## 4 Results
### PIV Flow Measurements  
Phase-locked PIV measurements can offer insight into the specifics of the control mechanisms behind NS-DBD actuators. The objective of this analysis was to observe the evolution of the flow over the airfoil when the DBD was active and to study the effect of different actuation frequencies on the structures of the flow.  
Figure 23: \(C_{p}\) distribution comparing applied voltages at \(Re=200,000\) and \(\alpha=16^{\circ}\), and actuation frequency \(f=266.6\) Hz.  
Figure 22: \(C_{p}\) distribution comparing applied voltages at \(Re=100,000\) and \(\alpha=16^{\circ}\), and actuation frequency \(f=66.6\) Hz.  
As mentioned above, re-attachment is an unstable phenomenon, which was shown by the pressure distributions obtained. To study how these instabilities evolve in time, the streamlines from six consecutive instantaneous velocity fields were produced. Each image pair obtained has a phase difference of \(3600^{\circ}\) with the actuation of the DBD, meaning that an image pair was obtained every ten actuations of the DBD. As shown in Figure 24, the flow over the airfoil was unstable, and therefore became attached and detached at different time instances. Furthermore, the mechanism at work behind this instability seemed to be the formation of a large vortex at the mid-chord of the airfoil. When the particular vortical structure broke down the flow re-attaches again. Note that the Reynolds number for the flow evolution presented was \(100,000\) and the actuation of the DBD was at \(F_{c}^{+}=1\).  
However, the existence of this instability seemed to be correlated with the Reynolds number. At the same actuation frequency of \(F_{c}^{+}=1\) but at \(Re=200,000\), this instability was not observed. Furthermore, this actuation frequency was observed to produce better results at a higher \(Re\), since, as shown in Figures 25 (right, corresponding to the higher \(Re=20^{+5}\)) and 26, where the Reynolds  
Figure 24: Evolution of different instantaneous flow structures and vortices with plasma actuation at \(F_{c}^{+}=1\) and \(Re=100,000\) (constant flow conditions).  
was \(Re=10^{+5}\), the size of the wake considerably decreased at the higher \(Re\). The dependence on the actuation frequency can be observed, as illustrated within the velocity field clearly in Figure 25 (top), for the conditions \(Re=200,000\) and \(\alpha=16^{\circ}\), where \(f=41\,\mathrm{Hz}\) for the top left hand side image and \(f=133\,\mathrm{Hz}\) (i.e., \(F_{c}^{+}=1\)) for the image on the top right.  
To obtain a better understanding of how the DBD actuator influences the existing characteristic structures in the flow field, images were taken at \(\alpha=24^{\circ}\) and \(Re=200,000\) where the instabilities were lower and the changes in the flow structure more pronounced. After the acquisition of 500 image-pairs, a time-averaged representation of the swirling strength was obtained. The frequencies of actuation used for the DBD were 69.0 Hz and 266.6 Hz, of which the latter corresponded to \(F_{c}^{+}=2\). Note that the frequency of 69.0 Hz is a characteristic frequency of the flow, which was obtained through analysis of the power spectra (Figures 13-15). The first image of Figure 27a corresponds to no actuation, whereas in Figure 27b,c, the actuation is on with frequencies of 69 Hz and 266 Hz, respectively. In Figure 27b, at frequency 69 Hz, the most likely excited structure is the separation vortex. Compared to Figure 27c, where the actuation frequency is 266.6 Hz, it was observed that different excitation mechanisms exist, which form distinct vortical structures that diffuse as they move downstream in the direction of the flow. The maximum swirling strength of the shedded vortices, however, were three times higher for  
Figure 26: Velocity field at \(Re=100,000\) and \(\alpha=16^{\circ}\) and DBD actuation at \(F_{c}^{+}=1\).  
the actuation frequency of 266.6 Hz. This clearly shows how the frequency of actuation influences the flow mechanisms.