Abstract

Even in low-turbulence environments, aerofoils can radiate substantial levels of noise from the sole interaction between the boundary layers and the wake: experiments show that for moderate-to-high Reynolds number and small angles of incidence, the sound spectrum is characterised by discrete tones that are commonly perceived as a whistle. Previous investigations have suggested that the acoustic emission is correlated to the ringing of coherent structures near the trailing edge, suggesting a nontrivial interplay between acoustics and hydrodynamics. Although this problem has received considerable attention since the mid-seventies, a satisfactory explanation for the physical origins of the tones is still under debate.

In this presentation, we address the instability and receptivity mechanisms involved in the tonal noise problem by means of global stability theory. It is found that the flow response to incoming disturbances exhibits important transient-growth effects that culminate into the onset of aeroacoustic feedback loops, involving instability processes 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.