# Active Flow Control of a Supercritical Airfoil and Flap with Sweeping Jets
## 3 Results and Discussion
### Aerodynamic Characteristics of the NASA SC(2)-0410 2D Straight-Wing Model without Flow Control  
The basic flow-field characteristics of the NASA SC(2)-0410 model were investigated using the calibration of the sweeping jet actuator. The lift coefficient of the model is defined according to the following formula:  
\[C_{L}=\frac{L}{0.5\rho_{\infty}.V\cdot S} \tag{2}\]  
Figure 6: Sweeping frequency of the sweeping jet for different mass flow rates. Figure 7: The velocity and total pressure at the outlet. where \(L\) is the lift of the wing model measured by the six-axis force-torque sensor, \(\rho_{\infty}\) is the density of the incoming flow, \(V\) is the velocity of the incoming flow, and \(S\) is the reference area of the wing model, respectively. The lift and wing surface pressure data at different angles of attack (\(\alpha\)) and flap deflection angles (\(\delta\)) are shown in Figure 8.  
It can be seen from the relationship between lift coefficient, angle of attack, and flap deflection angle in Figure 8 that the slope of the lift coefficient curve of the model starts to decrease beyond \(\alpha=9^{\circ}\) without flap deflection (black line), which is caused by the local partly separated flow on the wing surface. However, with a continual increase in the angle of attack, the lift coefficient increases and reaches a maximum at \(\alpha=15^{\circ}\). By analyzing the lift curves of different flap deflection angles, with an increase in the flap deflection angle, the lift coefficient of the wing can be significantly increased (dashed lines). For example, when the flap deflection angle changes to \(\delta=10^{\circ}\), the lift coefficient is increased by approximately 0.3, and the maximum lift coefficient changes from 0.7 (\(\alpha=15^{\circ}\)) to 0.94 (\(\alpha=12^{\circ}\)). However, when the flap deflection changes from \(\delta=20^{\circ}\) to \(\delta=30^{\circ}\), the lift yield decreases significantly, which indicates that there is a possible flow separation on the flaps at a lower angle of attack. In addition, at a high angle of attack, such as \(\alpha=9^{\circ}\) and above, the benefit obtained by flap deflection is clearly less than that at low angles of attack. To further analyze the flow field on the wing surface, the pressure data on the upper wing surface at different angles of attack and different flap deflection angles were further analyzed. The static characteristics of the wing surface pressure are expressed using the pressure coefficient, \(C_{p}\), the calculation of which is shown as follows:  
\[C_{p}=\frac{p_{i}-p_{\infty}}{q_{\infty}}, \tag{3}\]  
where \(p_{i}\) is the wing surface pressure (measured from the pressure tappings), and \(p_{\infty}\) and \(q_{\infty}\) are the static and dynamic pressures of incoming flow, respectively. The upper-surface pressure distributions at different conditions are shown in Figure 9.  
It can be seen from the pressure coefficient curve shown in Figure 9a, when \(\alpha=9^{\circ}\), that flap deflection can increase the negative pressure of the whole upper wing surface, especially in the leading edge area (i.e., as shown by the green arrow), which is one of the important sources of lift coefficient improvement in this situation. However, when the flaps are deflected from 20 to \(30^{\circ}\), the pressure change of the main wing is relatively weak, and the pressure on the flaps even drops a little, which indicates that the flaps may have serious flow separation in this condition; it is difficult to obtain further lift by increasing the deflection angle at this point. Figure 8: Variation of lift coefficient with angle of attack (\(Re=2.0\times 10^{5}\), \(V=10\) m/s). Furthermore, when \(\alpha=12^{\circ}\), flap deflection can decrease the negative pressure near the leading edge area of the upper wing surface (i.e., as shown by the purple arrow) but increase the negative pressure of the upper wing surface of the middle and aft area (i.e., as shown by the green arrow).