# Numerical Study of Flow Separation Control over a Hump Airfoil Using a Novel Sweeping Jet Actuator
## 3 Results
The locations of these monitoring points are illustrated in Figure 14.  
Figure 11: Size of the separation vortex of the Hump airfoil. Figure 12: Under F\({}^{+}\) = 0.375, 1, and 10 control, the HUMP airfoil’s average flow field at various VR. Figure 14: The location of monitoring points. \begin{table}
\begin{tabular}{c c c c c c} \hline
**VR** & **F\({}^{+}\)** & **The Separation** & **The Reattachment** & **Separation Vortex** & **Relative** \\  & **Point, x/c** & **Point, x/c** & **Size** & **Improvement, \%** \\ \hline
0 & 0 & 0.65 & 1.2 & 0.55 & \(-\) \\  & F\({}^{+}\) = 0.375 & 0.68 & 1.11 & 0.43 & 21.82 \\ VR = 1.1 & F\({}^{+}\) = 1 & 0.68 & 1.03 & 0.35 & 36.36 \\  & F\({}^{+}\) = 10 & 0.68 & 1.11 & 0.43 & 21.82 \\  & F\({}^{+}\) = 0.375 & 0.68, 0.78 & 0.73, 0.91 & 0.05, 0.11 & 70.91 \\ VR = 1.8 & F\({}^{+}\) = 1 & 0.68 & 0.76 & 0.08 & 85.45 \\  & F\({}^{+}\) = 10 & 0.68 & 0.9 & 0.22 & 60 \\  & F\({}^{+}\) = 0.375 & 0.68, 0.79 & 0.71, 0.84 & 0.02, 0.05 & 87.27 \\ VR = 2.3 & F\({}^{+}\) = 1 & 0.68 & 0.73 & 0.05 & 90.91 \\  & F\({}^{+}\) = 10 & 0.68 & 0.71 & 0.03 & 94.55 \\  & F\({}^{+}\) = 0.375 & 0.68, 0.76 & 0.71, 0.82 & 0.02, 0.06 & 85.45 \\ VR = 3.1 & F\({}^{+}\) = 1 & 0.68 & 0.78 & 0.1 & 81.82 \\  & F\({}^{+}\) = 10 & 0.68 & 0.7 & 0.02 & 96.36 \\ \hline \end{tabular}
\end{table} 
Table 2: The separation point positions under SWJ actuator control. Figure 13: Under F\({}^{+}\) =0.375, 1 and 10 control, the time-averaged Cp at VR = 3.1. As shown in Figure 15, the influence of SWJ actuators at various frequencies on the flow field at monitoring point 1 is illustrated. In this study, the velocity variation overtime at this point and the corresponding Fast Fourier Transform are investigated. It can be observed that the SWJ actuator effectively aligns the frequency of the flow field near the actuator with the frequency of the SWJ actuator itself. The impact of SWJ actuators at various frequencies on the flow field at monitoring point 2 is illustrated in Figure 16. It can be observed that at a distance from the SWJ actuator, F\({}^{*}\) = 0.375 and 1 continue to ensure consistency between the frequency of the  
Figure 15: The variation of velocity over time at monitoring point 1 and the corresponding Fast Fourier Transform at VR = 1.8.  
entire flow field and the oscillation frequency. However, at F\({}^{+}\) = 10, the periodicity at this point diminishes. By comparing the frequency information at two monitoring points, it was observed that at VR = 1.8 and F\({}^{+}\) = 10, the impact on the flow field far from the SWJ actuator was minimal. However, at F\({}^{+}\) = 0.375 or F\({}^{+}\) = 1, the flow field frequency remained consistent with the oscillation frequency, ensuring that the frequency of the separated vortices matched  
Figure 16: The variation of velocity over time at monitoring point 2 and the corresponding Fast Fourier Transform at VR = 1.8.  
the SWJ actuator frequency. This likely explains why F\({}^{+}\) = 1 achieved better control effectiveness when VR \(\leq\) 1.8. The reasons for the less effective control at F\({}^{+}\) = 0.375 require further investigation of the flow field. In addition, this paper investigates the periodic flow field under the control of the oscillating jet device and explores the working mechanism of the oscillating jet. As illustrated in Figure 17, the periodic flow field for F\({}^{+}\) = 1 is shown. At time T\({}^{*}\) = 0, two separated vortices, V1 and V2, appear on the surface of the airfoil. The smaller-sized vortex, V1, is generated due to the interaction between the oscillating jet attached to the lower surface of the airfoil at the exit location and the incoming flow from the external environment. From T\({}^{*}\) = 0 to T\({}^{*}\) = 1/6T, the size of V1 gradually increases,  
Figure 17: Periodic flow field of the HUMP airfoil under F\({}^{+}\) = 1 and VR = 1.8 control. as depicted in the upper right corner. V1 redirects the incoming flow from the external environment towards the surface of the airfoil, leading to a gradual reduction in the size of V2.