Research on Hydraulic Characteristics of Water Leakage Phenomenon of Waterproof Hammer Air Valve in Water Supply Pressure Pipeline Based on Sustainable Utilization of Water Resources in Irrigation Areas

Abstract

To investigate the causes of water leakage in the waterproof hammer air valve and its impact on sustainable water resource management, the DN100 waterproof hammer air valve was taken as the research object. By using the overset grid solution method of ANSYS Fluent 2021 R1 software, the flow field simulation of the waterproof hammer air valve was carried out. The transient action during the ascent phase of the key structural component floating ball, and the velocity and pressure distribution of the flow field inside the air valve are analyzed. The results showed that by giving different inlet flow velocities, the normal flow velocity range for the floating ball to float up was below 35 m/s and above 50 m/s. When the inlet flow velocity was between 35 m/s and 50 m/s, the growth rate of the pressure difference above and below the floating ball increased from 1.48% to 5.79% and then decreased to 0.4%. The floating ball would not be able to float up due to excessive outlet pressure above, which would cause the DN100 waterproof hammer air valve to leak water and fail to provide water hammer protection. When the inlet flow rate is 5 m/s, the velocity and pressure inside the valve body increase with time during the upward movement of the floating ball inside the waterproof hammer air valve and tend to stabilize at 400 ms. Through the generated pressure and velocity cloud maps, it can be observed that the location of maximum pressure is at the bottom of the buoy, directly below the floating ball, and at the narrow channels on both sides of the outflow domain. The location of the maximum velocity is at the small inlet of the bottom of the buoy. When the inlet speed of the valve is constant, a large amount of water flow is blocked by the floating ball, reducing the flow velocity and forming partial backflow below the floating ball, with an obvious vortex phenomenon. A small portion of the water flow passes through the air valve at a high velocity from both ends of the channel, and the water flow below the floating ball is in an extremely unstable state under the impact of high-speed water flow, resulting in a large gradient of water flow velocity passing through the valve. The research results not only help to improve the operational efficiency of water resource management systems but also reduce unnecessary water resource waste, thereby supporting the goal of sustainable water resource management.

1. Introduction

Water, energy, and food are the three major material foundations and strategic resources that human society relies on for survival and development. In the context of economic globalization, population growth and economic development are constantly expanding the global demand for water, energy, and food. Due to the fluidity and cyclicality of water resources, water continuously participates in a series of physical, chemical, and biological processes in the natural environment and flows widely through economic networks. Therefore, in the Water–Energy–Food linkage relationship, water resources are the core element, and their rational development and utilization play a crucial role in maintaining the healthy function of the natural water cycle, supporting sustainable economic and social development, and maintaining energy and food security. Pressure pipelines in irrigation areas are important infrastructure for ensuring food security, which not only meet the national food supply but also consume a large amount of water resources and energy. The implementation of water hammer safety protection decisions in irrigation pump station water delivery systems is an important guarantee measure for efficient water supply and increased grain production in irrigation areas. The schematic diagram of the water supply from the pumping station in the irrigation district is shown in Figure 1.

Water hammer is a hydraulic impact phenomenon that occurs in a pressure pipeline due to a rapid change in flow velocity causing momentum conversion, resulting in a series of sudden alternating pressure changes in the pipeline. The pump-stopping water hammer can cause excessive positive pressure of the water hammer, resulting in loud noise and strong vibration of the pipeline system, which may cause pipeline rupture. The negative pressure generated by the water hammer will cause the pipeline to sink and collapse, and the pressure at the local convex point of the pipeline will drop below the vaporization pressure, resulting in water column separation. When the positive pressure wave reflects back to that location, the water vapor in the air pocket condenses and the bubbles collapse, causing the separated water columns to collide with each other and form a bridging water hammer. The enormous pressure it generates may cause damage to water pump units, water pipelines, and valves, resulting in water supply interruption and significant economic losses [1]. Taking effective protective measures can suppress or eliminate negative pressure in pipelines and reduce positive pressure in pipelines. Common water hammer protection measures include air valves, air tanks, pressure regulating chambers, one-way pressure regulating towers, two-way pressure regulating towers, water hammer relief valves, hydraulic butterfly valves, etc. [2,3,4,5,6,7,8,9]. Different water hammer protection measures have their own advantages and disadvantages. In practical engineering, it is necessary to compare and analyze the water hammer protection effects of different water supply projects through numerical simulation calculations. Based on the calculation results and combined with the actual engineering situation, economical, reasonable, and effective water hammer protection measures should be selected. Compared with other protective equipment, air valves have the advantages of simple structure, low investment, convenient installation, and are not limited by geographical factors [10]. This has been widely applied in engineering practice.

Ensuring pressure stability in pipelines is a very important issue in complex pressurized water delivery systems with long distances and high flow rates. As a type of intake and exhaust equipment with suitable performance and simple structure, the air valve can discharge the accumulated air masses in the pipeline and provide supplementary air to maintain stable pipeline pressure, thereby achieving the effect of water hammer protection. The most commonly used one is the waterproof hammer air valve. Scholars at home and abroad have conducted extensive research on the control of transient pressure in air valves. Qiu et al. [11] discovered the fluctuation mechanism of pressure waves when water hammer occurs in the pipeline during pump shutdown by studying the problem of water hammer during pump shutdown. Zloczower [12] studied the characteristics of air valve intake and exhaust, as well as the control of airflow, and found its energy-saving and internal corrosion-delaying effects in water supply systems. Lee [13] and Stephenson [14] conducted a study on the reasonable selection of air valve size and installation location and found that unreasonable selection can lead to the inability to eliminate the water hammer and may cause secondary transients, increasing the transient positive pressure on the pipeline and unable to maintain stable pipeline pressure. McPherson [15] proposed that smaller air valves should be designed by reducing the volume of dissolved air in the water supply system during operation, by calculating the water body that releases 2% volume of air in the water supply pipeline at a certain pressure and temperature. Fuertes-Miquel [16] classified gases into two types: ideal gases and incompressible gases. Mathematical models were established for simulation under these two conditions, and experimental research was conducted on the water hammer pressure during the operation of air valves. The conclusion was drawn that the boundary conditions at lower pressures can be assumed to be incompressible gases, which provides new boundary conditions for establishing a mathematical model for water hammer resistance in air valves. Espert [17] studied the control of pipeline pressure by selecting different types of air valves, focusing on the control of peak water hammer pressure and the negative pressure caused by transient events. Through a combination of experiments and numerical simulations, it was concluded that using air valves with large inflow and small outflow has a better effect on controlling peak water hammer pressure and negative pressure. Coronado-Hernández et al. [18] conducted in-depth research on some problems that occur when there is no water in pipelines based on actual pipeline conditions. In addition, they analyzed the principle of water phase propagation through a rigid model and analyzed the cavitation effect using thermodynamic formulas. An experiment was designed for this model, and the proposed model was validated by measuring the absolute pressure of the airbag, water flow velocity, and the length of the emptying column in the experimental setup. The results indicate that the proposed model can accurately predict hydraulic characteristic variables.

The main parameters that affect the intake and exhaust performance of the waterproof hammer air valve during operation include the cross-sectional area of the intake and exhaust flow channels, the intake and exhaust flow coefficient, and the popping pressure of the buffer device in the waterproof hammer air valve. Reasonable design and parameter selection can ensure the efficient operation of air valves to the greatest extent possible. Scholars at home and abroad have conducted extensive theoretical and simulation research on these parameters, achieving certain results. Lee and Leow [19] proposed through research that the inlet and outlet characteristic parameters of air valves directly affect the accuracy of the water hammer calculation process and results. Lingireddy et al. [20] studied the effect of dual port air valves with large and small ports on pressure fluctuations in pipelines. The results showed that the inlet and outlet characteristics of air valves with different structures were different, directly affecting the water hammer protection effect. Small ports had a positive impact on pressure fluctuations inside the pipeline after exhaust. Martin and Lee [21] conducted an experimental study on the peak pressure of water column bridging after the air valve on the pipeline discharges air. The ratio of the orifice diameter to the pipeline diameter affects the magnitude of water hammer pressure. The experimental results showed that the maximum water hammer pressure value was achieved when the ratio was 0.14.

The flow changes of fluid in pressurized pipelines are a very complex process. At present, the computational analysis of complex flow problems is mostly based on computational fluid dynamics (CFD) prediction techniques, which simulate the flow conditions and predict performance through flow field analysis. The accuracy requirements of CFD technology are relatively low in order to make CFD prediction a reliable tool for valve design and guide equipment development [22]. Wu et al. [23] compared the relative dynamic behavior obtained from the joint simulation of MOC-CFD with the relative dynamic behavior calculated using MOC alone. The transient simulation results indicate that the MOC-CFD coupling analysis is closer to the real situation. García-Mares et al. [24] used CFD technology to numerically simulate air valves in water supply systems, analyzed the influence of turbulence models, and verified the numerical simulation results through experiments. Qu et al. [25] used CFD to numerically simulate liquid flow in pipelines and verified and calibrated the numerical simulation results and experimental results. Li et al. [26] conducted corresponding CFD numerical simulations based on the VOF model and studied the transient flow characteristics of trapped air in pipelines under different pump and valve operating conditions through experiments and numerical methods. The numerical simulation results were verified through experimental devices. Paternina-Verona et al. [27] used OpenFOAM v10 software to analyze the effect of different emptying operations with air inclusions in a single pipeline on negative pressure in water pipelines. The study found that in pipelines with air inlet holes, the percentage and frequency of opening the drainage valve are crucial for controlling negative pressure conditions. García-Todolí et al. [28] used CFD technology to characterize air valves and found that although CFD technology cannot completely replace measurement, it can significantly reduce experimental volume and total cost. Romero et al. [29] proposed a mathematical model to analyze the hydraulic transients generated in pipelines during the filling process of pressurized hydraulic systems. By comparing experimental measurements with model results, the effectiveness of air valves in avoiding excessive overpressure in large pipelines was verified. Hurtado-Misal et al. [30] used a two-dimensional computational fluid dynamics (2D CFD) model simulation with OpenFOAM software to evaluate the sensitivity of drainage valves to different openings and the variation of water column length during hydraulic phenomena.

In summary, researchers have conducted numerical simulations of various water hammer protection valves using CFD technology. However, current research on waterproof hammer air valves at home and abroad mostly focuses on the effect of air valve layout on water hammer elimination, and there is relatively little research on the structural characteristics and intake and exhaust effects of waterproof hammer air valves. As key components of the waterproof hammer air valve, the floating ball and throttle plug are prone to refusal during hydraulic transients, resulting in water leakage and affecting the water hammer protection effect of the entire pipeline. This article analyzes and studies the safe operation technology issues of waterproof hammer air valve leakage in water supply pumping stations. It not only makes up for the shortcomings of traditional waterproof hammer air valve design methods, providing theoretical support for the design, manufacturing, and selection of such valves in the future but also provides support for actively promoting sustainable water resource management. By reducing water resource waste, optimizing water resource allocation, improving energy utilization efficiency, and building a clean, low-carbon, safe, and efficient energy system, the energy needs of economic and social development can be met.

2. Structure and Working Principle of Waterproof Hammer Air Valve

2.1. Structure of Waterproof Hammer Air Valve

The waterproof hammer air valve is functionally equivalent to a combination of a high-speed intake and exhaust valve and a micro exhaust valve. It can not only exhaust gas to the outside under positive pressure conditions but also timely suck in gas to ensure pipeline safety under negative pressure conditions. Figure 2 is a schematic diagram of the structure of the waterproof hammer air valve studied in this article.

2.2. Working Principle of Waterproof Hammer Air Valve

This study takes the DN100 monolithic waterproof hammer air valve as the research object. The manufacturer of this equipment is Karon Eco-Valve Manufacturing Co., Ltd. in Shanghai, China. The valve body is not equipped with a pressure switch, and only the throttle plug is placed on the throttle plug pillar. Its structure is shown in Figure 3. The operation of the waterproof hammer air valve involves massive exhaust state, throttle exhaust state, micro exhaust state, and negative pressure intake state. Within the operating range of the throttling plug, the gas phase flow in the exhaust channel exhibits unstable flow, and complex motion occurs at the fluid–solid interface, involving fluid–solid coupling problems. Its dynamic behavior under different working states is as follows:

(1)

Massive exhaust state: When the water supply system is filled with water, the water pressure pushes the air to form a high-speed airflow. High-speed airflow enters the air valve through the inlet of the valve body and reaches the upper part of the valve body through the space between the air valve wall and the buoy. Finally, it is discharged into the atmosphere through the exhaust port and protective cover. Due to the presence of the buoy, the high-speed airflow is intercepted, preventing it from directly contacting the bottom of the floating ball and blowing it up. The buoy effectively protects against the phenomenon of floating ball blockage.

(2)

Throttle exhaust state: As the air in the pipeline continues to be discharged, the exhaust speed gradually increases. To prevent the occurrence of a secondary bridging water hammer in the pipeline due to excessive exhaust speed, the throttle plug will pop up, blocking a large number of exhaust ports and entering the micro exhaust state. In this state, the gas inside the pipeline is discharged outside the valve body through the trace exhaust hole on the throttle plug.

(3)

Micro exhaust state: When the water supply project enters the stable operation state, the entire water supply pipeline is filled with water, and the floating ball is lifted by the pressure of water, blocking the channel between the lower and upper chambers of the air valve. At this time, dissolved gases in the water still need to be discharged from the pipeline through the air valve, and the accumulated gases will accumulate in the upper part of the pipeline to form an airbag. When the pressure of the airbag is greater than the pressure of the water on the floating ball, the floating ball will briefly sink and discharge the gas in the airbag out of the pipeline. This cycle repeats to form the micro exhaust state of the air valve.

(4)

Negative pressure intake state: When the water supply system experiences negative pressure due to a power outage or other emergency conditions, the water level of the local high point waterproof hammer air valve will decrease. This will cause the external atmospheric pressure to be greater than the pressure inside the pipe, resulting in a negative pressure condition inside the pipe. At this point, the floating ball no longer receives pressure from the water and immediately sinks and opens up the air intake channel. The air valve will draw a large amount of air from the atmosphere into the water supply pipeline, and the waterproof hammer air valve will enter the state of mass intake.

3. Mathematical Model

3.1. Mathematical Model of Waterproof Hammer Air Valve

The intake and exhaust process of an air valve can be regarded as an isentropic process in which the nozzle flows through an ideal gas. The index of diatomic gas in the isentropic process n = 1.4. At the same time, the specific heat capacity of the ideal gas is constant, and the specific heat ratio k of the air diatomic molecule gas is 1.4. Therefore, the critical pressure ratio is as follows:

$${\displaystyle \frac{p_{cr}}{p}}={\left({\displaystyle \frac{2}{k+1}}\right)}^{{\displaystyle \frac{k}{k-1}}}=0.5283$$

(1)

The research object of this article is an integrated waterproof hammer air valve, where a large amount of exhaust and a small amount of exhaust are discharged from the valve body through the same outlet.

(1)

Under exhaust conditions:

The outlet pressure p₀ is atmospheric pressure, while the inlet pressure p is the gas pressure in the pipeline.

➀

When $0<{\displaystyle \frac{p}{p_0}}<1.8929$, the air flows out at subsonic speed, and at this time, the waterproof hammer air valve should be in a state of massive exhaust.

$$\stackrel{•}{m}=-C_{\mathit{out}}{A}_{\mathit{out}}\sqrt{2p{\rho }_0\left({\displaystyle \frac{k}{k-1}}\right)\left[{\left({\displaystyle \frac{p_0}{p}}\right)}^{{\displaystyle \frac{2}{k}}}-{\left({\displaystyle \frac{p_0}{p}}\right)}^{{\displaystyle \frac{k+1}{k}}}\right]}=-C_{\mathit{out}}{A}_{\mathit{out}}\sqrt{7p{\rho }_0\left[{\left({\displaystyle \frac{p_0}{p}}\right)}^{1.43}-{\left({\displaystyle \frac{p_0}{p}}\right)}^{1.71}\right]}$$

(2)

➁

When ${\displaystyle \frac{p}{p_0}}>1.8929$, the air flows out at supersonic speed, and at this time, the waterproof hammer air valve should be in the micro exhaust state.

$$\stackrel{•}{m}=-{C_{\mathit{out}}A}_{\mathit{out}}\sqrt{kp{\rho }_0{\left({\displaystyle \frac{2}{k+1}}\right)}^{{\displaystyle \frac{k+1}{k-1}}}}=-{C_{\mathit{out}}A}_{\mathit{out}}\sqrt{0.469p{\rho }_0}$$

(3)

(2)

Under suction conditions:

At this time, the waterproof hammer air valve is interchanged with the inlet and outlet ports under exhaust conditions, with the inlet pressure p₀ being atmospheric pressure and the outlet pressure p being the internal pressure of the valve.

➀

When $0.5283<{\displaystyle \frac{p}{p_0}}<1$, the air flows in at subsonic speed, and at this time, the waterproof hammer air valve should be in a large intake state.

$$\stackrel{•}{m}=C_{\mathit{in}}{A}_{\mathit{in}}\sqrt{2p_0{\rho }_0\left({\displaystyle \frac{k}{k-1}}\right)\left[{\left({\displaystyle \frac{p}{p_0}}\right)}^{{\displaystyle \frac{2}{k}}}-{\left({\displaystyle \frac{p}{p_0}}\right)}^{{\displaystyle \frac{k+1}{k}}}\right]}=C_{\mathit{in}}{A}_{\mathit{in}}\sqrt{7p_0{\rho }_0\left[{\left({\displaystyle \frac{p}{p_0}}\right)}^{1.43}-{\left({\displaystyle \frac{p}{p_0}}\right)}^{1.71}\right]}$$

(4)

➁

When ${\displaystyle \frac{p}{p_0}}\le 0.5283$, the air flows in at supersonic speeds, and air valves only operate under extreme conditions.

$$\stackrel{•}{m}=C_{\mathit{in}}{A}_{\mathit{in}}\sqrt{k{p}_0{\rho }_0{\left({\displaystyle \frac{2}{k+1}}\right)}^{{\displaystyle \frac{k+1}{k-1}}}}=C_{\mathit{in}}{A}_{\mathit{in}}\sqrt{0.469p_0{\rho }_0}$$

(5)

3.2. Realizable k − ε Turbulence Model

In numerical simulations, in order to make the flow more in line with the physical laws of turbulence, relevant studies [31,32] have linked the coefficient C_μ in the turbulence viscosity calculation formula to the strain rate and proposed the Realizable $k-\epsilon$ model.

The transportation equation for k is as follows:

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho k{u}_i\right)}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\right(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\left){\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k-\rho \epsilon$$

(6)

The transportation equation for $\epsilon$ is as follows:

$${\displaystyle \frac{\partial \left(\rho \epsilon \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho \epsilon u_i\right)}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\right(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\left){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+\rho C_{1}E\epsilon -\rho C_2{\displaystyle \frac{{\epsilon }^2}{k+\sqrt{v\epsilon }}}$$

(7)

In the three-dimensional numerical simulation of the waterproof hammer air valve, if the standard $k-\epsilon$ model is used for the turbulence model, the accuracy of the simulation results is limited. Here, the Realizable $k-\epsilon$ turbulence model is used for numerical simulation of the waterproof hammer air valve, providing technical support for the analysis of the hydraulic transition process of the pump station. A new turbulent viscosity formula is adopted in the Realizable $k-\epsilon$ model. The difference between the Realizable $k-\epsilon$ model and the standard $k-\epsilon$ model is that it introduces calculations related to rotation and curvature, and the Realizable $k-\epsilon$ model can effectively represent the energy conversion. The Realizable $k-\epsilon$ model satisfies the constraint conditions for Reynolds stress, thus maintaining consistency with real turbulence on Reynolds stress. This can simulate the diffusion velocity of planar and circular jets more accurately, and the calculation results are more in line with the real situation in problems such as rotational flow calculation, boundary layer calculation with directional pressure gradient, and separated flow calculation.

4. Numerical Simulation

4.1. Modeling

In this study, SolidWorks 2021 software was used to construct a geometric model of the air valve by modeling the sequence from the internal components to the external components. First, the key component floating ball is modeled, which consists of two steps. The first step was to establish a floating ball feature map, that is, a two-dimensional sketch of the semicircle upon which the feature rotates, divided into two semicircles to construct a hollow floating ball with an outer radius of 58 mm and a wall thickness of 2 mm. The second step was to rotate the semicircular structure and draw a hollow sphere. The same body can be formed using different configurations, such as a sphere resulting from both a stretched body and a rotating body. The material for the floating ball was chosen to be SUS316L, and its weight was 0.6646 kg. The geometric modeling of the floating ball is shown in Figure 4a. Then, a geometric model of the bonnet was constructed, following four steps: The first step was to model the hollow cylindrical part of the lower half of the bonnet using a two-dimensional sketch; the second step was to create a hollow cylinder via its rotation; the third step was to add a dome above the hollow cylinder; and the fourth step was to cut through the middle of the dome and to create a small exhaust hole. The geometric modeling of the bonnet is shown in Figure 4b. The material for the bonnet was chosen to be ultrahigh-molecular-weight polyethylene (UHMWPE), and its weight was 0.0033 kg. Finally, a geometric model of the buoy was constructed, divided into three steps: The first step was to create a two-dimensional sketch of the buoy; the second step was to turn it into a three-dimensional geometric buoy; and the third step was to perform orifice resection. Based on the air valve and observation of the physical model, four orifices were created on the upper part of the buoy and one orifice on the bottom of the buoy. The geometric modeling of the buoy is shown in Figure 4c. The orifice on the bottom of the buoy was circled in red in Figure 4c. The material for the buoy was chosen to be UHMWPE, which is the same as that for the bonnet, and the weight of the buoy was 0.5428 kg. The floating ball, bonnet, and buoy were combined, as shown in Figure 4d, and then, the valve body shell was constructed by continuing to use similar modeling methods. The diameter of the valve base was 220 mm. The final assembled three-dimensional geometric model of the air valve is shown in Figure 5, and the main geometric parameters of the waterproof hammer air valve are shown in

Table 1. The main geometric parameters of the waterproof hammer air valve.

Parameter Number	Parameter	Value
1	Jump spring	Φ6*35*90*11N
2	Throttle plug	100 mm
3	Inlet of buoy (single)	35 mm × 50 mm
4	Buoy wall thickness	2 mm
5	Floating ball outer radius	58 mm
6	Floating ball wall thickness	2 mm
7	Inner diameter of valve body inlet	100 mm
8	Flange connection plate aperture	Φ19 mm

.

The built geometric model was then imported into the SpaceClaim module of ANSYS 2021 R1 for fluid domain extraction. The flow channel through which the fluid passes from the inlet of the air valve to the point where the floating ball inside the valve reaches the vertex was selected as the calculation domain. Due to the presence of a buoy inside the air valve, the fluid domain established in this study was divided into an inner fluid domain and an outer fluid domain. The internal fluid domain refers to the part of the buoy that wraps around the floating ball, while the external fluid domain refers to the part where the fluid flows between the buoy and the outer wall of the valve. Excess component combinations were removed from the model in SolidWorks, and the model was simplified while retaining the fluid domain that needs to be calculated. The fluid domain is shown in Figure 6. Finally, the assembly in DesignModeler was opened; distinguished between the internal and external fluid domains as well as nested body domains; named them; and performed geometric preprocessing, including preparing the mapping surface settings.

4.2. Grid Partition

When using Fluent for fluid motion calculations, situations such as fluid motion inside the air valve, where a movable solid is added to the fluid, are common. In this case, the purpose is not simply to deal with the fluid motion but to calculate the interaction between the fluid and the solid. At this point, dynamic grid solutions such as laying, smoothing, and remeshing can be used. However, with the continuous development of ANSYS, a practical mesh function called overset mesh has emerged and can effectively handle motion problems in narrow spaces, and setting overset mesh is relatively convenient and simple compared to other dynamic mesh settings. Due to the narrow flow channel, high-speed water flow, and moving solid floating balls, the air valve perfectly meets the standard for using overset grids. Using overset grids can maintain a good mesh quality during the upward movement of the floating ball. Therefore, here, the overset grid scheme was used to simulate the motion of the floating ball inside the air valve.

An overset grid is composed of three parts: a background grid, a component grid, and overset boundaries. As shown in Figure 7, the background grid is the layer of the grid composed of identical small squares laid on the bottom layer, and the component grid is the radial part of the grid covering the circular ring on the background grid. The shape of the component mesh can be customized according to specific requirements and is not always circular. The background grid and component grid are two sets of grids, and both sets of grids need to be generated simultaneously when drawing the grid. Before importing them into Fluent for calculation, the overset grids need to be named; otherwise, Fluent cannot recognize the grids. The overset boundary is the boundary where the component mesh contacts the background mesh. The true boundary of the computational domain is the boundary of the moving object, which is represented by the small black circle in Figure 7.

The fluid domain was imported into ANSYS Meshing for meshing. The entrance, exit, inner and outer walls, as well as other small internal walls, were named, as was the cutting surface at the junction of two fluid domains, named the interior. In the air valve model, there are two fluid interfaces: one at the inlet of the bottom buoy and four at the inlet above the buoy. Then, the external fluid domain boundary conditions and the internal overset region boundary were named too. After the naming was completed, the model began to be meshed. First, a preliminary grid was generated and a coarse grid was drawn to check for any grid defects in the overall distribution. Then, the location of the maximum stress or maximum fluid flow was found, the correlation degree and correlation level were adjusted to perform an overall grid refinement, and the position was adjusted for changes to verify if the grid was suitable. The outer watershed cell size in this article was set to 10 mm, and then, the outer fluid domain was hidden. The internal volume was divided into grids, and the internal volume was used as the background grid to control the local grid of the internal volume. Because the internal fluid domain needs to be in contact with the floating ball, the grid needs to be finer to make the background grid more accurately connected to the overset grid so that more accurate calculations can be made. Therefore, the grid size was set to 4 mm.

Advanced size functions, including the boundary layer control functions and the curvature control functions, were set. The boundary layer control function is applicable to fluids, so here the number of element layers between the boundary layer and the edge is set to 5. Because the near-wall flow problem between the buoy and the ball inside the air valve, as well as the boundary between the buoy and the valve wall, is complex and where data transmission occurs, boundary control was used to ensure more accurate data transmission. The curvature control function is a function that controls the local encryption of circular arcs or defects. The layout of the internal boundary layer after cutting through the grid is shown in Figure 8.

During grid debugging, local size control required that the option to encrypt gaps be enabled, as narrow gaps in the positions were present inside the air valve. Therefore, encrypting the positions with gaps in the model was necessary. In this study, the internal flow of the air valve and the upward movement of the floating ball were assessed, setting the expansion layers in narrow areas where fluid flows were necessary to ensure a smooth flow in grid calculations. A diagram of the refined grid section after local grid control was set as shown in Figure 9. Finally, the output of the quality cloud map is shown in Figure 10. The interior of the air valve studied in this article was fluid, so the focus was on the degree of distortion. The average value should not exceed 0.5, and the maximum value should be below 0.96 before calculations can be carried out. The maximum distortion value of the grid in this article was 0.84944, and the average value was 0.19603, which met the requirements and could be solved and calculated. The orthogonal quality index takes 0.5 as a reference, and a value greater than 0.5 is sufficient. Because in this paper, the gas–liquid two-phase flow was studied in air valves, the fluid calculations generally required a reference to the orthogonal mass parameter.

Meshing was used to partition the mesh, and triangular and tetrahedral meshes were selected to perform non-structural mesh partitioning on the geometric models. Due to insufficient computer configurations and computing power, the mesh was converted into a polyhedral mesh. The initial number of grid nodes was 782,875, and the number of grids was 3,060,356. As the number of grids was relatively large, ordinary computers may not be able to meet the calculation requirements, so a grid transformation was needed. The advantage of polyhedral meshes over some tetrahedral meshes or mixed meshes is that the overall number is lower, and the shared faces of the partitioned hexahedral elements can be decomposed into multiple faces, becoming 12 or 16 faces to reduce the number of meshes. After grid conversion, the number of grids decreased to 821,396, as shown in Figure 11.

4.3. Grid Independence Verification

Grid independence verification refers to determining the uncorrelated relationship between the number of grids used in numerical calculations and the calculated results. The most suitable computational grid can ensure the minimum time, minimum computational workload, and optimal accuracy for numerical simulation calculations. To find the most suitable mesh density, the grids divided in Meshing are used for independence testing. The testing method is to continuously increase the mesh density, and after a certain simulated numerical calculation converges, there is no significant change with the increase in mesh density. It is considered that the mesh density at this time is the most suitable mesh. This study takes the inlet flow velocity of the waterproof hammer air valve at 10 m/s as the verification object for grid independence. By controlling the size of the internal fluid domain grid cells and changing the grid density, it is considered that the grid density is appropriate when the corresponding outlet gas average flow velocity no longer changes significantly with the grid density after convergence. The calculation results are shown in

Table 2. Grid independence verification calculation.

Grid Size (mm)	Number of Grids	Average Flow Velocity of Export Gas (m/s)
10	63,269	15.1603
9	86,102	15.5833
8	122,489	15.7932
7	180,896	15.5898
6	286,541	15.5789
5	495,747	15.4458
4	821,396	15.4296
3	2,277,533	15.4162

.

According to Table 2, for the fluid domain, as the grid size decreases from 10 mm to 8 mm, the outlet velocity increases from 15.1603 m/s to 15.7932 m/s, with a significant change in magnitude. When the grid size is reduced from 8 mm to 5 mm, the outlet flow velocity decreases from 15.7932 m/s to 15.4458 m/s. When the grid size is 4 mm and 3 mm, the change in outlet flow velocity is not significant, indicating that there is no correlation between the grid size and quantity and the calculated final average outlet gas velocity. In order to reduce the computational workload while ensuring sufficient accuracy of the calculation results, the mesh size for numerical simulation calculation was ultimately determined to be 4 mm.

4.4. Boundary Condition Setting

When the water pipeline operates normally, air is sucked in when the pressure inside the pipeline is lower than atmospheric pressure and air is discharged when the pressure inside the pipeline rises above atmospheric pressure. During the exhaust process, when the pipeline is filled with liquid, the valve can automatically close, preventing the liquid from leaking into the atmosphere. This process is known as suction and exhaustion. In this paper, the exhaust state is studied, which involves the flow of water in the pipeline. The air was present in front of the water, and when it reached the highest point or inflection point where the water flow needed to change directions, the air accumulated at the top and then continued to accumulate more. The air that precipitated from the water could not be eliminated in time and instead gathered at a high point in the pipeline, forming an air mass that reduced the efficiency of water delivery. In severe cases, it may cause water delivery interruptions, damage the pipeline, and even cause accidents. Therefore, the process by which a large amount of air is discharged from the valve and the water flow lifts the floating ball was simulated. The floating ball was pressed against the exhaust port to prevent water from escaping. When the floating ball blocked the exhaust ports, the next stage was the micro exhaust state. The gas–liquid two-phase flow filled the valve body, and the gas floated up, separated from the water body, and was discharged from the micro exhaust hole. The air in the pipeline was completely discharged, protecting the pipeline.

After opening Fluent, the grid was imported, the units were set, and the gravity was added; then, the divided grid file was imported. After reading the file, the grids were checked and displayed. Next, based on the model direction, gravity was added at 9.81 m/s² on the Z-axis. Then, a transient analysis was performed, and due to the large number of grids, ordinary computers may not be able to meet the computational requirements, so a grid transformation was also performed. Next, the materials were set to liquid water and air, the turbulence model was set to the Realizable $k-\epsilon$ model, and then the energy equation was activated. After activating the energy equation, the VOF multiphase flow model was activated and the implicit model was selected. Because the upward movement of the floating ball studied in this article is caused by the force exerted by the gas–liquid two-phase flow on the floating ball, the specific speed and acceleration of the floating ball inside the valve body were unknown, so the effect of the gas–liquid two-phase flow was used to determine its motion. Therefore, this is an implicit motion that requires the flow field to provide feedback parameters to the floating ball in order to determine its motion state. Afterwards, the overset grid was set and the corresponding command was entered to refresh the grid.

The inlet speed was entered, and the mixed inlet speed was checked in the Inlet option. According to the engineering data, the design flow rate of the water pump was 0.5 m³/s. The diameter of the water outlet pipe was 500 mm, and the calculated water flow velocity of the outlet pipe was about 2.55 m/s. The inlet velocity was set to four working conditions: 2 m/s, 3 m/s, 4 m/s, and 5 m/s. The default setting for the outlet was one atmosphere of pressure for the pressure outlet. Then, the overset grids were set up and the 6DoF model was selected. The internal floating ball is set to move along the Z-axis direction. The mass of the floating ball was set to 0.66 kg, and due to the limitations of the mechanical structure, the stroke height was also limited. Additionally, the stroke of the floating ball movement was set to 150 mm. The floating ball did not rotate, and the moment of inertia was not set. Then, the action grid area, including the overset areas and internal floating ball, was limited by six degrees of freedom. However, the balls move passively due to water flow impact, so when setting their movement, it is necessary to select Passive. The other settings remained at default, including the solver type and the selection of the SIMPLE solver. The settings were initialized; the time step was set to save the number of files and the time step; and then, grid calculations were performed. At the beginning of the comparison and after the trial calculation, the floating ball moved forward relative to its initial state. The small white cylindrical mesh surrounding the floating ball is the component mesh, and the internal fluid domain is the background mesh. The principle of this dynamic mesh scheme is that the component mesh wraps around the moving floating ball and moves forward, as shown in Figure 12.

5. Results and Discussion

5.1. Analysis of the Variation in Internal Flow Field with Time at a Constant Inlet Velocity

The fixed floating ball remains stationary at the lower limit position, and a gas–liquid two-phase flow with a certain flow rate is introduced from the valve inlet. The outlet condition is a pressure outlet, set to 101,325 Pa, and the velocity at the valve inlet is 5 m/s for calculation. The floating ball is set as a movable rigid body, and based on the mechanical structure limitation, the up-and-down motion stroke is 150 mm. The Fluent calculation type is changed to transient calculation, and the calculation time is initially set to 1 s with a time step of 0.001 s, and 1000 steps are calculated. The final pressure cloud map obtained is shown in Figure 13, the velocity cloud map is shown in Figure 14, and the streamline cloud map is shown in Figure 15. The transient simulation calculation data of floating ball motion is shown in

Table 3. Data sheet of transient simulation calculation of floating ball movement.

Transient Time /ms	Maximum Pressure Inside the Valve /Pa	Maximum Speed Inside the Valve /(m/s)
30	108,546	6.25
60	132,462	7.84
90	168,452	9.65
120	195,875	12.82
150	248,765	15.62
180	284,713	17.24
210	324,571	19.01
240	350,068	19.13
270	356,112	19.24
300	357,065	19.38
330	361,496	20.4
360	361,713	20.46
390	364,606	20.97
420	365,176	20.99
450	365,683	21.1
480	365,824	21.11
510	366,226	21.12
540	366,349	21.15
570	366,621	21.23
600	366,857	21.36
630	367,066	21.39
660	367,527	21.49
690	367,727	21.51
720	367,878	21.52
750	368,417	21.52
780	368,936	21.55
810	369,327	24.35
840	371,918	24.37
870	368,925	23.89
900	369,327	24.37

.

According to the data given in Table 3, a curve of the maximum pressure inside the air valve over time and the curve of the maximum velocity inside the air valve over time are drawn, as shown in Figure 16.

As shown in Figure 16, under the given operating conditions, the floating ball starts to move upwards under the action of gas–liquid two-phase flow. As time changes, the maximum pressure inside the valve body gradually increases and reaches stability at 400 ms. At the final moment, the maximum pressure inside the air valve is 369,327 Pa. From the pressure cloud map in Figure 13, it can be seen that the maximum pressure is located at the bottom of the buoy, directly below the floating ball, and at the narrow channels on both sides of the outflow domain. As time changes, the maximum velocity value inside the valve body gradually increases, with the growth rate first fast and then slow, reaching stability at 400 ms. At the final moment, the maximum velocity inside the air valve is 24.37 m/s. From the velocity cloud map in Figure 14, it can be seen that the position of the maximum velocity is at the small inlet at the bottom of the buoy. At 240 ms, the maximum pressure growth rate inside the valve is 222.5%, and at 240~900 ms, the maximum pressure growth rate inside the valve is 5.5%. The maximum velocity growth rate inside the valve is 206.1% at 240 ms, 9.6% at 240~400 ms, 2.7% at 400~780 ms, and 13.1% at 780~840 ms.

As shown in Figure 15, when the valve velocity inlet is constant, a large amount of water flow is blocked by the floating ball, reducing the flow velocity and forming partial backflow below the floating ball, with an obvious vortex phenomenon. A small portion of the water flows through the air valve at a high velocity from both ends of the flow channel. The water flow below the floating ball is in an extremely unstable state under the impact of high-speed water flow. The flow velocity gradient of the water passing through the valve is large, and the water flow also increases the impact on both ends of the buoy and the valve wall during the process of passing through the valve body. A large amount of water flow gathers at the inlet of the valve body to form a high-pressure zone. The inlet pressure of the valve body is relatively high, and the pressure drop distribution is obvious at the two ends of the outlet due to the fast flow velocity of the water flow and the low pressure.

5.2. Simulation of Internal Flow Field of Air Valve and Analysis of Floating Ball Force Under Different Inlet Flow Rates

This study takes a certain water supply pump station as an example. The pump station has a total of 4 units with a model number of 350DK175. Each unit has a design flow rate of 0.5 m³/s and a design head of 171 m. The water supply pipeline uses DN1200 mm steel pipes with a total length of 535.32 m. Selecting the operating condition of three water pumps running in parallel, with a pipeline flow rate of 1.5 m³/s and a pipeline cross-sectional area of 0.785 m², the average flow velocity inside the pipeline is 1.9 m/s. This is because the waterproof hammer air valve is installed above the pipeline, and the diameter of the waterproof hammer air valve is much smaller than that of the water supply pipeline. The gas–liquid two-phase flow entering the air valve from the pipeline enters the narrow pipeline through a wide pipeline, and the flow velocity will inevitably increase. Therefore, the inlet boundary flow velocity of the air valve must be greater than the pipeline flow velocity. The fixed floating ball remains stationary at the lower limit position. A certain flow velocity of gas–liquid two-phase flow is introduced from the valve inlet, and the outlet condition is a pressure outlet, set to 101,325 Pa. The inlet velocity of the valve is set to 5 m/s, 10 m/s, 15 m/s, 20 m/s, 25 m/s, 30 m/s, 35 m/s, 40 m/s, 45 m/s, and 50 m/s and calculations are performed.

The inlet velocity is controlled as a variable, simulated, calculated under 10 operating conditions, and analyzed and compared the changes in the pressure field and flow velocity field under different inlet velocities. Figure 17 shows the pressure cloud map inside the air valve at different inlet flow rates, and Figure 18 shows the flow velocity cloud map inside the air valve at different inlet flow rates.

As the inlet flow rate increases, the maximum pressure inside the air valve gradually increases, and the maximum flow rate inside is also positively correlated. The summary of the calculation results is shown in

Table 4. Summary table of simulation results under different entry velocities.

Inlet Velocity /(m/s)	Export Pressure /Pa	Maximum Pressure Inside the Air Valve /Pa	Maximum Pressure on the Upper Part of the Floating Ball /Pa	Maximum Impact Force at the Bottom of the Floating Ball /Pa	Maximum Speed Inside the Air Valve /(m/s)	Self-Weight of Floating Ball /N
5	101,325	369,327	267,598	368,122	24.37	6.468
10	101,325	1,122,300	1,100,000	1,179,658	39.05	6.468
15	101,325	2,318,471	2,300,000	2,307,589	56.49	6.468
20	101,325	3,783,295	3,700,000	3,712,589	77.32	6.468
25	101,325	5,754,936	5,700,000	5,715,698	193.30	6.468
30	101,325	8,068,909	8,000,000	8,026,879	110.95	6.468
35	101,325	4,100,263	4,059,756	4,000,453	126.02	6.468
40	101,325	13,827,330	13,758,963	13,005,643	156.65	6.468
45	101,325	16,406,650	16,394,565	16,078,563	178.93	6.468
50	101,325	20,153,000	20,136,587	20,056,746	202.62	6.468

. The relationship between inlet flow rate, maximum pressure, and maximum flow rate is shown in Figure 19.

As the inlet boundary velocity increases, the maximum pressure inside the air valve also increases. When the inlet velocity reaches 30 m/s, the maximum pressure inside the air valve suddenly decreases and continues to rise from 35 m/s. Therefore, there is a problem between 30 m/s and 40 m/s. As the inlet boundary velocity increases, the maximum velocity value inside the air valve also increases. When the inlet velocity reaches 20 m/s~30 m/s, the maximum velocity inside the air valve suddenly increases, and after 30 m/s, the velocity growth returns to the previous growth state.

By fitting the pressure values above and below the floating ball in Table 4, the trend chart of the changes is shown in Figure 20.

As shown in Figure 20, when the speed is below 35 m/s, the difference between the pressure above and below the floating ball is very small. From Table 4, it can be seen that the upper pressure is lower than the lower pressure, the floating ball can move normally, and the air valve operates normally. When the inlet flow rate is between 35 m/s and 50 m/s, it can be clearly seen that the pressure above the floating ball is greater than the pressure below, with a growth rate increasing from 1.48% to 5.79%, and then decreasing to 0.4%. At this time, the floating ball cannot float up normally to block the exhaust port due to the resistance of the upper pressure to the lower impact force, resulting in water leakage from the air valve. When the inlet flow rate reaches 35 m/s, a high-pressure zone appears above the floating ball inside the air valve in its initial state, as shown in Figure 21.

At this point, there is a pressure confrontation between the upper and lower parts of the floating ball, which prevents the floating ball from rising further to block the exhaust hole, resulting in water leakage from the air valve. As the inlet flow rate continues to increase, when it reaches 50 m/s, the force that impacts the floating ball becomes greater, and the floating ball speed becomes faster, quickly occupying the upper position of the air valve chamber, and the high-pressure zone disappears, as shown in Figure 22.

At this point, the high-pressure zone in the upper part disappears, and the pressure at the bottom of the floating ball is greater than that at the upper part. The floating ball can float up normally, thereby blocking the exhaust port of the air valve and performing a small amount of exhaust. The air valve can work normally.

6. Conclusions

This article takes the DN100 waterproof hammer air valve as the research object and analyzes and studies the safety operation technology problems of water leakage of the waterproof hammer air valve in the water supply pump station. Using SolidWorks software for geometric modeling of the air valve, numerical simulation of the micro exhaust state of the air valve was carried out through ANSYS finite element analysis software. The pressure field inside the air valve was analyzed at different flow rates, and a reasonable flow rate range for the normal operation of the waterproof hammer air valve was proposed. The main conclusions are as follows:

(1)

The reason for the water leakage of the waterproof hammer air valve in water supply engineering is that in actual engineering operation, the water flow velocity is often too high, causing rapid flow inside the valve body. Water containing trace gases quickly gathers above the floating ball, easily forming small vortices, resulting in excessive pressure on the floating ball, which cannot float normally and cannot block the exhaust hole. This can lead to water leakage, waste of water resources, and even endanger the safety of the water supply system.

(2)

Based on the finite volume method, nested grids were set up for numerical simulation and solution. It was found that the velocity and pressure of the floating ball inside the waterproof hammer air valve during the upward movement of the floating ball at each moment increased with time when the inlet flow velocity was 5 m/s and tended to stabilize at 400 ms. Through the generated pressure and velocity cloud maps, it can be found that the maximum pressure position is at the bottom of the float and directly below the float, as well as at the narrow channels on both sides of the outflow domain. The maximum velocity position is at the small inlet of the bottom of the float. At 240 ms, the maximum pressure growth rate inside the valve is 222.5%, and at 240~900 ms, the maximum pressure growth rate inside the valve is 5.5%. The maximum velocity growth rate inside the valve is 206.1% at 240 ms, 9.6% at 240~400 ms, 2.7% at 400~780 ms, and 13.1% at 780~840 ms.

(3)

By controlling different inlet flow rates, the internal pressure field of the air valve and the pressure values above and below the floating ball are obtained. The final pressure situation inside the air valve at different flow rates is analyzed to find that the flow rate range where the floating ball can float normally is below 35 m/s and above 50 m/s. When the inlet flow rate is between 35 m/s and 50 m/s, the floating ball will be unable to float due to excessive pressure above, resulting in water leakage and leakage of the DN100 waterproof hammer air valve, which cannot protect the pipeline. This is the innovation of this article.

In summary, the DN100 waterproof hammer air valve was taken as the research object, and the safety operation technology problem of water leakage of the waterproof hammer air valve was studied. The changes in the pressure field and velocity field inside the valve under different working conditions were compared and analyzed. In addition, there are some issues that can be further studied. This study only analyzed the waterproof hammer air valve theoretically using Fluent software, lacking experimental verification. Further in-depth analysis can be conducted through a combination of experiments and theory. This study is of great significance for water hammer protection in pressurized pipeline water supply in irrigation areas, which can ensure the safe, stable, and efficient operation of the system, thereby reducing equipment damage and maintenance costs, reducing water resource waste, and providing technical support for high and abundant grain production, promoting the sustainable use and management of Water–Energy–Food. In addition, conducting an ecological impact assessment during the optimization of the waterproof hammer air valve can help identify potential environmental impacts and make design decisions that are more in line with sustainable needs.