Abstract

Storm geysers increasingly occur in sewer systems under climate change and rapid urbanization. Mitigation measures are in great demand to avoid safety problems. In this study, three-dimensional computational fluid dynamics models of single-inlet and multi-inlet systems were established to investigate geysering induced by rapid filling and assess the effectiveness of potential mitigation methods. The modeling results suggest that increasing the capacity of the downstream pipe before the inflow front reaches the chamber can effectively reduce the maximum geyser pressure. The peak pressure can be significantly mitigated when the chamber size is designed with care and the drop height between the upstream and downstream pipes is reduced. A diversion deflector with air vents and an orifice plate at the riser top end can alleviate the maximum pressure by about 65% with about 75% of the entrapped air being released. The peak pressure during the geyser event in the multi-inlet model is less than that of a single-inlet model under the same total inflow condition, but more water can be released.

HIGHLIGHTS

  • A small drop height between the connecting pipes can effectively reduce the maximum pressure during rapid filling.

  • Mitigation measures including flow deflectors and orifice plates were studied to alleviate geyser intensity.

  • Intermittent air–water jets can be generated much more easily in a system with multiple inlets, and the peak pressure is generally small but more water can be released.

INTRODUCTION

Storm geyser events, where air–water mixtures eject from manholes, have been reported worldwide, in particular in the last 30 years as a result of urbanization and climate change (Guo & Song 1991; Wright et al. 2011; Vasconcelos et al. 2015; Bashiri-Atrabi et al. 2016). Pressure transients over the geysering can lead to unexpected damages to the pipeline system (Zhou et al. 2002) and safety problems for the public (Wright et al. 2011). A significant amount of work has been done in the field to address such problems and the rapid filling is found to be one of the main causes, which often results in transitions from free surface flow to surcharge flow, inertial surges, and air entrapment (Vasconcelos & Wright 2009; Wright et al. 2009; Zhou et al. 2011; Muller et al. 2017). Unfortunately, it is almost impossible to avoid rapid filling in urban sewer systems during intense rain events.

A number of geyser events have been reported in a manhole in Edmonton, Alberta, Canada since the sewer system was constructed in 2012 (Liu et al. 2020). Many mitigation measures have been examined, including using a properly designed orifice plate (Huang et al. 2018) and adding a water circulation chamber (Qian et al. 2020). However, despite the existing studies on geyser mitigation, such as Wright et al. (2011), Lewis (2011), and Wang & Vasconcelos (2017), almost no success in engineering practice has been reported. In fact, mitigation measures proposed in earlier studies often come at the cost of introducing other issues, such as inadequate removal of entrapped air. Thus, further study is needed to find effective methods.

The geyser mechanism in a single-inlet system has been extensively studied, while the geyser mechanism in a multi-inlet system has yet to be discovered. One mechanism of geysers in single-inlet systems is the release of trapped air pockets (Vasconcelos & Wright 2011; Cong et al. 2017; Muller et al. 2017; Leon et al. 2019). During flow transition from free surface flow to pressurized flow, the air pockets are entrapped and compressed at locations such as dropshafts and manholes (Vasconcelos & Wright 2011), and then moved downstream under the interaction of water and air (Wright et al. 2008). Factors that affect air pockets entrapment include the water depth in the pipe (Vasconcelos & Wright 2006, 2009), the filling ratio, and ventilation parameters (Huang et al. 2018). The shape parameters, such as the pipe diameter, the pipe diameter/length ratio (Hatcher & Vasconcelos 2017) and the configuration of the shaft (Cong et al. 2017; Muller et al. 2017), can also affect the geyser pressure. Based on the field data (Wright et al. 2009) and computational fluid dynamics (CFD) simulations (Muller et al. 2017), the geyser process in a prototype has been analyzed, and it is believed that the trapping of air pockets is an important part of the geyser process. These studies reveal in detail the geyser mechanism in a single-inlet system, but there is still a knowledge gap in the entrapment of air pockets and the influence of the inflow on the geyser in the multi-inlet system.

The present study is intended to assess chamber size, drop height, and multi-inlet on the geyser intensity, by using a CFD model based on the experimental model established by Liu et al. (2020). The CFD model is first validated by comparing with measured data in Liu et al. (2020) and then used as a tool to explore the geyser formation and mitigation measures, including diversion deflectors with or without air vents and orifice plates. Detailed analysis of the pressure and velocity patterns under various conditions is presented, and discussion on the influence of chamber design and multi-inlet on the geyser follows.

METHODS

ANSYS CFX was used to study the influence of chamber design and multi-inlet on geysers for the system in Edmonton where geysers were reported (Liu et al. 2020). The geometry model is shown in Figure 1(a), consisting of one or two upstream pipes, drop chamber, vertical riser, and downstream pipe. The two upstream pipes have an identical size, of which the length Lu = 5.80 m, diameter Du = 0.20 m, and slope Su = 0.01. The downstream pipe is horizontal, with a length Ld = 5.95 m and diameter Dd = 0.28 m. They are connected by a drop chamber, the size of which is 0.30 m × 0.30 m × 0.45 m (length × width × height). A riser of length Lr = 1.22 m and diameter Dr = 0.06 m is located above the drop chamber. The shear stress transfer k-ω turbulence model and the volume of fluid method (Hirt & Nichols 1981) are used to simulate the air–water flow in the pipe systems, where air is considered ideal gas and water incompressible. For numerical modeling, the single-inlet model includes only pipe 1, and the multi-inlet model has two upstream pipes, pipes 1 and 2.

Figure 1

Numerical model: (a) schematic diagram (not scaled); (b) deflector and orifice plate.

Figure 1

Numerical model: (a) schematic diagram (not scaled); (b) deflector and orifice plate.

The simulation cases of the single-inlet model are listed in Table 1, including cases A, B, and C, while those of the multi-inlet model are described in Table 2 (cases D and E). For convenience, two monitoring points, P1 and P2, are placed at the bottom of the chamber and the middle of the downstream pipe, respectively, as shown in Figure 1(a). The initial pressure at P1 and the initial water velocity at P2 of modeling cases are given. The single-inlet model is used to study the influence of chamber design on geysers. Case A was mainly intended to assess the influence of chamber heights on geyser intensity. The chamber heights in cases A0–A3 are 0.40 m, 0.45 m, 0.50 m, and 0.55 m, respectively. For case B, the influence of the drop height (defined as the elevation difference between upstream and downstream pipes) was examined. The downstream pipe diameter is set as 0.20 m, and the drop heights are 0.05 m, 0.10 m, 0.15 m, 0.20 m, and 0.25 m in cases B1–B5, respectively. Cases C1–C6 were modeled to evaluate the mitigation effects of deflectors with different cross-sectional angles, air vents, and orifice plates. The central angles of the tested deflectors in C1–C3 are θ = 90°, 120°, and 180°, respectively, as shown in Figure 1(b). Note that for these simulations, the flow at the inlet was increased rapidly (within 0.1 s), and the flow rate change is shown in Table 1.

Table 1

Simulated cases with single-inlet model

Case No.Initial pressure at P1 (kPa)Initial water velocity at P2 (m/s)Initial flow (L/s)Terminal flow (L/s)Note
A0 3.1 0.35 20 80 hL = 0.40 m 
A1 3.0 0.33 hL = 0.45 m 
A2 3.0 0.35 hL = 0.50 m 
A3 3.0 0.34 hL = 0.55 m 
B1 2.7 0.60 20 80 Δdh = 5 cm Dd = 20 cm 
B2 2.7 0.72 Δdh = 10 cm 
B3 2.8 0.70 Δdh = 15 cm 
B4 1.8 0.72 Δdh = 20 cm 
B5 1.9 0.74 Δdh = 25 cm 
C1 2.8 0.35 20 80 θ = 90° 
C2 2.7 0.33 θ = 120° 
C3 2.8 0.35 θ = 180° 
C4 2.7 0.35 Ah = 75.0 cm2, Do = 6 cm 
C5 2.8 0.36 Ah = 75.0 cm2, Do = 4 cm 
C6 2.8 0.35 Ah = 75.0 cm2, Do = 2 cm 
Case No.Initial pressure at P1 (kPa)Initial water velocity at P2 (m/s)Initial flow (L/s)Terminal flow (L/s)Note
A0 3.1 0.35 20 80 hL = 0.40 m 
A1 3.0 0.33 hL = 0.45 m 
A2 3.0 0.35 hL = 0.50 m 
A3 3.0 0.34 hL = 0.55 m 
B1 2.7 0.60 20 80 Δdh = 5 cm Dd = 20 cm 
B2 2.7 0.72 Δdh = 10 cm 
B3 2.8 0.70 Δdh = 15 cm 
B4 1.8 0.72 Δdh = 20 cm 
B5 1.9 0.74 Δdh = 25 cm 
C1 2.8 0.35 20 80 θ = 90° 
C2 2.7 0.33 θ = 120° 
C3 2.8 0.35 θ = 180° 
C4 2.7 0.35 Ah = 75.0 cm2, Do = 6 cm 
C5 2.8 0.36 Ah = 75.0 cm2, Do = 4 cm 
C6 2.8 0.35 Ah = 75.0 cm2, Do = 2 cm 

hL, chamber height; Δdh, flow drop height from upstream pipe to downstream pipe; θ, central angle of tested deflector; Ah, opening area on the deflector; Do, diameter of the orifice plate in the riser outlet; Dd, diameter of downstream pipe.

Table 2

Simulated cases with multi-inlet model

Case No.Initial pressure at P1 (kPa)Initial water velocity at P2 (m/s)Initial flow in Inlet 1 (L/s)Terminal flow in Inlet 1 (L/s)Initial flow in Inlet 2 (L/s)Terminal flow in Inlet 2 (L/s)Note
D1 2.9 0.35 20 80  
D2 3.2 0.33 10 40 10 40  
D3 2.9 0.35 20 80 80  
E1 3.2 0.33 10 50 10 50 Δt = 0.0 s 
E2 10 50 10 50 Δt = 2.0 s 
E3 10 50 10 50 Δt = 5.0 s 
E4 10 50 10 50 Δt = 10.0 s 
Case No.Initial pressure at P1 (kPa)Initial water velocity at P2 (m/s)Initial flow in Inlet 1 (L/s)Terminal flow in Inlet 1 (L/s)Initial flow in Inlet 2 (L/s)Terminal flow in Inlet 2 (L/s)Note
D1 2.9 0.35 20 80  
D2 3.2 0.33 10 40 10 40  
D3 2.9 0.35 20 80 80  
E1 3.2 0.33 10 50 10 50 Δt = 0.0 s 
E2 10 50 10 50 Δt = 2.0 s 
E3 10 50 10 50 Δt = 5.0 s 
E4 10 50 10 50 Δt = 10.0 s 

The multi-inlet model mainly focuses on the pressure variation over the geyser process and the mechanism for continuous ejections of the air–water mixture. Case D studied the characteristics of geysering under various inflow conditions. In case D1, the inflow at inlet 1 increased rapidly from 20 L/s to 80 L/s, and inlet 2 was blocked. In case D2, the inflow at inlet 1 and 2 both rapidly increased from 10 L/s to 40 L/s, and the inflow change for the system was identical to case D1. In case D3, the inflow of pipe 1 increased rapidly from 20 L/s to 80 L/s, and in the meantime pipe 2 from 0 L/s to 80 L/s. The effect of time lag for flow rate change of the two pipes was explored in cases E, and the time interval in cases E1–E4 were 0 s, 2 s, 5 s, and 10 s, respectively.

The mesh independence test for different mesh resolution and sensitivity analysis on the time step was conducted. The pressure at the bottom of the chamber (P1) was selected as an indicator. The mesh numbers of the CFD model were about 1.45, 1.62, 1.82, 2.02, and 2.25 million. The simulated results of the pressure at P1 are shown in Figure 2(a). When the mesh number is 2.02 million, the maximum pressure at P1 is 32.7 kPa, close to the experimental results (Liu et al. 2020); when the mesh number is 2.25 million, the maximum pressure at P1 is 33.5 kPa. The maximum pressure difference between the two mesh numbers is about 1.5%. Further increasing the number of mesh does not significantly improve the numerical results. Therefore, the mesh with 2.02 million elements was adopted.

Figure 2

Model verification: (a) mesh independence analysis; (b) time step sensitivity analysis; (c) pressure validation.

Figure 2

Model verification: (a) mesh independence analysis; (b) time step sensitivity analysis; (c) pressure validation.

Sensitivity tests were performed for time steps of 0.0005 s, 0.001 s, 0.005 s, and 0.01 s, and the results are shown in Figure 2(b). It can be seen that the maximum pressures at P1 are 33.4 kPa, 32.7 kPa, 31.7 kPa, and 30.8 kPa, respectively, and the maximum pressure difference between 0.0005 s and 0.001 s is about 2.1%, which indicates that further reducing the time step does not improve the modeling accuracy. Thus, the time step of 0.001 s was used for all the cases under study. Figure 2(c) shows the comparison between the numerical and experimental results of the pressure at the bottom of the chamber. The numerical results of pressure change are in good agreement with the experimental data. The pressure at P1 reaches the maximum value of 32.7 kPa at t = 2.03 s, close to the experimental data of 32.8 kPa, indicating that the numerical model is capable of predicting pressure transients induced by rapid filling.

RESULTS AND DISCUSSION

Influence of chamber design on geysering

At the initial stage of modeling, the flow in the upstream pipe had a free surface, and full pipe flow appeared downstream of the chamber. As the rapid filling began, the waterfront propagated along the pipe and pushed out air. The front curved back after hitting the downstream wall of the chamber and resulted in filling of the chamber and choking of the airflow through the riser. The entrapped air was continuously compressed until the pressure could push out the air–water mixture within the riser, generating a geyser. During the process, pressure oscillations were observed, and the flow achieved another steady state after the expulsion of air.

The pressure and velocity patterns for cases A0–A3 are presented in Figure 3. As the chamber height increases, the maximum pressure generated during the geyser event decreases. Compared with case A1, the chamber height in case A0 was decreased by 5 cm, and the maximum pressure was increased by 37.0% as the space for water and air interactions decreased; the chamber height in case A2 was increased by 5 cm, and the maximum pressure was reduced by 38.5%. However, further increasing the chamber height seems to have limited effect, as the comparison between A2 and A3 indicates. Three stages for the velocity change in the downstream pipe can be seen in Figure 3(b). At the first stage, the downstream pipe's water velocity increased slowly before the inflow front reached the chamber. The second stage started as the chamber was filled with the incoming water. Water velocity in the downstream pipe increased due to the pressure head buildup. Oscillations might occur during the air–water mixture being released through the riser at the third stage. If the chamber has a proper size, the acceleration process of water in the downstream pipe is oscillation-free, as shown in Figure 3(b). A chamber with appropriate size can provide sufficient space for air–water interactions so that the flow velocity in the third stage becomes oscillation-free, thereby reducing the maximum pressure. The reduced maximum pressure, in turn, slows down the acceleration of water in the downstream pipe. Further increase in the chamber space improves little the flow in the third stage, and only a slight difference in peak pressure between the cases A2 and A3 can be seen.

Figure 3

Influence of chamber height: (a) pressure at P1; (b) water velocity at P2.

Figure 3

Influence of chamber height: (a) pressure at P1; (b) water velocity at P2.

The drop height, defined as the invert elevation difference between the upstream and downstream pipes, has a remarkable effect on the chamber's flow regime, as illustrated in Figure 4(a). The different drop heights of the upstream and downstream pipelines lead to different water levels in the chamber. In the initial state, the flow in the upstream pipe of cases B1 and B2 was pressurized flow, and an air pocket was trapped upstream. As the elevation of the upstream pipe increased, the flows in the upstream pipe of cases B3–B5 were free surface.

Figure 4

Influence of drop height: (a) initial water volume fraction; (b) pressure at P1; (c) water velocity at P2.

Figure 4

Influence of drop height: (a) initial water volume fraction; (b) pressure at P1; (c) water velocity at P2.

Pressure variations at the bottom of the chamber and water velocity changes in the downstream pipe are shown in Figure 4(b) and 4(c). The initial water depths of the chamber in cases B1 and B2 were similar. In cases B1 and B2, the increased inflow compressed the air pocket trapped in the upstream pipe, causing the air pressure to rise. The pressure in the chamber increased correspondingly, which accelerated the water in the downstream pipe. Therefore, the increase in chamber pressure of the cases B1 and B2 caused the capacity of the downstream pipe to increase in the first stage. In case B1, the smooth flow transition due to the small difference between upstream and downstream pipe levels led to larger downstream velocity. As a result, the maximum pressure generated during the air–water interactions in the second stage was smaller.

In the initial states of cases B3–B5, free surface flow existed in the upstream pipe. The initially rapid filling did not change the pressure in the chamber and the water velocity in the downstream pipe. The downstream flow required a greater driving force to reach the same capacity as in case B1. More intensive pressure transients were generated during the interactions between water and air in the chamber at the second stage. In cases B4 and B5, the water flowed into the downstream pipe after falling in the chamber in the initial state. The rapid increase in inflow caused more air to enter the downstream pipeline. Therefore, although there was a large velocity oscillation in the third stage, the maximum pressure was lower than that of case B3.

From the above analysis, the drop height influences the magnitude of pressure transients during the geyser event. When it is small, the water level in the chamber after filling can be higher than the crown of the upstream pipe, causing air to be trapped in the form of an air pocket. The rapidly increasing inflow compresses the air pocket, which increases the pressure in the chamber and thereby improves the capacity of the downstream pipe. As a consequence, the peak pressure is reduced.

Influence of flow deflector inside the chamber on geysering

Different mitigation measures are evaluated in cases C1 to C6, where flow deflectors with different cross-sectional angle are analyzed. Initially, the deflector and the water in the chamber formed a sealed space connecting the upstream pipe and downstream pipe, and the air was trapped. Figure 5(a) shows the water volume fraction change in the chamber of case C3. With the rapid increase of inflow, the upstream pipe's air pocket was compressed and directed into the downstream pipe by the deflector (t = 1.00–1.63 s). The inflow front reached the drop chamber at about t = 1.63 s. A certain amount of water flowed over the deflector and filled the chamber. Over the filling process, water could enter the riser and might spill out. Figure 5(b) compares the pressures at P1 with deflectors of different angles (case A1 is original, without a deflector). The maximum pressures at P1 for cases A1, C1, C2, and C3 are 32.7 kPa, 27.8 kPa, 23.8 kPa, and 16.9 kPa, respectively, indicating that the relief effect on geyser pressure is more significant as the center angle of the deflector increases. Figure 5(c) shows the water velocity in the downstream pipe during the geysering. For case C3, as the inflow increased, the air was pushed into the downstream pipe, increasing the water velocity in the downstream pipe in the first stage. The larger flow rate implies that the downstream pipe has a greater capacity, which can be related to the reduction of the maximum pressure.

Figure 5

Influence of the deflector: (a) water volume fraction in case C3 (center profile); (b) pressure at P1; (c) water velocity at P2.

Figure 5

Influence of the deflector: (a) water volume fraction in case C3 (center profile); (b) pressure at P1; (c) water velocity at P2.

Although the deflector can reduce the maximum geyser pressure, it directs air from the upstream pipe into the downstream pipe, increasing the risk of geysering in downstream shafts. An air opening in the deflector and reducing the riser outlet area can result in air being stored in the chamber's upper space. Thus, it should be a better way to release as much air as possible, over the rapidly filling process. In cases C4–C6, opening areas of 75 cm2 were tested on the deflector, and plates with different orifice diameter at the riser outlet were placed to study the effect of the combined measure on geysers. The orifice plate diameters in cases C4, C5, and C6 are 6 cm, 4 cm, and 2 cm, respectively.

Figure 6(a) shows the pressure change under three cases (C4–C6). When the riser top was not restricted (case C4), the pressure at the chamber bottom and the water velocity change in the downstream pipe were the same as other cases, which could also be divided into three stages. When the orifice plate's diameter in the riser outlet was 2 cm (case C6), the smaller riser outlet limited the air release rate. During the rapid increase of inflow, the air stored in pipes and the chamber was compressed. As a result, the pressure at P1 rose in the first stage. The water velocity in the downstream pipe was also increasing rapidly, as shown in Figure 6(b). At t = 2.75 s, the water velocity at P2 increased rapidly again due to the inflow front's arrival. When the orifice plate's diameter in the riser outlet was 4 cm (case C5), the pressure at P1 did not increase rapidly with the increase in inflow. The water flowed into the downstream pipe under the deflector's action, increasing water velocity in the downstream pipe. At t = 2.4 s, there was a small peak in the pressure and a corresponding increase in the water velocity. During this process, the maximum geyser pressure was approximately 11.5 kPa, with only a small portion of the water flowing out of the riser. The water velocity in the downstream pipe did not increase sharply in the second stage. In the initial state of case C5, the volume of the entrapped air in the upstream pipe is around 115 L. The air released through the riser during the transient is about 87 L, which accounts for approximately 75% of the total volume.

Figure 6

Influence of the combined mitigation measures: (a) pressure at P1; (b) water velocity at P2.

Figure 6

Influence of the combined mitigation measures: (a) pressure at P1; (b) water velocity at P2.

Influence of multi-inlet on geysering

Cases D were modeled in order to study the mechanism of geysering in a system with two inlet pipes. Figure 7(a) shows the water volume fraction variation in the chamber for case D2. In the initial state, the water flow regime in the two pipes is free surface flow. Then the inflow simultaneously increased from the initial 10 L/s to 40 L/s. The inflow front in two pipes reached the chamber at about t = 2.8 s and then began to fill the chamber. At about t = 3.0 s, the water flow entered the riser and trapped the air in the chamber and upstream pipes. The air was then compressed and released through the riser. As air escaped, the water flowed towards the base of the riser and choked the airflow. Then the residual air was trapped again and the cycle repeated until the air was expelled completely, generating a series of geysers.

Figure 7

Parameter changes in multi-inlet model: (a) water volume fraction change (case D2); (b) pressure at P1 (cases D1–D3); (c) water flow rate of riser (cases A1 and D2).

Figure 7

Parameter changes in multi-inlet model: (a) water volume fraction change (case D2); (b) pressure at P1 (cases D1–D3); (c) water flow rate of riser (cases A1 and D2).

Figure 7(b) shows the pressure variation at P1 under three cases and compares them with the single-inlet model. For a system with two inlets, when the inflow in pipe 1 increased rapidly and there was no inflow in pipe 2 (case D1), pipe 2 operated as a storage space, storing the rapid inflow in pipe 1 and reducing the maximum pressure. When the inflow in the two pipes was changed at the same rate from 10 L/s to 40 L/s (case D2), the water velocity when the inflow front reached the chamber was less than that of a single-pipe system under the same total flow conditions (case A1), and the geysering pressure of 16.8 kPa also was smaller. With the same total flow in all three cases (cases A1, D1 and D2), the maximum pressure for the two-inlet system is less. In case D3, when the inflow change in pipe 1 was the same as that in the single-pipe system (case A1) but with additional inflow change in pipe 2, the maximum pressure in case D3 was 57.4 kPa, greater than the maximum pressure of 32.7 kPa in case A1.

Figure 7(c) shows the amount of water overflowing the riser in cases A1 and D2, in which the inflow was rapidly increased from the initial 20 L/s to the terminal 80 L/s. In case A1, the maximum flow rate of the riser outflow was 1.6 L/s, and the total outflow volume 0.48 L; in case D2, the maximum flow rate of the riser outflow was 6.6 L/s, and the total flow volume 2.2 L. The results suggest that a system with two inlet pipes results in more overspilling and a slightly smaller pressure than a single inlet pipe model.

In multi-inlet systems, the time for the filling front of each inlet to reach the chamber can be different. Cases E were simulated under the conditions that the lag time Δt for the increase in inflow was in a range from 0 to 10 s. When Δt in the two inlets is 0 s, 2 s, 5 s, and 10 s, the maximum geyser pressures generated during geysering are 22.6 kPa, 17.3 kPa, 22.1 kPa, and 17.3 kPa, respectively, as shown in Figure 8(a). In case E3 (i.e., Δt = 5 s), before the inflow change in pipe 2, the surge front from pipe 1 entered the chamber and then was discharged by the riser, resulting in small pressure fluctuations. The inflow in pipe 2 reached the chamber at approximately t = 7.5 s, when the water in the chamber sealed the end of pipe 2. Therefore, the inflow surge in pipe 2 would impact the water in the chamber, thereby generating the maximum geyser pressure in this case. For case E4 (i.e., Δt = 10 s), the chamber's water reached the top of pipe 2 when the inflow in pipe 2 started to increase. The air trapped in pipe 2 was driven by the flow from the chamber into the riser and discharged so that no significant pressure was generated.

Figure 8

Simulations under different time lags of the inflow increase: (a) pressure at P1; (b) water flow rate of the riser.

Figure 8

Simulations under different time lags of the inflow increase: (a) pressure at P1; (b) water flow rate of the riser.

The amount of overspilling water for cases E1–E4 is shown in Figure 8(b). The maximum flow rates of the riser outflow in the four cases were 14.9 L/s, 9.8 L/s, 8.9 L/s, and 5.2 L/s, and the total outflow volumes were 5.5 L, 4.4 L, 4.4 L, and 4.1 L, respectively. As the second pipe's inflow increased, the compressed air carried more water when discharged from the riser. As the modeling results indicate, only under the condition of a large volume of air being trapped in the pipe system can intermittent air–water jets (like geysers in the real world) occur. Compared to systems with only one inlet, multi-inlet systems are more susceptible to air entrapment and geysering.

CONCLUSIONS

In this paper, three-dimensional CFD models with single-inlet and multi-inlet were established to study factors affecting geyser generation and mitigations. The single-inlet model is used to analyze the effect of chamber design on geysers, and the multi-inlet model mainly studies the effect of multiple inlets on geysers. The main conclusions are as follows.

  • 1.

    Increasing the flow velocity in the downstream pipe before the inflow front reaches the drop chamber can significantly reduce the geyser pressure. A small drop between the upstream and downstream pipelines causes the air pocket to be trapped in the upstream pipeline, effectively reducing the maximum pressure during rapid filling.

  • 2.

    A deflector connecting the upstream and downstream pipes can reduce the maximum pressure in the geyser process, but it directs more air into the downstream pipe, increasing the risk of geysering for downstream risers. Combining a deflector with air vents and an orifice plate at the riser top can reduce the maximum geyser pressure by 65%.

  • 3.

    The time lag for inflow change in a multi-inlet system leads to significant air entrapment. The intermittent release of compressed air, accompanied by overshooting water and/or air–water mixture, can be observed. During such a geyser event in the two-inlet system, the peak pressure is lower and the released water volume through the riser is larger than the system with only one inlet.

The main findings in the present study allow us to better understand the mechanism of geysering and its coping strategies. However, the mitigation measures in real-world systems still need further investigation. The presented CFD simulation is based on a scaled physical model, and further study of geyser events in the prototype system is necessary.

ACKNOWLEDGEMENTS

The authors gratefully appreciate the financial support from the Natural Science Foundation of Ningbo (No. 202003N4132), the National Natural Science Foundation of China (No. 51809240), the Key Research and Development Program of Zhejiang Province (No. 2020C03082), and the Fundamental Research Funds for the Provincial Universities of Zhejiang (No. SJLZ2021004).

DATA AVAILABILITY STATEMENT

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

REFERENCES

REFERENCES
Bashiri-Atrabi
H.
Hosoda
T.
Shirai
H.
2016
Propagation of an air–water interface from pressurized to free-surface flow in a circular pipe
.
Journal of Hydraulic Engineering
142
(
12
),
04016055
.
Cong
J.
Chan
S. N.
Lee
J. H.
2017
Geyser formation by release of entrapped air from horizontal pipe into vertical shaft
.
Journal of Hydraulic Engineering
143
(
9
),
04017039
.
Guo
Q.
Song
C. C.
1991
Dropshaft hydrodynamics under transient conditions
.
Journal of Hydraulic Engineering
117
(
8
),
1042
1055
.
Hatcher
T. M.
Vasconcelos
J. G.
2017
Peak pressure surges and pressure damping following sudden air pocket compression
.
Journal of Hydraulic Engineering
143
(
4
),
04016094
.
Hirt
C. W.
Nichols
B. D.
1981
Volume of fluid (VOF) method for the dynamics of free boundaries
.
Journal of Computational Physics
39
(
1
),
201
225
.
Huang
B.
Wu
S.
Zhu
D. Z.
Schulz
H. E.
2018
Experimental study of geysers through a vent pipe connected to flowing sewers
.
Water Science and Technology
2017
(
1
),
66
76
.
Leon
A. S.
Elayeb
I. S.
Tang
Y.
2019
An experimental study on violent geysers in vertical pipes
.
Journal of Hydraulic Research
57
(
3
),
283
294
.
Lewis
J. W.
2011
A Physical Investigation of Air/Water Interactions Leading to Geyser Events in Rapid Filling Pipelines
.
PhD Thesis
,
University of Michigan
,
Michigan
,
USA
.
Liu
L.
Shao
W.
Zhu
D. Z.
2020
Experimental study on stormwater geyser in vertical shaft above junction chamber
.
Journal of Hydraulic Engineering
146
(
2
),
04019055
.
Muller
K. Z.
Wang
J.
Vasconcelos
J. G.
2017
Water displacement in shafts and geysering created by uncontrolled air pocket releases
.
Journal of Hydraulic Engineering
143
(
10
),
04017043
.
Qian
Y.
Zhu
D. Z.
Liu
L.
Shao
W.
Edwini-Bonsu
S.
Zhou
F.
2020
Numerical and experimental study on mitigation of storm geysers in Edmonton, Alberta, Canada
.
Journal of Hydraulic Engineering
146
(
3
),
04019069
.
Vasconcelos
J. G.
Wright
S. J.
2006
Mechanisms for air pocket entrapment in stormwater storage tunnels
. In
World Environmental and Water Resource Congress 2006: Examining the Confluence of Environmental and Water Concerns
, pp.
1
10
.
Vasconcelos
J. G.
Wright
S. J.
2009
Investigation of rapid filling of poorly ventilated stormwater storage tunnels
.
Journal of Hydraulic Research
47
(
5
),
547
558
.
Vasconcelos
J. G.
Wright
S. J.
2011
Geysering generated by large air pockets released through water-filled ventilation shafts
.
Journal of Hydraulic Engineering
137
(
5
),
543
555
.
Vasconcelos
J. G.
Klaver
P. R.
Lautenbach
D. J.
2015
Flow regime transition simulation incorporating entrapped air pocket effects
.
Urban Water Journal
12
(
6
),
488
501
.
Wang
J.
Vasconcelos
J. G.
2017
Preliminary assessment of a retrofit strategy in dropshafts impacted by geysering using CFD
. In
World Environmental and Water Resources Congress 2017
, pp.
230
239
.
Wright
S. J.
Vasconcelos
J. G.
Creech
C. T.
Lewis
J. W.
2008
Flow regime transition mechanisms in rapidly filling stormwater storage tunnels
.
Environmental Fluid Mechanics
8
(
5–6
),
605
616
.
Wright
S. J.
Vasconcelos
J.
Lewis
J.
Creech
C. T.
2009
Flow regime transition and air entrapment in combined sewer storage tunnels
.
Journal of Water Management Modeling. R
235
(
15
),
237
256
.
Wright
S. J.
Lewis
J. W.
Vasconcelos
J. G.
2011
Physical processes resulting in geysers in rapidly filling storm-water tunnels
.
Journal of Irrigation and Drainage Engineering
137
(
3
),
199
202
.
Zhou
F.
Hicks
F. E.
Steffler
P. M.
2002
Transient flow in a rapidly filling horizontal pipe containing trapped air
.
Journal of Hydraulic Engineering
128
(
6
),
625
634
.
Zhou
L.
Liu
D.
Karney
B.
Zhang
Q.
2011
Influence of entrapped air pockets on hydraulic transients in water pipelines
.
Journal of Hydraulic Engineering
137
(
12
),
1686
1692
.
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