## 1 Introduction
First, we showed that better \(L/D\) (lift-to-drag ratio) is obtained at cruise conditions than that of the well-recognized airfoil geometry [27]. Here, the detailed flow structure was discussed, but for only a single angle of attack \(\alpha=6\) deg. The result indicated that burst actuation tends to keep sequential spanwise vortex structures over the upper surface and keeps flow laminar until near the trailing edge in contrast to the promotion of turbulent transition at near stall angle [15]. The resultant flow field became similar to the flow over a well-recognized high-performance airfoil at a low Reynolds number flow regime. Second, a survey of several angles of attack was carried out [28]. Here, time-averaged aerodynamic characteristics were mainly discussed, and unsteady flow features were not discussed in conjunction with the aerodynamic characteristics at each angle of attack. The present study aims to understand the PA-controlled flow features by performing high-fidelity LESs at a broader range of pre-stall angles of attack and discuss the relation with the aerodynamic characteristics of the airfoil. The flow fields over an NACA0015 airfoil at angles of attack \(\alpha=4\), \(6\), \(8\), and \(10\) deg are considered. NACA0015 airfoil flows have been investigated in many previous studies [8; 23; 29; 30; 31], and a wealth of experimental  
Figure 1: Schematic diagram of the DBD plasma actuator (PA) and the example of practical applications. and numerical data are available for comparison. The thickness of this airfoil is not practical for actual flights. However, such a thick airfoil is less restrictive in structural design and has the advantage that a large amount of fuel can be loaded inside a wing. Therefore, the range of aircraft design possibilities will expand if the flow controls can improve the aerodynamic characteristics. The Reynolds number was set to 63,000, which was considered in the previous experimental and computational studies [8,29,30,32], and reliability of the flow simulations has been well established. Previous studies [8,30] show that small fluid fluctuations such as turbulence play an important role in fluid control using PA. In the Reynolds-averaged Navier-Stokes equation (RANS) method, the small fluctuations induced by PA are immediately damped. Therefore, in the present study, wall-resolved LES are conducted to resolve small fluid fluctuations properly. The obtained results are discussed together with the result of the post-stall condition (\(\alpha=12\)). Throughout the obtained results, the flow fields and the relationship between the aerodynamic characteristics are discussed. Focus is laid on the drag reduction, but the lift and the lift-to-drag ratio are also discussed. The results show the good flow control authority of PA for the aerodynamic characteristics of the airfoil at pre-stall angles of attack. In the cases of burst actuation, although the aerodynamic characteristics are improved at all angles of attack, the phenomena leading to the improvement are different between near-stall angles (including the post-stall angle) and lower angles. 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 suppresses the turbulent transition, allow the flow reattachment. Furthermore, the strategy of parameter settings of burst actuation of PA at angles of attack less than stall is indicated.