*3.3. Mesh Refinement and Grid Independence Verification Based on Velocity Gradient and y*<sup>+</sup> *Adaptive*

When simulating the flow of medium fluid in the valve at different opening, the velocity field cloud atlas shows that the velocity gradient at the valve opening is very large when the valve is half-open. The smaller the opening, the more concentrated the maximum velocity at the valve opening center, the more obvious the increase of the velocity gradient (Figure 9). In addition, when the opening is less than 40%, the height of the valve mouth is less than 6 mm, which can only accommodate 0 to 6 grids. It is necessary to take into account the insufficient development of turbulence in the boundary layer of the river basin. Especially when the opening is 1.5 mm at 10%, the scale of the turbulent viscous bottom layer is generally less than 1 mm. At this time, the influence of the flow boundary layer on the flow state cannot be ignored. However, it is not unnecessary to increase the overall grid density. Therefore, the velocity gradient adaptive method and y<sup>+</sup> adaptive method are adopted to solve the local mesh refinement based on the initial operation results (Figure 10).

It can be seen that with the alternating adaptive process, the mesh is continuously optimized, and the simulation results converge gradually. Therefore, the hybrid adaptive method of velocity gradient and y<sup>+</sup> adaptive has good applicability for reducing the error of simulation results of small opening state of valve body, and has guiding significance for grid optimization.

**Figure 9.** Cloud Map Display of Velocity Field at Different Openings shows that as the valve opening decreases, the velocity gradient increases. (**a**) for 40% opening; (**b**) for 30% opening; (**c**) for 20% opening; (**d**) for 10% opening.

**Figure 10.** The meshes of three-time velocity adaptation (**a**) velocity gradient and y<sup>+</sup> hybrid adaptation; (**b**) and their results of calculation (Tables 2 and 3), respectively.


**Table 2.** Result of Velocity gradient adaptive calculation.

**Table 3.** y<sup>+</sup> adaptive results at different mesh densities.

