# Solving the Moment Amplification Factor of a Lateral Jet by the Unsteady Motion Experimental Method
###### Abstract
According to the study, forced pitch oscillation data show negative interaction force amplification factors at a certain angle of attack, while interaction moment amplification factors indicate a pronounced decrease at a relatively high angle of attack. Researchers have conducted many wind tunnel tests and numerical simulations for jet problems, accumulated rich research experience, and played a guiding role in aircraft design. In addition to the above research on the impact of jets on air vehicles, leading universities have also conducted relevant research on jets. However, these universities focus more on the research aspects and frontiers of jet mechanisms. Research on the impact of jets on air vehicles, including air vehicle motion and aerodynamics, is generally lacking. Representative research from each leading university is as follows. At the University of Manchester, [PERSON] and [PERSON] [18] studied the mixing between two liquid flows with the same velocity in a plane mixing channel enhanced by three lateral synthetic jet pairs. The synthetic jet pair operates 180\({}^{\circ}\) out of phase and within a specific driving frequency and displacement range. [PERSON] et al. [19] at Imperial College proposed the application of a finite difference scheme to solve the hydrodynamic elliptic flow equations for the problem of vertical discharge of a turbulent reactive jet into an unconfined cross flow. At Nagoya University, [PERSON] et al. [20] used direct numerical simulation (DNS) to simulate the time evolution of a plane jet and a turbulent boundary layer by implicit large-eddy simulation (ILES). A plane jet and boundary layer ILES/DNS hybrid method was tested by comparing the results with the complete DNS from the initial laminar flow. At Nagoya University, the utility of the dielectric jet barrier controller was studied by [PERSON] et al. [21]. A rectangular nozzle (75 \(\times\) 10 mm) was used with an actuator placed on the longer side of the nozzle outlet. By changing the modulation frequency, duty cycle, and phase difference, unsteady driving of the actuator is realized. [PERSON] et al. [22] at the University of Poitiers used computational aeroacoustics to simulate a cold single flow jet at a Mach number of 0.9. Two mixed methods are used to calculate the jet sound field. Large-eddy simulation could be used for the jet flow domain to reduce computational costs. The primary source of cold jet noise in the acoustic perturbation equations system was shown to be the Lamb vector. However, the purpose of the jet is to make the air vehicle move, and the vehicle's movement inevitably leads to unsteady changes in the flow field and aerodynamic forces, which in turn lead to further movement of the air vehicle. A force analysis shows that when the air vehicle is flying, it activates the jet control in a relatively balanced state. Five action processes corresponding to 1-2 in Figure 1 can be identified by analyzing the jet process. These five processes can be summarized as follows: 1 The injection of jet gas causes the variation of the flow field around the air vehicle. Because the flow field is not immediately stable, the flow field around the nozzle must be unsteady for a short time. 2 The direct jet force acts on the air vehicle, and breaking its original force balance makes the air vehicle move differently. Because the direct jet force and the change in the flow caused by the jet occur simultaneously, the air vehicle begins to move (including linear motion and angular motion) before the flow is stable. In particular, the change in angle further changes the flow and produces unsteady flow. 3 When the flow around the air vehicle changes, it causes the aerodynamic forces on the air vehicle to change. 4 The original force balance state of the air vehicle is further broken, which again changes the air vehicle motion, including linear and angular motion. 5 The air vehicle angular displacement change further changes the flow field.