# Near-Field Aeroacoustics of Spanwise Forcing on a Transonic Wing: A DNS Study
## 5 Discussion
Their experimental study considered subsonic flow at moderate values of the Reynolds number, with almost zero turbulence intensity: instabilities due to laminar-turbulent transition above the laminar separation bubble were the cause for tonal noise development. Indeed, the interaction between the upper and lower surface boundary layers at the trailing edge can produce either tonal noise (if one flow is turbulent and the other is transitional) or broadband noise (if both flows are turbulent) [32]. [PERSON] et al. [33] studied experimentally the self-noise of a NACA0012 airfoil with both tripped and non-tripped boundary layers. In particular, they studied the tonal noise as a function of the Reynolds number and the angle of attack. When tripping was applied on both sides, they observed a drastic reduction in the tonal component, which becomes negligible for \(Re_{\infty}>10^{5}\) at \(\alpha=4^{\circ}\). Hence, since the current study involves a numerical tripping on both sides of the airfoil (see Section 2), the source of such tonal component is unclear. We hypothesize that either an instability in the separated trailing edge, pressure-side shear layer, or an additional fixed-frequency vortex shedding in the wake might explain the observed presence of tonal noise; other factors which may play a role are the asymmetric geometry of the V2C airfoil (as opposed to the symmetric NACA0012 profile), as well as the presence of the shock wave above the suction side. However, in Section 4 we have ruled out a connection between tonal noise observed at \(\theta\approx 225^{\circ}\) and buffeting, since the frequencies corresponding to the two peaks of the Fourier transforms are separated (see Figure 9). Broadband noise is perceived at \(\theta\approx 225^{\circ}\) (i.e., in the region of the maximum OASPL, see Figure 6). This kind of noise, generated by turbulence, characterizes four symmetric 'branches' at \(\theta\approx 45^{\circ},\theta\approx 135^{\circ}\), and \(\theta\approx 315^{\circ}\), together with the already mentioned \(\theta\approx 225^{\circ}\). Indeed, turbulence is probably the reason why most of the high-frequency contributions are perceived by the observers located at the angles \(\theta\in[-135^{\circ}\div 135^{\circ}]\): these, in fact, are the regions facing the turbulent boundary layers (downstream of the  
Figure 11: Magnitude of the Fourier coefficients \(|\widehat{p}^{\prime}|\) of the REF (**left**) and C10 (**right**) cases, as a function of the frequency (radial coordinate) and the azimuthal position of the probe. The three circles denote the peak frequency of the REF case (yellow), and the ‘equivalent’ and temporal frequencies of StTW (green and red, respectively). numerical tripping) and the wake. On the contrary, negligible contributions are perceived in front of the leading edge, where the incoming airflow is in fact laminar (see Section 2). It should be remembered that, at this relatively low value of \(Re_{\infty}\), the required artificial boundary layer tripping is quite large, and can therefore generate some noise by itself. For example, the two symmetric branches observed in front of the leading edge at \(\theta=135^{\circ}\) and \(\theta=215^{\circ}\) could be ascribable to the body force employed for tripping the boundary layer. Tonal noise due to tripping, however, can be ruled out, because of the random nature of the body force ([23]). In the controlled C10 case, shown in the right panel of Figure 11, the largest Fourier coefficients are detected in the direction opposite to the shock, albeit weak scattered spots appear above the suction side at \(\theta\approx 60^{\circ}\) and \(\theta\approx 130^{\circ}\). On the pressure side, the peak at \(\theta\approx 225^{\circ}\) previously observed is slightly intensified, whereas a reduction in the frequency content at \(\theta\approx 270^{\circ}\) is observed.