**1. Introduction**

Compared with the conventional layout aircraft, the flying wing has no flat tail and vertical tail, and the wing and the fuselage are highly integrated, so it is subjected to greater lift and less drag [1,2]. High aerodynamic efficiency, light weight structure, large loading space, and good stealth performance are the characteristics of the flying wing [3,4]. As the use of the air field is getting deeper, in future development, the aircraft of the flying wing layout seems to be the seed candidate [5]. However, just like the aircraft of the conventional layout, after the angle of attack exceeds the critical value, the surface boundary layer of the flying wing will be separated, the lift will drop sharply, and its maneuverability will deteriorate [6]. The flying wing is similar to a delta wing aircraft. At moderate angles of attack, both sides of the wing are subjected to a pair of asymmetric flow axial vortex systems. At high angles of attack, the left and right asymmetrical vortices are formed in the leeward area of the fore body, resulting in yawing and rolling moments, affecting its maneuverability [7,8].

Through the technical means of flow control, improving the stall characteristics of the wing surface and then improving the aerodynamic performance of the aircraft at a high angle of attack have become

an important research direction in the field of aviation [9,10]. At present, there are many research methods to improve the flow field by active flow control, such as acoustic excitation [11], oscillating jet [12], synthetic jet [13], blow and suction air [14], microelectromechanical system (MEMS) [15], and plasma flow control [16]. Plasma flow control has many types of research in the field of flow control because of its simple structure, no moving parts, rapid response and flexible function [17–20]. The plasma flow control technology is used to delay the flow separation under the low speed condition to improve the stall angle of attack and is also used to reduce the shock angle under the high speed condition to weaken the shock wave [21,22]. The common methods of using plasma to control the flow field are alternating current dielectric barrier discharge (ac-DBD) and nanosecond dielectric barrier discharge (ns-DBD). When the incoming flow velocity is low (less than 0.4 Ma), the ac-DBD control effect is good, mainly by generating body force in the flow field, inducing the near-wall airflow to accelerate, thereby suppressing flow separation [23]. When the incoming flow velocity is higher, it is more suitable for ns-DBD, which produces instantaneous heating in the flow field, and can e ffectively suppress airfoil flow separation at a large flow velocity (0.8 Ma) [24,25].

Servant et al. proposed a method for optimizing aerodynamic design, which was successfully applied to the design of 3D flying wing by parameterizing complex surfaces and removing invalid noise data by partial di fferential equation (PED) and response surface methodology (RSM) methods [26]. Huber et al. studied and analyzed the interaction between the vortex structure and the vortex on the upper surface of the DLR-F17 wing model by numerical simulation to evaluate the aerodynamic behavior in the flight envelope in order to study the requirements for stability and maneuverability [27]. Xu et al. used the synthetic jet control method to improve the lateral aerodynamic characteristics of the asymmetric vortex of the flying wing and control the lateral aerodynamic force through the interaction of the asymmetric vortex [28]. Han et al. studied the actuation frequency of ns-DBD to improve the aerodynamic performance of the flying wing under di fferent Reynolds numbers. The results show that there is an optimal actuation frequency and it is more e ffective to delay the breakdown of the leading edge vortex at low frequencies [29]. Yao et al. studied the optimal actuation position of the ns-DBD to improve the aerodynamic performance of the flying wing. When plasma actuation is applied to the leading edge of the inner and middle wing, the control e ffect is obvious. The actuation e ffect is best when the corresponding dimensionless frequency is 1 under low frequency conditions, and the variation of actuation voltage has little e ffect on the e ffect of the lift increasing [30].

In this paper, the microsecond pulse surface dielectric barrier discharge (μs-DBD) actuation method is used to carry out flow control experiment on two flying wings with di fferent sizes. The actuation effect of μs-DBD plasma flow control on improving the aerodynamic performance of the flying wing is compared. The energy of μs-DBD is analyzed in this paper. The optimal actuation frequency is studied from the dimensionless frequency by force measurement, and the variation of the flow field on the surface of the symmetric flying wing is analyzed by particle image velocimetry (PIV).
