# Numerical Investigation of Tonal Trailing-Edge Noise Radiated by Low Reynolds Number Airfoils
## 5 Discussion of Results  
High-accuracy 2D and high-fidelity 3D (ILES) numerical experiments were conducted to investigate the phenomena related to flow-acoustic resonant interactions at moderate Reynolds numbers characteristic of transitional airfoils. Numerical analyses were employed to examine the airfoil BL dynamics, including the statistical moments and surface pressure spectra, as well as the airfoil acoustic radiation in the far-field. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{16 m/s (128,000)} & \multicolumn{3}{c}{19 m/s (152,000)} \\ \hline \(f\), Hz computed (CFD) & 562 & 640 & 720 & \(f\), Hz computed (CFD) & 633 & 746 & 835 \\ \hline  & \(n=10\) & \(n=12\) & \(n=13\) & & \(n=10\) & \(n=11\) & \(n=12\) \\ \hline \(f\), Hz & & & & \(f\), Hz predicted, Equation (15) & 700 & 766 & 833 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{21 m/s (168,000)} & \multicolumn{3}{c}{25 m/s (200,000)} \\ \hline \(f\), Hz computed (CFD) & 699 & 820 & 939 & \(f\), Hz computed (CFD) & 963 & 1099 & 1218 \\ \hline  & \(n=8\) & \(n=10\) & \(n=11\) & & \(n=9\) & \(n=10\) & \(n=11\) \\ \hline \(f\), Hz & & & & \(f\), Hz predicted, Equation (15) & 992 & 1097 & 1202 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Computed (CFD) vs. predicted (Equation (15)) tonal frequencies. Figure 28: Dispersion analysis (Wavefront wavenumber-frequency spectra) for a NACA-0012 at mean flow velocities of 16–25 m/s. The first part of the study focused on thorough validation of the numerical model by comparing the unsteady responses of the NACA-0012 airfoil for selected flow regimes against the experimental data of [PERSON] et al. (2010). The results indicate that 2D and 3D ILES predictions compare well with experimental data. In particular, the conducted far-field spectral analysis showed a near perfect match of computational and experimental results at frequencies surrounding the peak tones. The predicted near field showed a good match of the tonal content but elevated broadband levels resulting from the unsteady hydrodynamic fluctuations that do not propagate into the far field. In addition, the similarities observed between the 2D and 3D ILES predictions vs. experimental data allowed the majority of the numerical experiments to be conducted using the 2D approach. The transition between the tone-producing and no-tone-producing flow regimes was thoroughly investigated for the NACA-0012 airfoil at a different AoA and \(Re_{c}\) and correlated with position and size of the LSB. At low AoAs (\(\alpha\leq 6^{\circ}\)), distinct tones were shown to be present that dominated the acoustics of the airfoil. However, the tones disappeared at higher AoAs (\(\alpha>6^{\circ}\)) due to the LSB migration towards the LE, which allowed sufficient time for the flow to transition to fully turbulent regime with subdued AFL interactions. On the other hand, for a fixed AoA, the increase in flow \(Re_{c}\) was associated with LSB shrinking on the suction side and an increasingly dominant contribution of the AFL on the pressure side to the tonal noise production. Additionally, a parametric investigation of the effect of \(Re_{c}\) allowed recreating [PERSON]'s dual ladder-type frequency structure. Overall, the results of the parametric studies involving high-fidelity numerical studies and linear stability analysis clearly demonstrate that the rapid growth of the BL instability modes is associated with the presence of separation regions (i.e., LSB) on either side of the airfoil. The switch from the slowly growing T-S modes (associated with the BL viscous effects) to the fast-growing K-H modes (associated with the velocity gradients in the LSB detached shear layer) thus appears as a necessary condition for the strong multiple-tone-producing flow-acoustic interactions.