## 4 Alleviation of Buffet Load by Tangential Slot Blowing
### Steady Blowing
#### 4.1.2 Flow Characteristics of the \"41% x/c\" Case  
From the above context, it can be interpreted that flow characteristics are altered under the \"41% x/c\" case. The airfoil surface pressure coefficient distributions corresponding to maximum, median, and minimum lift states under \"Blow_1.0_Ptot\" tangential blowing are plotted in Figure 15. It is seen that shockwave location nearly did not oscillate, but surface pressure in the separation zone downstream of the shockwave varied with time. Given that the most severe buffeting occurs at an incidence angle 6.0\({}^{\circ}\), it was selected to highlight the control effort. Three streamline contours corresponding to maximum lift, mean lift, and minimum lift for clean airfoil and \"Blow_1.0_Ptot\" blowing cases are plotted in Figure 16. It is seen that, for the clean airfoil without tangential blowing, the aspects depicting the unsteady shock/separation bubble interaction intensity can be summarized as follows [57]: (a) wedge effects--pressure rise due to the shock resulted in flow separation emanating from the shock foot, where this separated region behaved similar to a geometric wedge to strengthen the shock, as shown in Figure 16a; (b) dynamic effects--as the shock moved upstream, the velocity of the shock increased the relative Mach number of the upstream flow, as shown in Figure 16b; (c) airfoil curvature effects--the expansion of flow through the subsonic zone was dependent on the local surface curvature. The thick boundary layer decreased the camber, resulting in a reduction of the airfoil's circulation, as shown in Figure 16c. Under tangential slot-blowing conditions plotted in Figure 16d-f, by ejecting streamwise momentum into the boundary layer from tangential slot blowing, the adverse velocity of the separation bubble was evidently reduced, and the separation bubble could not move to the upstream location of the slot because of the strong ejection momentum. Hence, the shock/separation bubble interaction is evidently suppressed, resulting in (a) a reduced wedge effect as outlined as a smaller separation zone under the shock foot; (b) a weakened dynamic effect portrayed by the regularized bubble position. \begin{table}
\begin{tabular}{c c c c} \hline  & \(\mathbf{5.0^{\circ}}\) & \(\mathbf{5.5^{\circ}}\) & \(\mathbf{6.0^{\circ}}\) \\ \hline
41\% x/c & \(1.96\times 10^{-5}\) & \(1.16\times 10^{-5}\) & \(7.86\times 10^{-6}\) \\ \hline
46\% x/c & \(1.88\times 10^{-5}\) & \(1.36\times 10^{-3}\) & \(8.70\times 10^{-3}\) \\ \hline
51\% x/c & \(1.58\times 10^{-5}\) & \(5.49\times 10^{-3}\) & \(1.63\times 10^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 1: PSD peak values under the “Blow_1.0_Ptot” condition. Figure 15: Surface pressure distributions corresponding to maximum/median/minimum lifts with tangential blowing. (**a**) Surface pressure distribution; (**b**) zoomed version. To investigate the flow control mechanism, the Q-criterion results corresponding to those cases in Figure 16 were plotted in Figure 17, respectively. In the subsonic boundary layer, a feedback loop between the Kutta wave at the trailing edge and the location of the shock [58] was seen; the generated shear layer in the separation bubble under the shock foot warped pressure waves that propagated downstream, which interacted with the feedback of the Kutta waves travelling toward the shock from the trailing edge, completing the feedback loop. At the most upstream location, the shockwave shed its shear layer downstream and interacted with the shear layer under the shock foot as well as Kutta waves. These multiple interactions exchanged momentum and energy, sustaining oscillation of the periodic boundary layer, and unsteady buffet loads were generated, as shown in Figure 17a-f, the shear layer was generated by tangential slot blowing, and it continuously carried streamwise momentum. This shear layer prevented the upstream creeping of Kutta waves.