# 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  
The effect of the AoA and the mean flow velocity was previously shown by [PERSON] et al. [25] to have significant impacts on the tonal noise generation. To better understand the phenomenon of the airfoil entering and exiting the tone generating regime, several selected cases are chosen and presented in Table 2.  
Figure 6 illustrates the 2D time-averaged pressure contours for the NACA-0012 airfoil and the predicted LSB location along the airfoil surface (red line). At 0\({}^{\circ}\), symmetric LSBs exist on both the upper and lower surfaces of the airfoil covering approximately 25% of the aft section. As the AoA increases, the separation region on the suction surface advances forward while the pressure-side LSB shifts rearward. Note that LSBs exist on both the suction and pressure surfaces only for \(\alpha\) = 0\({}^{\circ}\) and 2\({}^{\circ}\) cases. For a higher AoA, trends reveal the LSB on the suction side shrinks in length and move towards LE. In contrast, \begin{table}
\begin{tabular}{c c c c} \hline
**Airfoil** & **AoA (degree)** & **Velocity (m/s)** & \(\mathbf{Re_{c}}\) \\ \hline NACA-0012 & 0, 2, 4, 6, 8, 10, 12 & 25 & 180,000 \\ \hline \end{tabular}
\end{table} 
Table 2: Geometric AoA investigated for the NACA-0012 airfoil. the separation region on the pressure surface starts in the same position as that on the suction surface at \(\alpha=0^{\circ}\) and moves rearward in the \(\alpha=2^{\circ}\) case. By \(4^{\circ}\), the pressure-side LSB disappears completely while the suction-side separation region remains present for all AoAs. Table 3 lists the exact locations of the separated regions in terms of percent chord. The presence of LSBs in these flow regimes, whether on the pressure or suction side, demonstrates the impact that LSBs have on triggering the AFL mechanism. In accordance with experimental observations of [PERSON] et al. (2018), the tonal noise emission is clearly observed for the cases with \(\alpha=0^{\circ}\), \(2^{\circ}\), \(4^{\circ}\), and \(6^{\circ}\), as seen in the acoustic spectra in Figure 7. Interestingly, all AoAs shown exhibit a single peak tone with the exception of the \(2^{\circ}\) case. The explanation for the dual tone can be tied to the formation of the LSB regions of Figure 6, which shows the \(2^{\circ}\) case to have an LSB on both the suction and pressure surface. To further investigate the roles of the airfoil suction and pressure surface LSBs in the mechanism of the airfoil tonal noise generation, LST is employed. For the \(\alpha=0^{\circ}\) case, the linear stability analysis was conducted for frequencies ranging from 0 to 4000 Hz with increments of 10 Hz, as well as for the peak tonal frequency. Based on the symmetric nature of the configuration, only the data for the upper surface is presented in Figure 8. The primary region of instability growth prediction corresponds well with the location of the LSB, as indicated by the dashed blue lines revealing flow separation and reattachment locations determined from the coefficient of friction plot shown in the bottom. The accompanying velocity contours provides visual evidences of the existence of the LSB and correlates well with the instability growth. \begin{table}
\begin{tabular}{c c c} \hline \hline
**AoA** & **Suction Side** & **Pressure Side** \\ \hline
0 & 70\%–96\% & 70\%–96\% \\
2 & 53\%–73\% & 82\%–100\% \\
4 & 35\%–48\% & No Separation \\
6 & 9\%–25\% & No Separation \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Laminar separation bubble (LSB) locations on the suction and pressure sides. Figure 6: Time-averaged pressure contours from 2D NACA-0012 simulations (**left**); corresponding separation regions (**right**). U = 25 m/s. To confirm the trends seen in Figure 8, data for \(\alpha=6^{\circ}\) is obtained and presented in Figure 9. Based on the results tabulated in Table 3, only results for the suction side are presented.