Numerical analysis of tonal airfoil self-noise and acoustic feedback-loops

In this study the role of acoustic feedback instabilities in the tonal airfoil self-noise phenomenon is investigated. First, direct numerical simulations are conducted of the flow around a NACA-0012 airfoil at Re = 1 × 10 5 and four angles of attack. At the two lowest angles of attack considered the airfoil self-noise exhibits a clear tonal contribution, whereas at the two higher angles of attack the tonal contribution becomes less significant in comparison to the broadband noise. Classical linear stability analysis of time-averaged boundary layer profiles shows that the tonal noise occurs at a frequency significantly lower than that of the most convectively amplified instability wave. Two-dimensional linear stability analysis of the time-averaged flowfield is then performed, illustrating the presence of an acoustic feedback loop involving the airfoil trailing edge. The feedback loop is found to be unstable only for the cases where tonal self-noise is prominent, and is found to self-select a frequency almost identical to that of the tonal self-noise. The constituent mechanisms of the acoustic feedback loop are considered, which appear to explain why the preferred frequency is lower than that of the most convectively amplified instability wave. ► The role of acoustic feedback instabilities in tonal airfoil self-noise is investigated. ► Direct numerical simulations of airfoil flows with and without discrete tones. ► Tonal noise cases exhibit acoustic feedback instability of the time-averaged flow. ► Acoustic feedback instability selects a frequency almost identical to the tonal noise. ► Stable loop frequency tends to that of most unstable shear-layer instability.