# 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\({}_{\rm c}\) = 180,000: No Tone-Producing Regimes  
To investigate the effects at higher AoAs, the simulations were conducted for \(\alpha\) = 8\({}^{\circ}\), 10\({}^{\circ}\), and 12\({}^{\circ}\). Unlike the previous results, acoustic peaks are no longer present; thus, only spectra for 8\({}^{\circ}\) and 12\({}^{\circ}\) are shown (Figure 12). Separation  
while the low-frequency counterparts continue to exist and grow mildly as they convect towards the TE. These results, however, may be influenced by 2D effects and are further discussed in the subsequent section. Figure 15 shows the instantaneous vorticity contours for all three cases, illustrating the formation of vortical instability modes through the separation regions close to the LE. The orderly formation of vortices convecting to the TE at the tone-producing lower AoA is now substituted with a much less regular street of vortices, which barely graze the airfoil surface as they convect downstream. Furthermore, the emergence of small-scale turbulence forming near the LE points to the necessity for 3D ILES studies with higher-fidelity to properly resolve such flow regimes. Nevertheless, it may be hypothesized that due to the geometry of the flow at a high AoA, any remaining coherent vortical structures would lack the opportunity to strongly interact with the TE and thus would not scatter into the acoustic modes. To test this hypothesis, full 3D ILES simulations (with grid dimensions shown in Table 1) were conducted for three cases at \(\alpha=0^{\circ}\), \(4^{\circ}\), and \(8^{\circ}\), with a fixed \(Re_{\epsilon}=180\),000, to elucidate the primary mechanism responsible for tonal noise suppression at an AoA greater than \(6^{\circ}\). At \(\alpha=0^{\circ}\), shown in Figure 16, the flow remains in the transitional regime and its behavior is similar to that proposed by [PERSON] et al. [29]. Upon closer inspection of the Z-vorticity contours, the BL dynamics clearly reveals that the unsteady oscillatory motion of the vortex street at the TE is responsible for generating pressure pulses and the subsequent propagation of acoustic waves into the far-field. In addition to the vortex shedding noise, the interaction of the airfoil surface instabilities scattering into the wake is responsible for the additional noise contributions (neighboring peaks) shown in the  
Figure 14: Instability chordwise amplification at various frequencies vs. statistical parameters for \(\alpha=12^{\circ}\). surface spectra. The accompanying dilatation field shown in Figure 16 further confirms the acoustic wave to be emitted from the TE of the airfoil. Increasing the AoA to \(\alpha=4^{\circ}\) forces the suction-side BL transition point to move further upstream, resulting in a larger separation region, while the pressure-side BL does not separate. However, the flow regime is still classified as transitional. \(Z\)-corticity contours in Figure 17 show coherent vortices and the resulting vortex shedding at the wake is still present. Therefore, it can be concluded that the mechanism responsible for the noise remains unchanged between the AoAs of \(0^{\circ}\) and \(4^{\circ}\). The acoustic field shown in the instantaneous dilatation plot exhibits behavior similar to the \(\alpha=0^{\circ}\) case and shows the noise source to originate at the TE. Figure 16: NACA-0012 at an \(\alpha=0^{\circ}\) AoA and \(Re_{c}=180,000\). (**Left**) Instantaneous \(Z\)-corticity contours; (**Right**) the dilatation field. Red circle indicates the origin of the acoustic wave to be at the trailing-edge (TE). Figure 15: Instantaneous vorticity contours for cases without tones. As the AoA is further increased to \(\alpha=8^{\circ}\), the results illustrated in Figure 18 reveal that the flow has transitioned to a fully turbulent regime. Unlike the previous transitional regime, the vortical structures convecting along the surface and its subsequent vortex shedding in the wake are no longer coherent.