Linear and weakly nonlinear boundary layer acoustics in a lined duct
In this thesis I look at the effect of boundary layer flow on the acoustics of an acoustic lining. Acoustic linings are used in aircraft engine ducts to reduce the sound they produce. They typically consist of an array of Helmholtz resonators that are characterised by their impedance - a linear relationship between the acoustic pressure and acoustic normal velocity. However in aircraft engines the air in the duct is moving quickly over the lining and so there is a boundary layer near the lining. The impedance boundary condition then needs to be modified to take into account the effect of the boundary layer flow on the acoustics. In this thesis I begin by considering the weakly nonlinear acoustics for a parallel viscothermal boundary layer flow with uniform geometry over an acoustic lining. This is done using a two layer matched asymptotics model that is solved numerically. It is known that certain linear acoustic components are amplified within the boundary layer and I show that this causes the weakly nonlinear acoustics to be amplified outside of the boundary layer. I also show that this model leads to some surprising large rapidly oscillating disturbances that propagate out into the centre of the duct in certain cases. I then consider the case of a non-parallel boundary layer with non-uniform geometry. This is done using a three-layer WKB asymptotic solution and the corresponding boundary condition is derived and shown be in agreement with previous work in certain limits. I also then show that for the non-parallel case the weakly nonlinear acoustics, while still amplified, do not display the large oscillating behaviour, suggesting that it is important that non-parallel effects are considered.
acoustics, aeroacoustics, duct acoustics, nonlinear acoustics, impedance boundary condition
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