Study on Explosion Venting Characteristics of L-Type Venting Duct

Abstract

The failure state of the natural gas pipelines in underground space may cause explosions, and an explosion flow field is affected by the structure of the venting duct. Based on FLACS software v9.0, the influence of the explosion vent and venting duct on temperature and pressure fields is studied. The results show that when the area of the explosion vent increases from 0 to 100 cm², the peak overpressure decreases by half, and the overpressure drops to zero within 0.3 s. For different L-type venting ducts, when the structural coefficient is less than 5, the peak overpressures and pressure variations are similar. When the structural coefficient is equal to 5, the peak overpressure significantly decreases, and the time to reach the peak value is extended by 50%. From the perspective of achieving a safe and efficient venting effect, the optimal structural coefficient is 5 for the L-type venting duct.

1. Introduction

With the rapid development of the social economics, people’s desire to live a green and safe life becomes stronger and stronger. More and more basic gas construction projects in China have been invested in and planned [1,2,3]. At the same time, the urban underground pipeline tunnel came into being. It is used to accommodate the structures and ancillary facilities of two or more types of urban pipelines, such as water supply, heating, gas, electricity, etc. The adjustment of China’s energy structure has led to the rapid development of natural gas production, transportation, storage, and other related industries. Meanwhile, gas leakage accidents caused by factors such as the aging of the gas pipelines, localized corrosion, and some illegal construction projects have occurred frequently in recent years. The leakage of the combustible gas spreads and accumulates in the underground space. Once detonated, cause tremendous death and injury and property loss [4,5,6,7]. For example, in June 2021, a natural gas pipeline leak in Shiyan City, Hubei Province, triggered an explosion that killed 25 people and injured 138. In view of the potential damage caused by the explosion in the underground space, the safety prevention method adopted in most areas is the early warning used at present [8,9].

Due to the fact that the natural gas pipeline tunnel is equipped with various openings such as vents, drains, and inspection ports, the venting technology in the tunnel is an important consideration. Many researchers have conducted gas explosion studies in cylindrical containers and long straight pipes [10,11,12,13,14,15,16,17,18]. Chow et al. [19] carried out a series of top venting tests on combustible gasses in a cylindrical vessel. They found that as the venting threshold increases, the first pressure peak gradually becomes the main peak. Chen et al. [20] proposed that the occurrence and intensity of secondary explosions mainly depend on the external structure, ignition energy, and ignition delay time. Kasmani et al. [2] studied the different explosion vents, and their results showed that due to turbulence, gas explosions in pipeline-connected containers have greater energy than that in isolated containers. Guo et al. [21,22,23] symmetrically installed exhaust pipes on both sides of a cylindrical container. They found that in the case of the same venting area, there is no significant change in the internal and external overpressure between two vents and a single vent. In addition, the internal pressure increases with the increase in the venting pressure and decreases exponentially with the increase in the venting area. Yu et al. [24,25] conducted methane explosion experiments in a square tube. Their results showed that the exhaust effect is affected by the induction of the opening end and the obstacle. Li et al. [26] studied the interaction between the flame propagation and obstacles. Sheng et al. [27] conducted gasoline explosion experiments in small square tubes with different opening areas. They proposed that the maximum propagation distance of the flame is mainly determined by the pressure gradient of the flow field. Ajrash et al. [28] conducted methane venting experiments in a semi-open circular tube. They found that lateral venting can significantly reduce the pressure in the tube, but its influence range mainly concentrates at the upstream of the vent. Yao et al. [29] carried out explosion experiments in square pipes. The experimental results showed that the increase in vent area can greatly reduce the pressure impulse, and the downward trend is more obvious when the number of vents increases. Luo et al. [30] studied the temperature distribution and shock wave propagation of the hydrogen explosion in the pipeline.

Based on the above research results, it can be found that although researchers have carried out relevant studies on the venting effect of the deflagration process in the confined space, they mainly focus on influencing factors such as the size and location of the vent, the ignition position, and the obstacles. The specific venting structure is not carefully considered, and the research conclusions considering the actual venting process are insufficient, which restricts the development of the explosion prevention and control technology.

For existing under-constructed and planned large-scale utility tunnels with gas compartments in China, there are currently no unified measures for isolating, suppressing, or venting gas explosions. For that reason, this paper adopted the L-type venting duct to achieve efficient control of natural gas explosion flames and overpressure within the gas pipeline tunnel. This approach seeks to manage explosions effectively near the source, prevent the escalation and expansion of explosions, and minimize casualties and property damage. It can also provide a theoretical basis and scientific guidance for exploring new venting technologies within utility tunnels.

2. L-Type Venting Duct

2.1. Layout of the Venting Duct

Considering the characteristics of the underground space, the L-type venting duct is proposed. Currently, the venting of gas explosions in utility tunnels mainly utilizes surface wellheads as venting channels. This method of releasing explosive energy poses significant explosion venting safety risks to the internal pipelines, walls, and structural components of the tunnel, and to people in the vicinity of the wellhead area. To avoid those problems, the L-type venting duct is used to guide the explosion energy to the tunnel’s side wall, and then discharge it into a safer area. Taking the DN300 natural gas pipeline tunnel as an example, as shown in Figure 1, the tunnel’s section size is 1.8 m × 2.7 m, and the distance from the center of the inlet vent to the tunnel’s top surface is 1.35 m. To meet the technical requirements of the explosion venting in gas pipeline tunnels, the L-type venting ducts are arranged in an orderly manner (1 to n) at a certain distance, as shown in Figure 2.

2.2. Structure of the Venting Duct

Although the relief area of the venting duct is important, the duct structure plays a decisive role. In view of this, when designing the L-type venting duct, not only should the vertical load be paid attention to, but so should the horizontal load. When selecting the structural coefficient, it is necessary to ensure the stability and economy of the duct structure. The structure of the L-type venting duct mainly includes the horizontal duct, the vertical duct, the water tank, and the buffer duct.

As shown in Figure 3, L_z is the length of the horizontal duct, L_x is the length of the vertical duct, S_c is the venting area of the horizontal and vertical duct, S_m is the venting area of the buffer duct ($S_m\le S_c$), and L_z/L_x is defined as the structural coefficient Z_x. The L-type venting duct is pre-embedded on one side of the natural gas pipeline tunnel. The inlet of the horizontal duct is connected to the tunnel, and the outlet of the vertical duct is connected to the water tank. The position of the water tank is higher than the ground, with a buffer duct installed on it.

2.3. Function of the Venting Duct

The natural gas explosion will result in a sharp pressure rise inside the natural gas pipeline tunnel. The L-type venting duct will alleviate the internal load of the tunnel and achieve the first buffer. In addition, water is an excellent buffer material. Based on the principle of the water sealing technology, the outlet of the venting duct is connected to a water tank, and the explosion flame entering the water tank will act as the second buffer. At last, the water in the tank will enter the buffer duct and be discharged into the air, so as to act as the third buffer. Through the water level detector, the fire alarm signal will be sent to the fire control department when the water level is abnormal. The specific working principle is shown in Figure 4.

3. Numerical Simulation

3.1. Governing Equations

FLACS software applies the finite volume method to solve the compressible conservation equations in the three-dimensional Cartesian coordinate system. The finite volume method is a discretization method that has developed rapidly in recent years. It is characterized by high computational efficiency and has been widely used in the field of CFD. In FLACS, the distributed porosity enables the detailed representation of complex geometries using the Cartesian grid, representing geometrical details as porosities for each control volume.

The explosive process satisfies the continuity equation, mass conservation laws, momentum conservation, and energy conservation. It also involves fuel’s mass fraction transport equation considering multiple compositions in the vapor cloud. All the conversation equations can be represented generally as

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \phi \right)+{\displaystyle \frac{\partial }{\partial X_j}}\left(\rho u_j\phi -{\rho \Gamma }_{\phi }{\displaystyle \frac{\partial \phi }{\partial x_j}}\right)=S_{\phi }$$

(1)

where $\phi$ is the general variable, including mass, momentum, energy, turbulent kinetic energy, etc.; $\rho$ is the gas density; $t$ is time; $u_j$ is the velocity in j direction; ${\Gamma }_{\phi }$ is the dispersion coefficient of the variable $\phi$; and $S_{\phi }$ is the source term.

The ideal gas relations can be expressed as

$$P=\rho RT$$

(2)

$$\gamma =c_p/c_v$$

(3)

$${\displaystyle \frac{P}{P_0}}={\left({\displaystyle \frac{\rho }{{\rho }_0}}\right)}^{\gamma }={\left({\displaystyle \frac{T}{T_0}}\right)}^{\gamma /\left(\gamma -1\right)}$$

(4)

where $P$ is the static pressure; $\rho$ is the gas density; $R$ is the gas constant of a mixture; T is the gas temperature; $\gamma$ is the isentropic ratio; $c_p$ is the specific heat capacity at constant pressure; and $c_v$ is the specific heat capacity at a constant volume.

Turbulence is modeled using the k-ε model, an eddy viscosity model that solves for turbulent kinetic energy and the dissipation of turbulent kinetic energy. An eddy viscosity is introduced to model the Reynolds stress tensor. These are shown as follows:

$${\displaystyle \frac{\partial }{\partial t}}\left({\beta }_v\rho k\right)+{\displaystyle \frac{\partial }{\partial X_j}}\left({\beta }_v\rho u_{j}k\right)={\displaystyle \frac{\partial }{\partial X_j}}\left\{{\beta }_j{\displaystyle \frac{u_{eff}}{{\sigma }_k}}{\displaystyle \frac{\partial k}{\partial X_j}}\right\}+{\beta }_v{P}_k-{\beta }_v\rho \epsilon$$

(5)

$${\displaystyle \frac{\partial }{\partial t}}\left({\beta }_v\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial X_j}}\left({\beta }_v\rho u_j\epsilon \right)={\displaystyle \frac{\partial }{\partial X_j}}\left\{{\beta }_j{\displaystyle \frac{u_{eff}}{{\sigma }_{\epsilon }}}{\displaystyle \frac{\partial \epsilon }{\partial X_j}}\right\}+{\beta }_v{P}_{\epsilon }-C_{2\epsilon }{\beta }_v\rho {\displaystyle \frac{{\epsilon }^2}{k}}$$

(6)

$$-\rho \overline{u_i^{″}{u}_j^{″}}=u_{eff}\left\{{\displaystyle \frac{\partial u_i}{\partial X_j}}+{\displaystyle \frac{\partial u_j}{\partial X_i}}\right\}-{\displaystyle \frac{2}{3}}\rho k{\delta }_{ij}$$

(7)

where $u_i$ is the velocity in i direction; $u_j$ is the velocity in j direction; $k$ is the turbulent kinetic energy; $\epsilon$ is turbulent kinetic energy dissipation rate; ${\beta }_v$ is volume porosity; ${\beta }_j$ is area porosity in the j direction; $u_{eff}$ is the effective turbulence viscosity; ${\delta }_{ij}$ is the stress tensor; $P_k$ and $P_{\epsilon }$ are the production of turbulent kinetic energy and the production of dissipation, respectively; ${\sigma }_k$ and ${\sigma }_{\epsilon }$ are Prandtl–Schmidt number of $k$ and $\epsilon$, taken as 1.0 and 1.3; and $C_{2\epsilon }$ is a constant taken as 1.92.

The initial high-pressure region is the sphere used to represent the explosive that generates the blast wave in FLACS-Blast. To calculate the region occupied by the sphere, a typical gas production rate, $V_{ex}$, is used to calculate the volume of gas produced from the specified explosive mass, $M_{ex}$:

$$V_{init}=V_{ex}\times M_{ex}$$

(8)

The temperature, $T_1$, and pressure, $P_1$, are set to ambient air properties and then heated to temperature, $T_{ex}$, following the ideal gas law. $T_{ex}$ is based on the heat of the reaction and the temperature of the combustion products. The new pressure, $P_2$, is then:

$$P_2={\displaystyle \frac{P_1\times T_{ex}}{T_1}}$$

(9)

After heating, the gaseous sphere is adiabatically compressed to a final pressure, $P_{ex}$, and the volume, $V$, is calculated using the gas expansion coefficient, $\kappa$, which is 1.4 for diatomic gasses:

$$V=V_{init}\times {\left({\displaystyle \frac{P_1\times \left(P_{ex}+1\right)}{P_2}}\right)}^{\left(-1/\kappa \right)}$$

(10)

3.2. Simulation Conditions

This study mainly analyzes the explosion venting characteristics. Before conducting simulations, some assumptions have been made.

(1)

In order to ensure the best compromise between the computational time and accuracy, the explosion simulations are conducted in a 1:5 reduced scale gas pipeline tunnel. Based on previous research [31,32], the parameter variation law obtained in the reduced-scale model still applies to the full-scale model.

(2)

In order not to be disturbed by other factors, the obstacles such as cables inside the natural gas pipeline tunnel are ignored.

(3)

In order to observe the venting effect, the explosion flame will be able to contact the outside only by the vent.

The simulated tunnel has a size of 0.4 m × 0.6 m × 2.0 m, and the internal space is 0.36 m × 0.56 m × 1.96 m. The methane/air gas mixture occupies the entire space, with a methane concentration of 11%. The methane concentration of 11% generates the maximum explosion pressure in the simulations. This concentration is chosen to more clearly compare the results of different conditions. The main objective of this study is to identify the optimal duct design. Thus, the methane concentration will not affect the results and conclusions. In the center of the tunnel, the gas mixture will be ignited. As shown in

Table 1. Different simulation conditions.

No.	Lz/m	Lx/m	L/m	Sc/cm2	Zx
1	—	—	—	0	—
2	—	—	—	36	—
3	—	—	—	100	—
4	0.2	1	1.2	100	1/5
5	0.4	0.8	1.2	100	2/4
6	0.6	0.6	1.2	100	3/3
7	0.8	0.4	1.2	100	4/2
8	1	0.2	1.2	100	5/1

, the simulation conditions are divided into the control group (1, 2, 3), with the explosion vent, and the experimental group (4, 5, 6, 7, 8) with the L-type venting duct. For the control group, the explosion vent is set in the center position of the model’s side wall and has different venting areas (S_c). For the experimental group, the venting duct is installed in the same position, and the venting area is fixed. The total length (L_z + L_x) of the venting duct is 1.2 m and has different structural coefficients (Z_x).

Five monitoring points (P1–P5) are used to analyze the temperature/pressure variation law in simulations. Among those points, two points (P1, P2) are located in the tunnel, two points (P4, P5) are located in the venting duct, and one point (P3) is located in the inlet of the venting duct. The specific position of those points is shown in Figure 5.

3.3. Mesh Division and Boundary Condition

FLACS software divides the mesh into three directions, which are direction X, direction Y, and direction Z. After the division, a rectangular mesh volume will be formed. As shown in Figure 6, when the explosion vent is used by the tunnel, the calculation area is a cuboid. The range of direction X is 0–2 m, the range of direction Y is 0–0.4 m, and the range of direction Z is 0–0.6 m. The size of the control volume is 0.1 cm × 0.1 cm × 0.1 cm, and the number of the control volume in the entire calculation area is 480,000. When the L-type venting duct is installed, the range of direction X is 0–2 m, the range of direction Y is 0–1.48 m, and the range of direction Z is 0–0.6 m. The size of the control volume is 0.1 cm × 0.1 cm × 0.1 cm, and the number for the control volume in the entire calculation area is 1,776,000. The initial temperature is set as 293.15 K, and the initial pressure is set as 101.325 kPa. To solve momentum and continuity equations in the boundary, the boundary conditions of the propagation of pressure waves are set as EULER, while the other boundary conditions are set as PLANE_WAVE. Other parameters are defaults.

3.4. Model Validation

Verifying the accuracy of the numerical model by the experiment is the most effective method. Due to the high risk of the gas explosion in the confined space, it is not possible to conduct an experimental validation. Therefore, this paper adopted the experiments conducted by Li et al. [33] to validate the effectiveness of the numerical model.

The experimental setup established by Li et al. [33] is shown in Figure 7. The size of the confined space is 30 m × 0.8 m × 0.8 m, and several pressure monitoring points are set along its length. In this section, a numerical model of the same size was established. The explosion pressure at the same position as the experiment was solved and compared with the experimental result.

As shown in Figure 8, the simulated pressure distribution is basically consistent with the experimental results, and the two curves match well. The maximum error between the simulation results and the experimental results is 9%, which falls within the engineering acceptable error range (0–20%). The good agreements between the experimental and simulation results show the reasonably accurate predictions utilizing FLACS to characterize gas explosion characteristics. Therefore, the reliability of the numerical model has been validated.

4. Result and Discussion

4.1. Simulation Results of the Control Group

4.1.1. Variation Law of Pressure

The pressure variations in different point positions (P1–P3) are shown in Figure 9a–c. In each position, the pressure variations under different venting areas are compared. It can be seen that when the venting area is 0, the pressure measured in each position rises rapidly after the explosion of the gas mixture. The pressure rises to the peak value after 0.2 s and then tends to be stable. When the venting areas are 36 and 100 cm², the pressure rises to its peak value in a short time, and then gradually decreases to 0 MPa. Obviously, the larger the venting area, the faster the pressure relief speed. In the same point position, it can be seen clearly that when the vent area is 0, the peak pressure of the gas mixture is the largest, and the time to reach the peak value is the longest. For the vent areas of 36 cm² and 100 cm², the gas mixture with the former has a higher pressure, and the time to reach the peak value is also shorter.

4.1.2. Variation Law of Temperature

The temperature variations with different venting areas (0, 36 cm², 100 cm²) are shown in Figure 10a–c. For each venting area, the temperatures measured by monitoring points rise rapidly before reaching the peak value. The fastest temperature rise rate is in the P2 position, while the slowest rate is in the P1 position. With the increased venting area, the temperature rise time will be delayed in the P1 position, but it will be advanced in the P3 position. When the venting area is 0, the temperatures rise to the peak value after 0.1 s. Then, the temperatures decrease slightly, and finally tend to be stable. When the venting area is 36 cm², the temperatures will continue to decrease after reaching the peak value. When the venting area is 100 cm², the temperatures will continue to decrease after reaching the peak value. However, they will tend to be stable after 0.3 s. Obviously, from the perspective of reducing peak pressure and temperature, the optimal venting area in the control group is 100 cm², and it is also used in the experimental group.

4.2. Simulation Results of the Experimental Group

4.2.1. Variation Law of Pressure

The pressure variations in different point positions (P1–P5) are shown in Figure 11a–e. In each position, the pressure variations with different structural coefficients are compared. In the P1 and P2 positions, the overall pressure variations are similar. In the P3-P5 positions, the peak value of pressure shows relatively large differences. In the same point position, it can be clearly seen that when the structural coefficient (Z_x) of the venting duct is 5, the peak pressure of the gas mixture is the smallest, and the time to reach the peak pressure is the longest. However, when the structural coefficient (Z_x) of the venting duct is 0.2, the peak pressure of the gas mixture is the largest, and the time to reach the peak pressure is the shortest.

It is worth noting that when the venting area is 100 cm², the gas explosion pressures with the explosion vent and the L-type venting duct (Z_x = 5) show some differences. For example, the peak pressure in the P1 position is about 0.3 MPa with the explosion vent. When using the L-type venting duct, the peak pressure increases to 0.35 MPa. Meanwhile, the time to reach the peak pressure in the P1 position is about 0.1 s with the explosion vent. When using the L-type venting duct, that time increases to 0.15 s. The pressure variation shows a similar trend in the P2 and P3 positions. It indicates under the ideal conditions, the optimal venting method for the tunnel is the explosion vent. The explosion vent has a better pressure relief effect, but it can also pose significant safety risks. Therefore, to achieve a similar venting effect to the explosion vent, the L-type venting duct should be used with the suitable structural coefficient.

4.2.2. Variation Law of Temperature

The temperature variations with different structural coefficients are shown in Figure 12a–e. For each structural coefficient, the temperatures measured by monitoring points rise rapidly before reaching the peak value. The fastest temperature rise rate is in the P2 position, while the slowest rate is in the P1 position. Temperatures will rise to their peak value within 0.15 s. When reaching the peak value, temperatures will continue to decrease within 0.3 s. It is worth noting that when the structural coefficient is less than 5, it has a minor effect on the temperature variations. However, when the structural coefficient is equal to 5, it has a significant effect on the temperature variations in different point positions.

When the venting area is 100 cm², the gas explosion temperatures with the explosion vent and the L-type venting duct (Z_x = 5) also show some differences. For example, the peak temperature in the P1 position is about 2250 K with the explosion vent. When using the L-type venting duct, the peak temperature increases to 2500 K. Meanwhile, compared to the L-type venting duct, the time to reach the peak temperature in the P1 position is slightly shorter with the explosion vent. The temperature variation shows a similar trend in the P2 and P3 positions. Overall, for the temperature relief effect, although some differences exist between the explosion vent and the L-type venting duct, the differences are not significant. From the perspective of achieving a safe and efficient venting effect, the optimal structural coefficient is 5 for the L-type venting duct.

4.3. Temperature and Pressure Distribution in the Venting Duct

The flame wave is a very important part in the process of methane explosion. Normally, it propagates slower than the pressure wave. In simulations, the 2D contour of the temperature distribution is used to show the flame propagation process. Taking the optimal structural coefficient as an example, the characteristics of the explosion flame in the tunnel can be analyzed. As shown in Figure 13, the flame wave propagates to the venting duct within the first 0.05 s, and the flame temperature can rise to 2250 K. In the time period of 0.05–0.1 s, the flame propagation in the venting duct is relatively stable. The flame temperature rises again and is close to 2500 K. In the time period of 0.1–0.15 s, the flame temperature in the center of the tunnel rises to the highest temperature, and the flame is continuously released to the venting duct. In the time period of 0.15–0.2 s, the flame temperature decreases rapidly in the venting duct. The temperature decrease rate is faster than that in the tunnel. In the time period of 0.2–0.3 s, the flame temperature in the tunnel and venting duct decreases to about 1500 K.

As shown in Figure 14, the pressure wave propagates to the entire venting duct within the first 0.05 s, and the pressure in the venting duct is relatively weak. In the time period of 0.05–0.1 s, the pressure in the venting duct gradually rises to 0.1 MPa. In the time period of 0.1–0.2 s, the pressure in the venting duct rises sharply. The peak pressure can easily reach 0.25 MPa. In the time period of 0.2–0.3 s, the pressure in the tunnel and venting duct decreases simultaneously. The pressure relief speed in the venting duct is faster than that in the tunnel. Eventually, the pressure in the tunnel and venting duct drops to 0 MPa.

5. Conclusions

In this study, a series of numerical simulations were carried out to analyze the explosion venting characteristics of the L-type venting duct. The effects of different venting areas and structural coefficients on the gas explosion pressure and temperature are clarified. The major conclusions are as follows:

(1)

When increasing the area of the explosion vent, the peak temperature and pressure will be reduced, and the pressure relief speed will be accelerated.

(2)

The explosion vent has a better pressure relief effect for the studied gas pipeline tunnel, but it can pose significant safety risks. From the perspective of achieving a safe and efficient venting effect, the optimal structural coefficient is 5 for the L-type venting duct.

(3)

Based on the temperature and pressure distribution, the flame and pressure wave released from the L-type venting duct will have certain impacts on the external environment. They can create multiple buffers when water sealing technology is adopted.

(4)

The obstacles inside natural gas pipeline tunnels are not considered in this study. However, they may have significant effects on the gas explosion characteristics in some cases. In the future, more work will be conducted to explore the optimal structural coefficient of the L-type venting duct in those cases.