Flow and geometry induced scattering of high frequency acoustic duct modes.

Abstract

a b s t r a c tCut-on cut-off transition of acoustic modes in hard-walled ducts with irrotational mean flow is well understood for Helmholtz numbers of order unity. Previous finite-element simulations of this phenomenon, however, appear to indicate the possibility of energy scattering into neighbouring modes at moderately large Helmholtz numbers. In this paper, such scattering phenomena are explained and predicted in slowly varying aeroengine ducts using a multiple-scales approach. It is found that, for sufficiently high frequencies, two mechanisms exist whereby energy can be scattered into neighbouring modes by an incident propagating mode. One mechanism occurs only when there is a mean flow inside the duct and induces scattering at significantly lower frequencies than the other mechanism which remains present without mean flow. A coupled system of ordinary differential equations is derived and then solved numerically for a number of example cases to obtain the corresponding transmitted and reflected amplitudes of the scattered modes as well as the overall acoustic pressure field. The theory appears to demonstrate that some exchange of energy between the acoustic and mean flow fields occurs during scattering.

Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

“…Such modifications include introduction of holes with sharp edges [2], barriers in the path of flow [3], or sudden contraction or expansion as is the case with the SEC [4]. Applications of this phenomenon in vortex motion have been successfully studied by Smith et al, [5] who identified two scattering mechanisms that allow neighbouring modes to interact; scattering occurs at significantly lower frequencies when the mean flow is present; an exchange of energy between mean flow and acoustic field occurs during scattering.…”

Effect of Shear on Ultrasonic Flow Measurement Using Nonaxisymmetric Wave Modes

“…Boucheron et al [2] made a comprehensive review of axisymmetric acoustic wave propagating in the rigid-walled pipeline. In the case of a lined-walled pipeline where the effect of acoustic impedance of the wall was considered, theoretical and numerical contributions were made by Rienstra and Darau [3], Rienstra [14], Smith et al [15], Brambley et al [16], and Buske et al [17]. Some experiment data can be found in the work of Marx et al [18].…”