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.

An efficient frequency-domain algorithm for wave scattering problems with application to jet noise

This paper presents a pseudo-time-step method to calculate a (vector) Green function for the adjoint linearised Euler equations as a scattering problem in the frequency domain, for use as a jet-noise propagation prediction tool. A method of selecting the acoustics-related solution in a truncated spatial domain while suppressing any possible shear-layer-type instability is presented. Numerical tests for 3-D axisymmetrical parallel mean flows against semi-analytical reference solutions indicate that the new iterative algorithm is capable of producing accurate solutions with modest computational requirements.

Effects of multi-scattering on the performance of a single-beam acoustic manipulation device.

The effects of multiple scattering on acoustic manipulation of spherical particles using helicoidal Bessel-beams are discussed. A closed-form analytical solution is developed to calculate the acoustic radiation force resulting from a Bessel-beam on an acoustically reflective sphere, in the presence of an adjacent spherical particle, immersed in an unbounded fluid medium. The solution is based on the standard Fourier decomposition method and the effect of multi-scattering is taken into account using the addition theorem for spherical coordinates. Of particular interest here is the investigation of the effects of multiple scattering on the emergence of negative axial forces. To investigate the effects, the radiation force applied on the target particle resulting from a helicoidal Bessel-beam of different azimuthal indexes (m = 1 to 4), at different conical angles, is computed. Results are presented for soft and rigid spheres of various sizes, separated by a finite distance. Results have shown that the emergence of negative force regions is very sensitive to the level of cross-scattering between the particles. It has also been shown that in multiple scattering media, the negative axial force may occur at much smaller conical angles than previously reported for single particles, and that acoustic manipulation of soft spheres in such media may also become possible.

On high-frequency noise scattering by aerofoils in flow

Abstract A theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local 'inner' regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated. © 2013 Cambridge University Press.

A comparative study of plasma-enhanced chemical vapor gate dielectrics for solution-processed polymer thin-film transistor circuit integration

This paper considers plasma-enhanced chemical vapor deposited (PECVD) silicon nitride (SiNx) and silicon oxide (SiOx) as gate dielectrics for organic thin-film transistors (OTFTs), with solution-processed poly[5, 5′ -bis(3-dodecyl-2-thienyl)-2, 2′ -bithiophene] (PQT-12) as the active semiconductor layer. We examine transistors with SiNx films of varying composition deposited at 300 °C as well as 150 °C for plastic compatibility. The transistors show over 100% (two times) improvement in field-effect mobility as the silicon content in SiNx increases, with mobility (μFE) up to 0.14 cm2 /V s and on/off current ratio (ION / IOFF) of 108. With PECVD SiOx gate dielectric, preliminary devices exhibit a μFE of 0.4 cm2 /V s and ION / IOFF of 108. PQT-12 OTFTs with PECVD SiNx and SiOx gate dielectrics on flexible plastic substrates are also presented. These results demonstrate the viability of using PECVD SiN x and SiOx as gate dielectrics for OTFT circuit integration, where the low temperature and large area deposition capabilities of PECVD films are highly amenable to integration of OTFT circuits targeted for flexible and lightweight applications. © 2008 American Institute of Physics.

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.