3.4.2. Dynamic Grid Design and Simplification for Flapper Deflection

In Section 2.3 we found and validated the reliability of the optimal grid size. Although the flow field of the main valve has been added to this chapter, the final goal of this chapter is to divide the grid model of the whole valve on the basis of the optimal grid size found in the above chapter because the force of the flapper in the nozzle pilot valve area is still the ultimate goal. It has 80,431 grid nodes and 78,741 grid elements. Its element quality, skewness and orthogonal quality are 0.927, 0.032 and 0.994, respectively, which meet the requirements of grid generation. In addition, in order to realize the motion characteristics of the main valve, a moving grid is needed. In this paper, Fluent is used to provide three dynamic grid models: smoothing, layering and regridding. The smoothing model chooses the spring method to smooth the transition; the layering model chooses the height base to set the split factor and collapse factor as default values; and the regridding model chooses the local cell regridding mode, with the maximum surface skewness set to 0.7, and the rest to remain as default.

3.4.3. Principal Frequency and Amplitude Change Rule in the Coupling of Main Valve

(1) Variation of flow field of servo valve with the change of inlet velocity

From Figures 19–22, it can be seen that the pressure trend of the flapper is the same as that of the previous one. Figure 23 shows that, with the increase of velocity, the average pressure of the flapper increases and the main frequency decreases, which is the same with the previous one. Unlike the previous one, the relative pressure amplitude does not increase linearly with the speed, but decreases linearly. Moreover, the comparison shows that the peak frequency is also reduced by adding the motion characteristics of the main valve. This is mainly due to the large inertia of the main valve, resulting in its low response frequency. Due to the existence of the feedback rod, this effect is reflected in the flapper, so that the flapper pressure frequency generated by fluid impact is reduced.

**Figure 19.** Pressure oscillation curve of the flapper considering the impression of the main valve and velocity of 5 m/s. (**a**) Time domain. (**b**) Frequency domain.

**Figure 20.** Pressure oscillation curve of the flapper considering the impression of the main valve and velocity of 10 m/s. (**a**) Time domain. (**b**) Frequency domain.

**Figure 21.** Pressure oscillation curve of the flapper considering the impression of the main valve and velocity of 25 m/s. (**a**) Time domain. (**b**) Frequency domain.

**Figure 22.** Pressure oscillation curve of the flapper considering the impression of the main valve and velocity of 50 m/s. (**a**) Time domain. (**b**) Frequency domain.

**Figure 23.** Pressure and main frequency of the servo valve flapper at different speeds.

#### (2) Variation of flow field of the servo valve with the change of the flapper displacement

Points 1 and 2 are taken as monitoring points. When the flapper deflects, the pressure curve of the pilot valve under the influence of the main valve is obtained, as shown in Figures 24–27. The pressure under displacement is summarized in Figure 28. The analysis shows that when the distance between the flapper and the nozzle increases, the pressure on the flapper decreases, the relative amplitude increases, and the main frequency increases. The overall trend is consistent with the previous one. It can be seen that the motion characteristics of the main valve do not affect the deflection characteristics of the flapper. At the same time, it can be seen that, whether the main valve exists or not, the pressure level of the pilot valve flapper is not affected at different distances, but the frequency of pressure oscillation is significantly reduced.

**Figure 24.** Pressure oscillation curve of the flapper under the influence of the main valve when the displacement of the flapper is *x* = 0.00 mm. (**a**) Point 1 in the time domain. (**b**) Point 1 in the frequency domain.

**Figure 25.** Pressure oscillation curve of the flapper under the influence of the main valve when the displacement of the flapper is *x* = 0.05 mm. (**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.

**Figure 26.** Pressure oscillation curve of the flapper under the influence of the main valve when the displacement of the flapper is *x* = 0.10 mm. (**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.

**Figure 27.** Pressure oscillation curve of the flapper under the influence of the main valve when the displacement of the flapper is *x* = 0.15 mm. (**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.

**Figure 28.** Pressure and main frequency of the flapper when the actual distance between the flapper and nozzle changes.
