Large eddy simulation and experimental study on vented gasoline-air mixture explosions in a semi-confined obstructed pipe

Accepted Manuscript Title: Large Eddy Simulation and experimental study on vented gasoline-air mixture explosions in a semi-confined obstructed pipe Authors: Guoqing Li, Yang Du, Shimao Wang, Sheng Qi, Peili Zhang, Wenzhuo Chen PII: DOI: Reference:

S0304-3894(17)30439-9 http://dx.doi.org/doi:10.1016/j.jhazmat.2017.06.018 HAZMAT 18639

To appear in:

Journal of Hazardous Materials

Received date: Revised date: Accepted date:

10-1-2017 8-6-2017 9-6-2017

Please cite this article as: Guoqing Li, Yang Du, Shimao Wang, Sheng Qi, Peili Zhang, Wenzhuo Chen, Large Eddy Simulation and experimental study on vented gasolineair mixture explosions in a semi-confined obstructed pipe, Journal of Hazardous Materialshttp://dx.doi.org/10.1016/j.jhazmat.2017.06.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Large Eddy Simulation and experimental study on vented gasoline-air mixture explosions in a semi-confined obstructed pipe Guoqing Li, Yang Du *, Shimao Wang, Sheng Qi, Peili Zhang, Wenzhuo Chen Chongqing Key Laboratory of Fire and Explosion Safety, Logistical Engineering University, Chongqing 401311, China (*Corresponding author (Y.D). E-mail address: [email protected])

Highlights 

1. LES and experimental studies were conducted to investigate vented gasoline-air mixture explosions in an obstructed pipe.



2. Interaction between flame propagation and obstacles was investigated by LES study.



3. Mechanism of overpressure dynamics was assumed to be associated with the mass flow rate and flame surface area.



4. Effects of initial gasoline vapor concentrations and obstacle number on gasoline-air mixture explosions were investigated.

Abstract: In this work, LES simulation coupled with a TFC sub-grid combustion model has been performed in a semi-confined pipe (L/D=10, V=10L) in the presence of four hollow-square obstacles (BR=49.8%) with circular hollow cross-section, in order to study the premixed gasolineair mixture explosions. The comparisons between simulated results and experimental results have been conducted. It was found that the simulated results were in good agreement with experimental data in terms of flame structures, flame locations and overpressure time histories. Moreover, the interaction between flame propagation process and obstacles, overpressure dynamics were analyzed. In addition, the effects of initial gasoline vapor concentration (lean (ϕ=1.3%), stoichiometric (ϕ=1.7%) and rich (ϕ=2.1%)), and the number of obstacles (from 1 to 4) were also investigated by experiments. Some of the experimental results have been compared with the literature data. It is found that the explosion parameters of gasolineair mixtures (e.g. the maximum overpressure peaks, average overpressure growth rates, etc.) are different from some other fuels such as hydrogen, methane and LPG, etc. Keywords: Vented gasoline-air mixture explosions; Large Eddy Simulation; Obstacles Nomenclature A model constant BR blockage rate c reaction progress variable Smagorinsky constant 𝐶𝑠 Di distance between two adjacent obstacles (dp/dt)ave average overpressure growth rate chemical equilibrium 𝑒𝑞 Heaviside function H(x) turbulence length scale 𝑙𝑡 Li distance between the first obstacle and the ignition point L/D aspect ratio N# order of literatures No. number of obstacles Pmax maximum overpressure peak PE maximum overpressure peak of experimental results PL maximum overpressure peak of LES results reaction progress source term 𝑆𝑐 ~ stain tensor rate 𝑆𝑖𝑗 𝑆𝑐𝑒𝑓𝑓 effective Schmidt number Sfmax maximum flame speed Sf flame speed t time to reach the maximum overpressure peak tE time to reach the maximum overpressure peak of experimental results tL time to reach the maximum overpressure peak of LES results unburnt reactant 𝑢 sub-grid velocity fluctuation 𝑢′ velocity u 1

𝜇𝑒𝑓𝑓 𝑈𝑡 𝑈𝑙 𝑉𝐶𝑉 xn+1-xn 𝑌𝑘 ρ 𝜌𝑢 α ∆ ∆tn

ϕ

−1 𝜏𝑠𝑔𝑠

effective viscosity turbulent flame speed laminar flame speed volume of the computational cell actual distance of two adjacent flame fronts the 𝑘 𝑡ℎ species mass fraction mass density density of unburnt mixture unburnt thermal diffusivity cell characteristic length arrival time difference of two adjacent flame fronts gasoline vapor concentration sub-grid mixing rate

1. Introduction

The premixed flammable gas explosion is a potential danger in chemical plants, coal mines, oil depots and other process industries and has caused economic losses, injuries, and fatalities. (Gourara, Roger et al. 2006, Zhu, Qian et al. 2015, Li, Du et al. 2016). The damage would be especially large when gas explosion happens in a space with solid obstacles or a congested area that can be treated as a large porous structure(Na'inna, Phylaktou et al. 2013). The interaction between gas flow and obstacles can result in the generation of turbulence, and hence the intense acceleration flame and severe overpressure rise. Therefore, it is essential to investigate and predict these phenomena in process industries in order to assess the risks and design suitable protection and mitigation measures against unsteady flammable gas combustion and explosion. Over the years, unsteady premixed flame propagation through obstacles has been investigated in many numerical and experimental studies (Patel, Ibrahim et al. 2003, Kindracki, Kobiera et al. 2007, Di Sarli, Di Benedetto et al. 2009, Di Sarli, Di Benedetto et al. 2012, Johansen and Ciccarelli 2013, Na'inna, Phylaktou et al. 2013, Ahmed and Swaminathan 2014, Xu, Cong et al. 2015). In the numerical studies, considerable attention has been paid on the development and validation of CFD codes. Most of the models were based on the RANS approach (Tang and Jiang 2011, Dong, Huang et al. 2012, Ahmed and Swaminathan 2014, Hu and Zhao 2016). However, Sarli, Benedetto et al. have indicated that the flame-vortex interaction is the key phenomenon driving the flame propagation during explosion, and thus it is essential to study such a phenomenon by coupling laser measurement and large eddy simulation (LES)(Sarli, Benedetto et al. 2012, Sarli and Benedetto 2013). Moreover, in recent years, due to the development of computer technology and CFD theory, LES has been applied by more and more researchers, and has shown stronger reliability in prediction than RANS (Abdel-Raheem, Ibrahim et al. 2015, Huang, He et al. 2015, Saghafian, Shunn et al. 2015). However, most of these LES cases were based on combustion chambers with small length/diameter (L/D) ratios (smaller than 5) (Di Sarli, Di Benedetto et al. 2009, Di Sarli, Di Benedetto et al. 2009, Di Sarli, Di Benedetto et al. 2012, Abdel-Raheem, Ibrahim et al. 2015), where the channels seemed not long enough that the flames were not able to develop fully after passing though the obstacles. Most of the experiments were conducted in a wide variety of initial conditions and with different geometrical configurations (Patel, Ibrahim et al. 2003, Kindracki, Kobiera et al. 2007, Park, Lee et al. 2008, Na’inna, Phylaktou et al. 2014, Wen, Yu et al. 2015), and several meaningful phenomena have been observed, such as the jet-like flame, growth of flame surface area and flame speed acceleration due to the interaction between flame and obstacle-generated turbulent vortices, etc.(Johansen and Ciccarelli 2009, Na’inna, Phylaktou et al. 2014, Wen, Yu et al. 2015). It should be noticed that most of the previous studies were conducted using methane, hydrogen, acetone, ethylene (Blanchard, Arndt et al. 2010, Wen, Yu et al. 2012, Na'inna, Phylaktou et al. 2013, Na’inna, Phylaktou et al. 2014, Hisken, Enstad et al. 2015) . In fact, the vapor of gasoline—an extensively used fossil fuel in industry is also a hazardous explosive gas, because once it mixes with air or other oxidants, a potential explosive atmosphere will be formed, which can lead to a destructive explosion along with damaging overpressures and high temperature, as pointed out by Yang, Li et al. (2013), Zhang, Du et al. (2013), Zhang, Du et al. (2015), and Li, Du et al. (2016), Qi, Du et al. (2016), Qi, Du et al. (2017), who are among the few researchers having studied the cases with the vapor of gasoline. However, their investigations were mostly 2

based on experiments, and were often conducted in straight pipes or standard vessels. Besides, none of them adopted LES technique to study gasoline-air mixture explosions in a pipe. Given above, numerical and experimental studies on gasoline-air mixture explosions in a pipe with obstruction are still needed to be conducted in order to investigate the effects of obstacles on the overpressures and flame behaviors during gasoline-air mixture explosion, which would provide guidance on explosion protection for oil and gas industry. The present work aims to investigate mechanisms of the flame acceleration and the overpressure development during vented gasoline-air mixture explosions in an obstructed pipe. Large Eddy Simulations are run of unsteady premixed flame propagation through four hollow-square obstacles with circular hollow a vented pipe. Vented gasoline-air mixture explosions under the conditions of various initial gasoline vapor concentrations and with different numbers of obstacles have also been investigated by experimental studies. 2. Numerical test case and experimental 2.1 Geometry of the pipe Simulations and experiments in the present work were conducted in a semi-confined pipe as shown in Fig.1, which is a 100mm×100mm×1000mm cube made of plexiglass 20mm in thickness. The right end of the pipe was closed with an ignition point on it. The left end was sealed by a thin polyethylene film whose rupture during the combustion process allowed the burned gases to escape. Four square obstacles, with a circle hollow through each of them, were mounted downstream of the right end at regular intervals of 100mm between them. The size of an obstacle was 100mm×100mm×3mm, and the radius of the hollow circle was 40mm, imposing an area blockage ratio of 49.8%.

2.2 Experiment setup Fig.2 shows the experimental system applied in the present work. Overpressure time histories were recorded by a dynamic data acquisition software called DAP 7.10 (Tai Site Technology Institution of Chen Du) coupled with a piezo-resistive pressure transducer (ZXP type 660, with a range of 0-200kPa and a total error <0.3%) located close to the ignition position. The gasoline-air mixtures were produced by a gasoline vapor generation system (Qi, Du et al. 2016), which consisted of an oil bottle, a vacuum pump, some confined rubber pipes and some valves. The oil bottle was used to hold liquid gasoline, and the vacuum pump was applied for gas circulation. Before each circulation, the circulation inlet and outlet were connected to port 4# and port 1#, respectively. Meanwhile, the gasoline vapor concentration was tested by a GXH-1050 infrared gas analysis apparatus (Jun Fang Physicochemical Science and Technology Institution of Beijing), whose test probes were connected to ports 2# and 3#, respectively. After a certain time (depended on the needed vapor concentration), values before and after the oil bottle were closed and the pump continued to work for 3 min to create a uniform mixture(Qi, Du et al. 2016). All the gas mixtures used in these experiments were at ambient pressure and temperature. Gas mixtures were ignited by an ignition system with an ignition energy varying from 2 J to 20 J. The position of the spark plug was constantly kept at the center of the blind plate, and a constant ignition energy was set at 6 J in case of the significant effects of ignition position and energy on the initial flame propagation and the resulting flame speed and overpressure (Li, Du et al. 2016). A high-speed camera (with a shutter of 1ms and at a speed of 1000 frames per second) was applied to record the images of flame propagation process during gas explosions.

2.3 Experiments of parameter changes In the present work, the influences of parameter changes on vented gasoline-air explosion characteristics were studied through experiments, which involved two types of parameters: initial gasoline-vapor concentration and the number of obstacles. As for the study of the effects of initial gasoline-vapor concentration, 1.3%. 1.7% and 2.1% of that was adopted in the experiments, which were conducted in a pipe in the presence of four sequential obstacles, as 3

shown in Fig.3 (d). In order to investigate the effects of the number of obstacles, one, two, three, four obstacles were respectively used in four kinds of experiments as shown as Fig.3(a), (b), (c) and (d), with an initial gasoline-vapor concentration of 1.7% for all. Most experiments were carried out for at least three times in order to ensure the accuracy of experimental results, depending on the reproducibility of the overpressures, flame speeds and flame shapes.

3. The Large Eddy Simulation(LES) and combustion model The LES model applied in this work has been described previously (Di Sarli, Di Benedetto et al. 2009, Di Sarli, Di Benedetto et al. 2012). The governing equations of the LES model were obtained by using a Favre-filter (i.e. a massweighted filtered) to the conservation equations of mass, momentum, energy and species, coupled to the constitutive and state equations. The species transport equation was recast in the form of a transport equation for the reaction progress variable c, which is defined as a normalized sum of the product species mass fractions, such that c=0 where the mixture is unburnt and c=1 where the mixture is burnt.

 (Y c  (Y k

k

 Yku )

k

eq k

k

Y ) u k



Yc Yceq

(1)

k

Where superscript 𝑢 denotes the unburnt reactant, 𝑌𝑘 denotes the 𝑘𝑡ℎ species mass fraction, superscript 𝑒𝑞 denotes chemical equilibrium, 𝛼𝑘 are constants that are typically zero for reactants and unity for a few product species. The LES Favre-filtered c-equation can be written as: 𝜇𝑒𝑓𝑓 ∂ −~ (2) ( 𝜌𝑐) + ∇ ∙ (−~~ ) + 𝑆−𝑐 𝑝𝑢𝑐 ) = ∇ ∙ ( ∂t 𝑆𝑐𝑒𝑓𝑓 Where ρ is the mass density, u is the velocity, 𝑆𝑐 is the reaction progress source term. The overbar (-) denotes a filtered quantity and the tilde (~) denotes a Favre-filtered quantity. 𝜇𝑒𝑓𝑓 denotes the effective viscosity, which is determined by the renormalization group (RNG) theory (Yakhot and Orszag 1986) and is equal to 𝜇𝑒𝑓𝑓 = 𝜇[1 + 𝜇𝑠2 𝜇𝑒𝑓𝑓

𝐻(

𝜇3

1/3

− 100)]1/3, where 𝜇𝑠 = 𝜌(0.157𝑉𝐶𝑉 )2 √2𝑆~𝑖𝑗 𝑆~𝑖𝑗 , 𝑉𝐶𝑉 is the volume of the computational cell,

~ 𝑆𝑖𝑗

is the stain

tensor rate, and H(x) is the Heaviside function (Molkov, Makarov et al. 2006). 𝑆𝑐𝑒𝑓𝑓 denotes the effective Schmidt

− 𝑆𝑐

number, and is equal to the effective Prandtl number (Yakhot and Orszag 1986). The reaction progress variable source terms is modeled as: = 𝜌−𝑢 𝑈𝑡 |∇ − (3) 𝑐| Where 𝜌𝑢 is the density of unburnt mixture, 𝑈𝑡 denotes the turbulent flame speed, and in this study, 𝑈𝑡 is obtained by a TFC model proposed by Zimont and Battaglia (Zimont and Battaglia 2006) or wrinkled and thickened flame fronts: 3

1

−1/4 1/4 𝑙𝑡

U𝑡 = 𝐴(𝑢′ )4 𝑈 2𝑙 α

(4)

−1 𝜏𝑠𝑔𝑠 = √2𝑆~𝑖𝑗 𝑆~𝑖𝑗

(7)

Where A is a model constant, and is equal to 0.5 recommended by Zimont (Zimont 2000), 𝑢′ is the sub-grid velocity fluctuation, 𝑈𝑙 is the laminar flame speed, α is the unburnt thermal diffusivity, 𝑙𝑡 is the turbulence length scale and in LES it could be modeled as: (5) 𝑙𝑡 = 𝐶𝑠 ∆ Where 𝐶𝑠 is the Smagorinsky constant (Lilly 1992), and ∆ is the cell characteristic length. The sub-grid velocity fluctuation is calculated as: −1 𝑢′ = 𝑙𝑡 𝜏𝑠𝑔𝑠 (6) −1 Where 𝜏𝑠𝑔𝑠 is the sub-grid mixing rate (inverse of the sub-grid scale time scale), and can be modeled as:

Where ~ 𝑆𝑖𝑗

~ 𝜕𝑢𝑖

~ 𝑆𝑖𝑗 is ~ 𝜕𝑢𝑗

the stain tensor rate calculated as:

1 = ( + ) 2 𝜕𝑥𝑗 𝜕𝑥𝑖

(8) 4

4. Numerical details The model equations were discretized by finite volume formulation, and the grid-independence of the solution was checked for the sgs combustion model. The solution domain was composed of two parts (i.e. inside the chamber and outside the chamber), for the solution domain outside the chamber, it was extended to form a dump vessel with a volume of 500mm×500mm×1000mm, in order to minimize the interference between the reflected pressure waves and the pressure field inside the chamber (Di Sarli, Di Benedetto et al. 2009, Di Sarli, Di Benedetto et al. 2010, Xu, Cong et al. 2015). A boundary condition of fixed gauge pressure (0 Pa) was specified at the boundaries of this extended domain. The grid of the whole solution domain consisted of about 1200,000 hexahedral cells, and about 950,000 cells were in the inside chamber with minimum and maximum resolutions equal to 2 and 2.5mm, respectively. Smaller cell size (2mm) was used close to the walls owning to the presence of steeper gradients of the solution field (Di Sarli, Di Benedetto et al. 2010). And the extended solution domain was characterized by around 250,000 cells with minimum and maximum resolutions equal to 2 and 10mm. It should be specially noted that once fixed the cell size, the role of the LES combustion sub-model is strictly dependent on the combustion regime experienced by the propagating flame(Sarli and Benedetto 2012). Adiabatic and no-slip boundary conditions were applied at the closed end, the horizontal faces of the pipe and the faces of the obstacles. It should be noticed that the thin polyethylene film that covered the open end could rupture at a low pressure, and had little influence on the explosion process, so the effect of it was ignored in the simulation study(Wen, Yu et al. 2012). The specific heats of the unburned and burned mixtures were approximated as piecewise fifth-powder polynomial functions of temperature. The molecular viscosities were calculated based on the Sutherland’s law for air viscosity. The initial fuel concentration was 1.7% which was near the stoichiometric concentration (Li, Du et al. 2016, Qi, Du et al. 2017), and the laminar burning velocity was assumed to remain constant with pressure and temperature and equal to 0.43 m/s (Mannaa, Mansour et al. 2015). Initial conditions consisted of gauge pressure, velocity components, temperature, and reaction progress. The initial temperature was set to 300K, and the other three initial parameters were set to zero everywhere. A hemispherical region with a radius equal to 5mm and reaction progress of 1 was patched at the center of the closed end of the chamber to simulate ignition(Wen, Yu et al. 2012). The LES simulations were realized by the ANSYS Fluent software which is based on a finite-volume discretization method. The SIMPLE method was used to couple the pressure and velocity fields. The second-order upwind scheme was applied to convection terms and the second order central difference scheme was used for the diffusion terms. The simulation computations were parallelized on a 64-bit computer Lenovo ThinkServer TD350 which consisted of one Xeon E5-2609 v4 CPU (8 processes) and an 8G RAM. The iteration time step size was set to 1×10-5s, and the solution for each time step required about 20 iterations to converge with the residual for energy equations less than 1×10-6, progress variable equations less than 1×10-4 , momentum equations less than 1×10-5. The time needed to complete one case was about 52h. 5. Results and discussion 5.1 Model validation In the present work, flame structures, overpressure time histories, flame front locations and flame speeds of simulated results have been compared with the experimental results, in order to evaluate the predictive capability of the numerical simulation model applied in this study(Patel, Jarvis et al. 2002, Xu, Cong et al. 2015). Fig.4 compares the flame structures at six different instants after ignition obtained from the experiment and the simulation, which reflects the change of flame shape under the influence of obstacles. The images obtained from simulation are chosen at the time when the location of the flame front is almost the same as the experimental measurements. Due to the limitation of the resolution of the high-speed camera used in the experiments, some of the detailed structures of the flame are not distinct. But from Fig.4, we can still clearly observe the hemisphere-shape flame structure before the flame fronts reached the first obstacle, the distortion of the flame structure since the front reached the first obstacle and the 5

obvious acceleration the front obtained during its propagation. The flame front locations along the pipe with respect to time are shown in Fig.6. The values of flame speeds are calculated by the Eq.(9), and their values got from experiments and simulations are compared in Fig.7, which indicates that the simulation is able to reflect the main features of flame speeds along the axial direction of the pipe, including the drops of flame speeds and the accelerations, although slight difference exists between the two results.

S f  ( xn1  xn ) / tn

(9)

where Sf is the flame speed, xn+1-xn is the actual distance of two adjacent flame fronts, ∆tn is the arrival time difference of two adjacent flame fronts. Fig.5 compares the experimental and simulated results of overpressure time histories at the measuring point on the closed end of the pipe. The black line represents the experimental overpressure profile and the red line represents the simulated result, respectively. As indicated by Fig.5, the overpressures in experiment and simulated peaked almost at the same time (27.4ms and 25.5ms respectively, with the deviation of 6.93%), and the value of the simulated maximum overpressure (about 165.35kPa) was close to the experimental result (about 194.77Kpa) with the calculation error of about 15.1%. However, Fig.5 also exhibits some differences between the simulations and the experiments: during the overpressure growth period, two overpressure peaks can be observed in the experiments, while there is only one in the simulation. This might be attributed to the rupture of the sealing membrane at the exit of the pipe in the experiment, which is not considered in the simulation. Overall, although some slight differences in overpressure profiles exist between the experiment and simulation, their overpressure histories agree with each other well. Moreover, in order to further evaluate the predictive capability of the models in the present work, the deviation between the LES simulation and experimental results in the present work are compared with those in some similar studies as listed in Table 1. It can be found that the calculation precision of the present model is close to those of the previous studies. Therefore, it could be verified that the simulation model applied in the present work is good and effective at capturing the main features of vented gasoline-air mixtures explosions in a semi-confined obstructed pipe. 5.2 Interaction between flame propagation and obstacles Fig.9 displays 3-D flame structures at different instants after ignition, with the flame fronts represented by the iso-surface of progress variable c=0.5(Wen, Yu et al. 2012, Xu, Cong et al. 2015). The flame structure remained hemispherical until the front reached the first obstacle at about 14ms after ignition, and in this early period the flame front remained smooth, and propagated in a laminar flame speed (0-9m/s). After the flame front passed through the first obstacle, it evolved into a mushroom-like structure, and the flame skirts began to propagate in the radial direction towards the pipe walls due to the vortices generated by the coupling of the unburned mixture flow pushed by the moving flame and the obstacle (t=18ms). Then as the flame front flowed through the second obstacle, the flame tip kept propagating along the pipe towards the open end, while a part of the flame skirts invert back due to the restrictions of the solid surface of the second obstacle (t=20ms). Continuously, flame tip propagated through the third and fourth obstacle, and the flame structures became profoundly distorted and wrinkled after passing through all the obstacles (t=23ms,25ms,26ms). It is obvious that flame speed increased significantly when it passed through each obstacle as shown in Fig.7 and Fig.9, which could be caused by the jetting effect and the enlarged flame surface area aroused by the distortion of the flame front, where the value of flame surface area is shown in Fig.8, which is calculated by simulated results based on Eq.(10): n

 dA   A

(10)

i

1

where Ai denotes the area of the cell zones on the iso-surface, and n denotes the total number of the cell zones on the isosurface. During flame propagating through the obstacles, two characteristic flame speeds (i.e. axial direction z and radial direction x-y) are observed. The flame speed increased in the axial direction because of the decrease in the cross-section and the flow vortices induced downstream of the obstacles. On the contrary, in the radial direction x-y, the flame propagated more slowly, as in a quasi-quiescent medium. This phenomenon was especially obvious after the flame passed through the second obstacle. 6

Therefore, due to the presence of a preferential direction along the z-axis direction, when the flame reaches the exit of the pipe at about 26ms, there are still some unburned mixtures left in the region between adjacent obstacles and close to the pipe walls, as shown in Fig.4 (b) and Fig.9. Similar results have been also reported in the study by V.Di Sarli et al. (Di Sarli, Di Benedetto et al. 2009) using a chamber (150mm×150mm×500mm) with one obstacle mounted 100mm downstream from the bottom end. V.Di Sarli considered that the more the flame accelerates towards the chamber exit, the higher the 𝑈𝑡 /𝑈𝑙 (where 𝑈𝑡 denotes the axial direction flame speed, 𝑈𝑙 denotes the radial direction flame speed) ratio increases along with the amount of fresh mixture trapped inside the chamber. In the present study, the value of 𝑈𝑡 was higher than 100m/s while the flame passing through the fourth obstacle, which is much higher than the result of V.Di Sarli (about 20m/s). Therefore, it is easily seen that the ratio of 𝑈𝑡 /𝑈𝑙 in the present study was much larger than that by V.Di Sarli, and thus some fresh mixtures could be trapped in the pipe even after the flame front exits the pipe. As analyzed above, hollow-square obstacles could exert great influence on the flame structure and the flame speed during the process of vented gasoline-air mixture explosions. In order to further investigate the mechanism of these phenomena, the interaction between flame propagation and obstacle-induced turbulent flow field is studied based on the result obtained from simulation. Fig.10 presents the profiles of flow fields and flame structures at six different instants after ignition. It can be seen that the velocity magnitude of the flow field was profoundly increasing when the flame propagated through the four obstacles, with the flame structure becoming more and more distorted. This can be attributed to the flame-vortex interaction, which would lead the initially laminar flame to burn through various turbulent combustion regimes, thus accelerating the flame speed(Wen, Yu et al. 2012). Furthermore, with the expansion of the flame, the unburned mixture in front of the flame front is pushed through the cross-section of the obstacles, generating turbulent eddies behind the obstacles. The eddies then would interact with the flame front, distorting and wrinkling the flame structures, increasing the flame surface area, and promoting the combustion rate and flame speed. As a result, the velocity in the flow field would increase as well, which shows a positive feedback mechanism between the flow field and the flame propagation.

5.3 Overpressure dynamics To gain insights into the mechanisms and phenomena that link the flame propagation to the overpressure time history, the overpressure time history has been divided into four stages as marked in Fig.11 (a), based on the different characteristic of the overpressure profile in each stage, and the four stages are assumed to be associated with two parameters: mass flow rate and flame surface area. It is easily observed in Fig.11 (a) that after ignition, there was no obvious overpressure increase until around 15ms (Stage I), corresponding to the laminar flame propagation stage. The Stage II presents a rapid pressure rise phenomenon until it obtains the maximum overpressure at around 25ms. At this stage, both the mass flow rate and the flame surface area increased sharply as shown in Fig.11(b) and (c), hence enhancing the combustion rate and heat release rate, which would lead to the flame acceleration and overpressure rise. Then around 25ms, the overpressure started to decrease dramatically until about 29ms as the mass flow rate dropped profoundly and the flame surface area decreased as well. During this period, the flame exited the pipe, which results in serious heat loss and overpressure decrease. Obviously, in the fourth stage, significant pressure oscillations are observed and several overpressure peaks are formed. It should be noticed that the first overpressure peak in this stage appeared simultaneously as the mass flow rate and the flame surface area reached the maximum values at about 32ms. In some previous studies(Patel, Jarvis et al. 2002, Wen, Yu et al. 2012), this phenomenon has been attributed to the ducting arrangement downstream the chamber, and the pressure oscillation was claimed to be caused by the pressure reflection by the close proximity of the extraction system. However, in the present work, the pressure oscillations are believed to be caused by the pseudo7

confined combustion phenomenon, which would be the result of the combustion of the remained fresh mixture that is wrapped by the heated burned gas, obstacles and the pipe walls after the flame has exited the pipe (Di Sarli, Di Benedetto et al. 2009, Xu, Cong et al. 2015). As can be seen from Fig.9, after the flame approaches the first obstacle, the flame propagated to the open end of the pipe without burning the whole mixture in the pipe due to the significant flame acceleration towards the pipe exit, and hence the remained mixture would be surrounded by the burned gas, obstacles and the pipe walls, forming a pseudo-confined combustion space (Di Sarli, Di Benedetto et al. 2009, Xu, Cong et al. 2015), as can be seen in Fig.12. The unburned mixture then could be heated and ignited by the burned gas, and its expansion would be limited by surrounding burned gas, obstacles and pipe walls, consequently leading to weak overpressure oscillations during the fourth stage. Another meaningful phenomenon could also be noticed in Fig.11 that during the whole development of the explosion, the overpressure, the mass flow rate and the flame surface area almost reached their peaks at the same time profiles. In summary, the first and second main overpressure peaks are closely associated with the mass flow rate and flame surface area, while the oscillations in the fourth stage are attributed to the effects of pseudo-confined combustion phenomenon.

5.4 Effects of the parameters 5.4.1 Initial gasoline vapor concentration In Fig.13, the overpressure histories obtained at the closed end of the pipe for three different initial gasoline vapor concentrations (ϕ=1.3%, ϕ =1.7%, ϕ =2.1%) are shown. The maximum overpressure peaks become more intense and occur earlier on ranging from rich (ϕ =2.1%) to lean (ϕ =1.3%) and stoichiometric (ϕ =1.7%) conditions. Fig.14 shows the flame speeds under different initial gasoline vapor concentrations. It is obvious that the variations of maximum flame speeds are similar to the overpressure time histories. These results are consistent with the former studies, which show that the unsteady flame propagation through obstacles is strongly dependent on the fuel concentrations, and the highest flame speed and overpressures are found at stoichiometric (or nearly stoichiometric, i.e. slightly rich) (Glassmeier 2001, Hargrave, Jarvis et al. 2002, Salzano, Marra et al. 2002). In addition, it is worth noting that some meaningful differences (as listed in Table 3) can be observed that for the explosions of methane-air mixture and hydrogen-air mixture, the maximum overpressure peaks and average overpressure growth rates of rich conditions are more intense than the lean conditions (Di Sarli, Di Benedetto et al. 2009, Guo, Sun et al. 2015), and the time taken to reach the overpressure peaks are shorter, while for the gasoline-air mixture, it is just the opposite, which has been also investigated by our former studies (Li, Du et al. 2016, Qi, Du et al. 2017). Moreover, it can be seen in Fig.13 that for the ϕ =1.7% condition, the pressure profile exhibits four dominant overpressure peaks, while only three peaks can be observed for the conditions of ϕ=1.3% and ϕ =2.1%.

The reason for the phenomenon that the maximum overpressure peaks of ϕ =1.7% and ϕ=1.3% are larger than that of ϕ=2.1% is as follows. The flame speeds along the axial direction for ϕ =1.7% and ϕ=1.3% were faster than that of ϕ=2.1% as shown in Fig.14. Therefore, it could lead to a faster speed for the exchange of burned and unburned 8

mixtures, and hence causes more intense combustion reactivity and enhance the burning velocity and flame surface area. Due to the factors above, more heat would be produced and accumulated to sustain the overpressure rise, and form greater maximum overpressure peaks for the stoichiometric and lean conditions than rich condition. Although the initial gasoline vapor concentration has significant effect on the maximum overpressure peak, it is worth noticing that for the overpressure peaks in the fourth stage as defined in section 5.3, the magnitudes of them are nearly the same. This indicates that the effects of pseudo-confined combustion on the overpressure peaks is not sensitive to the initial fuel concentrations, and the number of accumulated reactants might be probably the same by varying the equivalence ratio.

5.4.2 The number of obstacles Fig.15 shows the overpressure time histories with respect to the number of obstacles. The experimental results were obtained under an initial gasoline vapor concentration of ϕ =1.7%, and the distance between two adjacent obstacles was 100mm. As shown in Fig.15, the maximum overpressure peaks occurred more intensely with more obstacles and this trend can be also found in previous literatures (Wen, Yu et al. 2015). It is mainly caused by flameobstacle interaction, which can probably trigger a highly turbulent combustion, lead to higher burning rate, and hence bring about more intense overpressure rise. However, when to reach the peaks of overpressures is not fully dependent on the number of obstacles, and it doesn’t absolutely become shorter with the increase of the number of obstacles, as is shown in Fig.15, the time to reach the peaks was 27.6ms, 26.9ms, 28.2ms and 27.4ms, respectively for obstacle number varying from 1 to 4. Fig.16 presents the effects of the number of obstacles on flame speeds. It is observed that the maximum flame speeds increased with the growth of obstacle number. This can be explained by the fact that the flow turbulence become more intense with more obstacles mounted along the flame propagation channel, vortices are more easily formed downstream of flame fronts, and the flame structure can therefore become distorted and curved, which would enhance the flame surface area and burning velocity and hence result in significant flame acceleration ultimately.

5.4.3 Comparison with different fuel-air mixtures in terms of explosion parameters Previous studies on flammable gas explosions in an obstructed semi-confined vessel have been conducted using various fuels (e.g. gasoline, hydrogen, methane, etc.) air mixtures in terms of flame propagation speed, maximum overpressure peaks, location of flame front, etc., while few of them have investigated the differences of different gases. Therefore, it is essential to analyze the influence of different flammable gases on the explosion parameters. Table 3 shows an overview of the present work and multiple experimental results from the literatures. Maximum overpressure peaks, average overpressure growth rates and maximum flame speeds are chosen as the objects to do the comparison. It is easily found that the number of obstacles should have significant effects on the magnitude of explosion parameters both for gasoline-air mixtures and methane-air mixtures when comparing 1# with 2# and 3# with 4#, respectively. Concretely, the maximum overpressure peak, average overpressure growth rate and maximum flame speed for gasoline-air mixtures under the condition of three obstacles are enhanced by 445%, 454% and 22% respectively, compared with the results of one obstacle. Meanwhile, for methane-air mixtures, the maximum overpressure peak, average overpressure growth rate and maximum flame speed under the condition of three obstacles 9

are enhanced by 128%, 114% and 88% respectively, when compared with the results of one obstacle. Therefore, it is obvious that the enhancement for the maximum overpressure peak and average overpressure growth rate of gasolineair mixtures explosion is stronger than that of methane-air mixtures explosion with the growth of the number of obstacles. However, in terms of maximum flame speed, this trend is just the opposite. For 2#、4#、6# and 7#, one obstacle was mounted inside the vessel, and four different flammable gas mixtures (gasoline- air, methane-air, hydrogen-air and LPG-air) were applied in the experiments. It could be easily found that the values of maximum overpressure peaks for hydrogen-air mixtures, gasoline-air mixtures and LPG-air mixtures are enhanced by 1143%，266% and 255% when compared with that of methane-air mixtures. The average overpressure growth rates for hydrogen-air mixtures, gasoline-air mixtures and LPG-air mixtures are enhanced by 9044%，337.5% and 212.5% when compared with that of methane-air mixtures. The maximum flame speeds for hydrogen-air mixtures, gasoline-air mixtures and LPG-air mixtures are enhanced by 269%，202% and 78.6% when compared with that of methane-air mixtures. Ultimately, it is evident that the magnitudes of maximum overpressure peak, average overpressure growth rate and maximum flame speed for hydrogen-air mixtures are the greatest, followed by gasolineair mixtures, LPG-air mixtures and methane-air mixtures. However, the reasons for this phenomenon need to be further studied. Therefore, given the significant differences between the characteristics of gasoline-air mixture explosion and those of other fuel-air mixtures, when designing and placing safety protection devices such as explosion suppression devices, flame arresters and venting devices during an industry process, the variations should be taken into account as part of safety analysis.

6. Conclusions In the present work, LES simulation and experimental study on gasoline-air mixture explosions in a semi-confined pipe in the presence of obstacles have been performed. The TFC model proposed by Zimont and Battaglia was applied in the present simulation. The comparisons between simulated results and experimental results have been drawn. It is found that the models are able to predict the flame structures, flame speeds, flame front locations and overpressures behaviors effectively. The interaction between flame propagation and obstacles and the overpressure dynamics were studied according to the simulated results, and the effects of initial gasoline vapor concentrations and the number of obstacles were studied by contrast experiments. The interaction between flame propagation process and obstacles is profound, mainly due to the effects of the vortices generated by the coupling of the unburned mixture flow pushed by the moving flame and the obstacles themselves. The overpressure behaviors are closely associated with the variations of the mass flow rate and the flame surface area, and the overpressure time history can be described as four stages, and the overpressure oscillation phenomena in the fourth stage have been attributed to the effects of pseudo-confined combustion. Additionally, the maximum overpressure peaks and the flame speeds increase with the growth of the number of obstacles. Moreover, for the methane-air mixture and hydrogen-air mixture, the maximum overpressure peaks and average overpressure growth rates of rich conditions are more intense than the lean conditions, and the time taken to reach the maximum overpressure peaks are shorter, while for the gasoline-air mixture, this trend is just the opposite. The vented explosion parameters of several fuels in an obstructed vessel are compared with each other, and it is found that the magnitudes of maximum overpressure peak, average overpressure growth rate and maximum flame speed for hydrogen-air mixtures are the greatest, followed by gasoline-air mixtures, LPG-air mixtures and methane-air mixtures. In summary, the LES model applied in the present work has demonstrated itself as a useful tool to investigate the flow field characteristics, flame and overpressure behaviors of gasoline-air mixture explosions in a semi-confined obstructed space. And it would be suggested to be applied to the design tasks and operations in safety industry fields. 10

Acknowledgment Financial support for this work, provided by the National Natural Science Foundation of China (No. 51276195), and Chongqing scientific research innovation project (No. CYB16128) are gratefully acknowledged. Moreover, special thanks to my father for his long-standing support for my scholarship. References: Abdel-Raheem, M. A., S. S. Ibrahim, W. Malalasekera and A. R. Masri (2015). "Large eddy simulation of hydrogen–air premixed flames in a small scale combustion chamber." International Journal of Hydrogen Energy 40(7): 3098-3109. Ahmed, I. and N. Swaminathan (2014). "Simulation of turbulent explosion of hydrogen–air mixtures." International Journal of Hydrogen Energy 39(17): 9562-9572. Blanchard, R., D. Arndt, R. Grätz, M. Poli and S. Scheider (2010). "Explosions in closed pipes containing baffles and 90 degree bends." Journal of Loss Prevention in the Process Industries 23(2): 253-259. Di Sarli, V., A. Di Benedetto and G. Russo (2009). "Using Large Eddy Simulation for understanding vented gas explosions in the presence of obstacles." J Hazard Mater 169(13): 435-442. Di Sarli, V., A. Di Benedetto and G. Russo (2010). "Sub-grid scale combustion models for large eddy simulation of unsteady premixed flame propagation around obstacles." J Hazard Mater 180(1-3): 71-78. Di Sarli, V., A. Di Benedetto and G. Russo (2012). "Large Eddy Simulation of transient premixed flame–vortex interactions in gas explosions." Chemical Engineering Science 71: 539-551. Di Sarli, V., A. Di Benedetto, G. Russo, S. Jarvis, E. J. Long and G. K. Hargrave (2009). "Large Eddy Simulation and PIV Measurements of Unsteady Premixed Flames Accelerated by Obstacles." Flow, Turbulence and Combustion 83(2): 227-250. Dong, B., P. Huang and X. Peng (2012). "Numeral Simulation on the Venting Explosion Process of Methane and Propane Gas in Closed Cylindrical Vessel." Procedia Engineering 45: 448-452. Glassmeier, K. H. (2001). "Experimental investigation of flame/solid interactions in turbulent premixed combustion." Experimental Thermal & Fluid Science 24(3): 99-106. Gourara, A., F. Roger, H. Wang and J. Most (2006). "Assessment of ignition hazard in turbulent flammable gas mixers combining a Lagrangian approach and large eddy simulation." Combustion and Flame 144(3): 592-604. Guo, J., X. Sun, S. Rui, Y. Cao, K. Hu and C. Wang (2015). "Effect of ignition position on vented hydrogen–air explosions." International Journal of Hydrogen Energy 40(45): 15780-15788. Hargrave, G. K., S. Jarvis and T. C. Williams (2002). "A study of transient flow turbulence generation during flame/wall interactions in explosions." Measurement Science & Technology 13(7): 1036-1042. Hisken, H., G. A. Enstad, P. Middha and K. van Wingerden (2015). "Investigation of concentration effects on the flame acceleration in vented channels." Journal of Loss Prevention in the Process Industries 36: 447-459. Hu, K. and Y. Zhao (2016). "Numerical simulation of internal gaseous explosion loading in large-scale cylindrical tanks with fixed roof." Thin-Walled Structures 105: 16-28. Huang, Z.-w., G.-q. He, F. Qin and X.-g. Wei (2015). "Large eddy simulation of flame structure and combustion mode in a hydrogen fueled supersonic combustor." International Journal of Hydrogen Energy 40(31): 9815-9824. Johansen, C. and G. Ciccarelli (2009). "Visualization of the unburned gas flow field ahead of an accelerating flame in an obstructed square channel." Combustion and Flame 156(2): 405-416. Johansen, C. and G. Ciccarelli (2013). "Modeling the initial flame acceleration in an obstructed channel using large eddy simulation." Journal of Loss Prevention in the Process Industries 26(4): 571-585. Kindracki, J., A. Kobiera, G. Rarata and P. Wolanski (2007). "Influence of ignition position and obstacles on explosion development in methane–air mixture in closed vessels." Journal of Loss Prevention in the Process Industries 20(4-6): 551-561. Li, G., Y. Du, S. Qi, Y. Li, S. Wang and B. Wang (2016). "Explosions of gasoline-air mixtures in a closed pipe containing a T-shaped branch structure." Journal of Loss Prevention in the Process Industries 43: 529-536. Lilly, D. K. (1992). "A proposed modification of the Germano sub-grid‐scale closure method." Physics of Fluids A Fluid Dynamics 4(4): 633-633. Lv, X., L. Zheng, Y. Zhang, M. Yu and Y. Su (2016). "Combined effects of obstacle position and equivalence ratio on overpressure of premixed hydrogen–air explosion." International Journal of Hydrogen Energy 41(39): 17740-17749. Mannaa, O., M. S. Mansour, W. L. Roberts and S. H. Chung (2015). "Laminar burning velocities at elevated pressures for gasoline and gasoline surrogates associated with

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RON." Combustion & Flame 162(6): 2311-2321. Masri, A. R., S. S. Ibrahim and B. J. Cadwallader (2006). "Measurements and large eddy simulation of propagating premixed flames." Experimental Thermal and Fluid Science 30(7): 687-702. Molkov, V., D. Makarov and H. Schneider (2006). "LES modelling of an unconfined large-scale hydrogen–air deflagration." Journal of Physics D Applied Physics 39(39): 4366. Na'inna, A. M., H. N. Phylaktou and G. E. Andrews (2013). "The acceleration of flames in tube explosions with two obstacles as a function of the obstacle separation distance." Journal of Loss Prevention in the Process Industries 26(6): 1597-1603. Na’inna, A. M., H. N. Phylaktou and G. E. Andrews (2014). "Effects of Obstacle Separation Distance on Gas Explosions: The Influence of Obstacle Blockage Ratio." Procedia Engineering 84: 306-319. Park, D. J., Y. S. Lee and A. R. Green (2008). "Experiments on the effects of multiple obstacles in vented explosion chambers." J Hazard Mater 153(1-2): 340-350. Patel, S., S. S. Ibrahim, M. A. Yehia and G. K. Hargrave (2003). "Investigation of premixed turbulent combustion in a semi-confined explosion chamber." Experimental Thermal and Fluid Science 27(4): 355-361. Patel, S. N. D. H., S. Jarvis, S. S. Ibrahim and G. K. Hargrave (2002). "An experimental and numerical investigation of premixed flame deflagration in a semiconfined explosion chamber." Proceedings of the Combustion Institute 29(2): 1849-1854. Qi, S., Y. Du, S. Wang, Y. Zhou and G. Li (2016). "The effect of vent size and concentration in vented gasoline-air explosions." Journal of Loss Prevention in the Process Industries 44: 88-94. Qi, S., Y. Du, P. Zhang, G. Li, Y. Zhou and B. Wang (2017). "Effects of concentration, temperature, humidity, and nitrogen inert dilution on the gasoline vapor explosion." J Hazard Mater 323(Pt B): 593-601. Saghafian, A., L. Shunn, D. A. Philips and F. Ham (2015). "Large eddy simulations of the HIFiRE scramjet using a compressible flamelet/progress variable approach." Proceedings of the Combustion Institute 35(2): 2163-2172. Salzano, E., F. S. Marra, G. Russo and J. H. Lee (2002). "Numerical simulation of turbulent gas flames in tubes." Journal of Hazardous Materials 95(3): 233-247. Sarli, V. D. and A. D. Benedetto (2012). "Sensitivity to the Presence of the Combustion Submodel for Large Eddy Simulation of Transient Premixed Flame–Vortex Interactions." Ind.eng.chem.res 51(22): 7704-7712. Sarli, V. D. and A. D. Benedetto (2013). "Effects of non-equidiffusion on unsteady propagation ofhydrogen-enriched methane/air premixed flames." International Journal of Hydrogen Energy 38(18): 7510-7518. Sarli, V. D., A. D. Benedetto, E. J. Long and G. K. Hargrave (2012). "Time-Resolved Particle Image Velocimetry of dynamic interactions between hydrogen-enriched methane/air premixed flames and toroidal vortex structures." International Journal of Hydrogen Energy 37(21): 16201-16213. Tang, P. and J. Jiang (2011). "Numerical Simulation of Duct-vented Gas Explosion." Procedia Engineering 18: 25-30. Wen, X., M. Yu, W. Ji, M. Yue and J. Chen (2015). "Methane–air explosion characteristics with different obstacle configurations." International Journal of Mining Science and Technology 25(2): 213-218. Wen, X., M. Yu, Z. Liu and W. Sun (2012). "Large eddy simulation of methane–air deflagration in an obstructed chamber using different combustion models." Journal of Loss Prevention in the Process Industries 25(4): 730-738. Xu, C., L. Cong, Z. Yu, Z. Song and M. Bi (2015). "Numerical simulation of premixed methane–air deflagration in a semi-confined obstructed chamber." Journal of Loss Prevention in the Process Industries 34: 218-224. Yakhot, V. and S. A. Orszag (1986). "Renormalization group analysis of turbulence. I. Basic theory." Journal of Scientific Computing 1(1): 3-51. Yakhot, V. V. and S. A. Orszag (1986). 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"Analysis and assessment of the Qingdao crude oil vapor explosion accident: Lessons learnt." Journal of Loss Prevention in the Process Industries 33: 289-303. Zimont, V. and V. Battaglia (2006). "Joint RANS/LES approach to premixed flames modelling in the context of the TFC combustion model - Engineering Turbulence Modelling

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13

Fig.1 Schematic diagram of the explosion pipe (unit: mm).

Fig.2 Schematic of experimental system

(a) Configuration 1

(b) Configuration 2

(c) Configuration 3

(d) Configuration 4

Fig.3 Four configurations varying in terms of obstacle number

14

12ms 18ms 21ms 23ms 25ms 26ms (a)Experimental results (b)Simulation results Fig.4 Comparison between experimental and simulated flame structures at different instants after ignition.

15

220

1.0 (27.4ms,194.77kPa)

200

Experimental result Simulated result

(25.5ms,165.35kPa)

180

0.8

140

Simulated result Experimental result

120 100

Flame location/m

Overpressure/kPa

160

80 60 40 20

0.6

The fourth obstacle

0.4 The third obstacle The second obstacle

0

0.2

-20

The first obstacle

-40 -60

0.0 0

5

10

15

20

25

30

35

40

45

0

5

10

Time/ms

Fig.5 Comparison between experimental and simulated overpressure time histories of the monitor point at the closed end.

20

25

30

Fig.6 Comparison between experimental and simulated flame front locations along the pipe versus time.

0.5

300

Experimental result Simulated result

0.4

Flame surface area/m2

250

Flame speed/m/s

15

Time/ms

200

150

100

0.3

0.2

0.1

50

0.0

0 0

5

10

15

20

25

0

30

Fig.7 Comparison between experimental and simulated flame speeds along the pipe versus time.

5

10

15

20

25

30

35

40

45

Time/ms

Time/ms

Fig.8 Flame surface area versus time computed through simulated results (c=0.5).

14ms

18ms

20ms

21ms

23ms

25ms

16

26ms Fig.9 3-D flame structure images ( iso-surface of progress variable c=0.5) at different instants after ignition.

5ms

12ms

18ms

20ms

21ms

23ms

Fig.10 Velocity vector and flame structure maps obtained by LES calculations when the flame propagates sequentially through the four obstacles.

17

Fig.11 Overpressure time history at the closed end of the pipe (a); mass flow rate of the pipe (b), flame surface area (c).

z=50mm

z=150mm

z=280mm

z=350mm z=500mm z=800mm Fig.12 Reaction progress at different cross section (t=37ms)

(27.4ms,194.77kPa)

200

1.3% 1.7% 2.1%

150

z=250mm

250

1.3% 1.7% 2.1%

225 200 (32.5ms,119.91kPa)

Flame speed/m/s

175

Overpressure/kPa

z=180mm

125 (44.9ms,87.0kPa)

100 75 50 25

175 150 125 100 75

0

50

-25

25 0

-50 0

10

20

30

40

50

0

60

10

20

Time/ms

30

40

50

Time/ms

Fig.13 Overpressure time histories at the closed end of the pipe at different initial gasoline vapor concentrations.

Fig.14 Flame speeds versus time at different initial gasoline vapor concentrations. 275

（ 27.4ms,194.77kPa）

200

125

1 obstacle 2 obstacles 3 obstacles 4 obstacles

225 200 （ 28.2ms,109.52kPa）

Flame speed/m/s

150

Overpressure/kPa

250

1 obstacle 2 obstacles 3 obstacles 4 obstacles

175

100 （ 26.9ms,50.25kPa）

75 50 25 0

175 150 125 100 75 50

（ 27.6ms,19.40kPa）

-25

25 0

-50 0

5

10

15

20

25

30

35

0

40

Fig.15 Overpressure time histories in terms of the number of obstacles(ϕ =1.7%)

5

10

15

20

25

30

35

Time/ms

Time/ms

Fig.16 Flame speeds versus time in terms of obstacle number

18

Table 1. Overview of the calculation errors between the LES simulation and experimental results in the present work compared with those reported in similar studies done previously Calculation error (%)

Pmax(kPa) N#

1# 2# 3#

Gas

Present work A.R. Masri (Masri, Ibrahim et al. 2006) Chaoyi Xu(Xu, Cong et al. 2015)

Experimental

LES

Gasolineair mixtures

194.77

165.35

LPG-air mixtures

26.5

Methaneair mixtures

11.5

PE  PL

100%

Calculation error (%)

t (ms)

tE  tL

100%

Experimental

LES

15.1%

27.4

25.5

6.93%

29.2

10.1%

29.8

31.2

4.69%

9.3

19.1%

37.8

34.6

7.67%

PE

tE

Table 2 Overview of Pmax, t and (dp/dt)ave of the present work, Methane-air mixture and Hydrogen-air mixture explosions

N#

1#

2#

3#

0.8 (0.6 for 3# ) Pmax (dp/dt)ave t(ms) (kPa) (kPa/ms)

Equivalent ratio 1 Pmax (dp/dt)ave t(ms) (kPa) (kPa/ms)

Gasolineair mixtures

119.91

32.5

3.69

194.77

27.4

7.1

87

44.9

1.94

Methane-air mixtures

1.2

47

0.026

3.3

32

0.10

2.3

36

0.064

Hydrogenair mixtures

66

35

1.89

150

20

7.5

225

12.5

18

Gas

Present work Di Sarli, Di Benedetto et al.(Di Sarli, Di Benedetto et al. 2009) Guo, Sun et al.(Guo, Sun et al. 2015)

1.2 (1.6 for 3#) Pmax (dp/dt)ave t(ms) (kPa) (kPa/ms)

Table 3 Overview of some experimental results in the literatures in terms of different fuel-air mixtures and parameters N# 1# 2#

3#

4#

5#

6#

Equivalent ratio

BR (%)

No. (-)

Di (mm)

L/D

Pmax (kPa)

(dp/dt)ave (kPa/ms)

Sfmax (m/s)

1

49.8%

3

100

100

10

105.92

3.88

196.4

1

49.8%

1

100

100

10

19.4

0.70

160.7

Methaneair

1

50%

3

100

100

3.3

12.1

0.342

99.8

L=500mm D=150mm

Methaneair

1

50%

1

100

-

3.3

5.3

0.16

53.2

L=500mm D=100mm

Methaneair

1

50%

3

100

100

5

30

1.3

150.3

L=500mm D=100mm

Hydrogenair

1

50%

1

100

-

5

65.86

14.63

198.9

Reference

Geometry

Gas

Present work Present work Wen, Yu et al.(Wen, Yu et al. 2015) Wen, Yu et al. (Wen, Yu et al. 2015) Zheng, Yu et al. (Zheng, Yu et al. 2017) Lv, Zheng

L=1000mm D=100mm L=1000mm D=100mm

Gasolineair Gasolineair

L=500mm D=150mm

19

Li (mm)

(Lv, Zheng et al. 2016) 7#

A.R. Masri (Masri, Ibrahim et al. 2006)

L=860mm D=150mm

LPG-air

1

50%

1

20

350

-

5.7

18.8

0.5

95