## 4 Alleviation of Buffet Load by Tangential Slot Blowing
### Steady Blowing
#### 4.1.1 Buffet Load Alleviation  
As with the buffeting margin, the load characteristics of the transonic buffet are also of great concern in the aviation industry. From the above context, it is seen that when the incidence angle exceeds 3.9\({}^{\circ}\), transonic buffet will occur. At different buffeting states, namely at incidence angles of 5.0\({}^{\circ}\), 5.5\({}^{\circ}\), and 6.0\({}^{\circ}\), the time histories of unsteady lift coefficients of the clean airfoil are plotted in Figure 10, and their corresponding PSD (power spectrum density) results are plotted together in Figure 11. From these two groups of figures, it is seen that with the increase of incidence angle, both the amplitude and peak frequency of the unsteady buffet load increased. Moreover, it should be noted that the peak frequency resides in the frequency range of 88-99 Hz. In the wind-tunnel test of the NACA0012 airfoil given by [PERSON] and [PERSON] (2016), by referring to the flow parameters and the reduced frequency  
Figure 8: Comparison of unsteady numerical results (**a**) without tangential blowing and (**b**) with tangential slot blowing. Figure 9: Streamlines at a 5.0\({}^{\circ}\) incidence angle (**a**) without tangential blowing and (**b**) with tangential slot blowing. equation, the dimensional frequency was about 89 Hz. Thus, the calculated dominant frequency agreed with that of the wind tunnel test. Accounting for the problem of transonic buffet load alleviation, 27 cases were simulated (i.e., flow fields under three different blowing locations (namely, the \"41% x/c\" case, \"46% x/c\" case, and \"51% x/c\" case) at three different incidence angles with three different blowing total pressures). In the present paper, \"Blow_10_Ptot\", \"Blow_11_Ptot\", and \"Blow_12_Ptot\" denote that the total pressure ratio of blowing to that of freestream flow is 1.0, 1.1, and 1.2, respectively. The time histories of unsteady airfoil lift coefficients of \"41% x/c\" under different blowing pressure ratios at incidence angles 5.0\({}^{\circ}\), 5.5\({}^{\circ}\), and 6.0\({}^{\circ}\) are plotted in Figure 12. It is indicated that, for these incidence angles, the average airfoil lift increased and buffet loads decreased by using steady blowing with these three blow pressure ratios. Figure 11: Power spectrum density (PSD) results at different incidence angles. Figure 12: Unsteady lift coefficient histories under different total blowing pressures at different incidence angles: (**a**) 5.0\({}^{\circ}\), (**b**) 5.5\({}^{\circ}\), and (**c**) 6.0\({}^{\circ}\). Figure 10: Unsteady lift coefficients at different incidence angles: (**a**) 5.0\({}^{\circ}\), (**b**) 5.5\({}^{\circ}\), and (**c**) 6.0\({}^{\circ}\). The PSD results of unsteady airfoil lift coefficients are plotted in Figure 13. It is shown that transonic buffet was suppressed by tangential slot blowing under the \"Blow_10_Ptot\" condition. With the increase of total pressure ratio from 1.0 to 1.1 and 1.2, the PSDs of unsteady airfoil lift coefficients were nearly the same, and buffet load alleviation was not apparently improved; thus, these two groups of PSD curves were not plotted. With the blowing slot placed at 41% x/c chord location, the PSDs of airfoil lift coefficients at incidence angles 5.0\({}^{\circ}\), 5.5\({}^{\circ}\), and 6.0\({}^{\circ}\), corresponding to different blowing total pressure ratios, are plotted in Figure 14. It is seen that all these blowing cases with different blowing total pressure ratios can evidently depress buffet loads. For the \"5.0 deg\" case, an increase of blowing ratio could slightly improve the control effect, while for \"5.5 deg\" and \"6.0 deg\" cases, their control effectiveness slightly deteriorated by increasing the total pressure ratio. The PSD results plotted in Figure 14 also suggest that, for all these blowing cases, the buffeting frequencies were nearly 100 Hz, which indicates that the transonic buffet was alleviated, but the buffeting frequency was not evidently modified.