**1. Introduction**

The diaphragm valves are extensively used in various industrial applications, including breweries, pharmaceutical chemical, dairy, food, petroleum and mining etc. [1]. This is due to several unique advantages: the ability to handle solids, the low resistance coefficient, no dead areas where particles may collect, easy maintenance, and automation [1–3]. Traditionally, the diaphragm valves are commonly used as shut-off valves for non-Newtonian fluids with variable viscosities [4], such as suspensions, mixed solutions, and the like, because diaphragm valves in such applications do not need and are not easy to achieve accurate flow control. With the rapid development of information technology, diaphragm valves have been widely used in the precise control of Newtonian fluids with downsizing technology trend [5,6]. In order to obtain higher integration and smaller feature sizes of the chip, immersion lithography is the cutting-edge technology and key step in the semiconductor industry [7,8]. The fluid control requirements for ultra-pure water treatment and liquid injection systems are becoming more stringent, which mainly reflects the water purity of ultra-pure water and the stability of immersion flow field [9,10]. Diaphragm valves are the key components of ultra-pure water systems due to their excellent cleanliness and low resistance loss, ensuring a stable flow balance of the infusion flow and the immersion flow field [11].

The diaphragm valve structure and diaphragm material affect the throttling characteristics and sealing performance [12]. From the structural point of view, the most widely used diaphragm valves are straight-through type and weir type [1,13]. Although the flowing resistance in straight-through type valve body is lower and the flow performance is better than that in weir type valve body, the diaphragm travels longer in straight-through type, which means that under the condition of frequent opening and closing control, the life of the straight-through type valve body diaphragm will be much lower than that of the weir type valve body diaphragm. In addition, during the closing process in weir type valve body, the diaphragm forms a vertical coincident seal with the sealing table without any mechanical friction, thereby meeting the sanitary level cleaning requirements. Based on the special advantages of the weir type, the diaphragm valves used in the semiconductor industry are mostly weir type valve bodies. From the material point of view, the properties of rubber diaphragm such as high temperature resistance and oil resistance in the field of chemical industry are not the key points to be considered in ultra-pure water system. The surface quality, tensile strength, fatigue strength and shape retention of rubber are more suitable for evaluating diaphragm valve diaphragm in ultra-pure water system. Currently NBR, HNBR, ACM, FKM, etc. are the most widely used rubber material [14]. Nickel or silicon or bimorph materials are also used as diaphragm materials [15,16]. In addition, The diaphragm made of fluoroplastics (PTFE as an example) or rubber and fluoroplastics composite materials has better elasticity and strength, and its surface is smoother [17].

The throttling characteristics and flow control performance of the diaphragm valve are expressed in the form of valve flow coefficient *Cv* (or *Kv*) value, local resistance coefficient and valve flow characteristic curve [18,19]. The valve flow coefficient *Kv* value is the unit of measurement in metric units (the valve flow coefficient in English units is called the *Cv* value) and is defined as: under the standard pressure drop of 1 bar, the volume flow rate of water (the fluid severity at 1 N/m3) through the valve per hour, as expressed in Equation (1).

$$K\_{\upsilon} = Q \sqrt{\frac{\rho\_0}{\Delta p}} \tag{1}$$

where, *Kv*—valve flow coefficient; *Q*—volume flow rate (m3/h); Δ*p*—pressure drop (1 bar); ρ0—density of water (kg/m3).

The resistance coefficient is the index to measure the pressure loss of the valve. It is a dimensionless coefficient representing the pressure loss of the valve. It depends on the type, diameter, structure and cavity shape of the valve, and is calculated by the experimental data of the valve. According to the Bernoulli equation, the formula for calculating the drag coefficient can be deduced as Equation (2) [20],

$$
\zeta = \frac{2\Delta p}{\rho v^2} \tag{2}
$$

where, ρ—density of medium (kg/m3); *v*—average velocity of inlet (outlet) (m/s); Δ*p*—pressure drop (Pa).

The flow characteristic curve of the valve shows the flow through the valve at different openings in the process of opening and closing [21]. It is an index to describe the flow control performance of the valve. The higher the linearity of the curve, the larger the linearity range, the better the flow control performance of the valve. The curve was obtained experimentally.

At present, there are many experimental studies and valve body structure improvement studies on diaphragm valves, mainly focusing on sealing performance and operability. There are also studies on throttling characteristics of diaphragm valves and simulation studies on flow field [6,22,23] and pressure characteristics [24,25], but not in the ultra-pure water system of the semiconductor industry. Various studies based on other types of valves have confirmed that the change of flow path shape and the use of pilot valves can improve flow control characteristics, reduce vibration and cavitation [26–29]. The weir type diaphragm valve has become the mainstream for the sake of better cleanliness, longer diaphragm life, and better flow control characteristics. However, due to its large flow resistance and lack of design criteria for internal flow channel surface structure, it is difficult to obtain optimization methods to further improve valve control performance. In addition, the outlet of diaphragm valves in ultra-pure water treatment system is generally atmospheric back pressure environment, but the pressure in the pipeline of ultra-pure water treatment system is generally about 5 times atmospheric

pressure, so it is easy to produce cavitation and jet under the condition of diaphragm valve micro-orifice, leading to flow saturation and further increase pressure loss.

In order to solve the above problems, based on the structure of the weir type diaphragm valve body, the numerical simulation analysis of two-dimensional flow field is carried out. By comparing the flow coefficient, resistance coefficient and flow characteristic curve, the flow control performance of valves with different profiles is evaluated, and the structural optimization scheme is proposed and verified. Using the local grid encryption techniques based on velocity gradient adaptive and y<sup>+</sup> adaptive the accuracy of simulation results are improved [30]. The flow field of diaphragm valve was simulated and analyzed, and the cavitation phenomenon of small valve opening of diaphragm valve was explored under the condition of ultra-pure water system.
