*2.3. Grid Generation and Independence Analysis*

The runner belongs to the regular geometric model, so the grid module of ANSYS software, mesh (ANSYS 19.0, ANSYS, Inc., Canonsburg, PA, USA, 2018) is selected to divide the runner with the Quadrilateral Dominant method. Since there are a few trapezoidal areas in the runner, the type of grid division is Quad/Tri. At the same time, the nozzle part of the key research area has a larger grid density in order to capture as many transient details as possible. The partitioned grid is shown in Figure 2, and the grid parameters are shown in Table 3.

**Figure 2.** Grid model with a grid size of 0.012 and the flapper at the zero position when *L*<sup>1</sup> = 0.02.



For a servo valve, flow and pressure are the ultimate indicators, so pressure and flow can be used to determine whether the grid size is appropriate. The outlet flow and average pressure on flapper at different grid sizes are shown in Figure 3.

**Figure 3.** Flow and pressure at different grid sizes.

It can be seen that when the grid size is 0.010/0.012 and 0.015, the average pressure of the flapper is not much different, only within 0.005 MPa, while the mass flow of the outlet is almost the same, the difference being only 0.000048 kg/s. Therefore, when the grid size is in the range of 0.010–0.015, the grid quality has no effect on the simulation results. The median value of range of 0.012 is taken as the grid size when grid is independent.

After finding the optimal grid size, the channel model with different flappers are meshed. Since the distance between the flapper and the two nozzles is 0.2 mm when the flapper is located at the zero position, the number and quality parameters of the grid at different positions are obtained as shown in Table 4. The displacement of the flapper is in the right direction, i.e., the X direction shown in Figure 1 is in the positive direction.


**Table 4.** Grid model parameters of different spacing between nozzle and flapper.
