Study on the factors influencing air valve protection against water hammer with column separation and rejoinder

A water hammer is a phenomenon of unsteady flow caused by sudden changes in the velocity in a water transmission pipeline from inappropriate valve opening and closing procedures or the sudden starting and shutting down of a pump. This phenomenon leads to a series of positive and negative water hammer pressures in the water transmission system. In particular, a water hammer with column separation and rejoinder in the pipeline can lead to destructive water pressures, which seriously threaten the safe and efficient operation of the water transmission system (Ramos & De Almeida 2002; Bergant et al. 2006; Duan et al. 2020). Studies have shown that a high positive water hammer pressure can cause excessive noise, pipeline fatigue or rupture, and even valve failure. Similarly, a high negative water hammer pressure may cause pipeline collapse, leakage, service outages, and pipeline pollution (Pozos-Estrada 2017; Triki & Chaker 2019). Therefore, controlling the water hammer pressure in the water transmission system has been the main focus of hydraulic system designers and pipeline administrators. To prevent the occurrence of a water hammer with column separation and rejoinder, a water supplement system or air supply and pressure stabilizing equipment, such as one-way surge tanks (Moghaddas et al. 2017; Wan & Zhang 2018), an air tank (Besharat et al. 2016a, 2016b), and air valves (Zhuqing et al. 2011; Tasca et al. 2021) is typically used. In particular, air valves have the advantages of a simple structure, low cost, convenient installation, and large-scale air discharge and inflow during water filling and drainage in the pipeline. Thus, they have been widely applied in various water transmission systems (Phu 2017; Coronado et al. 2019, 2020).

Air valves have been widely used in different water transmission systems to improve the safety and efficiency of the operation of water transmission projects (Ramezani et al. 2015; Tijsseling et al. 2015; Wang et al. 2017). However, because of the improper selection and use of air valves, their actual benefits are not ideal. Accidents frequently occur due to insufficient air discharge, leakage, and pipeline explosion, which can lead to enormous economic and social losses (Fuertes-Miquel et al. 2019a, 2019b). Selecting an air valve involves three main factors, namely the type of air valve, the inlet and outlet orifice diameters, and the inflow and outflow discharge coefficients.

There are the following three primary types of air valves: (1) high-pressure micro-release valves or micro-hole release valves (e.g., US Air Release Valves, European Air Venting Valves), (2) low-pressure high-speed intake/release valves or large-hole intake/exhaust valves (e.g., US Air/Vacuum Valves, European Air Release/Intake Valves), and (3) the combination air valves (AWWA 2001; AWWA C512 2008). Balutto (1996) pointed out that traditional powerless air valves suffer from a poor sealing performance at low pressures, deformation of the float, blockage, and a limited orifice size. In contrast, powered air valves can cause sudden pressure changes during high-speed discharge, damaging the float and resulting in leakage. In addition, the seal might malfunction from pressure fluctuations. Related studies (Wu et al. 2015) have shown that lightweight free-float air valves have a low starting pressure and a poor release performance. Lever air valves have a low discharge speed and a small discharge capacity, which is not suitable for large pipeline networks. In comparison, composite air valves can achieve microlevel air release and are suitable for large air releases during repair. To reduce the water hammer pressure caused by high-speed air release, engineers and manufacturers have designed various types of air valves, such as two-stage or three-stage anti-slam air valves that are based on the ‘blowing and blocking’ effect of airflow, which ensures that the outflow area of the air valve is gradually reduced, and the pressure difference is kept in a reasonable range. The transient high pressure generated during air release is thus avoided.

The inlet and outlet orifice sizes of an air valve are the main factors affecting the water hammer pressure in the transient process caused by air release. Zhou et al. (2002a, 2002b, 2004) systematically tested how release vents with different orifice sizes lead to secondary transients. They divided the pressure oscillation during the release process into three types according to the relative orifice size (orifice diameter/pipe diameter = 0–0.566). (1) Small orifices (⁠ < 0.086) are affected by the buffer function of the air cushion and show a long period of pressure oscillation and small water hammer. The maximum pressure is 1.5–3 times the acting head. (2) With medium orifices (0.086 < < 0.2), pressure oscillation occurs in two stages, including a long period of pressure oscillation at the beginning of release and water hammering, such that water flow impacts the end of the pipeline after air release. The transient pressure increases as the orifice size increases, with the maximum pressure reaching 15 times the acting head. (3) For large orifices (⁠ > 0.2), after air is rapidly released, the buffer function of the air cushion disappears. Specifically, during the water hammering process, the maximum surge pressure decreases the orifice size. De Martino et al. (2008) tested the relative release vent size = 0.023–0.042. The result was similar to that of Zhou et al. (2002b), and the maximum transient pressure was 2.7 times the acting head (⁠ = 0.042). For comparison, they also installed a single-chamber release valve at the end of the pipeline. The water hammering pressure oscillation has been shown to be affected by the remaining air in the air valve chamber and to have a longer period of oscillation and a lower pressure peak than the release at the orifice. The maximum transient pressure is 2.5 times the acting head. A formula for calculating the duration of the long period of pressure oscillation and the maximum transient pressure has been developed. Researchers have shown that cavitation can severely increase the maximum peak pressure during fluid transients – enough to cause pipe damage. A small cavitation volume causes a larger transient pressure (Pozos-Estrada et al. 2012). In contrast, a greater cavitation volume can act as an air cushion to absorb the transient pressure (Thorley 2004).

The air valve inflow and outflow discharge coefficients, as characteristic air valve parameters, represent the air flow capacity of the air valve. Generally, the flow coefficients in the inflow and outflow stages are different, and the inflow coefficient is greater than the outflow discharge coefficient. According to American Water Works Association (AWWA) M57 (John 2011), the outflow discharge coefficient should be determined based on published standards. However, the value for each type of air valve is uncertain. To improve the numerical simulation results, Lucca et al. (2010) pointed out that the characteristic curve of the air valve must be tested and compared with that provided by the manufacturer. Therefore, studying the flow coefficients of the air valve is necessary. Lee (1999) used a physical experiment to show that a large inflow coefficient can effectively prevent a negative pressure in the pipeline. However, when the outflow discharge coefficient is also large, the fast air release can lead to a destructive water hammer with column separation and rejoinder.

In summary, the protection effect of an air valve against water hammer is mainly affected by factors such as the air valve type, the inlet and outlet orifice diameters, and the inflow and outflow discharge coefficients. An inappropriate air valve size can cause or aggravate the hydraulic transient process in the pipeline, especially during the discharge process. A large discharge velocity is likely to cause the cutoff water flow to collide at a similar flow rate, producing a severe water hammer with column separation and rejoinder. Therefore, selecting air valves with appropriate parameters to effectively suppress the negative pressure in the water transmission system and reduce the water hammer pressure is an urgent problem faced by designers and pipeline managers. In this study, numerical simulation is used to study the influences of the air valve type, the inlet and outlet orifice diameters, and the inflow and outflow discharge coefficients on protection against water hammers with column separation and rejoinder in an attempt to provide a theoretical reference for the selection of air valves for pressurized pipelines.

The intake and exhaust processes of an air valve are very complex. Wylie & Streeter (1993) and Chaudhry (2014) developed a detailed mathematical model of an air valve. This model is based on the following four basic assumptions. (1) Air enters and leaves the pipe through the valve under isentropic flow conditions. (2) The air mass within the pipe follows the isothermal law because the air mass in the pipeline is usually very small, whereas the area of the pipe and the surface area of the liquid are large. The large heat capacity causes the temperature of the gas to approach that of the liquid. (3) The air admitted to the pipe stays near the air valve so that it can be released through the air valve. (4) The elevation of the liquid level in the pipeline remains substantially constant, as the volume of air is much smaller than the liquid volume in the pipeline.

The mass flow rate of air passing through the air valve depends on the atmospheric absolute pressure and absolute temperature outside the pipe, as well as the absolute pressure and temperature within the pipe. Four conditions are possible (Wylie & Streeter 1993):

As shown in Figure 5, closing the valve at the end of the pipeline for 10 s causes a large transient pressure head of 26.10 m. Without an air valve, the reflected wave of positive pressure gives rise to a large negative pressure head of −16.84 m (theoretical calculated value, cavitation is not considered). Thus, the water column separates to produce a large secondary transient pressure head of 20.99 m.

Without the installation of an air valve at the highest point of the pipeline, there is severe negative pressure and the occurrence of a water hammer with column separation and rejoinder, causing a large water hammer pressure. Therefore, an air valve must be installed in the water transmission pipeline to suppress negative pressure.

Figures 6,⁷–8 show that for a traditional air valve, the minimum pressure head H_min at section i increases as the orifice diameter increases because a larger diameter enables a larger air mass flow M_air for the traditional air valve. Hence, a larger volume of air V_air enters the pipeline. Notably, a positive value of mass flow means air inflow, and a negative value indicates air release. Thus, the larger the diameter of the air valve is, the more significant the result of negative pressure suppression is. In contrast, a smaller diameter causes a smaller air mass flow and a smaller maximum air volume entering the pipeline V_max. Therefore, air cannot enter in a timely manner, and the effect of negative pressure suppression is not obvious. When the air in the pipeline is discharged through the traditional air valve, the water hammer pressure head H_max occurs with column separation and rejoinder. The water hammer pressure head first decreases and then increases with the air valve diameter because the small diameter air valve (d = 5 mm) has a small accumulative air volume, and the ‘air pocket’ at the highest point of the pipeline is small (V_max = 0.032 m³), which is not effective in reducing the water hammer pressure. Thus, the water hammer pressure head with column separation and rejoinder is large, H_max = 22.86 m. For the large diameter valve (d = 30 mm), the air intake volume is large. Although the air pocket at the highest point is also large (V_max = 0.124 m³), the large outlet orifice diameter enables high-speed air release (M_min = −0.082 kg/s), and the air pocket is rapidly released such that it is no longer able to buffer the occurrence of a water hammer, causing a large water hammer pressure head with column separation and rejoinder H_max = 18.63 m. The air pocket plays a certain role in delaying the occurrence of the water hammer with column separation and rejoinder. The larger the air pocket is, the longer the delay T_c is. Table 1 shows the results of traditional air valves with different inlet and outlet orifice diameters.

To study how different inflow and outflow discharge coefficients influence the transient control effect of a traditional air valve, inflow and outflow discharge coefficients of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 are used to numerically simulate the transient control effect of a traditional air valve. The minimum pressure head H_min of section i is −0.21 m when the inflow discharge coefficient of the air valve is 1.0 and −4.8 m when the inflow discharge coefficient of the air valve is 0.1. Given a reduction in the inflow discharge coefficient, the minimum pressure head of section i decreases. When the inflow discharge coefficient is a constant, a variation in the outflow discharge coefficient does not change the minimum pressure head. The results of water hammer pressure head H_max with column separation and rejoinder under different inflow and outflow discharge coefficients are shown in Table 2. According to Table 2, the water hammer pressure head of section i with column separation and rejoinder is mainly affected by the outflow discharge coefficient. When the inflow discharge coefficient is a constant, the water hammer pressure head with column separation and rejoinder decreases with a reduction in the outflow discharge coefficient.

Table 2

Changes in the water hammer pressure head with column separation and rejoinder with different inflow and outflow discharge coefficients (m)

.	Inflow discharge coefficient, .
	1 .	0.9 .	0.8 .	0.7 .	0.6 .	0.5 .	0.4 .	0.3 .	0.2 .	0.1 .
1.0	20.73	20.73	20.73	20.73	20.73	20.73	20.79	20.8	17.28	16.59
0.9	20.69	20.59	20.59	20.59	20.59	20.59	20.65	20.65	17.21	16.54
0.8	20.62	20.42	20.42	20.42	20.42	20.41	20.46	20.45	17.11	16.48
0.7	20.43	20.19	20.18	20.18	20.17	20.16	20.21	20.17	16.98	16.39
0.6	20.04	19.85	19.85	19.84	19.83	19.8	19.75	19.68	16.79	16.26
0.5	19.45	19.34	19.33	19.31	19.28	19.22	19.12	18.96	16.49	16.03
0.4	18.65	18.63	18.61	18.57	18.52	18.43	18.24	17.89	15.94	15.51
0.3	16.18	16.58	17.61	17.55	17.45	17.28	16.94	16.19	15.06	14.68
0.2	14.38	14.25	14.04	13.75	13.32	15.67	15.07	13.7	13.65	13.21
0.1	8.72	8.66	8.84	9.78	11.08	10.53	9.31	8.15	9.18	11.17

.	Inflow discharge coefficient, .
	1 .	0.9 .	0.8 .	0.7 .	0.6 .	0.5 .	0.4 .	0.3 .	0.2 .	0.1 .
1.0	20.73	20.73	20.73	20.73	20.73	20.73	20.79	20.8	17.28	16.59
0.9	20.69	20.59	20.59	20.59	20.59	20.59	20.65	20.65	17.21	16.54
0.8	20.62	20.42	20.42	20.42	20.42	20.41	20.46	20.45	17.11	16.48
0.7	20.43	20.19	20.18	20.18	20.17	20.16	20.21	20.17	16.98	16.39
0.6	20.04	19.85	19.85	19.84	19.83	19.8	19.75	19.68	16.79	16.26
0.5	19.45	19.34	19.33	19.31	19.28	19.22	19.12	18.96	16.49	16.03
0.4	18.65	18.63	18.61	18.57	18.52	18.43	18.24	17.89	15.94	15.51
0.3	16.18	16.58	17.61	17.55	17.45	17.28	16.94	16.19	15.06	14.68
0.2	14.38	14.25	14.04	13.75	13.32	15.67	15.07	13.7	13.65	13.21
0.1	8.72	8.66	8.84	9.78	11.08	10.53	9.31	8.15	9.18	11.17

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When a traditional air valve is installed at the highest point of the pipeline, with the same inlet and outlet orifice diameters, the larger its diameter is, the larger the air mass flow entering the pipeline is, allowing timely supply and suppression of the negative pressure. However, when the diameter is too large, the large volume air pocket is quickly discharged and is unable to buffer the occurrence of a water hammer, causing a large water hammer pressure head. In contrast, the smaller the orifice diameter is, the smaller the air mass flow is, causing insufficient air supply and an inadequate negative pressure suppression effect. Moreover, the small orifice diameter leads to a small air pocket at the highest point of the pipeline, which is unable to effectively buffer the water hammer with column separation and rejoinder, causing a large pressure head. In addition, the inflow and outflow discharge coefficients also play an important role in the protection against a water hammer with column separation and rejoinder for traditional air valves. Therefore, the traditional air valve cannot effectively protect against the water hammer phenomenon in the water transmission pipeline.

Figures 9,¹⁰–11 show that for the anti-slam air valve, the minimum pressure head at section i is H_min = −0.77 m and does not change with the orifice area ratio ε because the air valve inlet area is large and remains constant, causing a significant air mass flow. Notably, a positive mass flow value indicates air inflow, and a negative value indicates air release. Thus, the accumulated air volume is large, allowing for sufficient supply and thus suppressing negative pressures. The water hammer pressure head H_max increases with the orifice area ratio because the inlet diameter of the anti-slam air valve is constant, and the outlet orifice area increases with the orifice area ratio. As the outlet orifice area increases, the air mass flow also increases. Thus, the air pocket is rapidly released such that it is no longer able to buffer the occurrence of a water hammer with column separation and rejoinder. In contrast, the smaller the outlet orifice area is, the smaller the air mass flow during air release is. Thus, the large volume air pocket is slowly released, effectively avoiding the occurrence of a water hammer with column separation and rejoinder. In addition, the slow release of the air pocket plays a role in delaying the occurrence of a water hammer with column separation and rejoinder. The smaller the outlet orifice area is, the longer the delay T_c is. Table 3 shows the results of anti-slam air valves with different orifice area ratios.

To study how different inflow and outflow discharge coefficients influence the transient control effect of an anti-slam air valve, inflow and outflow discharge coefficients of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 are used to numerically simulate the transient control effect of an anti-slam air valve with a hole area ratio ε = 0.1. The minimum pressure head H_min of section i is −0.21 m when the inflow discharge coefficient of the air valve is 1.0 and −4.8 m when the inflow discharge coefficient of the air valve is 0.1. The minimum pressure head of section i decreases as the inflow discharge coefficient decreases but shows no sign of change as the outflow discharge coefficient varies. The results of water hammer pressure head from column separation and rejoinder under different inflow and outflow discharge coefficients are shown in Table 4. According to Table 4, the water hammer pressure head of section i from column separation and rejoinder is mainly affected by the outflow discharge coefficient. When the inflow discharge coefficient is constant, the water hammer pressure head from column separation and rejoinder decreases as the outflow discharge coefficient decreases.

Table 4

Changes in the water hammer pressure head from column separation and rejoinder with different inflow and outflow discharge coefficients (m)

.	Inflow discharge coefficient, .
	1 .	0.9 .	0.8 .	0.7 .	0.6 .	0.5 .	0.4 .	0.3 .	0.2 .	0.1 .
1.0	8.72	8.66	8.84	9.78	11.08	10.53	9.31	8.15	8.88	11.17
0.9	8.49	8.46	8.38	8.31	8.13	8.50	9.12	7.85	8.56	10.35
0.8	7.96	7.96	8.00	7.77	8.00	7.84	7.60	7.48	8.23	7.97
0.7	5.59	5.61	7.95	7.73	7.42	6.97	7.64	7.04	7.54	7.62
0.6	5.58	5.60	5.63	5.67	5.88	5.78	7.12	5.38	6.92	7.03
0.5	5.57	5.59	5.61	5.64	5.67	5.70	5.65	5.24	6.43	7.12
0.4	5.57	5.58	5.60	5.62	5.63	5.63	5.53	5.44	5.96	7.20
0.3	5.58	5.58	5.59	5.60	5.61	5.58	5.44	5.63	5.82	7.30
0.2	5.59	5.60	5.60	5.60	5.59	5.55	5.38	5.74	5.68	7.42
0.1	5.62	5.62	5.62	5.62	5.60	5.54	5.35	5.82	5.54	7.56

.	Inflow discharge coefficient, .
	1 .	0.9 .	0.8 .	0.7 .	0.6 .	0.5 .	0.4 .	0.3 .	0.2 .	0.1 .
1.0	8.72	8.66	8.84	9.78	11.08	10.53	9.31	8.15	8.88	11.17
0.9	8.49	8.46	8.38	8.31	8.13	8.50	9.12	7.85	8.56	10.35
0.8	7.96	7.96	8.00	7.77	8.00	7.84	7.60	7.48	8.23	7.97
0.7	5.59	5.61	7.95	7.73	7.42	6.97	7.64	7.04	7.54	7.62
0.6	5.58	5.60	5.63	5.67	5.88	5.78	7.12	5.38	6.92	7.03
0.5	5.57	5.59	5.61	5.64	5.67	5.70	5.65	5.24	6.43	7.12
0.4	5.57	5.58	5.60	5.62	5.63	5.63	5.53	5.44	5.96	7.20
0.3	5.58	5.58	5.59	5.60	5.61	5.58	5.44	5.63	5.82	7.30
0.2	5.59	5.60	5.60	5.60	5.59	5.55	5.38	5.74	5.68	7.42
0.1	5.62	5.62	5.62	5.62	5.60	5.54	5.35	5.82	5.54	7.56

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When the anti-slam valve is installed at the highest point of the pipeline (the inlet and outlet orifice areas are different), the inlet orifice area is relatively large and remains constant, and the air mass flow is large. Thus, the air supply is sufficient to suppress the negative pressure in the pipeline. The water hammer pressure head H_max with column separation and rejoinder increases with the orifice area ratio ε. The larger the outlet orifice area is, the higher the air mass flow is, and the quicker the air pocket is discharged, causing an increase in the pressure head. In addition, the inflow and outflow discharge coefficients also play an important role in protecting against water hammers with column separation and rejoinder. Therefore, selecting the appropriate inlet and outlet orifices of the anti-slam air valve can effectively protect against water hammers in water transmission pipelines.

The transient flow theory and the characteristic method are used to numerically simulate a gravity flow water delivery system in MATLAB 2014 to study the influences of the air valve inlet and outlet orifice diameters and the inflow and outflow discharge coefficients on preventing water hammers.

Without the installation of an air valve at the highest point of the pipeline, there is a severe negative pressure and the occurrence of water hammer with column separation and rejoinder, causing large water hammer pressure.

The traditional air valve with the same inlet and outlet orifice area cannot meet the requirements of rapid large air intake and slow air exhaust. Therefore, this will not achieve simultaneously the purpose of suppressing negative pressure and preventing water hammer with column separation and rejoinder. The inlet/outlet orifice area and the inflow/outflow discharge coefficients play an important role in the protection against water hammer with column separation and rejoinder for traditional air valves. The anti-slam valve with the different inlet and outlet orifice areas can meet the requirements of rapid large air intake and slow air exhaust. Therefore, this will achieve simultaneously the purpose of suppressing negative pressure and preventing water hammer with column separation and rejoinder. The inlet/outlet orifice area and the orifice area ratio ε play an important role in the protection against water hammer with column separation and rejoinder, and the inflow and outflow coefficients have a limited effect on preventing water hammers with column separation and rejoinder for anti-slam air valves.

In practical engineering applications, the anti-slam valve with a large inlet orifice area and a small outlet orifice area (the orifice area ratio ε = 0.05) should be selected as important equipment for long-distance pressurized pipelines to solve air storage and air supply problems. The inflow and outflow discharge coefficients should have a weaker influence on water hammer with column separation and rejoinder.

The results show that the inflow and outflow coefficients of anti-slam air valves have a limited effect on preventing water hammers. Therefore, the inlet and outlet orifice diameters of anti-slam air valves have a significant impact on preventing water hammers, so the suitable sized air valve anti-slam air valves can be used as a solution to the problem of gas storage and air supply in long-distance pressurized water transmission pipelines and are important equipment to prevent water hammers with column separation and rejoinder. However, the results of this study need to be corroborated by laboratory experiments and field applications, which will be done in future research.

This work was financially supported by the Natural Science Foundation of Shaanxi Provincial Department of Education (Grant No. 19JS046) and the Natural Science Foundation of Shaanxi Province (Grant No. 2021JQ-479).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.