# Recent Advances in Acoustics of Transitional Airfoils with Feedback-Loop Interactions: A Review
## 1 Introduction  
The unusual unsteady response of transitional airfoils subjected to moderate Reynolds number (Re) flows has been studied for nearly half a century since the pioneering experimental work by [PERSON] et al. [1]. Nevertheless, the controversy surrounding the interpretation of physical mechanisms triggering such response still persists, largely due to the high sensitivity of the transitional airfoil response to minute changes in flow conditions. For instance, in a recent study by [PERSON] et al. [2] correlating lift and drag measurements collected from multiple wind-tunnel and computational experiments, the findings proved to be highly contradictory due to the sensitive nature of the transitional airfoils and the resulting abrupt changes in airfoil response associated with it. Efforts to control such sensitivity using acoustic forcing to help improve aerodynamic performance have been attempted experimentally by [PERSON] et al. [3]. Earlier, the same technique was employed computationally by [PERSON] et al. [4] to examine the boundary-layer receptivity in the process of establishing the acoustic feedback loop (AFL) resulting in possibly the most distinct signature of the transitional airfoils, the highly pronounced tonal noise radiation with characteristic dual-ladder type frequency spectrum structure. The transitional airfoil's tonal noise signature was first comprehensively presented by [PERSON] et al. [1]. Through experimental testing, they successfully investigated the acoustics emitted by symmetric NACA airfoils in the Re range corresponding to full-scale helicopter rotors. Their key finding (reproduced in Figure 1) shows an unusual ladder-type structure (staging) of tones wherein the peak frequencies are scaled -\(U^{1.5}\) (\(U\) is the freestream velocity) with sudden jumps appearing between the rungs of the ladder scaled -\(U^{0.8}\). During this effort, [PERSON] et al. [1] successfully correlated the relationshipbetween the peak tonal frequencies with the natural vortex shedding characteristics of the airfoil, which scaled at - \(U^{1.5}\). However, the reason for the tones scaling with - \(U^{0.8}\) was at that time still unknown. Subsequently, [PERSON] [5] suggested his version of the acoustic feedback-loop (AFL) mechanism to explain the tonal staging. The proposed AFL consists of unstable laminar separation bubbles (LSBs) on both the pressure and suction sides of the airfoil merging at the trailing-edge (TE) to form the unsteady near-wake sheared flow profile. As the flow is convected from the sharp TE, the naturally occurring disturbances (free-shear K-H instabilities) resulting from the vortex shedding develop and amplify until their amplitudes become sufficiently large to manifest as tonal acoustic source. At this moment, the generated sound waves propagate in all directions, but most importantly, convect upstream and interact with induced TE instabilities. This interaction of the upstream-propagating acoustic waves and TE instabilities force the boundary layer (BL) to oscillate resulting in further amplification of the initial disturbances and subsequent tonal acoustic emission. The process is then repeated to complete the AFL. Interestingly, while such an AFL scenario was later rejected, [PERSON] and [PERSON] [6] have recently re-visited the problem to propose the TE scattering of near-field wake K-H instability as the primary source of the vortex-shedding self-noise generation mechanism for low-_Re_ airfoils with distinct shedding-tone signature, as further discussed below. [PERSON]'s [5] AFL scenario was later re-visited by [PERSON] [7] who suggested a different perspective on the feedback-loop mechanism based on the hypothesis of [PERSON] [8] and [PERSON] and [PERSON] [9]. Instead of considering the AFL to occur in the wake, [PERSON] [7] hypothesized that the process actually began very early on the airfoil surface. As illustrated in Figure 2, the proposed AFL appears as a result of instabilities incepted near the airfoil's leading-edge (LE) in the form of T-S waves.