# Numerical Investigation of Tonal Trailing-Edge Noise Radiated by Low Reynolds Number Airfoils
## 4 Results of the Parametric AFL Sensitivity Study
### Variation in Angle of Attack for Re\({}_{c}\) = 180,000: Tone-Producing Regimes
Additionally, the fact that the LST-predicted peak instability tones may not be the ones radiating in the far-field as acoustics may be addressed using several arguments. On one side, LST predicts a certain frequency for maximum growth but in determining this peak frequency assumes that the initial amplitudes of all frequency components are identical. This peak amplitude thus could change if the initial level of the disturbance is not uniform and is a function of frequency. One may argue that the scattered acoustic waves, through the BL receptivity process, excite some frequency disturbances more than the others; this was elucidated by [PERSON] et al. [26], who suggested that the BL receptivity process becomes increasingly more efficient at lower frequencies. Furthermore, while LST predicts a wide spectrum of rapidly-growing convected modes scattering at the TE into acoustic waves, the strength of the latter decreases with increasing frequency, as indicated by [PERSON] and [PERSON] [27] based on the application of [PERSON]'s TE noise theory [28]. Thus, one may expect that a particular low-frequency mode may be selected for optimum acoustic generation. Such a mode appears to be at the shedding frequency as it is naturally selected by the vorticity dynamics at the TE and its pattern of shedding into the wake. Another tone-selecting mechanism is the acoustic feedback determined by matching the phases of the acoustic and vortical modes. However, such mechanism described by the feedback-loop formula (further discussed below) produces many modes falling within the \"unstable\" category as determined by LST, and the fact that only a few of them are observed as primary peaks in the acoustic spectra appears to be solely determined by their proximity to the shedding tone. Indeed, the observed spectra indicate that the peak \"cut-on\" frequencies are the nearest to the shedding tone. This superposition also explains the dual-ladder tonal structure of [PERSON] et al. [1] since the scaling of the feedback-loop \"cut-on\" tone and the shedding tone is different with respect to the flow velocity. Note that for the moderate \(Re_{c}\) laminar flow around a symmetric NACA-0012 airfoil, [PERSON] and [PERSON] [9] identified the shedding frequency with that of the most amplified near-wake K-H instability in the free shear layer. The TE scattering of such near-wake instability was claimed as the source of the shedding tone in the absence of AFL. Thus, such a wake instability mechanism may superimpose on the AFL mechanism of airfoil tonal noise production, with both related to the TE scattering of the free shear-layer K-H instabilities. This would point to the mutual resonance phenomenon where both mechanisms overlap and appear to enhance each other. When the flow past the airfoil is laminar with no AFL present, the remaining shedding tone appears at significantly lower amplitude, as demon  
Figure 11: LST-predicted (triangles), shedding (diamonds), and acoustic (squares) peak frequencies. strated by [PERSON] and [PERSON] [9]. On the other hand, when the AFL mechanism is suppressed due to BL tripping or a low-intensity upstream turbulence, the observed acoustic spectrum still reveals a broadband hump centered around the shedding frequency ([PERSON] et al. [8]). It appears that the shedding mechanism is dominant and amplified with AFL presence due to the mutual interference and resonant interaction of the AFL-selected frequencies with shedding tone.