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. 2023 Jan 11;8(3):2953–2964. doi: 10.1021/acsomega.2c05553

Numerical and Experimental Study on Flame Dynamics of the Premixed Methane–Air Mixture at Different Ignition Positions in a Two-Side 45° Branch Tube

Zhuangzhuang Xu 1, Haoxin Deng 1,*, Xiaoping Wen 1, Fahui Wang 1, Guoyan Chen 1, Mengmeng Yan 1, Shengnan Wei 1
PMCID: PMC9878620  PMID: 36713713

Abstract

graphic file with name ao2c05553_0012.jpg

The combustion characteristics of premixed methane–air flames in a half-open tube with a two-sided 45° branch structure at different ignition positions were investigated by experiments and large eddy simulations. The numerical results were compared with the experimental results to verify the correctness of the model. The results show that the simulation results are highly consistent with the experiment. This study provides a basic understanding of the effects of the branch tube structure and the ignition position on flame dynamics. When the flame propagates to the branch interface, it forms a symmetrical vortex structure at the branch tube with the opposite rotation direction. When the ignition position is at IP0 and IP900, the maximum overpressures obtained in the experiment are 10.1 and 10.7 kPa, respectively, and 9.2 and 10.4 kPa in the simulation, respectively. At IP0, the Karlovitz number indicating the interaction intensity between the flame surface and the turbulence during flame propagation is a maximum of 9.2 and a minimum of 0.04. The premixed flame has a folded small flame, a corrugated small flame, and a thin reaction zone.

1. Introduction

Premixed methane–air is potentially dangerous in industries such as natural gas transmission, coal mining, and plant operations and can cause significant harm to personnel and production equipment.1−4 When the premixed gas explodes in a space with complex structure, the complex structure interacts with the gas flow generated by the explosion to generate a vortex. The vortex structure leads to serious wrinkles on the flame front, increasing the flame surface area. Pressure and flame propagation velocity increase with the increase in surface area, which can cause more serious damage. It is of great significance to study the gas explosion characteristics in complex structure tubes for industrial production safety protection.

The explosion process of premixed gas in tubes is usually unstable, and it would be affected by various fluid dynamics and combustion instabilities, such as Darrieus–Landau,5 acoustic waves, Rayleigh–Taylor instability, vortices, etc.6,7 Many experiments have been conducted to show that the premixed gas deflagration process in the tube is influenced by factors such as the initial temperature,8 the gas concentration,9 the ignition location,10 the tube aspect ratio,11 and the branching structure.12

In the process of industrial production, complex tube structures may increase the harm caused by the explosion. Many scholars have conducted a lot of experimental and numerical simulation studies on gas explosion characteristics in different tube structures and ignition locations. Sato et al.13 studied the flame propagation characteristics in a small-scale open square tube with a 90° bend through experimental and numerical simulations and found that the flame flow pattern and flame dynamics near the bend were mainly determined by the potential flow characteristics. Tagawa et al.14 experimentally studied the heat transfer characteristics of turbulent flames in a curved rectangular duct (180° bend) and found that the phenomenon of inverse gradient heat transfer occurs when the radial pressure gradient of the bend was large. Blanchard et al.15 conducted a study in a confined duct containing a 90° bend and showed that the bend could increase the flame velocity and overpressure, and shorten the distance to the deflagration to detonation transition to varying degrees. Xiao et al.16,17 found through experiments and numerical simulations that in a confined tube containing a 90° bend structure, four stages of flame propagation structure occurred in the early stages: spherical, finger-shaped, wall-touching flame, and tulip flame, which were consistent with the case of a straight tube. However, in the presence of a bend, the flame behavior after tulip formation was different from that of a straight tube in that the structure of the bend influence, the flame reached the inner wall of the bend first. Li et al.18 studied the effect of hollow square obstacles on the overpressure characteristics of oil and gas pressure relief explosions and found that the maximum overpressure and the flame speed increased with the number of obstacles, the oxygen-rich conditions to reach the maximum overpressure peak time were shorter, and the overpressure growth rate was greater. Sun et al.19 studied the effect of the membrane thickness and the blocking ratio on the methane–air explosion characteristics in a linked vessel and found that the smaller the membrane thickness and the blocking ratio, the smaller the explosion overpressure.

The ignition position has a great influence on the flame combustion characteristics. Cao et al.20 studied the explosion characteristics of different ignition positions on the hydrogen–air mixture in the tube and found that there was a maximum overpressure in the middle position. Xiao et al.21 experimentally investigated the kinetic properties of the hydrogen–air premixed gas at different ignition positions in a confined space and found that the ignition position had an important effect on the combustion characteristics and performance of the flame. Many studies22,23 have shown that fuel composition and hydrogen fraction significantly affect the flame velocity and pressure, and an increase in the hydrogen fraction leads to an increase in the laminar burning velocity. Mitu et al.24,25 studied the effects of various initial pressures and compositions on the laminar burning velocity of methane–air–inert mixtures in a centrally ignited spherical vessel. It was found that when the number of additives increased, especially CO2, the laminar burning velocity and maximum flame temperature of all studied components decreased.

In recent years, large eddy simulation (LES) is also widely used in numerical combustion simulation work due to its greater predictive power and the use of small mesh models to simulate turbulence. Sarli et al.26−28 used a validated large vortex simulation model with nonconstant premixed flame propagation for explosion characteristics in the presence of obstacles and investigated the effect of grid resolution on the effect of combustion submodels and found that on a fine grid even without combustion submodels, quantitatively and qualitatively, the simulation results agreed better with experimental results. Wen et al.29,30 proposed the evaluation of different subgrid scale combustion models and determined the most suitable propagation model for predicting nonconstant flame and for premixed deflagration flame propagation in a tube with the presence of three continuous obstacles.

In this study, premixed methane–air is used as the object of study with different ignition positions, and the experimental platform with a two-sided 45° branch tube is built independently. The flame shape evolution, the flame front velocity, and the overpressure are verified with the experimental results to analyze the premixed gas explosion process in the tube. Numerical simulation verifies the experimental results and analyzes the flame dynamics of premixed gas explosions in a tube.

2. Experimental Setup

The experimental setup is mainly composed of experimental tubes with 45° double-sided branches, an ignition system, a premixed gas distribution system, a pressure acquisition system, and a flame image acquisition system, and the experimental setup system is shown in Figure 1. The experimental tube with 45° double-sided branches consists of two main tubes of 300 mm length at both ends and a tube of 300 mm length with double-sided 45° branches in the middle, where the branches are also 300 mm and the double-sided 45° branches are located 70 mm away from the right end of the middle tube. The cross-section of the tube is 50 mm × 50 mm and the wall thickness is 20 mm. A stainless-steel plate is placed at the right end of the experimental tube completely closed. The left end and both sides of the branch port are closed using polyvinyl chloride (PVC) film. The PVC film will be broken in the combustion process, and the gas outlet is placed 20 mm from the left end. The ignition system consists of an ignition source, an ignition head, and an ignition switch. The ignition method selects the high-energy method, characterized by high ignition intensity. The ignition head is placed in the middle of the stainless-steel plates at the right end. The premixed gas distribution system is composed of two cylinders with different gases, two high-precision mass flow meters, and a gas mixer with three connections. The flow of gas from the cylinder is controlled by setting a highly sensitive mass flow meter, and the outflow gas is mixed by a gas mixer and enters the experimental tube together from the inlet at the right end of the tube. Gas distribution will be complete when the volume of the premixed gas is five times the volume of the experimental tube. During the gas injection process, the tube outlet is opened to ensure that the gas in the tube is at atmospheric pressure. It is static for 30 s to reduce the impact of turbulence on the explosion.31,32

Figure 1.

Figure 1

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Schematic diagram of the experimental equipment.

The pressure acquisition system contains a data acquisition card and a high-frequency pressure sensor. The pressure sensor is located at the right end of the stainless-steel plate 10 mm from the ignition head and records the overpressure generated by the explosion process. The high-frequency pressure sensor used in the experiment is the MH-90 series, the range is −0.1 to 0.1 MPa, and the acquisition frequency is 100 kHz. The flame image acquisition system is composed of a high-speed camera and a computer side. The high-speed camera is a Phantom Miro M310 type high-speed camera, and the experiment uses a shooting rate of 1000 fps, with high sensitivity. While recording the pressure, the data acquisition card and the high-speed camera are triggered simultaneously to deliver the acquired pressure data and images to the computer side.

In this study, the experiments were conducted at an equivalence ratio of 1.0, with an initial temperature and an initial pressure of 300 K and 101325 Pa, respectively. Ignition positions were located at the two ends of the main tube, IP0 = 0 mm and IP900 = 900 mm, respectively. Experiments were conducted at different ignition positions, and each experiment was repeated at least three times to ensure accuracy.

3. Numerical Model

3.1. Large Eddy Simulation (LES) and Combustion Model

The large eddy simulation (LES) control model equations are obtained by Favre filtering the N–S equations and then solving them computationally only for the large-scale turbulent pulsations and coupling the mass conservation, momentum conservation, energy conservation, and component conservation equations with the instanton equations and the equation of state.33 These filtered large eddy simulation control equations are as follows:

Continuity equation

3.1. 1

Momentum equation

3.1. 2

To calculate the subgrid turbulent heat flow in the energy equation, we used the dynamic Smagorinsky–Lilly eddy viscosity model in the study. The component transport equations are transformed to obtain the transport equation for the progress variable c, which is 0 in the fresh reactants and 1 in the combustion products.

3.1. 3

In eq 3, Yf is the partial combustion mass fraction, Yf0 is the fuel mass fraction in the unburned mixer, and the initial conservation equation for the progress variable c is

3.1. 4

In the above eq 4, the first term on the left corresponds to the nonconstant term and the second term corresponds to the convective flow; the two terms on the right correspond to the molecular diffusion and the reaction rate, respectively. The filtering process is to obtain the large-scale kinetic control equations, but the filtering operation generates unknown terms, and the subgrid-scale stress tensor and subgrid-scale heat flow are the unknown terms generated by the momentum and energy equations, respectively. The conservation equation of the Favre filtered reaction feed variable c is

3.1. 5

In eq 4, the upper corner marker (∼) is the Favre filtration amount, and (−) is the physical space filtration amount. The third term on the left side of the equation is an unknown term, which represents the variable flux of subgrid-scale reaction progress; the two terms on the right side of the equation are also unknown terms, which represent subgrid-scale molecular diffusion and subgrid-scale reaction rate, respectively. The so-called subgrid combustion model problem is the closure problem of these two terms.

To analyze the interaction between the flame and turbulence, the two terms on the right-hand side of eq 5 can be expressed according to the flame surface theory as

3.1. 6

Where Σ denotes the flame surface density (SGS flame surface ratio per unit volume), w denotes the displacement velocity of the flame surface, and ⟨ρw⟩s denotes the average mass-weighted velocity of the flame surface. It can be approximated as ρ0SL, with ρ0 and SL representing the fresh gas density and laminar flame velocity, respectively. By adding the fold factor ΞΔ, flame surface density can be expressed by the product of the progress variable c gradient and the correction factor. Using the above method, the equation can be rewritten as

3.1. 7

The energy equation solved by substituting the progress variable is

3.1. 8

Where k represents the thermal conductivity of the fuel, kt represents the turbulent thermal conductivity, Hcomb represents the heat released by the complete combustion of 1 kg of fuel, and Yfuel represents the mass fraction of fuel in the unburned gas. The expression for the creasing factor ΞΔ in the present work is the turbulent combustion model given by Charlette et al.33,34 To consider the effect of subgrid scale turbulence on the creasing of the flame front

3.1. 9

In eq 9, the fold factor ΞΔ is obtained by correlating the thickening factor Inline graphic the turbulence factor Inline graphic, the subgrid Reynolds number ReΔ and the exponent β. where the thickening factor Inline graphic is the ratio of the grid size Δ to the flame thickness δf; the turbulence factor Inline graphic is the ratio of the turbulent pulsation velocity to the flame propagation velocity; the efficiency function Γ can be expressed by the thickening factor and the turbulence factor and the subgrid Reynolds number, expressed as

3.1. 10

Where

3.1. 11
3.1. 12
3.1. 13
3.1. 14
3.1. 15

Based on the dimensional analysis between the viscosity coefficient, density, and integration length, the sublattice pulsation velocity can be expressed as

3.1. 16

In the above eq 16, Cs is the coefficient in the subgrid turbulence model. According to the analysis of the flame propagation velocity on the flame, flame thickness, and diffusion coefficients obtained from the dimensional analysis, it is known that

3.1. 17

This leads to the Reynolds number at the subgrid-scale expressed as

3.1. 18

3.2. Numerical Details

The computational domain calculated by large eddy simulation is consistent with the tube size in Figure 1. The simulation was set to be filled with premixed methane–air with an equivalent ratio of 1. The ignition is closed and the other ports are open. The boundary conditions of adiabatic and no-slip were used for the walls of all tubes. The structured grid is a hexahedral grid with a mesh size of 1 mm. The initial temperature is set to 300 K, and the initial pressure is set to atmospheric pressure.

The initial progress variable in the calculation domain is set to 0 to represent fresh gas. The hemispherical region with a radius of 3 mm is set at the ignition position, and the parameters of the hemispherical region are set as the combustion equilibrium parameters. The burned regional progress variable is set to 1. The SIMPLE algorithm is used for pressure–velocity coupling in the parameter setting process. The terms in the equation are discretized by different methods, where the convection term is discretized in bounded central difference format. The diffusion term is discretized in second-order central difference format, and the nonconstant term is discretized in second-order implicit format.

4. Results and Discussion

4.1. Flame Structure Characteristics

Figure 2 shows the experimental and simulated flame shape evolution at ignition positions of IP0 and IP900. It can be seen that the simulation results obtained by the turbulent combustion model given by Charlette can better verify the shape changes during flame propagation. The classic “tulip flame” will be formed in a tube with a large enough aspect ratio. The flame propagation process contains four stages: the first stage of flame propagation in the form of a hemispherical flame. The flame is not affected by sidewalls and propagates at the rate of gas produced by combustion. The second stage of the flame side will be affected by the sidewall of the tube, but the flame front will continue to propagate forward. The flame shape will gradually develop into a finger shape. The flame surface area and velocity will be exponential growth, resulting in a rapid increase in overpressure. The third stage of the flame occurs after the flame skirt touches the wall. The flame sidewall began to disappear, resulting in a decrease in flame surface area. The flame front gradually decelerates to form a plane flame. In the fourth stage, the flame front reverses to form the classic tulip flame. There are different explanations for the appearance of the tulip flame. Clanet and Searby35 found that the tulip flame is caused by the inversion of the flame front curvature due to the deceleration caused by the loss of flame surface area through an experimental study of a quasi-constant pressure half open tube. Ponizy et al.36 concluded that the tulip flame is a purely hydrodynamic phenomenon by visualization experiments with PIV images and processes, which is formed by the reverse flow of combustion gas and the velocity difference between the accelerated forward flow of unburned gas.

Figure 2.

Figure 2

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Comparison between experimental and simulated flame shapes at different ignition positions: (a) IP0 and (b) IP900. (The experimental flame shape is shown on the left side and the simulated flame shape is shown on the right side under the same ignition position.)

Figure 2 shows that there are only three stages of flame propagation: hemispherical, finger-shaped, and flame wall contact. This may be the influence of the branch structure in the experimental device. The spherical flame stage occurs in the t = 0–11 ms of IP0 and t = 0–10 ms of IP900, respectively. The flame propagation velocity in the axial direction is gradually greater than the radial propagation speed due to the restraining effect of the sidewall of the tube, and the flame surface area is continuously increasing. The flame structure in the tube is gradually stretched into a finger shape. This stage of flame velocity is an exponential form of growth after the flame side makes contact with the tube sidewall.

In Figure 2a, the flame spreads to the branch interface at t = 32 m. After the branch interface due to the action of the pressure wave from both sides of the branch and the left side of the main tube, resulting in the case of the flame front occurring inward concave. The shape of the concave on both sides is similar. There are no tulip flames due to the existence of the branch tube on both sides. The flame propagation process will be subject to the interference of the branch tube effect. In the formation of the tulip flame before the branch, the role of the flow field changes the flame propagation structure. The flame at the branch interface lacks the restraint of the tube sidewalls and increases the restraint of the branch tip and sidewalls. The flow field structure at the interface changes, resulting in the flame front occurring in serious folds. The flame starts to propagate along both sides of the branch and the left side of the main tube, forming an approximately symmetrical structure in the branch tube. Due to the constraining effect of the branch wall, the flame bends from left to right. The bending structure touches the right branch wall at t = 36 ms, and then the unburned gas on both sides of the branch is ignited. The flame front is severely folded and deformed, and the flame propagates to the end of the branch at t = 38 ms.

In Figure 2b, when the flame propagates to the interface at t = 30 ms, the front concave of the flame was also caused by the branch tube. Because of the lack of the role of the main tube sidewall and the increase in the branch tip restraint, the flame front structure becomes wider than the right side of the structure. The flame front structure changes into a serious fold, and the role of the branch sidewall made the flame also occur from left to right bending. The unburned gas on both sides of the branch ignited and passed rapidly to the end of the branch.

Panels a and b in Figure 2 also show the change in flame shape versus time at ignition positions IP0 and IP900. The simulation results at the branch tube interface can also verify the structure and position of the concave flame front more accurately. When the flame enters the branch pipe, the structure also bends from left to right. By comparing the experimental and simulation results, it can be seen that the large eddy simulation of this turbulent combustion model can qualitatively predict the overall characteristics of flame propagation.

Figure 3 shows the change in three-dimensional flame structure versus time by simulation. The simulation results are obtained by using the isosurface of the progress variable c = 1 to represent the flame structure. The flame propagation form is hemispherical and the propagation speed is approximately laminar flame speed. The flame is restrained by the sidewall of the tube and develops into a finger-shaped structure to propagate forward. At the branch tube interface, the flame structure is still affected by the branch tube and forms an inwardly depressed frontal structure. The flame front encounters a serious fold phenomenon and first propagates near the left side wall, after which a bending from the left side to the right side occurs, after which it propagates along both sides of the branches and the left side of the main tube. By comparing the three-dimensional structure diagram of the flame and the experimental flame images, it is found that the turbulent combustion model has a good prediction of the evolution of the flame structure during the explosion of methane–air premixed gas.

Figure 3.

Figure 3

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Three-dimensional flame structure images versus time (isosurface of progress variable c = 1.0). (a) IP0 and (b) IP900.

4.2. Flame Front Position

Figure 4 shows the development of flame front position at different ignition positions. The error bars are represented by the standard deviation of the flame front position. It can be seen from Figure 4 that the trend of repeated experiments is highly consistent.

Figure 4.

Figure 4

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Error analysis diagram of the flame front position.

Figure 5 shows the variation in flame front position versus time. This part only considers the position of flame propagation in the main tube and does not consider the flame propagation position in the branch tubes on both sides. The maximum distance from the flame tip to the ignition end in the main tube is taken as the flame front position. Different ignition positions have a greater effect on the experimental flame front position. The early flame propagated at the speed of burning gas with little difference. The gas involved in the reaction then increases, and the flame front surface area increases. The flame propagation speed is exponentially higher form, so the slope of the flame front position curve gradually becomes larger. When the flame propagation in the direction of the vent, at the same moment there is a gap between the flame front position. This is because the distance between the two ignition positions from the branch interface is different. The flame propagation process is subject to the different size of the branching effect. At IP0 under t = 32 ms, the flame surface area suddenly increases when the flame propagates near the branching interface. The explosion generated by the expansion wave quickly to the direction of the branch tube propagation, both sides of the branch pressure relief effect result in the slow propagation of the flame phenomenon. At IP900, the slow propagation of the flame phenomenon occurs slightly later than at IP0. This is because IP900 is farther away from the branch interface. The premixed gas in the branch tube is ignited, increasing the flame burning area, and then the combustion speed increases rapidly. When the flame passes the branch interface and enters the left end of the main tube, the flow field is stable and spreads rapidly in a finger shape.

Figure 5.

Figure 5

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Flame front position versus time under different ignition positions.

Figure 6 shows the calculated flame front position obtained by using a large eddy simulation for comparison with the experimental results. We found that the simulation was better at capturing the flame front position at IP0. The experimental results agree well with the simulation results. However, the maximum error occurred at 28 ms, and the simulated value was higher than the experimental value. This error occurs due to the flame propagation to the branch interface near the branch tube interference, the explosion generated by the flow field is more complex and variable. The flame front appears complex folded edge, resulting in a large difference in the results obtained. In Figure 6b, as the premixed gases involved in the reaction increase, the flame front surface area increases, the flame propagation speed exponentially increases, and the flame front position also exponentially increases. In the branch interface near the experimental and simulated values, although there is a small difference, the trend of the flame front position is consistent with the experimental one.

Figure 6.

Figure 6

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Comparison between experimental and simulated flame front position at different ignition positions: (a) IP0 and (b) IP900.

4.3. Overpressure Dynamics

The variation of overpressure with time at different ignition positions is shown in Figure 7. In the stage of 0 ≤ t ≤ 8, the pressure presents a relatively slow rising stage, which is the stage when there is less premixed gas involved in the reaction after ignition. The pressure curves at the early stage of flame propagation in the two ignition position cases coincide and are not affected by the reflected overpressure wave. As the reaction continues, the premixed methane–air involved in the reaction increases when the flame propagates in the tube, and the flame shape is axially stretched from spherical to finger-shaped by the constraint of the tube sidewall during the flame propagation. The flame front surface increases rapidly, and the overpressure quickly reaches the first peak at the ignition position IP0 and IP900 cases, respectively. At t = 16 ms and t = 18 ms to reach this peak, indicating that the rising rate of pressure under different ignition positions is different, and the peak pressure is larger under the ignition position IP900. After that the flame occurs touching the wall leading to a reduction in the flame front area, resulting in lower overpressure. When the flame propagates to both sides of the branch interface, the flame front surface by both sides of the branch and the left side of the main tube, resulting in flame front surface depression. The flame surface area increased, and overpressure appeared to be a small increase. The branch interface at the flow field is more complex, the flame front surface experienced serious fold deformation, resulting in a rapid increase in the flame surface area. At the same time, the unburned gas in the branch tube is ignited rapidly, resulting in the overpressure rising rapidly to reach the maximum overpressure.

Figure 7.

Figure 7

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Overpressure versus time under different ignition positions.

At IP900, the overpressure reached the maximum earlier than at IP0, reaching the maximum overpressure of 10.7 kPa at t = 35 ms, while the maximum overpressure is 10.1 kPa at the ignition position IP0. Because of the different ignition positions, the combustion situation at the branch interface is different in the flame propagation process, which leads to the difference in the maximum overpressure achieved. As the flame spreads to the end of the tube, a large amount of combustion gas from the vent to the outside of the tube. Heat loss leads to a reduction in overpressure. Due to the inertia of pressure relief, the pressure drops to negative pressure. When the pressure outside the tube is greater than the pressure inside the tube, resulting in the return of gas outside the tube, making the combustion more full. This cycle makes the pressure produces a Helmholtz oscillation with decreasing amplitude until the premixed gas inside the tube is burned out and the pressure becomes normal. The study of premixed methane–air pressure characteristics under different ignition positions in tubes with two-sided 45° branches is of great significance for safety and environmental issues in industrial applications and transportation of combustible gas.

The comparison between the pressure obtained by using a large eddy simulation at different moments and the experimental results are shown in Figure 8. The flame structure gradually develops from hemispherical to finger-shaped, and the pressure rises slowly. At t = 19 ms, the flame touches the wall, after which the flame front area decreases, and the pressure decreases, at which time the pressure in the tube reaches the first pressure peak. The pressure value of the experimental results is higher than the simulated results, which is because the existence of a PVC film is not considered in the simulation, resulting in a slightly lower simulated pressure than in the experiment. When flame continues to propagate to the branch interface, in the combustion of the expansion wave, the role of unburned premixed gas from the explosion vent further contributes to the pressure reduction. At t = 27 ms, under the action of the complex flow field, the flame front at the branch interface folds into deformation, and the flame surface area increases. When the unburned gas in the branch tube is also ignited, the flame propagation speed also increased rapidly, and the pressure rose sharply to reach the maximum overpressure. The simulated maximum overpressures are 9.2 and 10.4 kPa, respectively, and the values are not different (see Table 1). The maximum overpressures obtained in the experiments at the two ignition positions are 10.1 and 10.7 kPa, respectively, which are slightly higher than the values achieved in the simulations. There is a small deviation between the experimental and simulated time to reach the maximum overpressure. When the atmospheric pressure outside the tube is greater than the pressure inside the tube, the gas released will flow back, the combustion will become more complete and the pressure will rise again, producing a pressure oscillation with decreasing amplitude.

Figure 8.

Figure 8

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Comparison between experimental and simulated overpressure versus time at different ignition positions: (a) IP0 and (b) IP900.

Table 1. Calculation Errors of Pressure Peaks between the LES and Experiments, And Comparison with Results Reported in Previous Similar Studiesa.

      Pmax (kPa)
  
no. refb tube structure experimental LES calculation error (%) ((|PE – PL|/PE)100%)
1 present work (a) branch tube 10.1 9.2 8.91
2 present work (b) branch tube 10.7 10.4 2.80
3 Xiaoping Wen29 obstructed tube 11.4 10.8 5.26
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a

To verify the pressure characteristics of premixed methane–air in a tube with a two-sided 45° branch structure, the pressure peaks obtained by the LES and experiments in this study were compared with those in some previous similar studies. Study (3#) was conducted in a tube containing obstacles. It can be found that the pressure obtained by the branch pipe (1# and 2#) is close to the peak pressure obtained by the obstacle pipe (3#). Therefore, the results obtained by the model used in this study are effective.

b

Present work: (a) IP0; (b) IP900.

4.4. Flame Structure and Flow Field

To deeply study and analyze the change in flame structure during the explosion of premixed methane–air inside the branch tube containing double-sided 45° branches, the structure of the flame morphology and the flow field interaction at different moments during the flame propagation were obtained using a large eddy simulation containing the Charlette turbulent combustion model. Figure 9 shows the flame morphology and flow field changes when the flame front passes near the branch interface during the combustion process. The plane in the figure is the center plane of the tube (x–y plane with z = 0.025 m), and the colored flame plane is obtained by taking the equivalent plane of the progress variable c = 1. The convenience of viewing the flow, the field is indicated by white arrows, and the denser the arrow the greater the velocity.

Figure 9.

Figure 9

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Flame shapes and flow field versus time at different ignition position.

Figure 9a shows the change in the flame shape and the flow field distribution at ignition position IP0. At t = 25 ms, the flame is about to enter the branch interface. Due to the constraint effect of the tube sidewall on the flame, the internal propagation speed of the flame front increases along the axial direction. At the branch interface, the flow field is disturbed by the obstacle at the top corner of the branch tube and the branch wall, and an asymmetric vortex structure is formed here. The upper rotation direction is clockwise, and the lower rotation direction is counterclockwise. The airflow at the branch is contracted to the left side of the main tube by the influence of the vortex structure, and the flow field at the end of the branch tube is still distributed along the branch. The flow field at the end of the branch tube is still distributed axially along the branch tube. The premixed gas in the unburned area on the left side of the main tube is propagated axially along the tube under the action of the expansion wave generated by the flame combustion. The flame then propagates to the interface; influenced by the flow field distribution, the flame structure suffers from a strong turbulent flow field, which also presents the same curved flame front as the vortex direction. The turbulence intensity inside the tube becomes larger and the propagation speed increases, with the change in the flame structure, the flow field is also stretched. Due to the pressure relief of the branch tube, the flow field becomes sparse and the rising trend of the propagation speed slows down. When the flame propagates to the branch tube, the flame stretches to the right wall under the action of the vortex on both sides, at this time, the left unburned gas in the branch tube is ignited, forming the flow field to the left. The flame extends to the left wall and finally forms a shape similar to a “bending arm”. After that, the flame along the branch tube propagates to the vent, and the branch tube interface on both sides of the unburned gas body is ignited. The expansion wave generated by flame combustion promotes the interface of the flow field to the left side of the main development, resulting in the entrance to the left side of the main tube forming a “hilltop-like” convergence. The flow field then flows axially along the tube.

As shown in Figure 9b, at t = 27 ms, before the flame propagates into the branch tube interface, it also forms an up-and-down symmetrical vortex structure at the entrance of the branch tube. The flame enters the interface and forms a concave flame front under the action of the flow field at the branch tube, and the vortex flow field inside the branch is stretched and extended along the left sidewall. The left side wall of the branch burned, and the flame front was seriously folded. The unburned gas on the right side of the branch tube flowed to the unburned area of the main tube under the action of the flow field vortex, forming a flame shape similar to the “arrow” shape of the flame, and then the flame propagated to the main vent.

4.5. Turbulent Combustion Model Analysis

During the flame propagation in the tube, the flame and turbulence are coupled to form different turbulent premixed combustion models. Turbulent premixed combustion can be described as the interaction between the flame front and a collection of vortices representing different scales of turbulence. The Karlovitz number (Ka)37 can accurately represent the turbulence intensity and the degree of interaction between the flame front and the turbulence. The introduction of the Ka number can further investigate the methane–air premixed gas in a double-sided 45° branching tube. The Ka number is related to the minimum vortex (Kolmogorov) and is the ratio of the time scale τf of the flame surface to the time scale τk of the minimum vortex, and the Ka number is expressed as

4.5. 19

where μ′Δ is the subgrid turbulence velocity, SL is the laminar combustion velocity, δf is the laminar flame thickness, and Δ is the grid characteristic scale. Figure 10 shows the distribution of Ka numbers on the flame surface at different moments at the ignition position IP0. The flame surface is obtained by taking the equivalence surface of the progress variable c = 1. From Figure 10, it can be seen that t = 25 ms flame propagation to the front of the branch interface, the turbulence intensity is small due to the constraint effect of the tube sidewall. The flame front is still finger-shaped and the Ka number is low, while the Ka number at the flame front touching the wall is higher than that at the flame front, indicating that the flame touching the wall causes the turbulence intensity to increase. As the flame propagates to the branch interface, a symmetrical vortex structure with opposite direction is formed in the tube, the turbulence intensity becomes larger, and the Ka number appears to increase; when the flame propagates in the branch tube, the Ka number keeps rising, and after experiencing the symmetrical vortex structure at the branch interface, the flame propagation process touches the branch tip and the branch tube sidewall, which makes the strain rate and subgrid viscosity of the fluid in the branch tube higher. Therefore, the maximum value of the Ka number at different moments can be used to indicate the degree of interaction between the flame front and turbulence. The study of the Ka number at different positions in the tube plays an important role in industrial safety protection.

Figure 10.

Figure 10

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Distribution of Ka on the flame surface (c = 1) at different time instants at ignition position IP0.

Figure 11 shows a schematic diagram of turbulent flame regimes, in which the dots indicate the numerical points of Ka–Δ/δf at different moments of the methane-air premixed gas combustion flame in the case of ignition position IP0 in the duct containing 45° branches on both sides, corresponding to moments 19, 27, 28, 30, 33, 35, and 37 ms of the large eddy simulated flame propagation process, respectively, and the Ka numbers taken are all the maximum values of the flame propagation at that moment. The maximum value of Ka at the surface. According to Figure 11, it can be seen that in the process of methane-air premixed gas combustion in the branch tube containing double-sided 45°, when the flame front is still finger-shaped, the Ka number is less than 0.01, and it is in the folded flame surface mode. At t = 28 ms, the flame propagates to the branch interface, the flame front is influenced by the vortex, the flame front is seriously deformed, the Ka number gradually increases, and the flame mode turns to the corrugated flame surface; when t = 30 with 33 ms, the flame propagates in the branch tube, Ka number reaches the maximum of 9.2, and the flame turns to the thin reaction zone; then the flame on the left side of the main tube continues to propagate in the process, the flame mode still belongs to the thin reaction zone. In the 45° branch tube containing double sides, the methane–air premixed gas explosion flame has gone through three flame modes: a folded small flame surface, a corrugated small flame surface, and a thin reaction zone.

Figure 11.

Figure 11

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Schematic diagram of turbulent flame regimes at ignition position IP0.

5. Conclusion

In this study, the flame propagation characteristics of premixed methane–air in different ignition positions in a half-open tube containing two-sided 45° branches were investigated using large eddy simulation and experimental methods. The flame structure, the flame front position, and the pressure dynamics obtained from the simulation were compared with experimental results. The applicability of the turbulent combustion model to methane–air deflagration in special tube structures was verified. The influence of the branch tube structure and the ignition position on flame combustion characteristics can not only provide basic understanding for flame dynamics but also provide data support for industrial safety. The following conclusions can be drawn:

  • (1)

    In the tube with a two-sided 45° branch, a symmetrical vortex structure with the opposite rotation direction is formed at the branch interface, and the vortex structure causes a complex change in the flame front.

  • (2)

    The ignition location has a significant effect on the flame propagation characteristics. When ignited at IP900, the symmetrical vortex structure is deflected into the branching structure on both sides, resulting in a more complex flame structure. The maximum pressure and flame propagation velocity reached at IP900 is higher than at IP0.

  • (3)

    The Charlette turbulent combustion model can accurately reproduce the experimental results. The coupling of flow field and flame structure can better investigate the relationship between flow field and flame structure in the branch tube.

  • (4)

    The Karlovitz number represents the flame surface–turbulence interaction relationship to distinguish the flame mode in a tube containing a two-sided 45° branch structure. When the ignition position is at IP0, the flame undergoes a folded small flame, a corrugated small flame, and a thin reaction zone.

Acknowledgments

This work was supported by the National Natural Science Foundation of China [52004085].

The authors declare no competing financial interest.

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