## 3 Results and Discussion
### Study on Flow Control of Vertical Tail under Different Momentum Coefficients  
First, the gain of three gradually increasing momentum coefficients on the vertical tail lateral force coefficient is studied. Since the jet's direction is perpendicular to the direction of the vertical tail's lateral force, the jet does not directly increase the vertical tail's lateral force. Figure 12 shows that when \(\beta\) = 0\({}^{\circ}\) and \(Re\) = 2.12 \(\times\) 10\({}^{5}\), the vertical tail model lateral force coefficient and lateral force coefficient increment under different momentum coefficient controls. After the oscillating jet flow control is applied to the vertical tail model, the lateral force coefficient is significantly increased, and the lateral force coefficient increases with the increase in the momentum coefficient of the actuator. Within the range of 0\({}^{\circ}\)\(\sim\)10\({}^{\circ}\) rudder deflection angle, the three curves applied with flow control are relatively close, because when the rudder deflection angle is small, flow separation does not occur on the rudder, and the oscillating jet flow control applied at this time obtains the lateral force increment by increasing the vertical tail circulation. When the momentum coefficient of the actuator is 0.083%, the maximum increment of the vertical tail lateral force coefficient is 55.2%. As can be seen from the baseline, the lateral force coefficient is low at a small rudder deflection angle. When a jet with a velocity much greater than the incoming velocity is applied, the lateral force increment is considerable compared to the baseline. Then, with the increase in the rudder deflection angle, the increment of the lateral force coefficient decreases gradually. When the rudder deflection angle is 40\({}^{\circ}\), the increment of the lateral force coefficient is only 23.2%. When increasing the momentum coefficient of the actuator to 0.166%, the rudder deflection angle is 15\({}^{\circ}\), and the maximum lateral force coefficient increment is 69.4%. When the momentum coefficient of the actuator is increased to 0.332%, the lateral force coefficient is further improved. When the rudder deflection angle is 20\({}^{\circ}\), the maximum lateral force increment reaches 81.1%. Under the flow control of this momentum coefficient, when the rudder deflection angle is less than 25\({}^{\circ}\), the lateral force coefficient increment can reach nearly 80%, which is a very ideal control effect. Figure 13 shows that \(\beta\) = 0\({}^{\circ}\) and \(Re\) = 2.12 \(\times\) 10\({}^{5}\), the pressure coefficient curves of the rudder surface under different momentum coefficient jet controls when the rudder deflection angle is 5\({}^{\circ}\) and 25\({}^{\circ}\). When the rudder deflection angle is 5\({}^{\circ}\), there is attached flow on the vertical tail rudder. With the increase in the applied oscillating jet momentum coefficient, except for the increase in the negative pressure measured by the pressure-measuring hole near the outlet of the actuator, the downstream pressure coefficient changes little, and the rudder is attached. When the rudder deflection angle is 25\({}^{\circ}\), the pressure coefficient curve without flow control shows an obvious \"platform\", indicating that the airflow on the rudder is completely separated at this time. After the flow control is applied, a significantly increased negative pressure is measured at the pressure-measuring hole at the outlet of the actuator, and a \"suction peak\" appears. With the increase in the momentum coefficient of the oscillating jet, the negative pressure measured by the pressure measuring  
Figure 11: Velocity cloud diagram and streamline diagram of vertical tail upper surface without control: (**a**) \(\delta\) = 15\({}^{\circ}\); (**b**) \(\delta\) = 30\({}^{\circ}\) (\(\beta\) = \(-\)10\({}^{\circ}\), \(Re\) = 2.12 \(\times\) 10\({}^{5}\)). hole closest to the outlet of the actuator continues to increase, and the whole pressure coefficient curve shows an obvious slope.