Process of Natural Gas Explosion in Linked Vessels with Three Structures Obtained Using Numerical Simulation

processes

Article Process of Natural Gas Explosion in Linked Vessels with Three Structures Obtained Using Numerical Simulation

Qiuhong Wang 1,*, Yilin Sun 1, Xin Li 1, Chi-Min Shu 2, Zhirong Wang 3,*, Juncheng Jiang 3, Mingguang Zhang 3 and Fangming Cheng 1

1 College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China; [email protected] (Y.S.); [email protected] (X.L.); [email protected] (F.C.) 2 Process Safety and Disaster Prevention Laboratory, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan; [email protected] 3 Jiangsu Key Laboratory of Hazardous Chemicals Safety and Control, College of Safety Science and Engineering, Nanjing Tech University, Nanjing 210009, China; [email protected] (J.J.); [email protected] (M.Z.) * Correspondence: [email protected] (Q.W.); [email protected] (Z.W.)

Received: 9 December 2019; Accepted: 30 December 2019; Published: 2 January 2020

Abstract: Combinations of spherical vessels and pipes are frequently employed in industries. Scholars have primarily studied gas explosions in closed vessels and pipes. However, knowledge of combined spherical vessel and pipe systems is limited. Therefore, a flame acceleration simulator was implemented with computational fluid dynamics software and was employed to conduct natural gas explosions in three structures, including a single spherical vessel, a single spherical vessel with a pipe connected to it, and a big spherical vessel connected to a small spherical vessel with a pipe. These simulations reflected physical experiments conducted by at Nanjing Tech University. By changing the sizes of vessels, lengths of pipes, and ignition positions in linked vessels, we obtained relevant laws for the time, pressure, temperature, and concentrations of combustion products. Moreover, the processes of natural gas explosions in different structures were obtained from simulation results. Simulation results agreed strongly with corresponding experimental data, validating the reliability of simulation.

Keywords: combination system; ﬂame acceleration simulator (FLACS); pipe length; ignition position

1. Introduction Flammable gases are employed extensively in the production of petrochemicals, and regularly stored and transported using linked vessels. A typical linked system comprises closed vessels connected with pipelines [1]. However, widespread fires and explosions frequently occur in such structures because the flames and shock waves that result from local gas explosions can propagate through the pipeline [2–4]. Although the prevention and mitigation techniques for fires and explosions have been continuously improving, the number of accidents has not decreased in recent years. For instance, an explosion and a fire accident caused by a gas leak considerably damaged two nearby buildings, on 23 December 2008, in a coal gasification plant in Hunan province in China [5]. Furthermore, an explosion occurred in 2013 in Dalian Bay, China, due to an operation that violated safety protocols and ignited flammable gases in a vessel, which caused the death of two individuals and severely injured two others. The explosion that occurred in natural gas pipes in 2017 in Guizhou Province, China, caused the death of eight individuals and injured 35 individuals. Therefore, conducting further

Processes 2020, 8, 52; doi:10.3390/pr8010052 www.mdpi.com/journal/processes Processes 2020, 8, 52 2 of 16 studies on gas explosions occurring in linked vessels is of substantial importance for preventing and mitigating the damage caused by gas explosions. Research on the structure of linked vessels has been conducted in past decades. Generally, compared with methane explosions occurring in vented single vessels, gas explosions in linked vessel systems constitute a complex process. This complexity can lead to high explosion strength in linked vessels [6]. Furthermore, numerous influential factors, including venting sizes and positions, ignition positions, and pipe lengths, could affect this process, among which ignition positions or obstacles could considerably change flame propagation, accelerate the speed of fire, and rapidly increase explosion pressures [7–12]. The venting size and position also play a prominent role in gas explosions [13–18]. Studies have demonstrated that the pressure piling exists in linked vessels, and the explosion strength is principally affected by the pipe length to volume ratio [19–25]. Currently, along with the development of computer techniques, numerical simulations have become more advanced. Numerical simulation has numerous advantages over physical testing; numerically simulated experiments are cost-effective, user-friendly, and compatible with a limitless number of experimental devices. Some scholars have examined gas explosions by using numerical simulations. With experimental data collected from the literature and the computational fluid dynamics (CFD) software AutoReaGas, Maremonti et al. [24] simulated gas explosions in two linked vessels. They not only demonstrated that turbulence induced in the second vessel was a major factor influencing violence of the explosion but also verified the validity of their CFD code. Deng et al. [25] conducted an explosion experiment with a CH4 and CO mixture in a 20-L nearly-spherical tank and then used flame acceleration simulator (FLACS) software to mimic the gas explosion of the experiment. They compared their simulation results with experimental data to prove the reliability of the simulation. Ferrara et al. [26] modeled gas explosions vented through ducts by using a two-dimensional (2D) axisymmetric CFD model based on the unsteady Reynolds-averaged Navier–Stokes approach. Simulation results evidenced that the severity of ducted explosions is mainly influenced by vigorous secondary explosions occurring in the duct. Valeria et al. [27] used a validated large-eddy simulation model to study the mechanism underlying vented gas explosions in the presence of obstacles. Methane–air mixtures with different composition ratios, variously shaped obstacles, and area block ratios were investigated. The influences of the combustion rate and venting rate on both the number and intensity of overpressure peaks were observed. In this study, to systematically analyze how the vessel size, vessel structure, ignition position, and length of connection pipes influence natural gas explosions, the strongly validated N–S solver tool of FLACS [28], which has been developed continuously for more than 40 years for predicting the consequences of gas explosions [29,30], was employed. This tool includes a three-dimensional CFD code that solves Favre-averaged transport equations for mass, momentum, enthalpy, turbulent kinetic energy, rate of dissipation of turbulent kinetic energy, mass-fraction of fuel, and mixture-fraction on a structured Cartesian grid using a finite volume method. The Reynolds-averaged Navier-Stokes equations are closed by invoking the ideal gas equation of state and the standard k–ε model for turbulence. Furthermore, one of the key features that distinguishes FLACS from most commercial CFD codes is the use of the distributed porosity concept for representing complex geometries on relatively coarse computational meshes [28]. With this approach, large objects and walls are represented on-grid, whereas smaller objects are represented sub-grid. The pre-processor Porcalc reads the grid and geometry files and assigns volume and area porosities to each rectangular grid cell. In the simulations, the porosity field represents the local congestion and confinement, and this allows sub-grid objects to contribute with flow resistance (drag), turbulence generation and flame folding in the simulations. Simulated-pressure data were compared with the experimental results received from Nanjing Tech University, where the explosion experiment with 10 vol% methane was conducted [13]. In addition, results revealed the distributions of temperature and concentrations of gas products occurring during gas explosions. This study mainly aimed to contribute to this research field by exploring the characteristics of gas explosion in linked vessels. Processes 2020, 8, x FOR PEER REVIEW 3 of 16

2. Simulation Objects

2.1. Experimental Apparatus and Geometric Model The special-designed experimental device and its size and structure are displayed in Figure 1. ProcessesThis experimental2020, 8, 52 system consisted of two different spherical vessels, where one is big and the other3 of 16 is small comparatively, and they connected each other with pipes having a varied length [13]. Two spherical vessels were fabricated from steel with a design pressure of 20 MPa and their 2. Simulation Objects internal diameters were 0.6 and 0.35 m (0.113 m3 and 0.022 m3 in volume, respectively). Seamless steel pipes,2.1. Experimental with an inner Apparatus diameter and and Geometric a thickness Model of 0.06 and 0.015 m, respectively, were connected using flanges and bolts. The pipes were divided into three parts (each part was 2 m in length), so that they couldThe be combined special-designed into pipes experimental with varied device lengths and of 2.45, its size 4.45, and and structure 6.45 m between are displayed the big in and Figure small1. Thisspherical experimental vessels. systemSuitable consisted monitor of points two di wereﬀerent pl sphericalaced as dictated vessels, whereby the one experiment. is big and theThe other entire is explosionsmall comparatively, reactor with and three they different connected struct eachures other and withthe mesh pipes are having given a in varied Figure length 2. [13].

(a)

(b)

Figure 1. Picture and schematicschematic diagramdiagram ofof the the experimental experimental device device for for the the gas gas explosion. explosion. (a )(a Photo) Photo of ofthe the experimental experimental device; device; (b )(b scheme) scheme structural structural diagram diagram of linkedof linked vessels. vessels.

AlthoughTwo spherical only vesselspressure were data fabricated could be fromobtained steel from with the a design experiment, pressure the of data 20 MParegarding and their the temperatureinternal diameters and explosion were 0.6 products and 0.35 mwere (0.113 determined m3 and 0.022 through m3 innumerical volume, respectively).simulation. It provided Seamless furthersteel pipes, analysis with and an inner prediction diameter dealing and with a thickness unidentified of 0.06 explosion and 0.015 processes m, respectively, in linked were vessels. connected usingBased flanges on andthe physical bolts. The experiments, pipes were dividedthis study into conducted three parts natural (each gas part explosions was 2 m in in length), three systems, so that whichthey could were be a combinedsingle spherical into pipes vessel, with a variedsingle lengthsspherical of 2.45,vessel 4.45, connected and 6.45 with m between a pipe, the and big a andbig sphericalsmall spherical vessel vessels. connected Suitable to a sm monitorall spherical points werevessel, placed individually. as dictated Meanwhile, by the experiment. multiple Theinfluence entire factors,explosion including reactor with different three distrufferentctures, structures sizes of andthe thevessels, mesh lengths are given of in the Figure connection2. pipes, and ignitionAlthough positions only were pressure investigated data could in detail. be obtained from the experiment, the data regarding the temperature and explosion products were determined through numerical simulation. It provided further analysis and prediction dealing with unidentified explosion processes in linked vessels.

Based on the physical experiments, this study conducted natural gas explosions in three systems, which were a single spherical vessel, a single spherical vessel connected with a pipe, and a big spherical vessel connected to a small spherical vessel, individually. Meanwhile, multiple inﬂuence factors, Processes 2020, 8, 52 4 of 16 including diﬀerent structures, sizes of the vessels, lengths of the connection pipes, and ignition positions Processeswere investigated 2020, 8, x FOR in PEER detail. REVIEW 4 of 16

(a)

(b)

(c)

Figure 2. GridGrid division division on on the model of the three structures. ( (aa)) Grid Grid division division on on the the model model of of the spherical vessel; ((bb)) gridgrid divisiondivision on on the the model model of of the the single single sphere sphere with with a pipe; a pipe; (c) ( gridc) grid division division on theon themodel model of the of the big big vessel vessel connected connected with with the smallthe small vessel. vessel.

2.2. Boundary Boundary ConditionsConditions and and Initial Initial Conditions Conditions According toto the the experimental experimental conditions conditions and theand FLACS the FLACS User’s ManualUser’s Manual [28], the initial[28], the conditions initial conditionswere set as standardwere set pressureas standard and pressure temperature and andtemp theerature boundary and conditionsthe boundary were conditions set as Euler were equations set as Euler(inviscid equations flow equations), (inviscid which flow iseq suitableuations), for which most explosionis suitable simulations. for most explosion In FLACS, simulations. Euler equations In FLACS,are discretized Euler forequations a boundary are discretized element. Namely, for a theboundary momentum element. and continuityNamely, the equations momentum are solved and continuityon the boundary equations in theare casesolved of on outflow. the boundary The concentration in the case of of outflow. methane The used concentration in the experiment of methane was used10 vol% in ,the and experiment the vessel was was 10 filled vol%, entirely and the with vessel the was gas mixture.filled entirely The parameterwith the gas for mixture. the relative The parameterfuel–oxygen for concentration the relative fuel employed–oxygen in concentration FLACS is denoted employed by equivalence in FLACS ratiois denoted (ER), which by equivalence is defined ratioin Equation (ER), which (1): is defined in Equation (1):

mfuel⁄moxygen Vfuel⁄Voxygen ER = actual = actual (1) mfuel⁄moxygen Vfuel⁄Voxygen stoichiometric stoichiometric where m is the gas mass and V is the gas volume. Accordingly, the ER of methane–oxygen was 1.058. In addition, the default choice of heat switch is close in FLACS, as large-scale explosions are not much influenced. Activating radiation model will let walls and objects have background temperature, and gas heat loss from radiation will calculate as well as radiation from hot objects around. This is useful

Processes 2020, 8, 52 5 of 16

m /moxygen V /Voxygen fuel actual fuel actual ER = = (1) m /moxygen V /Voxygen fuel stoichiometric fuel stoichiometric where m is the gas mass and V is the gas volume. Accordingly, the ER of methane–oxygen was 1.058. In addition, the default choice of heat switch is close in FLACS, as large-scale explosions are not much Processesinfluenced. 2020, 8 Activating, x FOR PEER radiation REVIEW model will let walls and objects have background temperature,5 of and 16 gas heat loss from radiation will calculate as well as radiation from hot objects around. This is useful for small-scale confined explosions with important heat effects and is suitable to apply in this study. for small-scale confined explosions with important heat effects and is suitable to apply in this study. Furthermore, based on the experiment results in small closed vessels, Luo et al. [31] confirmed that Furthermore, based on the experiment results in small closed vessels, Luo et al. [31] confirmed that adding a radiation model is an effective way to improve the precision of calculated results. They adding a radiation model is an effective way to improve the precision of calculated results. They found found that the simulation results without adding the radiation model had a large error with an that the simulation results without adding the radiation model had a large error with an average average error of 10.05%, while the simulation results with adding the radiation model had a small error of 10.05%, while the simulation results with adding the radiation model had a small error with error with an average error of 1.88%. Therefore, adding a radiation model to the simulation of gas an average error of 1.88%. Therefore, adding a radiation model to the simulation of gas explosions explosions was able to produce a sound agreement with experimental results. As a result, to examine was able to produce a sound agreement with experimental results. As a result, to examine a realistic a realistic situation, this study included a radiation model to improve the accuracy of the results. situation, this study included a radiation model to improve the accuracy of the results.

3. Simulation Simulation Results with Different Diﬀerent Structures

3.1. Simulation Simulation Results Results in in the the Single Single Spherical Spherical Vessel Vessel

3.1.1. Influence Inﬂuence of Vessel Size on the Explosion Pressure The center ofof thethe largelarge spheresphere waswas at at (0.35, (0.35, 0.35, 0.35 0.35);, 0.35); the the sensor sensor mounted mounted on on the the sidewall sidewall was was at (0.075,at (0.075, 0.35, 0.35, 0.35); 0.35); the the center center of smallof small sphere sphere was wa ats (0.19,at (0.19, 0.19, 0.19, 0.19); 0.19); and and the the sensor sensor mounted mounted on theon thesidewall sidewall was was at(0.025, at (0.025, 0.19, 0.19, 0.19). 0.19). The The simulation simulation was was performed performed following followingthe the methanemethane explosion experiment at 10 vol% in two single vessels. The results of the simulation are plotted in Figure3 3..

49.3 ms 8 7.78 barg

53.6 ms 102.9 ms (barg)

P 4

2 Small vessel Big vessel

0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Figure 3. NaturalNatural gas gas explosion pressure varying with time in two single vessels.

The results revealed that the pressure plots at the center of the spheres and the sensor on the sidewall couldcould be be superposed. superposed. As As shown shown in Figure in Figu3, are nearly 3, a consistentnearly consistent maximum maximum explosion explosion pressure pressurecan be observed can be observed in the big in/small the vessel,big/small which vessel, were which 7.78 were and 7.797.78 barg,and respectively.7.79 barg, respectively. However, However,the maximum the maximum explosion expl pressureosion in pressure two vessels in two peaked vessels at peaked 102.9 and at 102.9 53.6 ms, and respectively, 53.6 ms, respectively, and there wasand athere considerable was a considerable diﬀerence of differ 49.3ence ms, whereof 49.3 the ms, amplitude where the can amp belitude attained can to be 48%. attained Therefore, to 48%. the Therefore,rate of pressure the rate rise of in pressure the big vesselrise in wasthe lowerbig vessel than was that lower of the than small that vessel. of the As small a result, vessel. without As a result,changing without the initial changing conditions the initial of the conditions scenario, the of peakthe scenario, pressure the was peak same, pressure but by contrast, was same, the but rate by of contrast, the rate of the pressure rise was only relevant to the vessel size. Additionally, this finding was consistent with the “explosion cubic law” [32].

3.1.2. Simulation Results of the Explosion Parameters in the Single Vessel The distributions on the X-Y section of explosion parameters containing pressure, temperature, and explosion products at the 10 vol% CH4 mixture in the big vessel are presented in Figure 4.

Processes 2020, 8, 52 6 of 16 the pressure rise was only relevant to the vessel size. Additionally, this ﬁnding was consistent with the “explosion cubic law” [32].

3.1.2. Simulation Results of the Explosion Parameters in the Single Vessel The distributions on the X-Y section of explosion parameters containing pressure, temperature, and explosion products at the 10 vol% CH mixture in the big vessel are presented in Figure4. Processes 2020, 8, x FOR PEER REVIEW 4 6 of 16

(a)

(b)

(c)

FigureFigure 4. 4. ContoursContours of of the the natural natural gas gas explosion explosion parame parametersters containing containing pressure, pressure, temperature, temperature, and and concentrationconcentration ofof products products in thein largerthe larger vessel. vessel. (a) Distribution (a) Distribution of pressure; of pressure; (b) distribution (b) distribution of temperature; of temperature;(c) distribution (c) ofdistribution the concentration of the concentration of products. of products.

AsAs evidenced inin FigureFigure4a, 4a, the the pressure pressure in the in largerthe larger vessel vessel was practically was practically uniform uniform at any speciﬁcat any specifictime. The time. explosion The explosion wave expandedwave expanded into a into spherical a spherical wave wave and theand temperaturethe temperature was was high high near near the theigniter igniter but but gradually gradually decreased decreased until until it it approached approached the the leading leading edgeedge ofof thethe combustion wave wave in in FigureFigure 44b.b. Here, the combustion wave reached the sidewall at 125 ms.ms. The temperature in the big vesselvessel began to decreasedecrease whenwhen thethe explosion explosion ended. ended. As As indicated indicated in in Figure Figure4c, 4c, when when more more natural natural gas gasparticipated participated in the in reaction,the reaction, the distribution the distribution of the of explosion the explosion products products spread spread further further until the until gas wasthe gasconsumed. was consumed. The laws The of thelaws distribution of the distribution of pressure, of pressure, temperature, temperature, and explosion and explosion products products in the small in thevessel small were vessel the samewere the as those same in as the those big in vessel. the big vessel. The changing temperatures and concentrations of the explosion products in the vessels are plotted in Figure 5. When the explosion occurred, the temperature at the center of the vessel enhanced rapidly, reaching 2161 K at 6 ms. Then the rate of the temperature rise dropped, and the temperature at the center of the small vessel reached 2580 K at 53 ms, whereas in the big vessel it reached 2581 K at 101 ms. The center and sidewall reached the highest temperature simultaneously, but the energy was lost when the combustion wave contacted the sidewall. The highest temperature near the sidewall was lower than that at the center of the sphere. After it was ignited at the center of the sphere, the concentration of products at the center escalated promptly, reaching its highest value (27.7%) at

Processes 2020, 8, 52 7 of 16

The changing temperatures and concentrations of the explosion products in the vessels are plotted in Figure5. When the explosion occurred, the temperature at the center of the vessel enhanced rapidly, reaching 2161 K at 6 ms. Then the rate of the temperature rise dropped, and the temperature at the center of the small vessel reached 2580 K at 53 ms, whereas in the big vessel it reached 2581 K at 101 ms. The center and sidewall reached the highest temperature simultaneously, but the energy was lost when the combustion wave contacted the sidewall. The highest temperature near the sidewall was lower Processesthan that 2020 at, 8 the, x FOR center PEER of REVIEW the sphere. After it was ignited at the center of the sphere, the concentration7 of 16 of products at the center escalated promptly, reaching its highest value (27.7%) at 12 ms in Figure5b. 12The ms theoretical in Figure concentration5b. The theoretical of products concentration reached 28.35%of products based reached on the methane28.35% based combustion on the methane chemical combustionequation. Accordingly, chemical equation. the simulation Accordingly, results the ﬁtted simulation the theoretical results values. fitted the theoretical values.

3000 0.30 (a) (b) c a 2500 d 0.25 a d b b

2000 0.20 c

1500 0.15 T (K) PROD

1000 0.10 a Center of big vessel a Center of big vessel b Side wall of big vessel b Side wall of big vessel 500 c Center of small vessel 0.05 c Center of small vessel d Side wall of small vessel d Side wall of small vessel

0 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s)

Figure 5. ProfilesProfiles of of the the natural natural gas gas explosion explosion parameters parameters in the single vessel. ( (aa)) Profiles Profiles of of explosion explosion temperaturestemperatures against against time time in in the the vessels; ( (bb)) concentration concentration profiles profiles against against time time for for the explosion products in the vessels. 3.2. Simulation Results in for Single Vessel with Pipes Connected to IT 3.2. Simulation Results in for Single Vessel with Pipes Connected to IT 3.2.1. Simulation Results of the Explosion Parameters in the Single Vessel with Pipes Connected to It 3.2.1. Simulation Results of the Explosion Parameters in the Single Vessel with Pipes Connected to It The big sphere with the 4.25-m pipe was adopted as an example; the igniter was located at the centerThe of big the sphere sphere. with The the distributions 4.25-m pipe of was the pressure,adopted as temperature, an example; and the concentrationigniter was located of products at the centerof the of methane the sphere. explosion The distributions are shown of in the Figure pressu6. There, temperature, plots of the and explosion concentration temperature of products and the of theconcentration methane explosion of products are are shown delineated in Figure in Figure 6. The7. plots of the explosion temperature and the concentrationFigure6a showsof products that the are peak delineated pressure in inFigure the single 7. vessel with a pipe connected to it was lower thanFigure that of 6a the shows single that vessel. the Aspeak provided pressure by in Figure the si6ngleb, because vessel ofwith the a oscillationpipe connected sparked to it by was the lower blast, thanthe gas that in of the the pipe single was vessel. carried As to theprovided vessel, by and Figure a jet flow6b, because formed. of Moreover, the oscillation from Figuresparked6c, by when the blast,the ignition the gas source in the waspipe locatedwas carried at the to center the vessel of the, and vessel, a jet the flow combustion formed. Moreover, wave spread from 2.3 Figure m in the6c, whenpipe when the ignition it spread source from thewas center located to theat the sidewall center inof the the vessel. vessel, Therefore, the combustion compared wave with spread the vessels 2.3 m inalone, the pipe thepipes when significantly it spread from accelerated the center the to the spread sidewall of the in explosion. the vessel. Therefore, compared with the vesselsIn alone, virtue ofthe the pipes oscillation significantly of the ac explosion,celerated the the plots spread of temperatureof the explosion. displayed a fluctuation at the center of the vessel (in Figure7a). Moreover, the energy was lost when the combustion wave contacted the sidewall. The highest temperature near the sidewall was low and the fluctuations were small comparatively. The plots in Figure7b reveal that as the explosion wave spread, the entire vessel was filled with combustion products, which reflected that the variation of products was not be affected by the oscillation.

(a)

Processes 2020, 8, x FOR PEER REVIEW 7 of 16

12 ms in Figure 5b. The theoretical concentration of products reached 28.35% based on the methane combustion chemical equation. Accordingly, the simulation results fitted the theoretical values.

3000 0.30 (a) (b) c a 2500 d 0.25 a d b b

2000 0.20 c

1500 0.15 T (K) PROD

0 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s)

Figure 5. Profiles of the natural gas explosion parameters in the single vessel. (a) Profiles of explosion temperatures against time in the vessels; (b) concentration profiles against time for the explosion products in the vessels.

3.2. Simulation Results in for Single Vessel with Pipes Connected to IT

3.2.1. Simulation Results of the Explosion Parameters in the Single Vessel with Pipes Connected to It The big sphere with the 4.25-m pipe was adopted as an example; the igniter was located at the center of the sphere. The distributions of the pressure, temperature, and concentration of products of the methane explosion are shown in Figure 6. The plots of the explosion temperature and the concentration of products are delineated in Figure 7. Figure 6a shows that the peak pressure in the single vessel with a pipe connected to it was lower than that of the single vessel. As provided by Figure 6b, because of the oscillation sparked by the blast, the gas in the pipe was carried to the vessel, and a jet flow formed. Moreover, from Figure 6c, when the ignition source was located at the center of the vessel, the combustion wave spread 2.3 m Processesin the pipe2020 ,when8, 52 it spread from the center to the sidewall in the vessel. Therefore, compared with8 ofthe 16 vessels alone, the pipes significantly accelerated the spread of the explosion.

Processes 2020, 8, x FOR PEER REVIEW (a) 8 of 16

(b)

(c)

Figure 6. 6. ContoursContours of of the the natural natural gas gas explosion explosion paramete parametersrs (pressure, (pressure, temperature, temperature, and and concentration concentration of products)products) inin the the single single vessel vessel with with a pipe a connectedpipe connected to it; (a )to distribution it; (a) distribution of pressure. of ( bpressure.) distribution (b) distributionof temperature; of temperature; (c) distribution (c) distribution of the concentration of the concentration of products. of products.

0.30 2500 0.27694

0.25 2000 12 ms 0.20 77 ms Center of vessel 1500 Side wall of vessel 0.15 T (K) 1000

0 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s)

Figure 7. Profiles of the natural gas explosion parameters (temperature and concentration of products) in the single vessel with a pipe connected to it.

In virtue of the oscillation of the explosion, the plots of temperature displayed a fluctuation at the center of the vessel (in Figure 7a). Moreover, the energy was lost when the combustion wave contacted the sidewall. The highest temperature near the sidewall was low and the fluctuations were

Processes 2020, 8, x FOR PEER REVIEW 8 of 16

(b)

(c)

Figure 6. Contours of the natural gas explosion parameters (pressure, temperature, and concentration of products) in the single vessel with a pipe connected to it; (a) distribution of pressure. (b) Processes 2020, 8, 52 9 of 16 distribution of temperature; (c) distribution of the concentration of products.

0.30 2500 0.27694

0.25 2000 12 ms 0.20 77 ms Center of vessel 1500 Side wall of vessel 0.15 T (K) 1000

PROD (b) Concentration profiles against (a) Profiles of explosion temperatures 0.10 time for the explosion products against time in the vessels in the vessels 500 Side wall of vessel 0.05 Side wall of vessel Center of vessel Center of vessel Processes 2020, 8, x FOR PEER REVIEW 9 of 16 0 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 small comparatively. TheTime plots (s) in Figure 7b reveal that as the explosion waveTime spread, (s) the entire vessel was filled with combustion products, which reflected that the variation of products was not be Figure 7. Proﬁles of the natural gas explosion parameters (temperature and concentration of products) affectedFigure by 7.the Profiles oscillation. of the natural gas explosion parameters (temperature and concentration of products) in the single vessel with a pipe connected toto it.it. 3.2.2. Influence Inﬂuence of of Changing Changing the the Ignition Ignition Position Position In virtue of the oscillation of the explosion, the plots of temperature displayed a fluctuation at the centerThe bigbig of vessel vesselthe vessel with with the(in the 4.25-mFigure 4.25-m pipe7a). pipe wasMoreover was adopted adopted, the as anenergy as example, an wasexample, thelost gas when the was gas the ignited was combustion atignited the sidewall atwave the sidewallcontactedof the big of the vessel, the sidewall. big the vessel, center The the highest of center the sphere,temperature of the sphere, location near location 1, the and sidewall location1, and was location 2(in low Figure and2 (in the 2Figure). fluctuations The 2). plots The of plotswere the ofexplosion the explosion pressure pressure as it changed as it changed with time with are time illustrated are illustrated in Figure in Figure8. 8.

4 (barg)

P 3

2 Center of big sphere Side wall of big sphere Location 1 1 Location 2 Location 4 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) FigureFigure 8. 8. NaturalNatural gas gas explosion explosion pressure pressure versus versus time by changing the ig ignitionnition positions.

As revealed in Figure 88,, changingchanging thethe ignitionignition positionposition substantiallysubstantially influencedinfluenced thethe explosionexplosion pressure inin thethe big big vessel. vessel. The The peak peak pressure pressure locations locations in the in big the vessel big withvessel di ffwitherent different ignition positionsignition positionscould be sortedcould be from sorted highest from to highest lowest asto follows:lowest as location follows: 4, location location 4, 2, location the center, 2, the location center, 1, location and the 1,sidewall, and the orderly.sidewall, By orderly. contrast, By thecontrast, maximum the maximum rate of pressure rate of risepressure could rise be could sorted be as sorted follows: as follows: location location4, location 4, location 2, location 2, location 1, the center, 1, the center, and the and sidewall, the sidewall, orderly. orderly. The combustionThe combustion wave wave contacted contacted the thesidewall sidewall during during the explosionthe explosion when when the ignitionthe ignition source source was was located located at the atsidewall. the sidewall. Due Due to the to wall the walleffect, effect, the abundant the abundant energy energy was consumed, was consumed, which resulted which inresulted the explosion in the intensityexplosion to intensity be weaker to than be weakerat the other than ignition at the positions.other ignition Accordingly, positions. the Acco explosionrdingly, pressure the explosion and the pressure rate of pressure and the rise rate were of pressurediminished. rise were Locations diminished. 1, 2, and Locations 4 were located 1, 2, and within 4 were the located pipe, within where the the pipe, explosion where occurred the explosion with occurreda tighter constraintwith a tighter and constraint the pipes acceleratedand the pipes the a explosionccelerated wave.the explosion Location wave. 4 was Location at the end 4 was of the at thepipe, end at whichof the pipe, the acceleration at which the distance acceleration was the dist longest.ance was The the explosion longest. intensityThe explosion was mostintensity vigorous was mostwhen vigorous the combustion when the wave combustion spread to wave the big spread vessel. to Therefore,the big vessel. the explosionTherefore, pressure the explosion and the pressure rate of andpressure the rate rise of were pressure the largest rise were when the the largest ignition when source the ignition was at location source was 4. at location 4.

3.2.3. Influence of the Length of the Connection Pipes The ignition source was located at the center of the vessel. The explosion pressure in different lengths of pipe is shown in Figure 9. Figure 9 shows that the size effect [33] of each pipe length had a noticeable influence on the explosion intensity in the vessel. The peak explosion pressure lessened as increasing length of the connection pipe, with the influence being the greatest in the small vessel. In any single vessel with a connected pipe, the energy from the explosion was consumed by the wall. More energy was lost when the lengths of the connected pipes increased on account of the greater area of the inner wall. Consequently, the peak explosion pressure decreased with the increase in the lengths of the connected pipes.

Processes 2020, 8, 52 10 of 16

Processes 2020, 8, x FOR PEER REVIEW 10 of 16 3.2.3. Inﬂuence of the Length of the Connection Pipes 8 8 (a) Big vessel with pipes connected to it The ignition source was located at the center of the(b) vessel. Small vessel The with explosion pipes connected pressure to it 2.20 in m diﬀerent Processes7 2020P, 8 ,of x 7.22 FOR barg PEER REVIEW 7 10 of 16 lengths of pipemax is shown in Figure9. 4.20 m 6.20 m 6 Pmax of 6.45 barg 6 8 8 P of 5.73 barg (a) Big vessel with pipes connected to it max 5 5 (b) Small vessel with pipes connected to it 2.20 m 7 7 Pmax of 7.22 barg 4.20 m 4 4 6.20 m (barg) (barg) 6 Pmax of 6.45 barg 6 Pmax of P P 3 3 3.90 barg Pmax of 5.73 barg 5 5 2 2 4 2.25 m 4 (barg) (barg) 1 4.25 m 1 Pmax of P P 3 6.25 m 3 3.90 barg 0 0 20.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 20.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 2.25 m Time (s) Time (s) 1 4.25 m 1 6.25 m Figure0 9. Natural gas explosion pressure versus time by0 changing the length of the pipe connected to 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 the single vessel. Time (s) Time (s)

3.3. SimulationFigure 9. NaturalNatural Results gas gas ofexplosion explosion the Big pressure Vessel Connected versus time to by the changing Small the Vessel length of the pipe connected to the single vessel. 3.3.1. Simulation Results of the Explosion Parameters in the Big Vessel Connected to the Small Vessel Figure9 shows that the size e ffect [33] of each pipe length had a noticeable influence on the 3.3. Simulation Results of the Big Vessel Connected to the Small Vessel explosionRegarding intensity the simulation in the vessel. of the The big peak vessel explosion with the pressure 4.45-m pipe lessened and the as small increasing vessel, length the ignition of the sourceconnection was pipe,located with at thethe influence center of being the big the vesse greatestl. Changes in the small in the vessel. distribution In any single of the vessel pressure, with 3.3.1. Simulation Results of the Explosion Parameters in the Big Vessel Connected to the Small Vessel temperature,a connected pipe,and concentration the energy from of products the explosion are presented was consumed in Figure by10. theThe wall.plots of More the temperature energy was andlost whentheRegarding concentration the lengths the simulation profiles of the connected of the bigexplosion vessel pipes increasedwithproducts the 4.45-m are on depicted account pipe and ofin theFigurethe greatersmall 11. vessel, area ofthe the ignition inner wall.sourceAs Consequently, wasillustrated located in at theFigure the peak center 10a, explosion the of peak the pressure pressurebig vesse decreasedwasl. Changes attained with in in the small increasedistribution vessel in the atof 75 lengthsthe ms pressure, and of was the considerablytemperature,connected pipes. higherand concentration than that in of the products big vessel. are presentedThe temperature in Figure in 10.the Thepipe plots was oflower the temperaturethan that in andthe sphere the concentration because energy profiles was of absorbed the explosion by the products wall in arethe depictedlong pipe in in Figure Figure 11. 12b. Gas at a lower temperature3.3. SimulationAs illustrated was Results brought in Figure of the into Big10a, the Vessel the sphere peak Connected pressureas a result to the was of Small theattained Vesseloscillation in the originatedsmall vessel from at 75 the ms explosion and was considerablywave. Here, the higher low-temperature than that in thejet cutsbig vessel.the temperat The temperatureure distribution in the in pipethe sphere was lower to a symmetricalthan that in 3.3.1. Simulation Results of the Explosion Parameters in the Big Vessel Connected to the Small Vessel thestructure. sphere because energy was absorbed by the wall in the long pipe in Figure 12b. Gas at a lower temperatureInRegarding Figure was 11a, the brought the simulation explosion into ofthe wave the sphere big reached vessel as a result withits highthe ofest the 4.45-m temperature oscillation pipe and originated (2700 the small K) at from vessel,70 ms the in the explosion the ignition small wave.vessel.source Here, By was contrast, locatedthe low-temperature the at thetemperature center jet of cutswas the the big2400 temperat vessel. K in theure Changes big distribution vessel in at the thein distribution the same sphere time. to of Because a thesymmetrical pressure, of the structure.oscillationtemperature, of the and combustion concentration wave, of products the temperature are presented at the center in Figure of the 10. big The vessel plots plummeted of the temperature to 1300 Kand at the74In msFigure concentration after 11a, the thecombustion profilesexplosion of wave thewave explosion spread reached into productsits the high smallest are temperature vessel, depicted which in (2700 Figure then K) formed 11 at. 70 ms a second in the peak.small vessel. By contrast, the temperature was 2400 K in the big vessel at the same time. Because of the oscillation of the combustion wave, the temperature at the center of the big vessel plummeted to 1300 K at 74 ms after the combustion wave spread into the small vessel, which then formed a second peak.

(a)

Figure 10. Cont.

(a)

Processes 2020, 8, 52 11 of 16 Processes 2020, 8, x FOR PEER REVIEW 11 of 16 Processes 2020, 8, x FOR PEER REVIEW 11 of 16

(b) (b)

(c) (c) Figure 10. Contours of the natural gas explosion parameters in the big vessel connected to the small Figure 10. Contours of the natural gas explosion paramete parametersrs in the big vessel connected to the small vessel. (a) Distribution of pressure; (b) distribution of temperature; (c) distribution of the vessel. (a(a)) Distribution Distribution of pressure;of pressure; (b) distribution (b) distribution of temperature; of temperature; (c) distribution (c) distribution of the concentration of the concentration of products. concentrationof products. of products.

0.30 (a) 0.30 (b) d (b) 2500 (a) The maximum of 0.2770 d 0.25 2500 c The maximum of 0.2770 c 0.25 2000 0.20 2000 0.20 b b a a 1500 0.15 1500 b 0.15 b PROD c T (K) PROD c

T (K) 1000 0.10 1000 0.10 a d a Side wall of big vessel a a Side wall of big sphere d ba SideCenter wall of ofbig big vessel vessel 500 ba CenterSide wall of bigof big sphere sphere 0.05 cb CenterCenter ofof smallbig vessel vessel 500 cb CenterCenter ofof smallbig sphere sphere 0.05 c Center of small vessel dc SideCenter wall of ofsmall small sphere sphere d Side wall of small vessel d Side wall of small vessel 0 d Side wall of small sphere 0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0 0.00 0.00 0.02 0.04 0.06 0.08Time 0.10 (s) 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08Time 0.10 (s) 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s)

Figure 11.11. ProfilesProfiles of of the the natural natural gas explosiongas explosion parameters parame (temperatureters (temperature and concentration and concentration of products of Figure 11. Profiles of the natural gas explosion parameters (temperature and concentration of productsversus time) versus in the time) big vessel in the connected big vessel to the connected small vessel. to the (a) Profilessmall vessel. of explosion (a) Profiles temperatures of explosion against products versus time) in the big vessel connected to the small vessel. (a) Profiles of explosion temperaturestime in the vessels; against (b )time concentration in the vessels; profiles (b) against concentration time for profiles the explosion against products time for in the the explosion vessels. temperatures against time in the vessels; (b) concentration profiles against time for the explosion products in the vessels. productsAs illustrated in the vessels. in Figure 10a, the peak pressure was attained in the small vessel at 75 ms and wasFigure considerably 11b shows higher that than the that concentration in the big vessel.of products The temperatureenhances rapidly in the at pipe 62 ms. was Namely, lower than the Figure 11b shows that the concentration of products enhances rapidly at 62 ms. Namely, the combustion wave spread into the small vessel through the connected pipe at that moment. combustion wave spread into the small vessel through the connected pipe at that moment.

Processes 2020, 8, x FOR PEER REVIEW 12 of 16

Furthermore, the combustion wave spread to the sidewall of the big vessel at 65 ms. This result again demonstrated the fact that the pipes accelerated the combustion wave.

Processes3.3.2. How2020 ,Changing8, 52 the Ignition Position Influenced the Gas Explosion 12 of 16 Considering the big vessel with the 4.45-m pipe and small vessel as an example, the ignition positionsthat in the were sphere the sidewall because energyof the big was vessel, absorbed the center by the of wallthe big in vessel, the long location pipe in 1, Figurelocation 12 2,b. location Gas at 4,a lowerlocation temperature 6, the center was of the brought small intovessel, the and sphere the sidewall as a result of ofthe the small oscillation vessel, as originated depicted in from Figure the 2.explosion A methane wave. mixture Here, with the low-temperaturea concentration of jet 10 cuts vol% the was temperature intentionally distribution selected in in the the simulations. sphere to a Thesymmetrical plots of the structure. explosion pressure in the large and small vessels are shown in Figure 12.

9 g (a) Explosion pressure 16 (b) Explosion pressure a Side wall of big sphere f b Center of big sphere e d c b in big vessel in small vessel a c Location 1 8 14 d Location 2 a e Location 4 7 12 f Center of small sphere b g Side wall of small sphere 6 c 10 5 e f g 8 (barg) (barg) d P P 4 a Side wall of big sphere 6 3 b Center of big sphere c Location 1 4 2 d Location 2 e Location 4 1 f Center of small sphere 2 g Side wall of small sphere 0 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s) Figure 12. NaturalNatural gas gas explosion explosion pressure pressure versus versus time time in in the the large and small vessels at different diﬀerent ignition positions.

AsIn Figureexhibited 11a, in the Figure explosion 12a, the wave peak reached pressure its highest was attained temperature in the (2700big vessel K) at when 70 ms the in the ignition small vessel.was positioned By contrast, at the the sidewall temperature of the small was 2400 vessel. K inThe the minimum big vessel pressure at the same value time. was obtained Because ofwhen the theoscillation ignition of was the combustionpositioned at wave, the sidewall the temperature of the big at vessel. the center Figure of the 12b big shows vessel that plummeted the peak topressure 1300 K decreasedat 74 ms after when the the combustion ignition was wave moved spread from into the smallsidewall vessel, in the which big thenvessel formed to location a second 2, then peak. the peakFigure pressure 11 increasedb shows thatslightly the when concentration the ignition of was products moved enhances from location rapidly 2 to at the 62 sidewall ms. Namely, in the smallthe combustion vessel. Therefore,wave spread the pressure into the piling small [21,22] vessel originated through from the connectedthe oscillation pipe was at the that weakest moment. at locationFurthermore, 2. the combustion wave spread to the sidewall of the big vessel at 65 ms. This result again demonstrated the fact that the pipes accelerated the combustion wave. 3.3.3. How Changing the Length of the Connection Pipe Influenced the Gas Explosion 3.3.2. How Changing the Ignition Position Influenced the Gas Explosion In the experiment, the vessel that contained the ignition source was defined as the initiating Considering the big vessel with the 4.45-m pipe and small vessel as an example, the ignition vessel, and the other was defined as the secondary vessel. The explosion results were determined positions were the sidewall of the big vessel, the center of the big vessel, location 1, location 2, location variably with the change in the length of the pipe, as drawn in Figure 13. 4, location 6, the center of the small vessel, and the sidewall of the small vessel, as depicted in Figure2. Figure 13a,b exhibited that the length of the pipe affected the pressure in the initiating vessel. A methane mixture with a concentration of 10 vol% was intentionally selected in the simulations. The peak pressure in the initiating vessel was reached when the length of the connecting pipe was The plots of the explosion pressure in the large and small vessels are shown in Figure 12. 4.45 m. As the length increased, the peak pressure in the initiating vessel increased, yet decreased As exhibited in Figure 12a, the peak pressure was attained in the big vessel when the ignition when the pipe was longer than 4.45 m. The acceleration from the pipes on the combustion wave was positioned at the sidewall of the small vessel. The minimum pressure value was obtained when reinforced the explosion intensity, but as the length of the pipe increased, more energy was dissipated the ignition was positioned at the sidewall of the big vessel. Figure 12b shows that the peak pressure by the cause of the wall. When the length of the connecting pipe was excessive, a more momentous decreased when the ignition was moved from the sidewall in the big vessel to location 2, then the influence on the acceleration from the wall than that from the pipes could be demonstrated. peak pressure increased slightly when the ignition was moved from location 2 to the sidewall in the Comparing Figure 13a together with Figure 13c,b together with Figure 13d revealed that the peak small vessel. Therefore, the pressure piling [21,22] originated from the oscillation was the weakest at pressure in the initiating vessel was lower than that in the secondary vessel. Moreover, when the location 2. initiating vessel was the big vessel, the peak pressure in the second vessel was considerably higher. 3.3.3. How Changing the Length of the Connection Pipe Influenced the Gas Explosion In the experiment, the vessel that contained the ignition source was defined as the initiating vessel, and the other was defined as the secondary vessel. The explosion results were determined variably with the change in the length of the pipe, as drawn in Figure 13. Figure 13a,b exhibited that the length of the pipe affected the pressure in the initiating vessel. The peak pressure in the initiating vessel was reached when the length of the connecting pipe was 4.45 m. As the length increased, the peak pressure in the initiating vessel increased, yet decreased when the pipe was longer than 4.45 m. The acceleration from the pipes on the combustion wave reinforced Processes 2020, 8, 52 13 of 16 the explosion intensity, but as the length of the pipe increased, more energy was dissipated by the cause of the wall. When the length of the connecting pipe was excessive, a more momentous influence on the acceleration from the wall than that from the pipes could be demonstrated. Comparing Figure 13a together with Figure 13c,b together with Figure 13d revealed that the peak pressure in the initiating vessel was lower than that in the secondary vessel. Moreover, when the initiating vessel was the big Processesvessel, the2020 peak, 8, x FOR pressure PEER REVIEW in the second vessel was considerably higher. 13 of 16

8 8 6.45 m 6.45 m 7 4.45 m 7 4.45 m 2.45 m 2.45 m 6 6

5 5 (barg) 4 (barg) 4 P P

3 3

2 2 (b) In small vessel with the ignition 1 (a) In big vessel with the ignition 1 sources located at the center sources located at the center 0 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s) 14

6.45 m 12 8 6.45 m 4.45 m 4.45 m 2.45 m 2.45 m 10 6 8 (barg) (barg) P 6 P 4

4 2 2 (c) In small vessel with the ignition (d) In big vessel with the ignition sources located at the center sources located at the center 0 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time (s) Time (s)

Figure 13. NaturalNatural gas gas explosion explosion pressure-time pressure-time curves curves in inthe the vessels vessels with with changing changing the thelength length of the of pipe.the pipe. 4. Error Analysis 4. Error Analysis The simulation results and experimental data were compared for two diﬀerent structures, which The simulation results and experimental data were compared for two different structures, which were the big vessel connected to the small vessel with the 4.45-m pipe and the 6.45-m pipe. The peak were the big vessel connected to the small vessel with the 4.45-m pipe and the 6.45-m pipe. The peak pressure values at diﬀerent ignition positions from the simulation and experiment are shown in pressure values at different ignition positions from the simulation and experiment are shown in Figure 14. Figure 14. In Figure 14a, “A1” to “A7” correspond to the adopted ignition positions: the sidewall of the big vessel, the center of the big vessel, location 1, location 2, location 4, the center of small vessel, and the 2.0 2.0 sidewall of the smallPeak vessel. pressure in Similarly, large sphere by simulation in Figure 14b, “B1” to “B8” representPeak pressure in the largeadopted sphere by simulation ignition 1.8 1.8 Peak pressure in large sphere by experiment Peak pressure in large sphere by experiment positions: the sidewall of the big vessel, the center of the big vessel, locationPeak pressure 1, in location small sphere by 2, simulation location 4, 1.6 Peak pressure in small sphere by simulation 1.6 location 6, the center ofPeak the pressure small in small vessel, sphere by experiment and the sidewall of the small vessel.Peak pressure in small sphere by experiment Figure1.4 14 shows that the variation that depended with1.4 the ignition positions of the peak pressure in the1.2 simulation and experiment were analogous.1.2 From Figure 14a, the average error between

(MPa) 1.0

1.0 the (MPa) simulation and experimental data is 7.7% in the big vessel with the 4.45-m pipe connected to it. max max 0.8 P 0.8 The average error is shown in Figure 14b is 8.04%. Overall,P 70% of the simulation data were marginally 0.6 0.6

0.4 0.4 (a) Big vessel connected to the (b) Big vessel connected to the 0.2 small vessel with a 4.45–m pipe 0.2 small vessel with a 6.45–m pipe

0.0 0.0 A1 A2 A3 A4 A5 A6 A7 B1 B2 B3 B4 B5 B6 B7 B8 -- Ignition position Ignition position Figure 14. Comparison between the simulation data and experimental data of the natural gas explosion pressure versus time in the linked vessels.

Processes 2020, 8, x FOR PEER REVIEW 13 of 16

8 8 6.45 m 6.45 m 7 4.45 m 7 4.45 m 2.45 m 2.45 m 6 6

5 5 (barg) 4 (barg) 4 P P

3 3

6.45 m 12 8 6.45 m 4.45 m 4.45 m 2.45 m 2.45 m 10 6 8 (barg) (barg) P 6 P 4

4 Processes 2020, 8, 52 2 14 of 16 2 (c) In small vessel with the ignition (d) In big vessel with the ignition sources located at the center sources located at the center 0 0 larger0.00 than 0.02 those 0.04 0.06 of the 0.08 experimental 0.10 0.12 0.14 data 0.16 0.18 in all 0.20 the compared0.00 0.02 0.04 points, 0.06 in 0.08 which 0.10 0.12 the average 0.14 0.16 di0.18fference 0.20 was 6.97%. Generally, anTime experiment (s) was controlled by more factors in comparisonTime (s) with a simulation. Even though the radiation model was employed, with the aim of improving simulated accuracy, some Figure 13. Natural gas explosion pressure-time curves in the vessels with changing the length of the degree of discrepancy still could be observed. The increase of the temperature in the wall of the pipes pipe. was limited in the physical experiment. A considerable temperature difference existed between the 4.combustion Error Analysis products and the wall of the pipe. The energy was dissipated on account of thermal convection, thermal conduction, and thermal radiation. As a result, the simulation data had higher valuesThe than simulation the experimental results and dataexperimental [34]. Consequently, data were compared on the one for hand, two different the simulation structures, effectively which werereproduced the big vesselthe development connected to of the the small gas explosion vessel with inthe linked 4.45-m vessel. pipe Onand the the other 6.45-m hand, pipe. it The correctly peak pressurepredicted values the variations at different of pressure, ignition temperature,positions from and the the simulation changing concentrationand experiment of productsare shown with in Figuredifferent 14. factors.

2.0 2.0 Peak pressure in large sphere by simulation Peak pressure in large sphere by simulation 1.8 1.8 Peak pressure in large sphere by experiment Peak pressure in large sphere by experiment Peak pressure in small sphere by simulation 1.6 Peak pressure in small sphere by simulation 1.6 Peak pressure in small sphere by experiment Peak pressure in small sphere by experiment 1.4 1.4

1.2 1.2

(MPa) 1.0

1.0 (MPa) max max 0.8 P 0.8 P

0.6 0.6

0.4 0.4 (a) Big vessel connected to the (b) Big vessel connected to the 0.2 small vessel with a 4.45–m pipe 0.2 small vessel with a 6.45–m pipe

0.0 0.0 A1 A2 A3 A4 A5 A6 A7 B1 B2 B3 B4 B5 B6 B7 B8 Ignition position Ignition position

FigureFigure 14. ComparisonComparison betweenbetween the the simulation simulation data data and experimentaland experimental data of data the naturalof the gasnatural explosion gas explosionpressure versuspressure time versus in the time linked in the vessels. linked vessels. 5. Conclusions In this study, natural gas explosions were conducted, employing the simulation tool of FLACS in three systems, including a single vessel, a single vessel with a pipe connected to it, and a big vessel connected to a small vessel with a pipe. The main conclusions of this study are as follows:

When the explosions occurred in the same initial conditions, the peak explosion pressure • maintained unchanged. However, the maximum rate of pressure rise decreased when the volume of the closed vessels increased, which is following the explosion cubic law. The length of the connecting pipe profoundly affected the explosion intensity in the single vessel • with a pipe connected to it and in the big vessel connected to the small vessel. Furthermore, an oscillation of the explosion wave developed in the linked vessels. The ignition position affected the explosion intensity in the linked system extremely. The explosion • intensity was weakest when the ignition source was positioned at the center of the system. When the explosions occurred in the linked system, the explosion intensities in the secondary • vessels were stronger than those in the initiating vessels. Using FLACS software for the simulation of the small–scale linked system, the average difference • attained 6.97%. Accordingly, the simulation results agreed reasonably well with the experimental results and the actual explosion conditions were reflected in the FLACS simulation to an acceptable extent. Processes 2020, 8, 52 15 of 16

Author Contributions: All authors contributed equally to the research presented in this paper and to the preparation of the final manuscript. Conceptualization, Q.W.; Formal analysis, Y.S. and X.L.; Methodology, Z.W. and M.Z.; Supervision, J.J.; Software, F.C.; Writing—original draft, Y.S. and X.L.; Writing—review, Q.W. and C.-M.S. All authors have read and agreed to the published version of the manuscript. Funding: The study was financially supported by the National Key R &D Program of China (2016YFC0800100); the National Nature Science Foundation of China (51504190); and the Natural Science Basic Research Plan in Shaanxi Province of China (2017JM5068). Conflicts of Interest: The authors declare no conflict of interest.

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