Tonal noise generation in flows around aerofoils: a global stability analysis
The generation of discrete acoustic tones in the compressible flow around an aerofoil is addressed in this thesis by means of nonlinear numerical simulations and global stability analyses. To this end, a nonlinear simulation code featuring a novel technique for gaining access to the linearized direct and adjoint dynamics has been developed and applied to the flow around an aerofoil. The nonlinear simulations confirm the appearance of discrete tones in the acoustic spectrum, and for the chosen flow case, the global stability analyses of the mean-flow dynamics reveal that the linearized operator is stable. However, the flow response to incoming disturbances exhibits important transient growth effects that culminate into the onset of aeroacoustic feedback loops, involving instability process on the suction- and pressure-surface boundary-layers together with their cross interaction by acoustic radiation at the trailing edge. The features of the aeroacoustic feedback loops and the appearance of discrete tones are then related to the features of the least stable modes in the global spectrum: on the one hand, the spatial structure of the direct modes display the growth of hydrodynamic instabilities on the suction surface and the near wake; on the other hand, the associated adjoint modes display increased receptivity of the flow on the pressure surface. Finally, the analysis of the wavemaker region highlights, in agreement with previous experimental investigations, the sensitivity of the flow to the pressure-surface boundary layer.