the 488 nm line shows the superposition of Raman features on a photoluminescence (PL) background. The direct relationship of the sp2 content and the optical band gap has been confirmed. The difference in the PL background for samples of the same optical band gap (sp2 content) and different hydrogen content was demonstrated and an empirical relationship between the visible Raman spectra PL background slope and the corresponding hydrogen content was extracted. © 2004 American Institute of Physics.

Fabrication and electrical characteristics of carbon nanotube-based microcathodes for use in a parallel electron-beam lithography system

The development of the Nanolith parallel electron-beam writing head was discussed. The fabrication and electrical characteristics of carbon nanotube-based microcathodes for use in the lithographic system were described. The microcathode exhibited a peak current of 10.5 μA at 48 V when operated with a duty cycle of 0.5 percent.

Efficient line launch for bandwidth improvement of 10 Gbit/s multimode fibre links using elliptical Gaussian beam

A novel elliptical Gaussian beam line launch is shown to allow improved system capacity for high speed multimode fibre links. This launch maintains higher bandwidth than dual launch even with misalignment of ±6 μm despite not requiring testing at installation. ©2010 IEEE.

Fabrication of 25nm wide gold lines using nanometer scale lithography and ionized cluster beam deposition

It becomes increasingly difficult to make continuous metal lines with well defined thickness and edges by the lift-off technique as the line width is decreased. We describe in this paper a technique in which the combination of high resolution electron beam lithography and ionized cluster beam (ICB) deposition has enabled very high quality gold lines ({all equal to}25nm wide) to be obtained on thick single crystal silicon substrates. © 1990.