4.3.1. The Influence of Opening Degree

Under the given boundary conditions, cavitation begins to appear near the lower boundary of the valve orifice and the corner of the outlet bending when the opening of the diaphragm valve drops to 50%. With the opening decreasing, the cavitation area gradually expands and develops to the upper boundary of the valve orifice (Figure 14). When the opening is below 20%, the cavitation area shrinks to the valve orifice and cavitates near the corner of the outlet bending. When the opening is less than 10%, the cavitation area continues to shrink near the center of the valve opening.

(**b**) Two-phase volume fraction (**left**) and gas content distribution (**right**) at 40% opening

(**c**) Two-phase volume fraction (**left**) and gas content distribution (**right**) at 30% opening

(**d**) Two-phase volume fraction (**left**) and gas content distribution (**right**) at 20% opening

(**e**) Two-phase volume fraction (**left**) and gas content distribution (**right**) at 10% opening

**Figure 14.** *Cont*.

(**f**) Two-phase volume fraction (**left**) and gas content distribution (**right**) at 5% opening

**Figure 14.** Volume fraction α of two phases and void fraction distribution of cavitation phase in valve flow field.

4.3.2. Effect of Entrance Boundary Conditions (at 10% Opening)

The inlet is still set as pressure inlet, the setting value increases from *pin* = 500 kPa to *pin* = 100 kPa intervals, and the outlet is set as pressure outlet with *pout* = 100 kPa back pressure. Two-phase volume fraction nephogram of observed time-averaged cavitation results can be obtained by processing and calculating the data of outlet flow rate, pressure difference at both ends and inlet flow rate, and the change of mass flow rate at both ends of inlet and outlet can be obtained with the increase of pressure boundary conditions (Figure 15).

**Figure 15.** With the increase of inlet pressure, the inlet flow rate and outlet flow rate increase almost linearly, but when the inlet pressure *pin* increases to more than 900 kPa, the increase of outlet flow rate slows down, resulting in a larger flow loss.

The reason is that when the pressure difference between the two ends Δ*p* is greater than 800 kPa, the cavitation phenomenon becomes serious and more cavitation bubbles are blocked at the valve mouth, which leads to flow saturation and deviates from the theoretical flow input. And Figure 16 shows a volume fraction nephogram at different inlet pressures.

(**a**) Aqueous phase volume fraction at inlet pressure of *pin =* 600 kPa (**left**) and *pin =* 900 kPa (**right**)

**Figure 16.** *Cont*.

(**b**) Aqueous phase volume fraction at inlet pressure of *pin =* 1200 kPa (**left**) and *pin =* 1500 kPa (**right**)

**Figure 16.** Volume fraction nephogram at different inlet pressures.

#### *4.4. Shape Optimization and Verification*

According to the conclusion analysis of the influence of the structure of the runner profile on the throttling characteristics and the flow control characteristics, the following optimization ideas can be obtained: Increasing the lateral flatness of the ridge, appropriately increasing the width of the ridge top and reducing the protrusion of the inner wall of the valve at the diaphragm installation can increase the flow coefficient and reduce the local resistance coefficient of the valve, and appropriately reduce the diaphragm stroke, the central area of the inner surface of the diaphragm approximates the plane at the maximum opening, and give the diaphragm a pre-stroke during installation. The flow control characteristics of the diaphragm valve can be improved appropriately and the linear range of the flow control zone can be enlarged. The improvement of various surface structures should be carried out on the premise of ensuring the overall size ratio of diaphragm valves.

The optimized prototype is based on the well-behaved surface e, and further flattens the ridge ridge, reduces the obstacles at the protrusions, and modifies the shape of the inner surface of the diaphragm so that the central area of the inner surface of the diaphragm is planar in the fully open state, thus reducing the diaphragm travel. The comparison between the optimized profile F and profile E is shown in Figure 17.

**Figure 17.** The optimized surface F and the optimized surface E.

The flow coefficient and local resistance coefficient (Figure 18) of the optimized profile are improved to a certain extent compared with the prototype profile E before optimization; with the increase of the opening of the profile F valve, the flow coefficient shows an increasing trend, and no longer decreases with the increase of the opening when approaching full opening (Figure 19a). In addition, some improvements have been made in the flow control characteristics of the valve under profile F. In addition to the good linearity, the linearity range has also been enlarged at large valve ports (Figure 19b).

As can be seen from the streamline diagram (Figure 20), the vortices on the right side of the ridge are compressed to a great extent, which hardly hinders the main flow. The vortices near the upper wall of the valve outlet are almost non-existent, indicating that the reduction of the flow path hindrance has a great effect on the reduction of the vortices.

(**b**)

**Figure 18.** Comparison on flow characteristics (**a**) and drag characteristics (**b**) between profile E and the optimized profile F.

(**a**) Flow coefficient *Cv* and *Kv* under different openings of profile F.

**Figure 19.** *Cont*.

(**b**) Flow rate at different openings of profile F.

**Figure 20.** Streamline diagram of profile F at full opening.

#### **5. Conclusions**

The deformation mechanism of diaphragm valve diaphragm is analyzed and simulated by the finite element method. The influence of diaphragm thickness and the loading mode of stem loading on diaphragm deformation are explored. The conclusion is drawn that the diaphragm with thin and moderate loading area had better sealing and control characteristics. The effect of velocity gradient adaptive and y<sup>+</sup> adaptive methods on mesh optimization in some regions and the effect of refined mesh on simulation accuracy are verified by means of mesh adaptive technology.

In the way of design comparison, the influence of the sill-shaped diaphragm structure on the flow coefficient and the drag coefficient of the valve is discussed. Combined with the simulation of the cloud map and the simulation of the flow field under different opening degrees of the valve, the optimized diaphragm flow is obtained. The theoretical idea of the pavement surface structure: smoothing the side wall of the ridge, increasing the width of the ridge, reducing the obstruction of the pipeline and smoothing the lower surface of the diaphragm. Optimize the design in this direction and further simulate to analyze the correctness of the verification optimization.

Through the analysis of gas-liquid two-phase flow nephogram, it is concluded that with the valve closing cavitation gradually occurs and expands, and with the increase of inlet boundary conditions, the small valve opening cavitation becomes more and more serious.

In this paper, the factors influencing the flow characteristics of diaphragm valves and the method of optimizing the flow profile are systematically studied. The main technical indexes of diaphragm valves, such as controllability, flow performance, diaphragm life, cleanliness, and sealing, are comprehensively studied. The improvement of Throttling Characteristics and control characteristics is beneficial to

ultra-pure water system and submerged photolithography. The improvement of technology is of great benefit and constructive and forward-looking to the development of semiconductor industry.

**Author Contributions:** Investigation Y.L. and L.L; Simulation and Analysis Y.L.; Methodology L.L.; Software Y.L.; Writing and Editing Y.L. and L.L.; Validation L.L. and K.W.

**Funding:** The authors are grateful to the National Natural Science Foundation of China (no. 51605333 and no. 51805317) for financial support.

**Conflicts of Interest:** The authors declare no conflict of interest.
