# Near-Field Aeroacoustics of Spanwise Forcing on a Transonic Wing: A DNS Study
## 3 The Near-Field Flow  
We start by describing the effects of flow control via StTWs on the wall stresses close to the trailing edge of the wing, linking them to the modifications of the near-field velocity field, with a particular emphasis on its wake. Our previous analysis described in Ref. [13] was focused on the aerodynamic forces acting on the wing, and did not consider the flow field around it. Figure 3 plots an instantaneous snapshot of the spatial distribution of the pressure fluctuations of the transonic flow around the wing in the reference uncontrolled (REF) simulation. The figure gives an overview of the rich physics of the flow, and of how well it can be captured with a DNS. A thorough description of the flow was already given in [12; 13] and will not be repeated in detail here. In a nutshell, the initially subsonic flow is compressed and slowed down by approaching the leading edge. Then, on the suction side the airflow undergoes an abrupt acceleration (or 'expansion') and rapidly becomes supersonic, remaining so for about half the profile chord. The supersonic region (delimited by the white sonic line) is terminated by a shock wave, which results from  
Figure 2: Position of the probes employed for extracting the pressure fluctuations. \(\theta\) represents the angle of the observer. the compression of the supersonic flow in the aft part of the wing. The shock interacts with the boundary layer, increasing its thickness and enhancing pressure fluctuations downstream of the interaction. Close to the trailing edge, the flow is further slowed down by the adverse pressure gradient, which eventually causes flow separation. On the pressure side, instead, the flow is accelerated downstream of the leading edge, but does not reach supersonic conditions. The most intense pressure fluctuations are detected in the post-shock region above the suction side, and below the pressure side. Large-scale eddies, visualized as pressure fluctuations of alternating signs, characterize the wake and the boundary layers. The latter, which become turbulent downstream of the tripping (see Section 2), feature different characteristics depending on the wing side: on the suction side, fluctuations are relatively weak down to the shock wave/boundary layer interaction region, which enhances turbulence (a common source of noise, together with the trailing-edge separation). Beneath the profile, instead, pressure fluctuations are significant only in the trailing-edge region. Figure 4 plots, for cases REF, C10, and C12, a detail of the mean pressure (\(C_{p}=2(p-p_{\infty})/\rho_{\infty}U_{\infty}^{2}\)) and friction (\(C_{f}\)) coefficients, together with the \(x\)-derivative of the pressure gradient (\(\partial C_{p}/\partial x\)), close to the trailing edge of the wing on its pressure side. StTWs, albeit applied on the suction side only, do have a minimal influence on the flow properties of the pressure side too, as a consequence of the changes to the airfoil circulation. On the upper panel, the pressure coefficients of cases REF and C12 basically overlap. The curve relative to simulation C10, instead, features slightly higher values of \(C_{p}\). In the lower panel, a region of separated flow is detected by the negative values of the friction coefficient: the regions where \(C_{f}<0\) in cases REF and C12 overlap, while the one relative to case C10 is larger by some percent chord units. In Ref. [13], it was shown for the suction side how the StTWs contribute to the generation of a recirculation bubble in the region of the shock foot. In particular, it was shown that spanwise forcing induces a separation, whose extension is enlarged in a measure that depends on the the position of the shock and on the skin-friction reduction rate. Here, on the contrary, we observe that on the opposite pressure side, separation is already present in the unmanipulated flow. Interestingly, StTWs modify  
Figure 3: Instantaneous fluctuating pressure distribution around the wing in a \(x-y\) plane, for the reference uncontrolled simulation.