## 1 Introduction  
The vertical tail is essential for aircraft lateral stability and yaw damping, crosswind landing, and resistance to asymmetric dynamics [1, 2]. To ensure the aircraft's controllability and meet the flight quality requirements in the case of asymmetric engine failure, the vertical tail size of most commercial aircraft is larger than the size required for static heading stability [3]. In addition, the aircraft has low airspeed and steering efficiency during takeoff and landing, so it is necessary to design a large vertical tail to provide sufficient lateral force. However, the large area of the vertical tail will increase the weight and resistance of the aircraft, fuel consumption, and the burden of the control mechanism. Flow control changes the flow state by applying force, mass, heat, electromagnetic, and other physical quantities to the moving fluid, thereby changing the moving object's force state or motion state. Using active flow control technology to improve steering efficiency, reduce the size of the vertical tail, and provide the same control capability as the large vertical tail can enhance the safety and economy of civil aircraft. Active flow control traditionally enables the smaller vertical tail to provide the required control capability in an emergency while operating in the rest of the flight envelope [4]. An oscillating jet flow control technology is one of the most popular active flow control technologies. The self-excited oscillating jet actuator [4] has the advantages of a fixed and reliable structure, strong control ability, and wide control frequency band. It is widely used in separation flow control, enhanced mixing, and other aspects. The self-excited oscillating jet actuator causes the main flow in the mixing chamber to swing due to the control of the feedback channel, and the periodic unsteady jet sweeping will be generated at the outlet of the actuator. Many scholars have made a lot of research achievements regarding the oscillating jet and its application. Scholars such as [PERSON] [5] and [PERSON] [6] have used high-speed schlieren to study the coupling relationship between the internal flow structure of the oscillating jet actuator and the actuator's performance. [PERSON] et al., (1989) [7] studied the separation flow control of a two-dimensional airfoil upper surface using a periodic perturbation active flow control method. [PERSON] et al., (2012) [8] of Pennsylvania State University conducted an experimental study on improving the S903 airfoil's aerodynamic performance with an oscillating jet actuator. [PERSON] et al., (2014, 2017) [9; 10; 11; 12] of the National Aeronautics and Space Administration (NASA) Langley Research Center conducted a comparative study on oscillating jet, micro vortex generator, steady blowing, and other flow control methods on the pressure gradient slope model in the 15-inch wind tunnel. The experimental results show that the momentum utilization efficiency of the steady direct jet is the lowest. An unsteady oscillating jet has the best control efficiency by increasing the pressure recovery and reducing downstream flow separation. [PERSON] et al., (2016, 2018) [13; 14; 15] of the University of Halifa studied the change in the height and width of the feedback channel and the influence of the mass flow rate on the jet velocity distribution and jet span. The two-dimensional Unsteady Reynolds Averaged Navier Stokes (2D-URANS) simulation of the unsteady flow field generated by the oscillating jet actuator was carried out using Fluent software. They studied the unstable flow fields on several internal Coanda surfaces. They gave the effects of different Coanda surfaces and mass flow rates on the jet velocity and spanwise distribution. Under the sponsorship of NASA ERA project, [PERSON] et al., (2015, 2019) [1; 16; 17; 18] carried out active flow control research on a general vertical tail model with a relative thickness of 12%.