# Active Flow Control of a Supercritical Airfoil and Flap with Sweeping Jets
## 3 Results and Discussion
### Analysis of Aerodynamic Characteristics of the Wing Model with Sweeping Jet Control  
In AFC, the momentum coefficient of the jet is a key dimensionless parameter to indicate the flow control effectiveness. In this paper, the following formula is used to calculate the momentum coefficient:  
\[C_{\mu}=\frac{\dot{m}^{2}}{\rho_{n}\cdot A_{n}\cdot q_{\infty}\cdot S} \tag{4}\]  
where \(\dot{m}\) is the total mass flow rate used for flow control, \(\rho_{n}\) is the gas density at the outlet throat of the actuator, \(A_{n}\) is the area at the outlet throat of the actuator, \(q_{\infty}\) is the dynamic pressure, and \(S\) is the reference area of the wing. According to Equation (4), the momentum coefficients corresponding to the three groups of mass flow rate are 0.9% (\(\dot{m}=0.0003\) kg/s), 3.7% (\(\dot{m}=0.0007\) kg/s), and 8.2% (\(\dot{m}=0.0010\) kg/s), respectively. Figure 10 shows the wing lift coefficient and lift increment for different momentum coefficients of the sweeping jet when the flap deflection angle is fixed at the maximum position, \(\delta=30^{\circ}\). It can be seen from the figure that the flow control for the three groups of momentum coefficients can produce significant lift increments at both angles of attack under testing. With an increase in the angle of attack, the flow-control effect at a small momentum coefficient gradually weakens. This may be caused by the large angular deflection of the flaps at high angles of attack, causing flow separation to occur on the main wing, which reduces the efficacy of the sweeping jet flow. However, when the momentum coefficient reaches 8.2%, the increase in the lift coefficient of the sweeping jet can be maximized to \(\Delta C_{L}=34\%\) @ \(\alpha=6^{\circ}\); also, it remains greater than 30% over the full range of the angle of attack, which indicates that a jet injection with large energy can not only inhibit separation flow on the flap but also have a significant effect on the flow field over the main wing surface. Figure 9: Pressure coefficient for different percentage chord lengths of upper wing surface (\(Re=2.0\times 10^{5}\), \(V=10\) m/s). (**a**) \(\alpha=9^{\circ}\). (**b**) \(\alpha=12^{\circ}\). To study the mechanism and influence of flow control in more detail, the surface pressure data on the upper wing surface are analyzed for the condition after the jet flow is applied, which is shown in Figure 11.  
The wing surface pressure coefficient curve shows that before stall, sweeping jet AFC benefits are mainly attributable to the \"new\" strong peak of pressure in the flap position (i.e., x/c = 0.7), which inhibits the generation of flow separation. In addition, the negative pressure on the main wing surface is increased by the sweeping jet, and the suction peak near the leading edge is increased. However, when the angle of attack is increased to \(\alpha\) = 9\({}^{\circ}\), only the flow control at \(C_{\mu}\) = 8.2% has a peak of pressure on the flaps (i.e., the red dash-dot line), which indicates that the sweeping jet with a small momentum coefficient cannot effectively change the flow field on the flaps. This is the main factor for the reduction in the control effect of the sweeping jet with a small momentum coefficient. In addition, owing to the introduction of a high-speed sweeping jet, flow separation at the leading edge of the main wing is partly inhibited, and the suction peak increases slightly (as shown in Figure 11b), which is the main reason why the sweeping jet can still produce a control effect in this condition. Figure 11: Pressure coefficient on the upper wing surface at different momentum coefficients (\(\delta\) = 30\({}^{\circ}\), \(Re\) = 2.0 \(\times\) 10\({}^{5}\), \(V\) = 10 m/s). (**a**) \(\alpha\) = 6\({}^{\circ}\). (**b**) \(\alpha\) = 9\({}^{\circ}\). Figure 10: Variation of lift coefficient of the wing model with angle of attack for different momentum coefficients (\(\delta\) = 30\({}^{\circ}\), \(Re\) = 2.0 \(\times\) 10\({}^{5}\), \(V\) = 10 m/s). (**a**) Lift coefficient at different angles of attack.