Flow and geometry induced scattering of high frequency acoustic duct modes

• Published in: Wave motion Vol. 49; no. 1; pp. 109 - 124
• Main Authors: Smith, A.F., Ovenden, N.C., Bowles, R.I.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.01.2012; Elsevier
• Subjects: Acoustics; Aeroacoustics, atmospheric sound; Differential equations; Duct modes; Ducts; Exact sciences and technology; Fundamental areas of phenomenology (including applications); High frequencies; Mathematical analysis; Mean flow; Neighbouring; Physics; Scattering; Standing waves; Structural acoustics and vibration; Unity; Standing waves; Mean flow; Duct modes; Scattering; Irrotational flow; Pipe flow; Turbojet; Large pipe; Acoustics; Modeling; Cut off frequency; Finite element method; Variable section; Coupling; High frequency; Aircraft; Energy transfer; Standing wave
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2011.07.006

Cut-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. ► This paper examines sound propagation in slowly varying ducts with flow at high frequency. ► Two scattering mechanisms are identified that allow neighbouring modes to interact. ► Scattering occurs at significantly lower frequencies when a mean flow is present. ► An exchange of energy between mean flow and acoustic field occurs during scattering.