## 5 Conclusions  
LES of the flows controlled by PA over an NACA0015 airfoil was performed at angles of attack before a stall. The flow control authority of PA was investigated, and the relationship between the aerodynamic coefficient and the flow field was clarified through the LES results.  
The Continuous and Burst cases using PA at the angles of attack before the stall improved \(L/D\) compared to PA-OFF. The improvement in \(L/D\) is mainly owing to the reduction in \(C_{\rm D_{p}}\) in addition to the improvement in \(C_{\rm L}\). The primary causes of the reduction in \(C_{\rm D_{p}}\) are (1) lower pressure at the suction peak and (2) reduction in the plateau region of \(C_{\rm P}\) as the separation bubble is moved or shrunk on the upper surface of the airfoil. The second effect is remarkable in the Burst cases with \(F^{+}=6\). Although, in the Bust case, the lift-to-drag ratio is improved at all angles of attack, the phenomena leading to the improvement differ between near-stall angles (\(\alpha=10\) and \(12\)) and other lower angles (\(\alpha=4\), \(6\), and \(8\)). At near-stall angles, the turbulent transition is rapidly promoted by PA, and the flow is reattached. Whereas, at lower angles, the transport of two-dimensional vortex structures, which maintain their structures downstream and suppress the turbulent transition, creates flow reattachment. At \(\alpha=4\) and \(8\), the \(L/D\) of the Continuous case was higher than that of the Burst case because the suction peak value of \(C_{\rm P}\) in the Burst case was not improved compared to the PA-OFF case due to the trailing edge separation. The trailing edge separation may be caused by the suppression of the turbulent transition by the two-dimensional vortices whose structures are maintained even near the trailing edge in addition to the reverse pressure gradient. Therefore, applying flow control methods that promote turbulence transition could possibly suppress the trailing separation and improve aerodynamic characteristics. Based on the results of the previous study [27], frequencies lower than \(F^{+}=6\) may be effective, and further investigation is required. In addition, a control method that dynamically changes the PA drive conditions according to the angle of attack is needed for robust control.  
It should be noted that these phenomena in the present study would depend on the airfoil geometry and flow conditions. Future studies on the influence of the airfoil geometry such as a thin airfoil and the flow conditions such as freestream turbulence are required.  
Conceptualization, T.O. and K.F.; Data curation, T.O.; Formal analysis, T.O.; Funding acquisition, K.F.; Investigation, T.O.; Methodology, T.O.; Project administration, T.O.; Resources, T.O. and M.S.; Software, T.O., K.A., T.T. and K.F.; Supervision, K.A. and K.F.; Validation, T.O.; Visualization, T.O.; Writing--original draft, T.O.; Writing--review & editing, K.A. and K.F. All authors have read and agreed to the published version of the manuscript.  
This research was supported by a JSPS Grant-in-Aid for Scientific Research No. 18H03816 in Japan.  
Figure 22: Power spectrum densities (PSDs) of the chordwise velocity fluctuation at the point of the maximum TKE directly above each code length in the Burst case at \(\alpha=12\).  
**Acknowledgments:** The flow field computations presented in the present study are performed on the \"JAXA Supercomputer System Generation 2 and 3 (JS82 and JS83)\" in the Japan Aerospace Exploration Agency (JAXA) and on the \"SX-Aurora TSUBASA\" in the Cyberscience Center, Tohoku University. Supports by the system and center staffs are very much acknowledged. The authors would like to thank [PERSON] of Tokyo University of Agriculture and Technology for conducting the experiments to validate the present simulations.  
**Conflicts of Interest:** The authors declare no conflict of interest.