Abstract
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.
Highlights
The propagation of unsteady disturbances in ducts of slowly-varying geometry, such as those typical of an aeroengine, can be successfully modelled using a multiple scales approach
A recent comparison paper [8] contains finite-element simulations of cut-on cut-off transition that appear to indicate the possibility of energy scattering into neighbouring modes at large Helmholtz numbers
A brief argument put forward by the authors of the paper was based on the smaller separation of neighbouring eigenvalues at high frequency and it was conjectured that scattering may occur at non-dimensional frequencies of the order of ε−2, where ε ≪ 1 is the so-called slowly-varying parameter
Summary
The propagation of unsteady disturbances in ducts of slowly-varying geometry, such as those typical of an aeroengine, can be successfully modelled using a multiple scales approach. A brief argument put forward by the authors of the paper was based on the smaller separation of neighbouring eigenvalues at high frequency and it was conjectured that scattering may occur at non-dimensional frequencies of the order of ε−2, where ε ≪ 1 is the so-called slowly-varying parameter (a typical feature of the nondimensional duct geometry variation as described below). We attempt to explain and predict such observed scattering phenomena in slowly varying aeroengine ducts using a multiple-scales approach. The straightforward application of the theory to ducts of both circular and annular cross-section is described towards the end of the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
