document: 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. From the first application [1] of multiple-scales analysis to sound propagation in ducts of rectangular and circular cross section without mean flow, more recent developments have extended the method to cases with uniform mean flow [2], mean swirling flow [3], ducts of arbitrary cross section [4] (with uniform mean flow) and strongly curved ducts [5]. The multiple-scales approach has a number of distinct advantages over full numerical methods as it is ideally suited to handle higher frequencies and the computational complexity is only marginally more than calculating the eigenmodes inside a straight parallel duct. The accuracy and usefulness of the multiple scales approach has been validated against finite-element methods [6] for realistic aeroengine configurations and acoustic frequencies [7,8].
doc_bio_tags: O B I I I O B O O O O O O O O O B O O O O O O B I I O O O O O O O O O B I O B O O O O O O O B I O O O O O O O O O O O B I O B I I O B O O O O O O O B I O O O B O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O B I I O O B I I O O O O O O B I I O O O O O O O O O B O O B I O
extractive_keyphrases: acoustic frequencies aeroengine calculating the eigenmodes ducts higher frequencies mean flow mean swirling flow multiple scales approach numerical methods propagation of unsteady disturbances sound propagation straight parallel duct
abstractive_keyphrases: aeroengine configurations finite-element methods multiple-scales analysis multiple-scales approach strongly curved ducts uniform mean flow