# Recent Advances in Acoustics of Transitional Airfoils with Feedback-Loop Interactions: A Review
## 1 Introduction
Due to the natural flow convection, the T-S waves were presumed to have sufficient time to amplify in strength as they approached the TE where they scattered into noise. This scattering mechanism, in addition to the airfoil natural vortex shedding, generated the acoustic waves propagating upstream to induce the BL vortical disturbances through the receptivity mechanism. In the established AFL process, the phase of the upstream-propagating acoustic wave must match the phase of the downstream-traveling instability waves so that a stronger acoustic wavefront could be deployed upstream to maintain the feedback loop. Figure 1: Airfoil ladder-type frequency structure (adapted from [PERSON] et al. [1]). The AFL scenario proposed by [PERSON] [7] was further elaborated by [PERSON] and [PERSON] [10] based on a series of experiments with NACA-0012 airfoils. Their recorded acoustic spectra generally confirmed the tonal ladder-type structure of [PERSON] et al. [1] to produce, for a given velocity in the range of \(U\) = 20... 40 m/s (_Re_\(c\) = 2... 6 \(\times\) 10\({}^{5}\)), a narrowband set of equidistant frequencies superimposed on a broadband hump (Figure 3). In agreement with the interpretation suggested by [PERSON] [7], [PERSON] and [PERSON] [10] concluded that such contribution was indeed attributed to T-S instability waves developing in BL and scattering as sound at the airfoil TE. The AFL was presumed generated between selected TE-radiated acoustic waves and the most amplified T-S waves based on the condition that both acoustic and convected instability waves are in phase at the point of the instability inception. Furthermore, [PERSON] and [PERSON] [10] proposed the first explanation for the tonal ladder staging of [PERSON] et al. [1] by correlating the _U\({}^{0,8}\)_ velocity dependence with diffraction of T-S instabilities at the airfoil TE. To supplement their measured data, the linear stability theory (LST) and a modified version of [PERSON]'s [5] AFL formula were employed to predict the peak and discrete frequencies, with results showing a good agreement, which further validated their findings. The early works on the subject of tonal noise produced by transitional airfoils (reviewed, e.g., in [PERSON] et al. [11], [PERSON] and [PERSON] [12], [PERSON] et al. [13], [PERSON] et al. [14], [PERSON] and [PERSON] [6], and [PERSON] et al. [15]) discussed AFL as the necessary and sufficient condition for generation of the airfoil tonal noise. Such discussion was particularly focused on the controversies observed between results of different experimental studies, which in some instances failed to observe the ladder-type acoustic tonal structure. Some authors, including [PERSON] et al. [11] and [PERSON] and [PERSON] [6], rejected the idea of the feedback loop (in the sense proposed by [PERSON] [7]) as a pre-requisite for airfoil tonal self-noise, while attributing other experimental claims to various installation effects. In their DNS study of NACA-0012 airfoil, [PERSON] and [PERSON] [6] observed only a single shedding tone, and at much lower amplitude compared to some other experimental and numerical studies. Figure 3: Airfoil frequency spectrum (adapted from [PERSON] [10]). Figure 2: Feedback loop in airfoil flow-acoustic interaction (adapted from [PERSON] [7]). They also demonstrated correspondence of the shedding frequency tone to TE-scattered most amplified near-wake K-H instability. However, their simulations were conducted for NACA-0012 airfoil at zero AoA with fully laminar flow conditions, with no LSB and AFL present. They also rightfully pointed to the fact that viscous T-S instabilities themselves are slowly growing and would not have sufficient magnitudes to produce a significant acoustic radiation through TE scattering. On the other hand, a number of investigators including [PERSON] et al. [16] and [PERSON] et al. [4] employed direct numerical simulations (DNS) and linear stability analysis in transitional regime to elaborate on AFL genesis including BL receptivity and tonal frequency selection process.