## 3 Experimental Results and Discussion  
Flow Characteristics without DBD-PA Actuation Classified by \(C_{l}\) and \(C_{p}\) Distributions  
Figure 6 shows the \(C_{l}\) curves without DBD-PA actuation, indicating the difference between the curve shapes of each \(Re\) number condition. Each \(C_{l}\) curve was calculated by integrating the time-averaged pressure distribution of the wing surface along the chord. Among the pressure distributions without DBD-PA actuation used in the integration, the results for the angles of attack of 13\({}^{\circ}\), 15\({}^{\circ}\), 18\({}^{\circ}\), and 24\({}^{\circ}\) in the pitch-up runs are shown in Figure 7. The integral for calculating each \(C_{l}\) was performed downstream from the 8.7% chord for all conditions because of the following reasons: (i) the DBD-PA electrode was covered by pressure ports at the leading edge of the wing model; and (ii) when \(Re=9.4\times 10^{5}\), the pressure at the 0-6.0% chord position exceeded the measurable limit of the pressure sensor. Figure 5: Voltage waveform and parameters for DBD-PA actuation. The \(C_{L}\) curves of the pitch-up run in Figure 6 exhibit peaks around a 13\({}^{\circ}\) AoA; simultaneously, the negative \(C_{p}\) near the leading edge shows a large peak during an increase in \(C_{L}\) with angles of attack of 1-13\({}^{\circ}\), as shown by the black curves in Figure 7 for 13\({}^{\circ}\). Considering the pressure distribution on the suction surface of the airfoil, this observation is attributed to the flow attached to the wing model and the negative \(C_{p}\) that increases based on [PERSON]'s theorem for accelerated flow. Downstream of the leading edge, the fully attached flow recovers pressure with deceleration toward the trailing edge, and the pressure at the trailing edge approaches the surrounding pressure. Therefore, \(C_{p}\) approaches zero for a 13\({}^{\circ}\) AoA. The \(C_{L}\) values for the region around angles of attack of 14-17\({}^{\circ}\) at \(Re=4.2\,\times\,10^{5}\), \(5.7\,\times\,10^{5}\), and \(9.4\,\times\,10^{5}\) decrease gradually. \(C_{p}\) does not recover as much at the trailing edge, and a flat \(C_{p}\) distribution is observed near the 40-50% chord location to the trailing edge for a 15\({}^{\circ}\) AoA under the Reynolds numbers, as shown by the blue curves in Figure 7. These results suggest a partial separation on the latter half of the airfoil at angles of attack of 14-17\({}^{\circ}\). For \(Re=9.4\,\times\,10^{5}\), the aforementioned range is extended to larger angles. At each angle in this range, a negative \(C_{p}\) peak is observed around the leading edge. The foot of the peak narrows, and the starting position of the flat \(C_{p}\) distribution moves toward the leading edge with an increase in the AoA. This phenomenon suggests that complete leading edge separation of the boundary layer does not occur up to 24\({}^{\circ}\) under this \(Re\) condition, and the separation point of the boundary layer moves up to the leading edge with an increase in the AoA. Figure 6: \(C_{L}\) curves without DBD-PA actuation. Figure 7: \(C_{p}\) distribution on the wing model surface without DBD-PA actuation on each \(Re\) number and AoA. A considerable difference in the pressure distribution exists between 14\({}^{\circ}\) and 17\({}^{\circ}\) angles of attack and at greater angles under _Re_ = 1.9 \(\times\) 10\({}^{5}\), 4.2 \(\times\) 10\({}^{5}\), and 5.7 \(\times\) 10\({}^{5}\). As indicated by the red curves in Figure 7, a negative \(C_{p}\) peak on the suction side is not observed at higher angles, which results in a flat \(C_{p}\) distribution. No pressure recovery occurs at the trailing edge, and a larger negative \(C_{p}\) is observed because a low-velocity area with almost no acceleration or deceleration is formed on the entire surface of the suction side because of the boundary layer separation at the leading edge.