*3.1. Flow Field Characteristics with Constant Velocity and Flapper Displacement*

The nozzle area is selected as the observation object, and the observation points on the flow channel model are shown in Figure 4a, while Figure 4b shows that the wall Y plus number along the wall position. The results show that nearly all the wall Y plus number is less than 1 as suggested by Fluent user's guide, except for the leftmost and rightmost boundaries; however, the Y plus numbers are still less than 2. Analogously, the simulation obtained Y plus numbers in 5 m/s, 25 m/s, and 50 m/s conditions are also less than 1, mostly, including the wall areas near points 1–6, in which the research is much concerned.

**Figure 4.** Nozzle structure with observation points and the Y plus distribution. (**a**) Nozzle structure with observation points. (**b**) The Y plus distribution when velocity of inlet is 10 m/s.

The flow field model with an inlet velocity of 25 m/s and the flapper at the zero position is used for overall analysis. Since the flapper is in the zero position, the distance between the nozzles on both sides and the flapper is equal, making the flow resistance the same. According to the theoretical calculation, the pressure loss of the nozzles on both sides is the same, and the flow velocity through the nozzles should be equal. In addition, because the flow state of the oil injection to the two sides of the flapper is exactly the same, without considering the wear of the nozzles, the pressure fluctuation curves generated by the flappers on both sides should also be the same. By observing Figure 5, it is found that the oil velocity on both sides of the nozzle is the same, which is in accordance with the theory. However, in the wake region, the oil continuously makes periodic whirlpool motions, which makes the flapper subject to periodic pressure oscillations through the disturbance of the oil cycle, and in order to observe the pressure oscillation on the left and right sides of the flapper, point 1 and point 2 of Figure 4 are selected as the comparison, and the pressure situation at the two points is measured as shown in Figure 6a–d. Pressure oscillation phenomena have been observed at both points. It can be seen that there exists a fluid self-excitation oscillation between the nozzle and flapper. Moreover, the pressure oscillation curves at both points are approximately the same, the average pressure is about 0.57 MPa, and the oscillation amplitude is 0.12 MPa. Observing the power spectrum, it is found that the pressure fluctuation is mainly high frequency, and the peak frequency appears at 3000 Hz.

It is known from the foregoing that when the flapper of the jet flapper valve is located at the zero position, the average pressure, velocity and pressure fluctuation of the flapper on both sides of the flapper are almost the same, so in order to observe the pressure situation at different positions of the flapper, according to Figure 4, only points 1, 3, and 5 on the right side are selected as the observation objects. The pressure fluctuation curves are shown in Figure 6a,b,e–h respectively. From the graph analysis, it can be seen that the pressure pulsation at point 1 and point 3 oscillates around 0.57 MPa and has positive pressure, while point 5 oscillates near −0.045 MPa and the pressure is negative. This is because point 1 is located in the central region of the oil injection, so its pressure corresponds to the highest, while point 5 is located in the wake region, so the pressure is low; besides point 1, point 3, and point 5, the main frequency is low. The performance is not obvious because point 1 is the main area to be impacted by the jet, so the pressure oscillation here is also the most significant. At the same time, the pressure fluctuations in the three locations are mainly high frequency, generally over 3000 Hz, and the maximum power size appears at 3000 Hz, which indicates that the main frequency of pressure oscillation is 3000 Hz. In addition, the pressure amplitudes of the three locations are very stable in the time domain, and there is no sudden change point, which indicates that pressure oscillation exists. It is not caused by accidental factors, but by the high-speed impact of oil on the flapper.

**Figure 5.** Velocity nephogram in one oscillating period.

**Figure 6.** Pressure oscillation curves at different points on flappers. (**a**) Point 1 in the time domain. (**b**) Point 1 in the frequency domain. (**c**) Point 2 in the time domain. (**d**) Point 2 in the frequency domain. (**e**) Point 3 in the time domain. (**f**) Point 3 in the frequency domain. (**g**) Point 5 in the time domain. (**h**) Point 5 in the frequency domain.

The simulation time step is 0.0001 s, and each step is saved automatically. As a result, a flow cycle is obtained as shown in Figure 5. It can be found that the fluid disturbance is very intense when it enters the nozzle flapper area. In Figure 5a, after the fluid is injected into the nozzle flapper, it intersects at the bottom of the flapper, and the phenomenon of reflux is intensified in Figure 5b. Then a small eddy current is initially formed in Figure 5c, which is generated in Figure 5d and completes a cycle in 0.0003 s. Figure 6b shows that the main frequency is about 2850 Hz and the calculated period is about 0.00035 s, which are in good agreement with each other, indicating that the intercepted period is correct. This is because the oil continuously forms eddy currents on the flapper, producing repetitive pulses on the flapper, and thus forming a pressure oscillation on the flapper.
