# Numerical Study of Flow Separation Control over a Hump Airfoil Using a Novel Sweeping Jet Actuator
## 4 Conclusions  
In this paper, a feedback-free sweeping jet actuator that can efficiently decouple frequency and velocity ratio was designed and applied to flow control for the HUMP airfoil. The study investigates the impact of frequency and velocity ratio on flow control. In the design of SWJ actuators, a novel approach has been proposed using a feedback-free configuration, where the basic shape and dimensions are similar to traditional dual-feedback SWJ actuators. However, instead of feedback channels, two synthetic jets are used to decouple frequency from velocity ratio and size. This design facilitates determining the SWJ actuator's frequency impact on flow control. In this study, numerical simulations validated the feasibility and effectiveness of this SWJ actuator. When applying the SWJ actuator to flow control on the Hump airfoil, the following observations were made:  
When VR \(\leq\) 1.8, the control effectiveness is optimal at F\({}^{+}\) = 1. Specifically, at VR = 1.1, the reattachment point shifted from x/c = 1.2 to x/c = 1.03. At F\({}^{+}\) = 10 and under VR = 1.1, the reattachment point shifted from x/c = 1.2 to x/c = 1.1. At F\({}^{+}\) = 0.375, the control effectiveness was similar to F\({}^{+}\) = 10. At VR = 1.8, F\({}^{+}\) = 1 effectively shifted the reattachment point from x/c = 1.2 to x/c = 0.76, significantly reducing flow separation. In contrast, at F\({}^{+}\) = 10 under the same VR control, the reattachment point shifted from x/c = 1.2 to x/c = 0.9. This demonstrates that by appropriately adjusting the frequency, better control effectiveness can be achieved with the SWJ actuator, validating its feasibility in practical applications. At VR > 1.8, the control effectiveness was highest at F\({}^{+}\) = 10, effectively preventing flow separation. Conversely, at F\({}^{+}\) = 1 during this process, the control effectiveness improved less and even led to an increase in separation area at VR = 3.1. This is because as the VR increases, more energy is provided to the flow field to suppress flow separation. At high VR, the energy provided by the SWJ actuator is sufficient to suppress flow separation, which explains why F\({}^{+}\) = 10 effectively prevents flow separation. At F\({}^{+}\) = 1, the mechanism involves the SWJ actuator attaching to the lower surface of the main jet flow, creating a clockwise vortex at the outlet that effectively entrains energy from both the SWJ actuator and the incoming flow to induce it onto the airfoil surface. This causes the separation vortex to move downstream while gradually diminishing in size. When the separation vortex  
Figure 19: The flow field of the HUMP airfoil under F\({}^{+}\) = 1 and VR = 3.1 control. disappears, this clockwise vortex becomes a new separation vortex. Similarly, when the SWJ actuator attaches to the upper surface of the main jet flow, it also creates a clockwise vortex with entrainment effects, but without enlarging in size, its role is to push the previously generated separation vortex downstream, effectively maintaining consistency between the flow field frequency and the SWJ actuator frequency. This is why F\({}^{+}\) = 1 achieves better control effectiveness at VR \(\leq\) 1.8. However, at VR \(>\) 1.8, the maximum size of the clockwise vortex created when the SWJ actuator attaches to the upper surface of the main jet flow also increases, matching the size of the final separation vortex, leading to an increase in separation area under control F\({}^{+}\) = 1. Throughout the process of applying the SWJ actuator to flow control on the Hump airfoil, it was observed that both velocity ratio and frequency can influence flow control. However, the optimal frequency is not fixed. Therefore, future studies will focus on ensuring that the SWJ actuator consistently maintains its optimal frequency in flow control. Writing--original draft, T.Z. ; Writing--review & editing, Y.B. All authors have read and agreed to the published version of the manuscript.