Smith, A.F. (2012) Transition and flow-induced scattering of acoustic modes in ducts. Doctoral thesis, UCL (University College London).
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The propagation of unsteady disturbances in ducts of slowly-varying geometry, such as those typical of an aero-engine, can be successfully modelled using a multiple scales approach. The multiple-scales approach has a number of distinct advantages over full numerical methods. Previous authors have validated the accuracy and usefulness of the multiple scales approach by comparing with results obtained using the finite element method, using realistic aero-engine configurations. Cut-on cut-off transition of acoustic modes in hard-walled ducts with irrotational mean flow is well understood. However, previous finite-element simulations of this phenomenon appear to indicate the possibility of energy scattering into neighbouring modes at large Helmholtz numbers. In this thesis, an attempt is made to explain such scattering phenomena in slowly varying aero-engine ducts using multiple-scales techniques. In order to model modal scattering a good understanding of cut-on cut-off transition is necessary. Here, the well known single turning point is revisited, and our understanding of cut-on cut-off transition is extended to include an analysis of a double turning point. Then using a similar apparatus, modal scattering in the case where a mode undergoes cut-on cut-off transition is investigated. It is found that, for sufficiently high frequencies, a mechanism exists whereby a propagating incident mode can be scattered into neighbouring modes provided that a mean flow exists within the duct. An asymptotic analysis of this mechanism is presented and, by solving numerically a composite solution, results in a duct of rectangular cross section are obtained. The energy distribution of the incident and neighbouring scattered modes reveals an interaction and exchange of energy with the mean flow. This work now allows greater insight as well as more accurate and fast computations of high frequency mode propagation in slowly-varying hard walled ducts using multiple-scales approaches.
|Title:||Transition and flow-induced scattering of acoustic modes in ducts|
|Open access status:||An open access version is available from UCL Discovery|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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