Acoustic radiation by vortex induced flexible wall vibration

Abstract

Sound radiation due to unsteady interaction between an inviscid vortex ͑which models a turbulent eddy͒ and a finite length flexible boundary in a two-dimensional space is studied using potential theory and the matched asymptotic expansion technique. The Mach number of the vortex propagation is kept below 0.15. Results suggest that the monopole field created by the volumetric flow induced by the vibrating flexible boundary dominates the overall acoustic power radiation. The longitudinal dipole directly due to the transverse vortex acceleration is only important when the vortex is moving over the flexible boundary. The longitudinal dipole resulting from the boundary vibration gains slightly in importance in the strong vortex case, but the corresponding transverse dipole remains negligible for the cases considered in the present study. The two longitudinal dipoles give rise to biased radiation directivities on both sides of the flexible boundary.

Vortex sound in the presence of a low Mach number flow across a drum-like silencer

“…The flexible walls are modeled as membranes with tension per unit length T, mass density m, and a damping coefficient D as in Huang 10 and in the previous investigations of the authors. 13,19 In the foregoing sections, a and (x o , y o ) represent the width of the duct and the instantaneous vortex position, respectively. The length and height of the cavity are denoted by L and h, respectively.…”

“…For small membrane vibration magnitudes, the vibrating membranes are modeled as rigid boundaries with distributed fluctuating normal velocities as in Tang et al 13 The complex flow potential at any position (x, y) inside a channel, W, due to a flow of velocity v into the channel through a tiny opening of width Dx at…”

“…11 However, flexible duct walls are also susceptible to excitation by flow turbulence and the flow as well. There are solid evidences showing that sound can be produced through the complicated interactions between flow turbulent eddies and pressure-releasing devices, such as flexible walls, 12,13 perforated screens, 14 and porous materials. 15 Such sound generations are expected to lower the performance of any duct noise control devices developed based on vibro-acoustic consideration.…”

“…The vortex motion and the mean flow give rise to fluctuating pressure forces on the two membranes. The equations of motion governing the vibrations of the membranes are 13 m @g…”

Simulation of Vortex Sound Using the Viscous/Acoustic Splitting Approach

“…Understanding the flow structure-acoustics interaction therefore is important for improved duct noise control design. Tang et al [13] developed a theoretical model to investigate the sound generated by the unsteady interactions between a vortex and a finite length flexible boundary in an otherwise rigid wall at low Mach numbers. It is concluded that the time fluctuating volumetric flow rate induced by the flexible boundary vibration and the vortex acceleration are two major sources of sound.…”