# Numerical Study of Flow Separation Control over a Hump Airfoil Using a Novel Sweeping Jet Actuator
## 3 Results  
The Cp of the Hump airfoil is shown in Figure 10. The numerical calculation results clearly fit the experimental data well, which proves the feasibility of the numerical simulation method and grid. As shown in Figure 11, the average flow field of the streamwise velocity is depicted. In the streamwise velocity field, it can be observed that under uncontrolled conditions, there is significant separation of the Hump airfoil. The separation point at x/c = 0.65. The reattachment point at x/c = 1.2. Figure 12 illustrates the average streamwise velocity field of the HUMP airfoil under SWJ actuator control. By comparing the average velocity fields of the HUMP airfoil under SWJ actuator control at different F\({}^{+}\), it is observed that both F\({}^{+}\) and VR have a certain impact on the size of the separation vortices. The separation point positions under SWJ actuator control are shown in Table 2. Due to the presence of two separation vortices on the surface of the Hump airfoil at F\({}^{+}\) = 0.375, two separation points and reattachment points have been added to the table. The specific mechanism of generation will be further described below. Figure 10: The time-averaged coefficient of pressure (C\({}_{\text{P}}\)) over the Hump airfoil in the no-flow-control scenario is compared with experimental data [40]. At VR = 1.1, F\({}^{+}\) has a relatively minor impact on the flow separation of the HUMP airfoil. Although at F\({}^{+}\) = 1, the reattachment point is slightly closer to the upstream region, this effect is not very pronounced. As VR increases, the influence of frequency on the flow separation of the HUMP airfoil becomes significantly different. At VR = 1.8, it is evident that at F\({}^{+}\) = 1, the flow separation control is most effective. It can shift the reattachment point from x/c = 1.2 to x/c = 0.76, an improvement of 0.14 compared to F\({}^{+}\) = 10. This demonstrates that frequency has a certain impact on flow control, and at this momentum coefficient, F\({}^{+}\) = 1 achieves the optimal flow separation control. However, with the continued increase in VR, F\({}^{+}\) = 10 becomes the best control frequency, effectively suppressing flow separation on the HUMP airfoil, with the separation vortex essentially disappearing. At VR = 3.1, for F\({}^{+}\) = 0.375 and 1, the separation vortex size increases with the increasing VR, indicating that F\({}^{+}\) may have an inhibitory effect on flow control during the operation of the SWJ actuator. Simultaneously, the control effects demonstrated by F\({}^{+}\) = 1 and 10 at different momentum ratios suggest that selecting the appropriate frequency at different VR can optimize the control effectiveness. In addition, at F\({}^{+}\) = 0.375, a distinct alteration in the separation vortex shape is apparent. The separation vortex at the separation point is smaller in size, and its vortex center is located farther away from the separation point. Moreover, at this frequency, with an increase in velocity ratio, a notable phenomenon can be observed: due to the smaller height near the separation point, the separation vortex splits into two vortices with increasing momentum. One vortex remains at the separation point with a smaller size, while the other is positioned above the airfoil. Figure 13 depicts the comparison of surface pressure coefficients under different F\({}^{+}\) controls at VR = 3.1, showing consistent results with the average streamwise velocity field. The optimal control effect is observed at F\({}^{+}\) = 10. In response to the phenomena observed in Figure 12, this paper conducts a detailed investigation into the flow field mechanisms of the SWJ actuator on the HUMP airfoil at F\({}^{+}\) = 0.375, 1, and 10. Initially, a study on the control of the flow field is conducted for SWJ actuators at different frequencies. Two monitoring points are established in the flow field:one (x/c = 0.8, y/c = 0.1) near the SWJ actuator and the other (x/c = 2, y/c = 0.1) at a distance of one chord length from the HUMP airfoil.