## 3 Experimental Results and Discussion
### Dependence of the Increase in \(C_{l}\) by DBD-PA Actuation on Flow Characteristics  
Figure 8a-d shows the dependence of \(C_{L}\) on the AoA at each Reynolds number without (as shown in \"w/o DBD-PA\") and with DBD-PA actuation, with \(F^{+}\) = 0.1, 1, 10, and 100. Each \(C_{L}\) value was calculated using the \(C_{p}\) distributions obtained under identical flow and plasma conditions. For example, each plot of the \"w/o PA\" condition at \(\alpha\) = 13\({}^{\circ}\), 15\({}^{\circ}\), 18\({}^{\circ}\), and 24\({}^{\circ}\) was calculated from the corresponding \(C_{p}\) distribution shown in Figure 7. Considering all \(C_{p}\) distributions under conditions without plasma actuation obtained in this experiment, including the examples shown in Figure 7, the ranges of the angles of attack in the top figures are colored gray, blue, and red for the first, second, and third flow patterns described in Section 3.1, respectively. Figure 8: \(C_{L}\) curves with \(F^{+}\) = 0.1, 1, 10, and 100 and without DBD-PA actuation for each \(Re\) number (**a–d**), and \(C_{L}\) increase with respect to \(F^{+}\) and the angle of attack with DBD-PA actuation for each \(Re\) number (**e–h**). Figure 8e-h shows the increase in \(C_{L}\) caused by the DBD-PA actuation with respect to \(F^{+}\) and the AoA. The value of \(C_{L}\) increased, and \(\Delta C_{L}\) was calculated using the following equation:  
\[\Delta C_{L}=C_{L}-C_{L_{NoPA}}. \tag{2}\]  
In Figure 8e-h, there is a negligible increase or decrease in \(C_{L}\) regardless of the \(Re\) number, in the range of angles of attack corresponding to the gray range shown in Figure 8a-d. In the range of angles of attack corresponding to the blue range, \(C_{L}\) is only slightly affected. For \(Re\) = 4.2 \(\times\) 10\({}^{5}\) (Figure 8b,f), the increase in \(C_{L}\) is negative at a high \(F^{+}\). For \(Re\) = 5.7 \(\times\) 10\({}^{5}\) (Figure 8c,g), the increase in \(C_{L}\) is slightly positive. Some peaks of \(C_{L}\) increase were observed for every \(Re\) number condition. At \(Re\) = 5.7 \(\times\) 10\({}^{5}\), these peaks are discrete with respect to \(F^{+}\). For \(Re\) = 9.4 \(\times\) 10\({}^{5}\) (Figure 8d,h), the increase in \(C_{L}\) depends on the AoA and \(F^{+}\), and the effect of DBD-PA actuation switches between positive and negative effects. At this \(Re\) number, for a 16-19\({}^{\circ}\) AoA, \(C_{L}\) decreased under almost all conditions. However, for higher angles of attack, there are some conditions in which \(C_{L}\) increases depending on \(F^{+}\). The most effective increase in \(C_{L}\) was obtained in the range of the AoA corresponding to the red range in Figure 8a-d. Figure 8e-g for \(Re\) = 1.9 \(\times\) 10\({}^{5}\)-5.7 \(\times\) 10\({}^{5}\) show that the flow field with lower \(Re\) numbers has a larger increase in \(C_{L}\) closer to the stall AoA. The dependencies of the increase in \(C_{L}\) on the \(Re\) numbers and angles of attack are explained as follows: the actuated DBD-PA placed in a flow field adds a body force into the flow field, changing the behavior of the fluids [41; 62; 63]. We considered the body force to be almost constant because the power consumption of DBD-PA was fixed in the current experiments. Therefore, the DBD-PA actuation is considered more effective with respect to the control of the flow field at a lower \(Re\) number, with a large ratio of the body force generated by the actuation to the main flow momentum. In addition, the result in which the flow field in the region of the AoA corresponds to the red region in Figure 8a-c shows a larger increase in \(C_{L}\) than in the other regions, thereby indicating that DBD-PA is more effective in controlling the stall when the body force is placed closer to the point of the boundary layer separation on the suction side of the wing. Considering that the condition when the separation point is set closer to the trailing edge (i.e., the blue region of the AoA in Figure 8b-d), the increase in \(C_{L}\) is discretely dependent on the condition.