# Near-Field Aeroacoustics of Spanwise Forcing on a Transonic Wing: A DNS Study
## 4 The Near-Field Acoustics  
### Overall Sound Pressure Level  
Figure 6 (upper panel) shows the time histories of the fluctuating part of the pressure signals for simulations REF, RREF, C10, and R10. The signals are extracted at the probes which detect the largest overall sound pressure level, namely \(\theta\approx 251^{\circ}\) for cases REF and C10, and \(\theta\approx 224^{\circ}\) for cases RREF and R10. Each signal is characterized by a wide range of low and high frequencies. For a quantitative analysis, the OASPLs at every azimuthal position are presented in the lower panel of Figure 6, comparing the four cases REF, RREF, C10, and R10. The latter pair feature StTWs with the same control parameters. On a global perspective, the largest OASPL values are found in simulation C10, while simulation RREF registers the weakest noise. The direction of the maximum OASPL is highlighted with a diamond on each curve: quite surprisingly, the largest intensity is not found at angles corresponding to the shock (i.e., \(\theta\approx 50^{\circ}\)), or located anywhere above the suction side of the wing. On the contrary, the direction of the maximum OASPL is in the diametrically opposite location, beneath the pressure side of the airfoil. This is probably due to the weak intensity of the shock (recall that \(M_{\infty}=0.7\)), as well as to its limited excursion around its equilibrium position, which consequently does not generate intense acoustic waves. In all cases, the weakest OASPL is obtained downstream of the trailing edge (\(\theta\approx 0^{\circ}\)). Other important information deduced from Figure 6 is that the minor change in the angle of attack between the two pairs of simulations is not visible in the directionality of the noise, since the shape of the directivity plots is essentially unchanged. Figure 5: The velocity profile in the wake for a subset of ten cases within simulations C1–C20. The left panel portrays the free-stream-parallel velocity component \(u_{t}\) on the segment illustrated in Figure 3, with the black line denoting the unmanipulated flow. The right panel depicts the percentage variation in the velocity profile with respect to the reference case. Lines are colored according to the increase in lift \(\Delta C_{L,\%}\). The variation \(\Delta\) in the OASPL between the forced and the reference cases is now computed for each observer. Figure 7 presents the relative changes as a function of the position of the observer \(\theta\). The polar axis of Figure 6 has been switched to a Carthesian axis. The horizontal solid lines show the mean OASPL value averaged across all the azimuthal positions. It is evident that, at least for the cases considered, controlling the flow via StTWs slightly increases the overall sound pressure level for almost every observer at both angles of attack, with changes that on average amount to a small 1-2 dB. The difference in noise intensity at \(\alpha=4^{\circ}\) appears to be marginally higher above the suction side of the wing (\(\theta\in[0^{\circ}\div 180^{\circ}]\)). The largest OASPL increase was obtained in case R10, indicating that the noise increase is larger at the reduced incidence when the control is applied. This is due to the fact that, as shown above for the OASPL when discussing Figure 6, at \(\alpha=3.45^{\circ}\) the uncontrolled simulation (RREF) features lower intensities than the corresponding case at \(\alpha=4^{\circ}\) (REF), while the intensities of case R10 are similar to those computed in case C10. Figure 6: Upper panel: temporal history of the pressure fluctuations, recorded at the position of the largest OASPL. Lower panel: the OASPL (expressed in decibels on the radial axis) of simulations REF, RREF, C10, and R10, as a function of the angular position of the observer \(\theta\) (expressed in degrees in the azimuthal direction). The colored diamond on each line represents the azimuthal position of the maximum OASPL.