#### Abstract

In order to research on gas exploration shock wave spread law via a one-way bifurcation pipeline, the gas exploration pipeline experimental system and numerical calculation model were established. By adopting the comparative analysis of experiments and numerical modeling, it conducted researches on the attenuation and shunt characteristics of the gas exploration shock wave via the one-way bifurcation pipeline and obtained the computational formulas for shock wave attenuation coefficients of branch pipelines and straight pipelines and shock wave shunt coefficients of branch pipelines. As the research result showed that when the pipeline bifurcation angle was fixed, the larger the shock wave overpressure was, the larger the overpressure attenuation coefficients of straight pipelines and branch pipelines were. When the shockwave overpressure was fixed and the one-way bifurcation pipeline angle increased, the shock wave overpressure attenuation coefficients of branch pipelines would be aggregated and the shock wave overpressure attenuation coefficients of straight pipelines would be decreased, which reflected the shunting action of the shock wave in branch pipelines and straight pipelines; the larger the branch pipeline bifurcation angle, the smaller the shunting action for straight pipelines. The research achievements in the paper had important significance for the assessment of structures damage in mine laneways gas exploration accidents and installation of the antiexploration manhole cover, which further enriched gas exploration spread theory.

#### 1. Introduction

Gas exploration accidents had the characteristics of strong complexity and large destructiveness. In general, mine gas exploration accidents always resulted in the damage of the underground ventilation system, structures, and inspection and monitoring systems, which could cause the disorder of underground airflow, further aggravate the accumulation of gas, and lead to continuous and repeated gas exploration accidents. In the meantime, the rapid spread of poisonous and harmful gas generated after gas exploration could cause a large amount of injuries and deaths among underground staff. Gas exploration accidents existed along with coal mining. With the increase of coal mining depth year by year, the emission of mine gas became increasingly more and the pressure which discharged gas also became more and more, which enlarged the possibility of triggering gas exploration [1–3]. This paper studies the law of attenuation and propagation of the shock wave after the gas explosion accident in general air districts, instead of the law of mutual association between shock wave and flame wave in the gas combustion area. The research achievements in the paper had important significance for the rescue decision-making of gas explosion accidents such as roadway damage and selection of disaster relief route. The shock wave pressure generally appears to be attenuating in general air districts. Therefore, the research results in this paper are of guiding significance to accident control rather than accident prevention, and it was of great significance to make research on the assessment of influence of gas exploration shock wave spread law on gas exploration accidents shock wave damage severity and on design of structures, such as mine ventilation facilities.

Some foreign countries with relatively developed industrialization had started researches on gas exploration early. From 1980s, there were many researches on the gas exploration mechanism from home and abroad. In America, Australia, Poland, Russia, Japan, etc., there were experimental researches on the exploration and spread characteristics of premixed combustible gas. In America, there were National Institute for Occupational Safety and Health (NIOSH), Pittsburgh research center and Lake Lynn experimental mine; in Australia, the London Dare safety research center was established; some European countries had established the premix flammable gas exploration experiment system and conducted experimental researches [4–6]. The gas exploration researches in China was a little late than European and American countries; however, China paid much attention on coal mine safety technology researches [7, 8]. With the great support of governments and technology departments, China had conducted fundamental researches on coal mine gas exploration mechanisms from 1980s. In recent thirty years, with the continuous development of coal mining technology and safety technology, the explosion prevention and control national key laboratory from Beijing Institute of Technology, gas explosion key laboratory from China University of Mining and Technology, Henan Polytechnic University, Fushun Branch of China Coal Research Institute, Institute of Mechanics, Chinese Academy of Sciences, Power Engineering College Explosion Laboratory of Nanjing University of Science and Technology, had established the premixed flammable gas explosion experiment pipeline system successively and obtained a large amount of achievements through researches. At present, scholars from home and abroad had conducted researches on the gas explosion occurrence mechanism, propagation process, influence factors, fire losses estimation, and rescue decision-making [9–16]. Lin Baiquan, professor of China University of Mining and Technology, had made researches on the influential factors of the shock wave and flame propagation in the pipeline gas explosion combustion area [17, 18]. Jing Guoxun, professor from Henan Polytechnic University, had led his team to research the gas explosion shock wave, flame, poisonous gas propaganda law influential factors in the pipeline air area [9, 10, 19, 20]. Currently, there was shortage of researches on pipeline gas explosion shock wave propaganda law. The factors which affected the pipeline gas explosion shock wave propaganda were complicated. The current research achievements were mainly about the shock wave affecting factors such as the roughness of pipeline wall, pipeline bend, pipeline cross section change, and barriers, but there were few researches on gas explosion shock wave propaganda law under the complicated bifurcation pipeline. However, most mine laneways were complicated network, and it was of practical significance to make researches on shock wave propaganda principles in complicated pipelines [21–23].

Under such circumstances, the paper conducted researches on the most common one-way bifurcation pipeline and adopted the shock wave attenuation law under laboratory one-way bifurcation pipeline to simulate shock wave attenuation law under the practical one-way bifurcation pipeline.

#### 2. Experimental Research on Gas Explosion Shock Wave Spread Law via the One-Way Bifurcation Pipeline in the Nongas Combustion Area

In the gas combustion area, the shock wave would have coupling spread with the combustion wave and interact with each other. Meanwhile, the shock wave overpressure had the trend of enlarging gradually. In the nongas combustion area, when the gas combustion finished, the shock wave showed decreasing tendency. The purpose of the paper was to research on the attenuation law of the shock wave in the pipeline in the nongas combustion area.

##### 2.1. Experimental System

The paper adopted gas explosion experimental platform from China University of Mining and Technology and established the one-way bifurcation pipeline gas explosion experimental system. The experimental pipeline contained five subsystems, i.e., high energy ignition device, air distribution device, vacuum meter, gas explosion experimental pipe system, and analysis system of dynamic data. The high energy ignition device was used to ignite gas, which was low pressure stored energy and high pressure discharge; the air compressor was composed of two parts: vacuum pump and air compressor. The air compressor was mainly for generating compressed air and preparing premixed flammable gas; the vacuum pump was used for delivering prepared flammable gas into the gas-filling area inside the pipeline; the experimental pipeline system was designed as a square-shaped pipeline with the cross section of 80 mm ∗ 80 mm and total length of 20.9 m; and TST6300 dynamic data collection and analysis system would integrate dynamic data storage device, various sensors, and computers and then collect pressure data.

The physical models are shown in Figure 1.

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##### 2.2. Experimental Scheme

The length of the gas explosion combustion area is usually 3 times that of the gas-filling area. The maximum length of the gas-filling area is set to 6 meters during the experiment. This paper studies the law of attenuation and propagation of the shock wave after the gas explosion accident in general air districts. In order to ensure that the gas explosion flame wave cannot reach the bend of the pipeline during the experiment, the experimental straight line pipeline is set to 19 meters and the total length of the pipeline is 20.9 meters, which was set up to simulate the actual mine roadway.

The experimental pipeline was a square-shaped pipeline with the cross section of 80 mm ∗ 80 mm and total length of 20.9 m. At the left end of the gas explosion test chamber, the gas-filling area was set and high energy ignition device could be used to ignite gas; at the right end, one-way bifurcation pipeline and pressure sensors were installed to test shock wave overpressure at pipeline bifurcation, as shown in Figure 2.

Normally, mine roadways are rare with more than 90 degrees. But the propagation direction of the gas explosion shock wave along the roadway may be reversed during the disaster and the shock wave does not propagate in the direction of wind flow, so the bifurcation angles more than 90 degrees of the experimental pipe for the gas explosion shock wave experiment was set up to simulate the actual situation in the mine roadway.

In order to simulate the spread law of underground gas explosion in roadway, the paper adopted the pipeline model with seven bifurcation angles: 30°, 45°, 60°, 90°, 120°, 135°, and 150°. Since shockwave had reflection stack phenomenon at the bifurcation or turning, there were high pressure area and low pressure area for the shock wave pressure in the area. The purpose of the paper was to research the general attenuation and shunt principle inside straight pipeline and branch pipeline after the shock wave had passed pipeline bifurcation, instead of shock wave reflection stack phenomenon in the regional area. Therefore, the pressure sensor was installed outside pipeline bifurcation reflection stack areas. The system experiments had proved that when the no. 1 and no. 2 pressure sensors were 0.5 m away from bifurcation and no. 3 pressure sensor was 1.5 m away from bifurcation, the reflection stack phenomenon could be almost ignored. Therefore, no. 1 and no. 2 pressure sensors shall be installed 0.5 m away from bifurcation and no. 3 pressure sensor 1.5 m away from bifurcation.

The main research on this paper is gas exploration shock wave spread law via the one-way bifurcation pipeline, so the concept of shock wave overpressure is that shock wave absolute pressure removes a standard atmospheric pressure, which is a parameter characterizing shock wave propagation in this paper. The unit of shock wave overpressure is Pascal. The experiment mainly focused on the shock wave attenuation and bifurcation laws under a different initial pressure and distinct pipeline bifurcation angles. Therefore, in the experiment, it filled 4, 5, and 6 m gas with volume fraction of 9.5% in the gas explosion combustion area (spherical valves in Figure 2) under the same bifurcation angle to change the shock wave initial pressure. The experiment was repeated for three times and nine times in total.

The pipeline shock wave attenuation coefficient represented for the attenuation principle of shock wave overpressure inside the pipeline, while the branch shock wave overpressure shunt coefficient stood for the influence of the shock wave spreading inside the branch pipeline on the straight shunt effect. By combining both indicators, it could represent the shock wave attenuation principles in bifurcation pipelines (branch and straight pipelines). The shock wave pressure tested at testing points no. 1, no. 2, and no. 3 were overpressure peak. It could define Overpressure at no. 1 testing point/overpressure at no. 2 testing point = straight pipeline shock wave overpressure attenuation coefficient *K*_{1} Overpressure at no. 1 testing point/overpressure at no. 3 testing point = branch pipeline shock wave overpressure attenuation coefficient *K*_{2} Overpressure at no. 3 testing point/overpressure at no. 2 testing point = branch pipeline shock wave overpressure bifurcation coefficient *M*

##### 2.3. Experimental Data Analysis

In the experiment, it made analysis of the shock wave overpressures at different testing points in the circumstances of seven bifurcation pipelines and three kinds of distinct gas-filling amount. The emphasis was put on the influence of shock wave initial overpressure and pipeline bifurcation angles on one-way bifurcation pipeline attenuation coefficient changes, as shown in Tables 1 and 2. In Table 1, it presented gas explosion shock wave experimental data; in Table 2, it showed gas coal dust explosion shock wave data. The reason why gas coal dust explosion was adopted was that the initial overpressure of shock wave generated through gas coal dust explosion was far larger than that from gas explosion. The purpose of the experiment was to verify the influence of shock wave initial overpressure on the shock wave attenuation coefficient and shunting coefficient via the one-way bifurcation pipeline.

By analyzing experimental data, it could be known that, under the same conditions, the larger the initial pressure was, the larger the straight pipeline attenuation coefficient *K*_{1} and branch pipeline attenuation coefficient *K*_{2} were. Since the shock wave was a kind of the air compression wave, the larger the shock wave initial overpressure was, the larger the oblique shock wave pressure generated by the shock wave at pipeline bifurcation was, and the faster the shock wave attenuation was because the energy loss was greater after strong reflection stack of the shock wave. No matter it was in pipeline bifurcation, pipeline bend, and straight pipeline, the characteristics of the shock wave attenuation coefficient would increase along with the enlargement of initial pressure when kept the same.

Under the same conditions, the main factor which affected shock wave attenuation coefficient change was the pipeline bifurcation angle, which had greater influence than initial overpressure. The influence of initial overpressure on the straight and branch pipelines shock wave attenuation coefficient was smaller than the influence of the pipeline bifurcation angle, so that the influence of initial overpressure could be almost ignored. In the data analysis process, it would select the average testing results of 4 m, 5 m, and 6 m gas-filling length. Therefore, in the pipeline bifurcation condition, the influence of initial overpressure on the attenuation coefficient could be ignored and only the influence of the pipeline bifurcation angle on the attenuation coefficient shall be analyzed, as shown in Figure 3.

Under pipeline bifurcation circumstance, when the bifurcation angle was in the range of 30°–90°, the branch pipeline attenuation coefficient *K*_{2} was between 1.4 and 1.9, while the straight pipeline attenuation coefficient *K*_{1} was between 1.5 and 1.0 and the branch bifurcation coefficient *M* was between 0.9 and 0.6; when the bifurcation angle was in the range of 90°–150°, the branch pipeline attenuation coefficient *K*_{2} was between 1.9 and 2.9, while the straight pipeline attenuation coefficient *K*_{1} was between 1.1 and 1.0 and the branch bifurcation coefficient *M* was between 0.6 and 0.3. When the branch pipeline attenuation coefficient *K*_{2} was enlarged, the straight pipeline attenuation coefficient *K*_{1} would decrease, which reflected the shock wave shunting effect in branch and straight pipelines, i.e., when the branch pipeline bifurcation angle was larger, the shunting effect for the straight pipeline was smaller. The both could have mutual influences. In pipeline bifurcation conditions, shock wave attenuation in branch pipelines was larger than that in the straight pipeline. Therefore, the coal mine antiexplosion manhole cover shall be installed in the branch roadway of return air shaft in order to protect main ventilators.

From Figure 3, it could be known that, under pipeline one-way bifurcation, the change of the gas explosion shock wave attenuation coefficient and shunting coefficient along with the pipeline bifurcation angle was shown below from Formulas (1)–(3). The formulas could provide reference for the shock wave overpressure attenuation after mine gas explosion accidents. Combined with the damage criterion of shock wave on human bodies, it could estimate the severity and damage scope of gas explosion accidents.

Straight pipeline shock wave attenuation coefficient:

Branch pipeline shock wave attenuation coefficient:

Branch pipeline shock wave shunting coefficient:

#### 3. Numerical Simulation Research on Gas Explosion Shock Wave Spread Law via the One-Way Bifurcation Pipeline in the Nongas Combustion Area

Based on FLUENT software numerical simulation, the paper researched on gas explosion shock wave spread law via the one-way bifurcation pipeline in the nongas combustion area adopted the method of combining experiments and numerical simulation and established the mathematic models which was the same with experiment conditions.

##### 3.1. Initial Conditions and Boundary Conditions

The initial conditions in the burned zone were as follows: *T* = 1600 K; *P* = 102325 Pa; *X*_{V} = 0, *Y*_{V} = 0; , , , and . The initial conditions in the unburned zone were as follows: *T* = 300 K; *P* = 0 Pa; *X*_{V} = 0, *Y*_{V} = 0; , , , and . The initial conditions in the air zone were as follows: , , , and . Boundary conditions: the boundary was set as the thermal insulated surface, and the temperature was 300 K; the two exit faces going through branch points were set as pressure exits.

##### 3.2. Analysis of Numerical Simulation Results

Through numerical simulation, it calculated the shockwave overpressure value at bifurcation under the circumstances that gas-filling lengths were 4 m, 5 m, and 6 m, respectively, and one-way bifurcation pipeline bifurcation angles were 30°, 45°, 60°, 90°, 120°, 135°, and 150°, as shown in Table 3.

From Table 3, it was known that, under pipeline bifurcation circumstance, when the bifurcation angle was in the range of 30°–90°, the branch pipeline attenuation coefficient *K*_{2} was between 1.4 and 2.8, while the straight pipeline attenuation coefficient *K*_{1} was between 1.1 and 1.4 and the branch bifurcation coefficient *M* was between 0.43 and 0.91; when the bifurcation angle was in the range of 90°–150°, the branch pipeline attenuation coefficient *K*_{2} was between 1.52 and 2.78, while the straight pipeline attenuation coefficient *K*_{1} was between 1.18 and 1.38 and the branch bifurcation coefficient *M* was between 0.36 and 0.43. When the branch pipeline attenuation coefficient *K*_{2} was enlarged, the straight pipeline attenuation coefficient *K*_{1} would decrease, which reflected the shock wave shunting effect in branch and straight pipelines, i.e., when the branch pipeline bifurcation angle was larger, the shunting effect for the straight pipeline was smaller. The both could have mutual influences.

The numerical simulation results were compared with the experimental data. The maximum pressure of the gas explosion shock wave measured at testing point no. 1 was 47.4209 KPa, while the maximum pressure from the numerical simulation result was 48.062006 KPa; the maximum pressure of the gas explosion shock wave measured at testing point no. 2 was 44.0654 KPa, while the maximum pressure from the numerical simulation result was 40.586941 KPa; and the maximum pressure of the gas explosion shock wave measured at testing point no. 3 was 26.6673 KPa, while the maximum pressure from the numerical simulation result was 29.938706 KPa. By comparing and analyzing numerical simulation results and experimental results, the deviations were in 8&, which implied that the simulation results were reliable. Through comparison and analysis of experimental data and numerical simulation data, the attenuation coefficient and shunting coefficient curves under different pipeline bifurcation conditions are shown in Figure 4. In the data analysis, it selected the average value under 4 m, 5 m, and 6 m gas-filling lengths.

From Figure 4, it could be known that the increase or decrease trend of numerical simulation calculation parameters matched with that of the results measured in experiments. However, the data from numerical simulation calculation were larger than that from the experiment, and the attenuation coefficient and shunting coefficient were larger than that from the experiment. The main reasons were as follows:(1)In numerical simulation, the conditions were ideal and the factors affecting gas explosion were not taken into consideration, such as air mass force, pipeline wall heat loss, and pipeline wall roughness, which made shock wave overpressure numerical simulation calculation results larger.(2)In gas explosion experiments, the pipelines were not completely sealed and the gas explosion shock wave was impeded at the place where ball valves were installed, so that there was energy loss when the shock wave spread to pipeline connections and ball valves, which made the numerical simulation calculation result larger than the experiment result.

#### 4. Conclusion

(1)Under the same conditions, the larger the initial pressure was, the larger the straight pipeline attenuation coefficient *K*_{1} and branch pipeline attenuation coefficient *K*_{2} were. The shock wave attenuation coefficient kept the same characteristics that it increased with the enlargement of initial pressure no matter in pipeline bifurcation, pipeline bend, and straight pipeline conditions.(2)Under the same conditions, the main factor which affected shock wave attenuation coefficient change was the pipeline bifurcation angle, which had greater influence than initial overpressure. Under pipeline bifurcation circumstance, when the bifurcation angle was in the range of 30°–90°, the branch pipeline attenuation coefficient *K*_{2} was between 1.4 and 1.9, while the straight pipeline attenuation coefficient *K*_{1} was between 1.5 and 1.0 and the branch bifurcation coefficient *M* was between 0.9 and 0.6; when the bifurcation angle was in the range of 90°–150°, the branch pipeline attenuation coefficient *K*_{2} was between 1.9 and 2.9, while the straight pipeline attenuation coefficient *K*_{1} was between 1.1 and 1.0 and the branch bifurcation coefficient *M* was between 0.6 and 0.3.(3)When branch pipeline attenuation coefficient *K*_{2} was enlarged, the straight pipeline attenuation coefficient *K*_{1} would decrease, which reflected the shock wave shunting effect in branch and straight pipelines, i.e., when the branch pipeline bifurcation angle was larger, the shunting effect for the straight pipeline was smaller. The both could have mutual influences. In pipeline bifurcation conditions, the shockwave attenuation in the branch pipeline was larger than that in the straight pipeline.(4)Without considering influences of initial pressure, it obtained the formula that the gas explosion shock wave attenuation coefficient and shunt coefficient in pipeline one-way bifurcation changed along with pipeline bifurcation angles.

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

The authors would like to thank the financial support from the National Natural Science Foundation for Young Scientists of China (51604096, 51704099, and 51774120), Basic and Frontier Technology Research Project of Henan Province in 2016 (162300410031), Hebei State Key Laboratory of Mine Disaster Prevention (KJZH2017K08), Doctoral Fund of Henan Polytechnic University (B2015-05), and Open Fund of Energy Platform Laboratory Project (G201609).