Skip to main content
NCBI home page
ACS Omega logoLink to ACS Omega
. 2022 Dec 26;8(1):1375–1388. doi: 10.1021/acsomega.2c06831

Study of Methane Explosion Suppression Characteristics of N2 and CO2 in Variable Cross-Section Ducts

Jian Wang †,‡,§,*, Yongxian Zhao †, Ligang Zheng †,‡,§, Rongkun Pan †,‡,§, Chang Lu †,‡,§, Guilong Liu †, Xiaoyan Liu ∥
PMCID: PMC9835181  PMID: 36643466

Abstract

graphic file with name ao2c06831_0018.jpg

To investigate the effect of concentration of N2 and CO2 (0, 10, 20, 30, 40, and 50%) on the flame propagation characteristics of CH4/air premixed gases with stoichiometric ratios in variable cross-section ducts, experiments were conducted in four combinations of ducts at initial conditions of 298 K and 1 atm. The results show that the flame propagation velocity, propagation time, and overpressure are greater in the suddenly contracted duct than in the suddenly expanded duct if the dimensions of the ducts are kept constant. However, an increase in inert gas concentration leads to a decrease in flame propagation speed, an increase in flame propagation time, and changes in flame structure and pressure. “Tulip” flames appeared when a duct with a cross section of 100 mm × 100 mm was combined with a duct with a cross section of 70 mm × 70 mm, whether N2 or CO2 was added or what its concentration was. However, when a duct with a cross section of 140 mm × 140 mm was combined with a 70 mm × 70 mm duct, a “tulip” flame is formed only at a CO2 concentration of 50%. As the concentration of inert gas increases, the explosion pressure first decreases and then stabilizes, while the rate of pressure increase showed a monotonically decreasing trend. The explosion pressure is minimized when the concentration of CO2 and N2 is 30 and 40%, respectively.

1. Introduction

As a major component of natural gas and widely used in modern industry, methane is an excellent alternative fuel.1−3 In practice, gas pipelines are constructed in many different ways. Connections between gas pipelines of different cross-sections can be found everywhere, and there are many differences in the flame propagation processes of premixed combustible gases in different forms of piping. Meanwhile, underground integrated pipelines are being built in many Chinese cities, and gas pipelines are in them. This requires comprehensive leak and fire prevention and protection. Therefore, accidental leakage and improper handling during the production, processing, storage, and transportation of methane can result in the formation of complex combustible gas mixtures. Once the explosion conditions are satisfied, the gas explosion can cause serious property damage and casualties.4−7 To prevent and control gas explosion accidents, effective measures need to be found to minimize the scope and intensity of gas explosion. Inert gases are often used as inhibitors of methane-air explosions. Common explosion suppressants are nitrogen, carbon dioxide, argon, and helium.8−10

Many studies have been conducted on the explosive properties of CH4 and the properties of inert gases to suppress CH4 explosion, such as flame structure, overpressure, flame propagation speed, and explosion limit. Gonzalez et al.11 analyzed different calculation results, such as wall friction, duct aspect ratio, and initial flame structure, in detail through numerical simulation and obtained a complete and detailed description of the “tulip” phenomenon. Clanet and Seardy12 proposed four stages of “tulip” flame development, i.e., spherical flame, finger flame, flat flame, and “tulip” flame. Xiao et al.13−15 proposed the fifth evolution stage, i.e., the distorting tulip flame (DTF) in a closed duct with an aspect ratio of 6.46 and a hydrogen concentration of 26–64%. It is believed that Rayleigh–Taylor instability played an important role in the onset of DTF. Some other scholars have experimentally studied the combustion characteristics of methane at different concentrations. Bao et al.16 conducted tests on the venting explosion of methane-air mixtures and investigated the effect of methane concentration in the range of 6.5–13.5% on the development of internal pressure. The results show that the number of pressure peaks is closely related to the methane concentration. Two pressure peaks were observed in the internal pressure curve at methane concentrations ranging from 7.5 to 11.5%. But the internal pressure history shows only one pressure peak when the methane concentration was 6.5 or 12.5%. Li et al.17 studied the effects of methane concentration and ignition position on pressure and flame. They observed three pressure peaks and two types of pressure oscillation. Larger duct sizes increase the combustion reaction rate and flame propagation velocity, but smaller duct sizes increase the peak overpressure.18,19 The addition of N2 and CO2 decreases the maximum overpressure20,21 and burning rate of methane explosion.22−24 Some researchers have studied the suppression of explosion pressure and pressure rise rate of methane-air mixtures by inert gas.25−27 Galmiche et al.28 investigated the effect of dilution on premixed methane/air combustion through experiments and numerical simulations. Xie et al.29 analyzed the effect of CO2 on the laminar burning velocity of premixed methane/air flames. And they obtained the influence of initial temperature and initial pressure on the dilution effect and the thermal effect. In addition, N2 and CO2 can reduce the laminar burning velocity.30,31

The explosion limit of O2/CO2/CH4 mixtures32 and CH4-air33,34 can be calculated based on thermal theory and thermal radiation effects. The upper explosion limit of methane was slightly reduced when the pressure was increased,35 and the addition of C2H6 reduced both the upper and lower explosion limits of CH4.36 Chen et al.37 investigated the dilution effect of CO2, N2, and Ar on various fuels and analyzed the impact of CO2 on combustion chemistry kinetics. Wang et al.38 studied the effect of sudden change of duct cross-sectional area on flame propagation of methane/air premixed gas. Compared to N2, CO2 can participate in important chain reactions during combustion and compete with free radicals, leading to stronger inhibition of combustion.39,40 Premixed combustion is unstable due to the influence of various flame instabilities. The presence of flame instability, equivalence ratio, oxygen concentration, and dilution have significant effects on flame structure and combustion characteristics. Xiang et al.41 investigated the effect of CO2 on the combustion characteristics of laminar premixed flames and analyzed the sensitivity and net reaction rate of the main reactions of radical OH. Xiao et al.14 proposed that the Rayleigh–Taylor instability is an important mechanism for distorting tulip flame (DTF) formation, while the Richtmyer–Meshkov instability transforms the DTF into a ripple flame through impact flame interactions.42 Zheng et al.43,44 studied the flame instability and combustion characteristics of CH4/O2/CO2 and CH4/O2/N2 mixtures.

Existing studies have focused on spherical vessels and homogeneous-sized ducts, which emphasize the effect of several different inactive gases on the explosion characteristics of premixed gases. In the actual production process, it is common to see ducts with changing cross-sectional sizes, such as mine tunnels, underground galleries, and gas transmission ducts. In addition, natural gas is widely used in industry. For the safe production and use of natural gas, inert gases need to be considered to suppress natural gas explosions. There are relatively few studies on flame propagation processes in variable cross-section ducts and the suppression characteristics of inactive gases. In this study, the effects of different concentrations of N2 and CO2 on the explosion process of methane/air premixed gas are studied by four variable cross-section ducts. And the change law of flame propagation velocity and overpressure is analyzed. The results can be used as guidelines for the installation of inert gas fire suppression and explosion suppression facilities in underground integrated corridors and other natural gas transmission pipeline systems, such as the selection of inert gas types, concentration settings, etc. For example, for underground integrated corridors, inert gas can be installed locally. The early release of gas is achieved through sensors and controllers to mitigate or stop the propagation of the explosion and protect the personnel and equipment in the rear.

2. The Experiment and the Composition of the Mixture

2.1. Experimental System

The experimental setup (Figure 1) similar to the previous study45 consisted of a gas distribution system, a Plexiglas duct, an ignition system, and a pressure and image acquisition system. The cross sections of the ducts used for the experiments were of three different sizes 70 mm × 70 mm (S), 100 mm × 100 mm (M), and 140 mm × 140 mm (L), respectively. The length of each section of the duct is 500 mm. The experimental ducts were combined with two sections of different cross-sectional dimensions as shown in Table 1. The first duct is defined as duct A and the second duct as duct B. In configurations S-L and L-S, the cross-sectional area of large ducts was four times that of small ducts, while it was about 2.04 times in configurations S-M and M-S. The right end of the combined ducts was used as the ignition end and was closed. The left end was the open end and was closed with a single layer of PVC film. The ignition system consists of an ignition electrode, a 6V DC power supply, and an ignition controller. The ignition electrode is located in the center of the plexiglass cover at the ignition end, and the initial ignition energy is about 100 mJ. The flame propagation process was captured using the Chinese-made Thousand-Eyes Wolf 5KF10 high-speed camera with an acquisition frequency of 4000 fps. The two pressure sensors (Shanghai MIND Ltd.) were installed at the right closed-end and the left semi-closed end of the duct, respectively. The data acquisition card model is USB-1208FS. The photodiode is located outside the transparent Plexiglas duct, pointing to the ignition source.

Figure 1.

Figure 1

Open in a new tab

Experimental system diagram.

Table 1. Composition and Structure of the Experimental Duct.

configuration size
S-M 70 mm × 70 mm × 500 mm + 100 mm × 100 mm × 500 mm
M-S 100 mm × 100 mm × 500 mm + 70 mm × 70 mm × 500 mm
S-L 70 mm × 70 mm × 500 mm + 140 mm × 140 mm × 500 mm
L-S 140 mm × 140 mm × 500 mm + 70 mm × 70 mm × 500 mm
Open in a new tab

2.2. Experimental Mixtures

In the experiment, the N2 and CO2 contents (0, 10, 20, 30, 40, and 50%) were varied so that the methane/air equivalence ratio was always 1 as shown in Table 2. The purity of methane, N2, and CO2 is over 99.999%. The volume fraction of each gas in the mixture was first calculated based on the chemical equivalence ratio (CH4, air, N2, and CO2 in this experiment are shown in Table 2). Then the volume flow rate for each operating condition was calculated based on the size of the pipe volume, and the flow rate value was set using a mass flow meter. The experiments were carried out using the exhaust air method for filling, and the filling volume was four to five times the volume of the duct. All experiments were performed at an initial pressure of 1.0 atm and an initial temperature of approximately 298 K. At least three tests were carried out for each component condition to ensure the accuracy and repeatability of the experiment.

Table 2. Composition of Mixtures.

volume fractions of N2 and CO2 (φ, %) CH4 (%) N2 or CO2 (%) air (%)
0 9.50 0 90.50
10 9.40 1.05 89.55
20 9.29 2.32 88.39
30 9.13 3.92 86.95
40 8.94 5.96 85.10
50 8.68 8.68 82.64
Open in a new tab

3. Results and Discussion

3.1. Effect of Duct Structure and N2/CO2 Content on Premixed Flame

In this section, the effects of different cross-sectional area ducts and inert gas (N2 and CO2) concentrations on premixed flames were studied. The effect of the duct structure on the flame was studied by changing the size of the duct cross-sectional area. Taking the addition ratio of CO2 as 30% as an example, Figure 2. shows the evolution of premixed flame propagation in four different variable cross-section ducts. The flames undergo only spherical and finger flames in the configurations of S-L and L-S ducts. While in the configurations S-M and M-S, the four types of flame are formed (i.e., spherical flame stage, finger-shaped flame stage, flame skirt touching the wall of the duct, and “tulip” flame stage).12 This may be caused by the different cross-sectional areas of the ducts. The difference in cross-sectional area between the configurations S-M and M-S is small, while the difference in cross-sectional area between the configurations S-L and L-S is large. This leads to an increase in flame propagation time in the configurations S-M and M-S, which slows down the flame structure evolution and results in a “tulip” flame. It has been suggested that the combined effect of overpressure and fluid flow,15 Rayleigh–Taylor instability,12 gas composition,46 combustion gas vortex close to the wall, and the interaction between the flame and the combustion fluid may all be responsible for the “tulip” flame.47 Although “tulip” flames appear in both configurations S-M and M-S, the compression flame fronts are different. The tip of the flame depression in the configuration S-M moves toward the ignition end, while the tip of the flame depression in the configuration M-S propagates toward the venting end. This is due to the different strengths of the vortex action and expansion action in these two cases. For the configuration S-M, the larger area of the vent end causes the explosion of the transition exhaust volume to make a large amount of outside air enter the duct in a short period, making the vortex effect stronger than the expansion effect. However, in the configuration M-S, less air enters the duct, making the expansion effect stronger than the vortex effect.

Figure 2.

Figure 2

Open in a new tab

Flame front evolution in the four different variable cross-section ducts under φ = 30%. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

At 500 mm of the duct, due to the sudden expansion of the duct cross section and the effect of sparse wave disturbance at the upper and lower walls, local turbulent vortex motion is formed, which accelerates the rate of gas transport near the upper and lower walls and makes the flame front become folded and distorted.45 Similarly, Sun and Li48 found that the initial turbulence acting on the flame front intensifies the positive effect of stretching, which wrinkles the flame front and thus promotes the formation of cells, thus increasing the flame propagation velocity. The cross-sectional area of the duct of the configuration M-S is suddenly reduced at 500 mm, causing the flame to be compressed and ejected into a smaller cross-section duct. The flame propagation time in the configuration M-S is 2.5 ms longer than that in the configuration S-M. But duct B of the configuration S-M is 5 ms longer than duct B of the configuration M-S. And the flame propagation time in the configuration L-S is 18 ms longer than that in the configuration S-L. While in duct B, it is 5 ms longer in the configuration S-L than that in the configuration L-S. The results show that the sudden expansion and contraction ducts affect the flame propagation time. The flame propagation time in the sudden contraction duct is longer than that in the sudden expansion duct. But in duct B, the flame propagation time in the sudden contraction duct is shorter than that in the sudden expansion duct.

Figure 3 shows the evolution of the flame front in a variable cross-section duct (L-S and S-L) for two concentrations of CO2, i.e., φCO2 = 40% (Figure 3a,b) and φCO2 = 50% (Figure 3c,d). As can be seen in Figure 3, when φCO2 = 40%, the flame front inside duct A maintains stability and smoothness. However, when φCO2 = 50%, the flame front is folded and twisted inside duct A. In addition, the flame structures of φCO2 = 50% and φCO2 = 40% are different in the conformation S-L. For example, when φCO2 = 40%, there are only spherical flames and finger flames, but when φCO2 = 50%, the flames formed a flat flames and “tulip” flames at 81 and 83 ms, respectively. Similarly, in the configurations S-L and L-S, the flame structures under other CO2 content (φ = 0, 10, 20, and 30%) are similar to that when φ = 40%.

Figure 3.

Figure 3

Open in a new tab

Flame front evolution of CO2 diluted in two different cross-section ducts. (a) 40% CO2-S-L; (b) 40% CO2-L-S; (c) 50% CO2-S-L; and (d) 50% CO2-L-S.

Figure 4 shows the evolution of the flame front in a variable cross-section duct (L-S and S-L) for two concentrations of N2, i.e. φN2 = 40% (Figure 4a,b) and φN2 = 50% (Figure 4c,d). The effect on the flame structure was studied by changing the N2 concentration. When φN2 = 40% and φN2 = 50%, it can be seen from Figure 4 that the flame front always remains smooth in duct A. The flame structures in configurations S-L and L-S have only spherical flame and finger-shaped flame for both contents. Similarly, the flame structures under the other N2 dilutions (φ = 0, 10, 20, and 30%) in the S-L and L-S configurations are similar to both contents. Only when φCO2 = 50%, premixed gas can form a “tulip” flame in S-L and L-S configurations. This is because the formation of “tulip” flames is affected by the flame tip deceleration. An experiment by several researchers supports the idea that the physical origin of the “tulip” phenomenon is flame deceleration.48 Clanet and Searby12 also suggested that the formation of the “tulip” flame is a manifestation of the Taylor instability driven by flame tip deceleration.

Figure 4.

Figure 4

Open in a new tab

Flame front evolution of N2 diluted in two different cross-section ducts. (a) 40% N2-S-L; (b) 40% N2-L-S; (c) 50% N2-S-L; and (d) 50% N2-L-S.

However, the concentrations of CO2 and N2 also have a certain effect on the flame propagation time. The flame propagation time in S-L and L-S increases with the increase of CO2 and N2 concentration. For example, when CO2 is added to the conformations S-L and L-S, the flame propagation time at 50% dilution is 43.5 and 27.75 ms longer than 40%, respectively. When N2 is added to the conformations S-L and L-S, the flame propagation time at 50% dilution is 9.5 and 5.25 ms longer than 40%, respectively. This indicates that the flame propagation time of CO2 is 43 and 44.5 ms longer than that of N2 dilution when the configuration S-L and L-S addition ratios are 50%, respectively. In summary, the flame structure is influenced by many factors. The flame propagation time increases with the increase of CO2 and N2 concentration, and the flame propagation time under CO2 dilution is longer than that of N2.

Figure 5 shows the local flames under inert gases (N2 and CO2) dilution in configurations S-M and M-S, where the numbers in parentheses indicate the locations of the characteristic flame formation. When φN2 = 40%, the premixed gas in the configuration S-M takes 7.5 and 8.5 ms longer to form a flat flame and “tulip” flame than when φ = 0. And its characteristic flame position is 53 and 45 mm closer to the ignition end. When φCO2 = 40%, the premixed gas in the configuration S-M takes 27 and 31.5 ms longer to reach the flat flame and “tulip” flame than when φ = 0, respectively. And its characteristic flame position is 121 and 130 mm closer to the ignition end. In the configuration M-S, when φ = 40%, the time to form a “tulip” flame under CO2 dilution is 1.5 ms longer and the distance is 21 mm shorter than that of N2. The result shows that with the increase in inert gas concentration, the time for premixed gas to form a flat flame and “tulip” flame increases and the position of characteristic flame formation is close to the ignition end.

Figure 5.

Figure 5

Open in a new tab

High-speed image of flame front in the configurations S-M and M-S at different concentrations. (a) N2: S-M; (b) CO2: S-M; (c) N2: M-S; and (d) CO2: M-S.

3.2. Effect of Duct Structure and N2/CO2 Content on Premixed Flame Propagation Velocity

Figure 6 shows the relationship between the position of the flame front and time under N2 dilution. The flame velocity is the time derivative of the flame front position. The flame front position is defined as the axial distance from the flame tip to the ignition position, i.e., x. The maximum propagation velocity is the maximum value of the time derivative of the position in front of the flame, i.e., Vmax = (dx/dt)max. As can be seen from Figure 6, the curve slope of the flame front position gradually decreases from left to right as the N2 addition ratio increases from 0 to 50% in the four ducts. It shows that the increase in inert gas concentration will slow down the flame front velocity and increase the time. For example, when the N2 addition ratio is 0 and 50% in Figure 6a, the time required for the flame to reach the end of the duct is 51.75 and 93.5 ms, which increased by 41.75 ms. As can be seen from the curve and the corresponding position in the picture, the sudden change in the duct causes a rapid increase in the position of the flame front. In Figure 6b, when φ = 0, the flame front position increases by 84 mm when the flame propagation time increases from 0 to 20 ms. But when the flame propagation time increased from 51 to 57 ms, the flame front position increased by 225 mm. The latter flame front position increased about 2.68 times compared to the former. It indicates that the sudden change in cross section accelerates the time and position change of the flame reaching the end of the duct.

Figure 6.

Figure 6

Open in a new tab

Relationship between the position of the flame front and time under N2. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

It can be seen from Figure 7 that the flame front position rises more slowly under CO2 dilution than that of N2 and the flame propagation time is longer. For example, the comparison of Figure 7a with Figure 6a reveals that the flame propagation time under CO2 dilution is 114 ms when the inert gas concentration is 50%, which is 20.5 ms more than that of N2.

Figure 7.

Figure 7

Open in a new tab

Relationship between the position of the flame front and time under CO2. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

Figure 8 shows the relationship between flame propagation velocity and flame front position under N2 dilution. It can be seen from Figure 8 that both the inert gas concentration and the duct structure have a certain effect on the flame propagation velocity. As shown in Figure 8a, when no N2 is added, the flame propagation velocity has only one deceleration, but when the N2 addition ratio is 20% or more, the flame propagation velocity has two decelerations. This indicates that an increase in the concentration of inert gas causes a change in the flame propagation velocity. In addition, the structure of the duct also affects the propagation pattern of flame velocity. When φN2 = 50%, the flame propagation velocity has only one deceleration in Figure 8c, but the flame propagation velocity has two decelerations in Figure 8d. Table 3 shows the flames arriving at the distance peak and velocity peak under N2 dilution. The inflection point of the flame propagation velocity is defined as the velocity peak, and the distance of the flame to reach the velocity peak is the distance peak. In general, the velocity peak decreases gradually and the distance peak becomes shorter as the addition ratio increases. For example, when the addition ratio is 0 and 50% in the configuration S-M, the flame distance peaks are 355 and 287 mm and the velocity peaks are 35 m/s and 10 ms, respectively. Its distance is reduced by 68 mm and velocity by 25 m/s.

Figure 8.

Figure 8

Open in a new tab

Relationship between the flame velocity and the position of the flame front under N2. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

Table 3. Flames Arriving at the Distance Peak and Velocity Peak under N2 Dilution.

φ (%) S-M M-S S-L L-S
0 355 mm (35 m/s) 259 mm (24 m/s) 494 mm (43 m/s) 274 mm (16 m/s)
10 330 mm (28 m/s) 249 mm (22 m/s) 473 mm (42 m/s) 241 mm (16 ms)
20 317 mm (26 m/s) 231 mm (18 m/s) 480 mm (41 m/s) 236 mm (16 m/s)
30 313 mm (23 m/s) 227 mm (15 m/s) 477 mm (37 m/s) 221 mm (15 m/s)
40 270 mm (15 m/s) 210 mm (13 m/s) 467 mm (33 m/s) 220 mm (13 m/s)
50 287 mm (10 m/s) 203 mm (11 m/s) 466 mm (26 m/s) 217 mm (12 m/s)
Open in a new tab

From Figure 9c with Figure 8c, it can be seen that the propagation velocity of the flame undergoes one deceleration when φN2 = 20%. But when φCO2 = 50%, the flame propagation velocity undergoes two deceleration. This indicates that CO2 has a stronger effect on flame propagation velocity than N2. In the configuration S-L, the flame velocity change is different from other ducts. Taking the ignition position as the starting point, the velocity from 0 to 400 mm takes longer to increase slowly than in the rest of the configuration duct. The flame propagation velocity rapidly increases from 400 to 500 mm, then decreases to a minimum velocity at 600 mm, and finally suddenly increases due to the turbulence in the duct. However, when φCO2 = 50%, the flame propagates from 400 to 500 mm, and due to the effect of flat flames and “tulip” flames, the flame first decelerates and then accelerates. Due to the influence of 50% CO2, there is a short deceleration of the flame propagation from 500 to 600 mm. After 600 mm, the velocity starts to increase linearly. Table 4 shows the flames arriving at the distance peak and velocity peak under CO2 dilution. It can be found that an increase in CO2 concentration decreases the peak velocity and shortens the peak distance of the flame. For example, when the addition ratio is 0 and 50%, the peak distance is reduced by 73 mm and the peak velocity is reduced by 28 m/s in the configuration S-M. By comparing the peak velocity and peak distance of CO2 and N2, it can be found that CO2 is more effective than N2 in suppressing the flame propagation velocity. In summary, the inert gas and duct structure not only changes the flame propagation velocity but also has an effect on the velocity curve law.

Figure 9.

Figure 9

Open in a new tab

Relationship between the flame velocity and the position of the flame front under CO2. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

Table 4. Flames Arriving at the Distance Peak and Velocity Peak under CO2 Dilution.

φ (%) S-M M-S S-L L-S
0 355 mm (35 m/s) 259 mm (24 m/s) 494 mm (43 m/s) 274 mm (17 m/s)
10 324 mm (30 m/s) 238 mm (20 m/s) 480 mm (40 m/s) 233 mm (17 m/s)
20 316 mm (24 m/s) 242 mm (18 m/s) 479 mm (35 m/s) 224 mm (14 m/s)
30 314 mm (21 m/s) 225 mm (15 m/s) 471 mm (34 m/s) 216 mm (12 m/s)
40 298 mm (18 m/s) 215 mm (13 m/s) 457 mm (23 m/s) 204 mm (10 m/s)
50 277 mm (12 m/s) 215 mm (12 m/s) 373 mm (13 m/s) 196 mm (8 m/s)
Open in a new tab

Figure 10 shows the variation of maximum flame propagation velocity (Vmax) with inert gas concentration. The flame propagation velocity in the sudden contraction duct is bigger than that of the sudden expansion duct. And the flame propagation velocity becomes faster as the cross-sectional area of the sudden change becomes larger. But the Vmax decreases with the increase of inert gas concentration. For example, when φ = 0, the flame propagation velocities of configurations S-M, M-S, S-L, and L-S are about 102, 108, 133, and 151 m/s, respectively. The Vmax in the configuration S-L is bigger than that of the configuration S-M. But the increase of inert gas concentration can lower the Vmax. When the addition ratio in the configuration L-S is 50%, the Vmax under N2 and CO2 dilution is about 109 and 73 m/s. The Vmax of CO2 is 36 m/s lower than that of CO2 (i.e., by 49.32%). Because CO2 has a higher heat capacity,9 a lower thermal diffusion coefficient actively participates in the dissociation reaction to compete for H radical.37 In addition, N2 can be regarded as an inert gas in the combustion process and hardly participates in chemical reactions, but CO2 is directly involved in some chemical reactions.32Figure 10c,d shows the error bars analysis of the Vmax and is similar to the corresponding Vmax change patterns in Figure 10a,b. The standard errors in the experimental Vmax were less than 6%.

Figure 10.

Figure 10

Open in a new tab

Relationship between the maximum flame propagation velocity and the concentration of N2 and CO2. (a) N2; (b) CO2; (c) N2: add error bars; and (d) CO2: add error bars.

It can be seen from Figure 11 that the time for the flame to reach the end of the duct increases with the concentration of inert gas. And the bigger the sudden change in cross-sectional area, the shorter the flame propagation time. When the N2 concentration is 0 and 50%, the flame arrival times at the end of the duct are 52 and 93.5 ms in the configuration S-M, respectively. The flame arrival times at the end of the duct are 43 and 65 ms in the configuration S-L. Compared with the time in the configuration S-M, the flame propagation time was reduced by 9 and 28.5 ms in the configuration S-L, which is about 50.93 and 43.85%, respectively. It can also be seen from Figure 11 that the flame propagation time in the sudden contraction duct is more than that in the sudden expansion duct. At the same concentration, the flame propagation time under CO2 dilution is longer than that of N2. When φ = 0, the flame propagation time is 57.5 ms in the configuration M-S, which is 5.5 ms longer than that of the configuration S-M. When the addition ratio of N2 and CO2 is 50%, the flame propagation time increases to 108 and 139 ms and the flame propagation time of CO2 is 29 ms longer than that of N2.

Figure 11.

Figure 11

Open in a new tab

Relationship between the time front takes to reach the downstream end and the concentration of N2 and CO2. (a) N2 and (b) CO2.

3.3. Effect of Duct Structure and N2/CO2 Content on Premixed Flame Explosion Overpressure

Figure 12 shows the relationship between overpressure and time under N2 dilution, exhibiting two types of pressure evolution curves under four types of ducts, single-peak and double-peak curves. As the curve in Figure 12d, there is a first overpressure peak Pmax1 and a second peak Pmax2. Cooper et al.49 studied the mechanism of overpressure in gas explosion exhaust. When the explosion occurs, the volume of gas in the duct expands rapidly and the pressure rises rapidly, which leads to the break of PVC film and the release of gas in the duct. The volume expansion rate and pressure drop suddenly, forming the first overpressure peak, which is also known as the “exhaust” pressure Pv. “Venting” pressure is not static pressure but dynamic pressure. After the first overpressure peak is formed, the explosion continues. The gas expansion rate is bigger than the gas release rate at the open end of the duct, so the overpressure continues to rise until the gas expansion rate is again equal to the gas release rate at the open end of the duct, resulting in the second overpressure peak Pmax2, which is the “overpressure” peak. Generally speaking, the maximum overpressure peak Pmax1 is controlled by the second peak Pmax2 when the gas expansion rate in the duct is always bigger than the gas release rate at the open end, forming a single-peak curve as shown in Figure 12a,c. It can be seen that the overpressure peaks Pmax1 and Pmax2 are both related to the expansion rate.

Figure 12.

Figure 12

Open in a new tab

Relationship between the overpressure and time in different ducts under the N2. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

In the premixed system, the increase in the concentration of inert gases (N2 and CO2) makes the reaction activity weaker and leads to a decrease in the expansion rate, which is the fundamental reason for the shift from single-peak to double-peak curves. It can be seen from Figure 12 that the overpressure curve changed from single-peak to double-peak when the addition ratio is 20% or more in the configuration M-S. And the Pmax2 time of formation also became longer with increasing concentration. Similarly, when the addition ratio is 10% in the configuration L-S, the overpressure curve also changes from single-peak to double-peak and Pmax2 is larger than Pmax1. But when the addition ratio is more than 10%, Pmax2 is smaller than Pmax1. In addition, the increase of the addition ratio makes Pmax2 gradually decrease and the time to reach Pmax2 increases.

As shown in Figure 13, when the addition ratio is 50% in conformations S-M and S-L, the overpressure curve changes from single-peak to double-peak. Similarly, when the addition ratio is 10% or more in configurations M-S and L-S, the overpressure curve also changes from single-peak to double-peak and Pmax2 is smaller than Pmax1. The comparison of Figure 13a with Figure 12a shows that the overpressure curves under CO2 dilution are different from that of N2. At the addition ratio of 50%, the dilution of CO2 changes the single-peak curve into the double-peak curve. In addition, CO2 inhibited the overpressure more than N2. For example, the added ratio is 10% in the configuration M-S, the overpressure under N2 dilution only produced a single-peak curve. But the overpressure under CO2 dilution produced a double-peak curve, and Pmax2 is smaller than Pmax1. This indicates that the weakened reactivity of the premixed gas and the reduced expansion rate made CO2 participate in the overpressure inhibition process more effectively than that of N2.

Figure 13.

Figure 13

Open in a new tab

Relationship between the overpressure and time in different ducts under the CO2. (a) S-M; (b) M-S; (c) S-L; and (d) L-S.

Figure 14 shows the relationship between the maximum explosion pressure and the concentration of inert gas. The explosion pressure decreases with the increase of inert gas concentration and stabilizes when the minimum explosion pressure is reached. When φN2 = 40% and φCO2 = 30%, the best suppression of pressure was achieved. For example, when φN2 = 40%, the maximum overpressure formed is 5.5 and 10.37 kPa in configurations S-M and M-S, respectively. Compared with the addition ratio of 0, it is reduced by 1.45 and 1.07 kPa. When φCO2 = 30%, the maximum overpressure formed is 5.54 and 11.40 kPa in configurations S-L and L-S, respectively. Compared with the addition ratio of 0, it is reduced by 1.69 and 3.35 kPa. This indicates that there is an optimal suppression concentration of inert gas in the variable-section duct.

Figure 14.

Figure 14

Open in a new tab

Relationship between maximum explosion pressure and inert gas concentration. (a) Two times the cross-sectional area of the duct. (b) Four times the cross-sectional area of the duct.

Figure 15 shows the relationship between the maximum pressure rise rate and the inert gas concentration. It can be seen from Figure 15 that the pressure rise rate gradually decreases with the increase of inert gas concentration. For example, when the addition ratio is 50% in the configuration S-L, the maximum pressure rise rates under N2 and CO2 dilution are 0.24 and 0.17 kPa/ms, i.e., a reduction of 18 and 42%, respectively. In a previous study, Mitu et al.27 investigated the rate of pressure rise of methane diluted with N2 and CO2 in a 0.52 L spherical vessel. It was found that the pressure rise rate decreased by approximately 30 and 52 kPa/ms or 40 and 69%, respectively, when the addition ratio of N2 and CO2 was 10%. The results of this study and the above study consistently show that CO2 is much more effective at suppressing explosion pressure than N2. The maximum pressure rise rates in the sudden contraction duct are higher than those in the sudden expansion duct. For example, when φ = 0, the maximum pressure rise rates are 0.42 and 0.70 kPa/ms in the configurations S-M and M-S, respectively. The larger the cross-sectional area of the sudden change, the higher the pressure rise rate. For example, when φ = 0, the maximum pressure rise rate in the configuration L-S is 0.87 kPa/ms, which is 0.17 kPa/ms higher in the configuration L-S than in the configuration M-S. But in the sudden expansion duct, the larger the sudden cross-sectional area is, the lower the pressure rise rate is. For example, when φN2 = 50%, the maximum pressure rise rate in the configuration S-L is 0.06 kPa/ms lower than that of the configuration S-M.

Figure 15.

Figure 15

Open in a new tab

Relationship between the maximum pressure rise rate and inert gas concentration. (a) N2 (b) CO2.

Figure 16 shows the relationship between the time for the flame to reach the pressure double-peak and the concentration of inert gas. The increase in inert gas concentration makes the flame take longer to reach the double-peak, and CO2 takes more time to reach the double-peak than N2. In the configuration M-S, Pmax2 does not appear when φ = 0. But when φN2 = 10%, the pressure curve does not form a complete overpressure peak so take the middle value of the sudden change in pressure as the overpressure peak. In Figure 16a, the arrival times of N2 for 10% are 47 and 63 ms. And those of N2 for 50% are 66 and 108 ms, an increase of 19 and 45 ms. The arrival times of CO2 for 50% are 70.5 and 118 ms or an increase of 23.5 and 55 ms. When φ = 50%, the time for CO2 to reach the double-peak increases by 4.5 and 10 ms more than that of N2.

Figure 16.

Figure 16

Open in a new tab

Relationship between the time required to reach pressure double-peak and inert gas concentration. (a) M-S and (b) L-S.

4. Conclusions

In this study, the effect of different concentrations of N2 and CO2 on the explosion characteristics of CH4/air premixed gas in a variable-section pipeline is experimentally investigated. The main conclusions are as follows:

  • (1)

    Premixed gases can form “tulip” flames in both S-M and M-S configurations, but only when the CO2 concentration is 50% in S-L and L-S configurations. The flame propagation time, maximum overpressure, and maximum flame propagation velocity in the suddenly contracted duct are larger than those in the suddenly expanded duct. The flame propagation time, flame propagation velocity, and overpressure rise as the cross-sectional area increases. However, the pressure rise rate is different. As the cross-sectional area of sudden change increases, it will increase in the suddenly contracted duct, while it will decrease in the suddenly expanded duct.

  • (2)

    Compared with N2, CO2 has a better suppression effect. At the same concentration, the time for the flame to reach the end of the duct under CO2 dilution is longer than that of N2, and the flame propagation velocity and explosion overpressure are lower.

  • (3)

    Increasing the concentration of inert gas leads to an increase in flame propagation time, a decrease in flame propagation speed and pressure rise rate, and stabilization of the explosion overpressure after it drops to a minimum value. When φCO2 = 30% and φN2 = 40%, the explosion overpressure decreases to the minimum value.

Acknowledgments

This work was supported by the Young Teacher Support Program of Henan Polytechnic University (2022XQG-16), the National Natural Science Foundation of China (No. 51974107), and the Innovative Scientific Research Team of Henan Polytechnic University (T2021-4).

The authors declare no competing financial interest.

References

  1. Elbaz A. M.; Roberts W. L. Investigation of the effects of quarl and initial conditions on swirling non-premixed methane flames: Flow field, temperature, and species distributions. Fuel 2016, 169, 120–134. 10.1016/j.fuel.2015.12.015. [DOI] [Google Scholar]
  2. Luo Z.; Liu L.; Cheng F.; Wang T.; Su B.; Zhang J.; Gao S.; Wang C. Effects of a carbon monoxide-dominant gas mixture on the explosion and flame propagation behaviors of methane in air. J. Loss Prev. Process Ind. 2019, 58, 8–16. 10.1016/j.jlp.2019.01.004. [DOI] [Google Scholar]
  3. Su B.; Luo Z.; Wang T.; Zhang J.; Cheng F. Experimental and principal component analysis studies on minimum oxygen concentration of methane explosion. Int. J. Hydrogen Energy 2020, 45, 12225–12235. 10.1016/j.ijhydene.2020.02.133. [DOI] [Google Scholar]
  4. Nishimura I.; Mogi T.; Dobashi R. Simple method for predicting pressure behavior during gas explosions in confined spaces considering flame instabilities. J. Loss Prev. Process Ind. 2013, 26, 351–354. 10.1016/j.jlp.2011.08.009. [DOI] [Google Scholar]
  5. QIAO L.; KIM C.; FAETH G. Suppression effects of diluents on laminar premixed hydrogen/oxygen/nitrogen flames. Combust. Flame 2005, 143, 79–96. 10.1016/j.combustflame.2005.05.004. [DOI] [Google Scholar]
  6. Liu J.; Yu R.; Ma B.; Tang C. On the Second Explosion Limits of Hydrogen, Methane, Ethane, and Propane. ACS Omega 2020, 5, 19268–19276. 10.1021/acsomega.0c02825. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Jia H.; Cui B.; Duan Y.; Zheng K. Study on the Influence of Vent Shape and Blockage Ratio on the Premixed Gas Explosion in the Chamber with a Small Aspect Ratio. ACS Omega 2022, 7, 22787–22796. 10.1021/acsomega.2c02367. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Pei B.; Yu M.; Chen L.; Zhu X.; Yang Y. Experimental study on the synergistic inhibition effect of nitrogen and ultrafine water mist on gas explosion in a vented duct. J. Loss Prev. Process Ind. 2016, 40, 546–553. 10.1016/j.jlp.2016.02.005. [DOI] [Google Scholar]
  9. Wang; Ni L.; Liu X.; Jiang J. C.; Wang R. Effects of N2/CO2 on explosion characteristics of methane and air mixture. J. Loss Prev. Process Ind. 2014, 31, 10–15. 10.1016/j.jlp.2014.06.004. [DOI] [Google Scholar]
  10. Zhang B.; Xiu G.; Bai C. Explosion characteristics of argon/nitrogen diluted natural gas–air mixtures. Fuel 2014, 124, 125–132. 10.1016/j.fuel.2014.01.090. [DOI] [Google Scholar]
  11. Gonzalez M.; Borghi R.; Saouab A. Interaction of a flame front with its self-generated flow in an enclosure: The “tulip flame” phenomenon. Combust. Flame 1992, 88, 201–220. 10.1016/0010-2180(92)90052-Q. [DOI] [Google Scholar]
  12. Clanet C.; Searby G. On the “ Tulip Flame ” Phenomenon. Combust. Flame 1996, 105, 225–238. 10.1016/0010-2180(95)00195-6. [DOI] [Google Scholar]
  13. Xiao H.; Wang Q.; He X.; Sun J.; Shen X. Experimental study on the behaviors and shape changes of premixed hydrogen–air flames propagating in horizontal duct. Int. J. Hydrogen Energy 2011, 36, 6325–6336. 10.1016/j.ijhydene.2011.02.049. [DOI] [Google Scholar]
  14. Xiao H.; Wang Q.; Shen X.; Guo S.; Sun J. An experimental study of distorted tulip flame formation in a closed duct. Combust. Flame 2013, 160, 1725–1728. 10.1016/j.combustflame.2013.03.011. [DOI] [Google Scholar]
  15. Xiao H.; Houim R. W.; Oran E. S. Formation and evolution of distorted tulip flames. Combust. Flame 2015, 162, 4084–4101. 10.1016/j.combustflame.2015.08.020. [DOI] [Google Scholar]
  16. Bao Q.; Fang Q.; Zhang Y.; Chen L.; Yang S.; Li Z. Effects of gas concentration and venting pressure on overpressure transients during vented explosion of methane–air mixtures. Fuel 2016, 175, 40–48. 10.1016/j.fuel.2016.01.084. [DOI] [Google Scholar]
  17. Li J.; Wang X.; Guo J.; Zhang J.; Zhang S. Effect of concentration and ignition position on vented methane–air explosions. J. Loss Prev. Process Ind. 2020, 68, 104334 10.1016/j.jlp.2020.104334. [DOI] [Google Scholar]
  18. Ajrash M. J.; Zanganeh J.; Moghtaderi B. Deflagration of premixed methane–air in a large scale detonation tube. Process Saf. Environ. 2017, 109, 374–386. 10.1016/j.psep.2017.03.035. [DOI] [Google Scholar]
  19. Tan B.; Liu Y.; Liu H.; Wang H.; Li T. Research on size effect of gas explosion in the roadway. Tunn. Undergr. Space Technol. 2021, 112, 103921 10.1016/j.tust.2021.103921. [DOI] [Google Scholar]
  20. Wang S.; Cai Y.; Guo H.; Wu D.; Xie Y. Effect of fuel concentration, inert gas dilutions, inert gas–water mist twin fluid medium dilutions, and end boundary condition on overpressure transients of premixed fuel vapor explosion. Fuel 2022, 309, 122083 10.1016/j.fuel.2021.122083. [DOI] [Google Scholar]
  21. Yu M.; Yang X.; Zheng K.; Zheng L.; Wan S. Experimental study of premixed syngas/air flame propagation in a half-open duct. Fuel 2018, 225, 192–202. 10.1016/j.fuel.2018.03.127. [DOI] [Google Scholar]
  22. de Persis S.; Foucher F.; Pillier L.; Osorio V.; Gökalp I. Effects of O2 enrichment and CO2 dilution on laminar methane flames. Energy 2013, 55, 1055–1066. 10.1016/j.energy.2013.04.041. [DOI] [Google Scholar]
  23. Di Benedetto A.; Di Sarli V.; Salzano E.; Cammarota F.; Russo G. Explosion behavior of CH4/O2/N2/CO2 and H2/O2/N2/CO2 mixtures. Int. J. Hydrogen Energy 2009, 34, 6970–6978. 10.1016/j.ijhydene.2009.05.120. [DOI] [Google Scholar]
  24. Khan A. R.; Anbusaravanan S.; Kalathi L.; Velamati R.; Prathap C. Investigation of dilution effect with N2/CO2 on laminar burning velocity of premixed methane/oxygen mixtures using freely expanding spherical flames. Fuel 2017, 196, 225–232. 10.1016/j.fuel.2017.01.086. [DOI] [Google Scholar]
  25. Giurcan V.; Razus D.; Mitu M.; Oancea D. Prediction of flammability limits of fuel-air and fuel-air-inert mixtures from explosivity parameters in closed vessels. J. Loss Prev. Process Ind. 2015, 34, 65–71. 10.1016/j.jlp.2015.01.025. [DOI] [Google Scholar]
  26. Mitu M.; Giurcan V.; Razus D.; Prodan M.; Oancea D. Propagation indices of methane-air explosions in closed vessels. J. Loss Prev. Process Ind. 2017, 47, 110–119. 10.1016/j.jlp.2017.03.001. [DOI] [Google Scholar]
  27. Mitu M.; Prodan M.; Giurcan V.; Razus D.; Oancea D. Influence of inert gas addition on propagation indices of methane–air deflagrations. Process Saf. Environ 2016, 102, 513–522. 10.1016/j.psep.2016.05.007. [DOI] [Google Scholar]
  28. Galmiche B.; Halter F.; Foucher F.; Dagaut P. Effects of Dilution on Laminar Burning Velocity of Premixed Methane/Air Flames. Energy Fuel 2011, 25, 948–954. 10.1021/ef101482d. [DOI] [Google Scholar]
  29. Xie M.; Fu J.; Zhang Y.; Shu J.; Ma Y.; Liu J.; Zeng D. Numerical analysis on the effects of CO2 dilution on the laminar burning velocity of premixed methane/air flame with elevated initial temperature and pressure. Fuel 2020, 264, 116858 10.1016/j.fuel.2019.116858. [DOI] [Google Scholar]
  30. Jithin E. V.; Varghese R. J.; Velamati R. K. Experimental and numerical investigation on the effect of hydrogen addition and N2/CO2 dilution on laminar burning velocity of methane/oxygen mixtures. Int. J. Hydrogen Energy 2020, 45, 16838–16850. 10.1016/j.ijhydene.2020.04.105. [DOI] [Google Scholar]
  31. Wang S.; Wang Z.; He Y.; Han X.; Sun Z.; Zhu Y.; Costa M. Laminar burning velocities of CH4/O2/N2 and oxygen-enriched CH4/O2/CO2 flames at elevated pressures measured using the heat flux method. Fuel 2020, 259, 116152 10.1016/j.fuel.2019.116152. [DOI] [Google Scholar]
  32. Hu X.; Yu Q.; Sun Y. Effects of carbon dioxide on the upper flammability limits of methane in O2/CO2 atmosphere. Energy 2020, 208, 118417 10.1016/j.energy.2020.118417. [DOI] [Google Scholar]
  33. Egolfopoulos F. N.; Holley A. T.; Law C. K. An assessment of the lean flammability limits of CH4/air and C3H8/air mixtures at engine-like conditions. Proc. Combust. Inst. 2007, 31, 3015–3022. 10.1016/j.proci.2006.08.018. [DOI] [Google Scholar]
  34. Wang T.; Liang H.; Luo Z.; Su B.; Liu L.; Su Y.; Wang X.; Cheng F.; Deng J. Near flammability limits behavior of methane-air mixtures with influence of flammable gases and nitrogen: An experimental and numerical research. Fuel 2021, 294, 120550 10.1016/j.fuel.2021.120550. [DOI] [Google Scholar]
  35. Huang L.; Pei S.; Wang Y.; Zhang L.; Ren S.; Zhang Z.; Xiao Y. Assessment of flammability and explosion risks of natural gas-air mixtures at high pressure and high temperature. Fuel 2019, 247, 47–56. 10.1016/j.fuel.2019.03.023. [DOI] [Google Scholar]
  36. Luo Z.; Wei C.; Wang T.; Su B.; Cheng F.; Liu C.; Wang Y. Effects of N2 and CO2 dilution on the explosion behavior of liquefied petroleum gas (LPG)-air mixtures. J. Hazard. Mater. 2021, 403, 123843 10.1016/j.jhazmat.2020.123843. [DOI] [PubMed] [Google Scholar]
  37. Chen Z.; Tang C.; Fu J.; Jiang X.; Li Q.; Wei L.; Huang Z. Experimental and numerical investigation on diluted DME flames: Thermal and chemical kinetic effects on laminar flame speeds. Fuel 2012, 102, 567–573. 10.1016/j.fuel.2012.06.003. [DOI] [Google Scholar]
  38. Wang J.; Fan Z.; Wu Y.; Zheng L.; Pan R.; Wang Y. Effect of Abrupt Changes in the Cross-Sectional Area of a Pipe on Flame Propagation Characteristics of CH4 /Air Mixtures. ACS Omega 2021, 6, 15126–15135. 10.1021/acsomega.1c01350. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Dong W.; Jin T.; Qiu B.; Chu H. Effects of carbon dioxide on the combustion characteristics of the laminar premixed n-heptane/air flames at elevated pressures. J. Energy Inst. 2021, 99, 127–136. 10.1016/j.joei.2021.08.011. [DOI] [Google Scholar]
  40. Liu F.; Guo H.; Smallwood G. J. The chemical effect of CO2 replacement of N2 in air on the burning velocity of CH4 and H2 premixed flames. Combust. Flame 2003, 133, 495–497. 10.1016/S0010-2180(03)00019-1. [DOI] [Google Scholar]
  41. Xiang L.; Chu H.; Ren F.; Gu M. Numerical analysis of the effect of CO2 on combustion characteristics of laminar premixed methane/air flames. J. Energy Inst. 2019, 92, 1487–1501. 10.1016/j.joei.2018.06.018. [DOI] [Google Scholar]
  42. Li X.; Xiao H.; Duan Q.; Sun J. Numerical study of premixed flame dynamics in a closed tube: Effect of wall boundary condition. Proc. Combust. Inst. 2021, 38, 2075–2082. 10.1016/j.proci.2020.08.032. [DOI] [Google Scholar]
  43. Zheng L.; Du D.; Wang J.; Dou Z.; Wang X.; Jin H.; Wang Y. Study on premixed flame dynamics of CH4/O2/CO2 mixtures. Fuel 2019, 256, 115913 10.1016/j.fuel.2019.115913. [DOI] [Google Scholar]
  44. Zhong; Zheng L.; Wang X.; Shao X.; Jia H.; Shi Z.; Zhang J. Comparative study on flame instability and combustion characteristics of CH4/O2/CO2 and CH4/O2/N2 mixtures. J. Energy Inst. 2022, 102, 70–81. 10.1016/j.joei.2022.02.009. [DOI] [Google Scholar]
  45. Wang J.; Wu Y.; Zheng L.; Yu M.; Pan R.; Shan W. Study on the propagation characteristics of hydrogen/methane/air premixed flames in variable cross-section ducts. Process Saf. Environ. 2020, 135, 135–143. 10.1016/j.psep.2019.12.029. [DOI] [Google Scholar]
  46. Zheng K.; Yang X.; Yu M.; Si R.; Wang L. Effect of N2 and CO2 on explosion behavior of syngas/air mixtures in a closed duct. Int. J. Hydrogen Energy 2019, 44, 28044–28055. 10.1016/j.ijhydene.2019.09.053. [DOI] [Google Scholar]
  47. Ponizy B.; Claverie A.; Veyssière B. Tulip flame - the mechanism of flame front inversion. Combust. Flame 2014, 161, 3051–3062. 10.1016/j.combustflame.2014.06.001. [DOI] [Google Scholar]
  48. Sun Z.; Li G. Propagation speed of wrinkled premixed flames within stoichiometric hydrogen-air mixtures under standard temperature and pressure. Korean J. Chem. Eng. 2017, 34, 1846–1857. 10.1007/s11814-017-0084-3. [DOI] [Google Scholar]
  49. Cooper M. G. On the Mechanisms of Pressure Generation in Vented Explosions. Combust. Flame 1986, 65, 1–14. 10.1016/0010-2180(86)90067-2. [DOI] [Google Scholar]

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES