Attenuation and Diffraction of Bending Waves at Gaps in Fluid Loaded Plates

The scattering of a bending wave by a finite number of parallelrectilinear gaps in an infinite fluid-loaded plate is discussed.For the purpose of analysis, the widths of the gaps are assumedto be infinitesimal, but there is no physical contact betweenabutting edges of neighbouring sections of the plate. A sectionedge may be restrained by resilient supports or loadings, eitherindividually or jointly with the neighbouring edge. The theorydetermines the attenuation of the bending wave by the gaps andthe sound radiated into the ambient fluid during the interaction.Specific results are given for a steel plate which has a singlegap in air and in water, such that either (1) the abutting edgesare free to vibrate independently, (2) both edges are clamped,or (3) one edge is clamped and the other free. In each of thesecases the coupling between the two halves of the plate is providedsolely by the fluid loading: the bending wave would be totallyreflected at the gap in vacuo. The results are relevant to thecontrol and suppression of structure-borne sound     

The Application of Numerical Methods to the Conformal Transformation of Polygonal Boundaries

This paper describes a highly efficient numerical method forevaluating the constants of the Schwarz-Christoffel transformationequation of complex polygonal boundaries. It uses a combinationof a direct search simplex technique to minimize the sum ofsquares of the errors in the dimensions of the polygon and Gauss-JacobiQuadrature formulae to evaluate the elements of the error function.The performance of the method as applied to a typical electricalengineering problem is discussed.     

INFLUENCE OF SEPARATION ON SOUND GENERATED BY VORTEX-STEP INTERACTION

An analysis of the sound produced when a line vortex interacts at low Mach number with forward or backward facing steps is made. The radiation is dominated by an aeroacoustic dipole whose strength is equal to the unsteady drag on the step. The drag is determined by the vorticity distribution, and a correct estimate of the sound must therefore include contributions from vorticity in the separated flow induced by the vortex. The separation is modelled by assuming that the shed vorticity rolls up into a concentrated core, fed by a connecting sheet from the edge of the step of negligible circulation. The motion everywhere is irrotational except at the impinging vortex and the separation core, and the trajectory of the core is governed by an emended Brown & Michael equation. For large steps it is found that estimates of the generated sound that neglect separation are typically an order of magnitude too large. The sound levels predicted for small steps with and without separation are of comparable magnitudes, although the respectivephasesare different.Turbulentflow over a step frequently involves separation and large surface pressure fluctuations at reattachment zones. The results of this paper suggest that numerical schemes for determining the noise generated by turbulent flow over a step must take proper account of “forcing” of the separation region by the impinging turbulence and of vorticity production via the no-slip condition.     

VORTEX-SURFACE INTERACTION NOISE: A COMPENDIUM OF WORKED EXAMPLES

Students attending a graduate course on the Theory of Vortex Sound given recently at Boston University were required to investigate the low Mach number unsteady flow and the accompanying acoustic radiation for a selection of idealized flow-structure interactions. These included linear and non-linear parallel blade-vortex interactions for two-dimensional airfoils, and for finite span airfoils of variable chord; interactions between line vortices and surface projections from a plane wall; bluff-body interactions involving line and ring vortices impinging on circular cylindrical and spherical bodies, and vortex motion in the neighborhood of a wall aperture. In all cases, the effective source region was localized in either two or three dimensions, and could be regarded as acoustically compact, and the sound was calculated by routine numerical methods using the theory of compact Green functions. The results are collected together in this paper as a compendium of canonical solutions that provide qualitative and quantitative insight into the mechanisms responsible for sound production, and a database that can be used to validate predictions of more generally applicable numerical schemes.     

NOISE GENERATED BY A COANDA WALL JET CIRCULATION CONTROL DEVICE

An analysis is made of the production of sound by a hydrofoil with a Coanda wall jet circulation control (CC-) device. Three principal sources are identified in the vicinity of the trailing edge of the hydrofoil. The radiation at very low frequencies is dominated by “curvature noise” generated by the interaction of boundary layer turbulence with the rounded trailing edge of the CC-hydrofoil; this is similar in character and magnitude to the low-frequency component of the conventional trailing edge noise produced by a hydrofoil of the same chord, but with a sharp trailing edge. Higher frequency sound is produced principally at the Coanda jet slot. “Passive slot noise” is caused by the “scattering” by the slot lip of nearfield pressure fluctuations in the turbulent boundary layer of the exterior mean flow past the slot. This is of comparable intensity to high frequency, sharp-edged trailing edge noise. However, the acoustic spectrum is greatly extended to much higher frequencies if the Coanda jet is turbulent; the sound produced by the interaction of this turbulence with the lip tends to dominate the spectrum at frequencies f (Hz) greater than about U_j/h, where h is the slot width and U_jthe Coanda jet speed. Sample numerical results are presented for a typical underwater application that indicate that at this and higher frequencies the slot noise can be 20 dB or more greater than conventional trailing edge noise, although the differences become smaller as the thickness of the slot lip increases.     

Damping of sound and vibration by flow nonlinearity in the apertures of a perforated elastic screen

An analysis is made of the influence of flow nonlinearity inthe apertures of a perforated elastic plate on the damping ofsound and flexural vibrations. Fluid is forced through the perforationsby the pressure differential established across the plate bythe incident disturbance. The Reynolds number is assumed tobe sufficiently large that separation occurs, and the reciprocatingaperture flows form ‘jets’ on alternate sides ofthe plate. The growth of these jets is modelled by means ofa nonlinear equation proposed by Cummings (1986). This equationis solved simultaneously with a generalized bending wave equationderived by the author (Howe, 1995a) which governs motions ofa perforated elastic plate whose lengths scales are large comparedto the aperture spacing. It is shown that significant attenuationsof large amplitude acoustic waves can occur except when thefrequency is so small that the plate is acoustically transparent.Bending waves are also damped provided the amplitude of theplate surface velocity is not too large and the frequency issmall enough to ensure the formation of substantial jets inthe apertures. Numerical results are given for large amplitudesound waves incident on a perforated screen in air, and forbending waves propagating over aluminium and steel screens immersedin either air or water.     

Production of Sound by Turbulent Flow over an Embedded Strut

An analysis is made of the sound produced during low-Mach-numberturbulent flow over a thin, two-dimensional rigid strut embeddedin a compliant layer. The layer is interposed between the flowand a plane rigid wall, and is modelled by ahomogeneous ‘blanket’of uniform thickness, whose properties are represented by thoseof a fluid of uniform mean density and sound speed. The strutis transverse to the mean flow and projects normally from thewall to an arbitrary distance, but does not make physical contactwith the fluid. Sound is produced by the diffraction by thestrut of the intensive convective pressure fluctuations of theboundary layer. Numerical predictions are made of the radiationinto the fluid, and of the extent to which the diffracted fieldstands out against the background noise of the turbulent boundarylayer.