## 3 Experimental Results and Discussion
### Particle Image Velocimetry for Characterizing the Flow Field
\(\xi/c=0.45\) was adopted because the position corresponding to \(\xi/c=0.45\) provides the most accurate estimation of the momentum thickness, and the positions downstream from \(\xi/c=0.45\) were not adopted  
Figure 9: PIV results for a typical flow field around the NACA0015 wing model at an angle of attack of 24\({}^{\circ}\) (**top**), and magnified images of the PIV result near the separation point of the boundary layer (**bottom**). The conditions in this figure are \(F^{+}=1\) and \(Re=9.4\times 10^{5}\). because there exist conditions under which the freestream region was not included in the field of vision. The ratio of the shear layer height, \(K_{h}\), was defined as the value of the change in shear layer height due to DBD-PA actuation normalized by the height without actuation; this index is expressed by the following formula:  
\[K_{h}=\frac{h}{h_{NoPA}}-1, \tag{4}\]  
where \(h\) and \(h_{NoPA}\) are the shear layer height with and without DBD-PA actuation at \(\xi/c=0.45\) and AoA = 24\({}^{\circ}\), respectively. (3) The ratio of increase in the maximum TKE \(K_{\text{TKE}}\): to calculate the ratio of increase in the maximum TKE, a TKE profile was obtained at \(\xi/c=0.45\), similar to the procedure for calculating the velocity profile described above; a maximum TKE value was extracted in that profile. This index was defined as the value of the maximum TKE increased by DBD-PA actuation divided by the value without actuation. The \(K_{\text{TKE}}\) is defined as follows:  
\[K_{\text{TKE}}=\frac{TKE}{TKE_{NoPA}}-1, \tag{5}\]  
where \(TKE\) and \(TKE_{NoPA}\) are the maximum turbulent kinetic energy with and without DBD-PA actuation at AoA = 24\({}^{\circ}\) and on a line perpendicular to the chord at \(\xi/c=0.45\), respectively. (4) The normalized displacement of the separation point of the boundary layer \(ND_{SP}\): the normalized displacement of the separation point of the boundary layer was determined as follows: velocity profiles in the direction perpendicular to the wing surface were calculated for each position along the chord. The velocity was evaluated along a vector tangential to the airfoil surface. The separation point was defined as the most upstream chord position where a velocity profile with a negative value was found. The displacement was defined as the result of subtracting the position of the separation without actuation from the position of the separation with actuation. As chord lengths were used for normalization, the \(ND_{SP}\) is expressed as follows:  
\[ND_{SP}=\frac{\xi_{SP}-\xi_{SP}^{NoPA}}{\text{c}}, \tag{6}\]  
where \(\xi_{SP}\) and \(\xi_{SP}^{NoPA}\) are the position of the separation with and without DBD-PA actuation, respectively. \(c\) is the chord length of the wing model. Figure 10: Schematic defining the position of the boundary layer separation on the \(\xi\) axis. Dependence of the Four Indices on Re and \(F^{+}\) under a Deep Stall Condition with DBD-PA Actuation  
The discussion is based on the data for each of the four indices defined in the previous section, which are summarized in the color maps in Figures 11-14. These figures, with the \(Re\) number on the \(x\)-axis and the normalized burst frequency, \(F^{+}\), of the plasma actuation on the \(y\)-axis, show the values of the indices defined by a color bar. The asterisks in Figures 11-14 indicate the conditions for which data was obtained by PIV measurement, and the results of the conditions indicated by triangle marks are discussed in the next section. Figure 11 shows a contour map of the \(C_{L}\) increase ratio by DBD-PA actuation, named the first index in the previous section, at a 24\({}^{\circ}\) AoA. The broken line in the figure connects the data points of the maximum value of each \(Re\). Figure 11 illustrates the region where increases in \(C_{L}\) clearly exist in the range of \(F^{+}\) = 0.1 - 5.0 and their peak exists at \(F^{+}\) = 0.5 or 1.0.