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Quantitative research on gas explosion inhibition by water mist
Journal of Hazardous Materials 363 (2019) 16–25
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Journal of Hazardous Materials journal homepage: www.elsevier.com/locate/jhazmat
Quantitative research on gas explosion inhibition by water mist Yifan Song, Qi Zhang
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T
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Explosion inhibition Spraying concentration Droplet size Flame temperature Numerical simulation
Water mist as an effective explosion inhibitor has wide application prospect to prevent and reduce gas explosion hazard. The quantitative study of gas explosion inhibition with water mist provides the groundwork for the design of gas explosion suppression system. In this paper, the influence of the initial droplet sizes and spraying concentrations on explosion inhibition were numerically studied in a 2D numerical model. Under the initial spraying concentrations in the range of ∼1.5 kg/m3, the inhibition effect of water mist on the explosion overpressure was not significant. The inhibition effect of water mist was mainly reflected in the suppression of the explosion flame temperature. When the initial droplet sizes were in the range of 50–150 μm, the flame length was obviously reduced. But when the initial droplet sizes were less than 50 μm or more than 150 μm, the inhibition to reduce flame length begin to weaken. The results of this study provide the theoretical basis of the suppression technology for gas explosion.
1. Introduction Gas explosion accidents result in large directly and indirectly economic loss every year in China, which seriously limits the development of coal industry [1]. The key to solve this problem is to find a material which can control the gas explosion efficiently combining with suppressing explosion techniques to prevent the disaster occurrence. The active explosion suppression as one effective technology has been widely used in coal mine and other industry concourses [2–4]. Active suppression technologies are mainly by means of spraying inhibitor to suppress the scope and intensity of explosion to avoid excess pressure and temperature in limited spaces. The detectors are used to induct the initial explosion in order to inhibit the process of explosion and eliminate or weaken the harmful factors of explosion, that is, high temperature flame, shock wave and harmful gas. However, coal mine production system is usually too huge to make the explosion suppression device spread in all over the corner. The effective use range of each device is limited, which makes the explosion suppression to be greatly limited resulting in vicious gas explosion occasionally happening. Due to the fine dispersity, high heat capacity and ease of evaporation, water mist has got widely used in building fire, ship fires and other fire types [5,6]. A number of researches have been conducted to develop the theory and technology of explosion suppression by water mist [7–9]. Liang and Zeng [10] used the SENKIN code of chemical kinetics package to analyze the mole fraction profiles of reactants, free radicals and catastrophic gases in the process of gas explosion suppression by
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water mist. Zhu et al. [11] developed an Eulerian–Lagrange model to study the extinguishing effect of ultra-fine water mist in total flooding experiment in confined space. The cooling and suffocation effects and the smaller average diameter of ultra-water mist were the main factors to extinguish fire. The effects of fine water mist on laminar flame speeds of propane-air mixtures are investigated both experimentally and numerically by Yoshida et al. [12]. The results showed that the large radial acceleration of the flow induced the mist droplet accumulation around the stagnation stream line, leading to the negative dependence of flame speed on stretch rate. Compared with the normal water mist, the gas explosion could be more effectively suppressed by the positively charged water mist [13]; the inhibition effect became stable with the increase of the nitrogen fraction in the ultrafine water mist [14]. However, the influence of spraying concentration on the changes in explosion flame structure and the relationship between the pressure rising and flame propagation have not been mentioned in the open literatures. Feasibility study of explosion suppression by ultra fine water mist (diameter＜10 μm) has been discussed in literatures [15]. Sub-10-μm water drops were found to be an effective flame suppressant in a coflow cup burner flame [16]. The ultra fine water mist was able to successfully extinguish all pool fires [17]. The water mist (20 μm＜ diameter＜200 μm) having strong engineering application background, however, has been fewer studies made on its fire suppression mechanism [18]. Moreover, the secondary breakup process of water mist is researched insufficiently. In literatures, researches on premixed gas
Corresponding author. E-mail address: [email protected] (Q. Zhang).
https://doi.org/10.1016/j.jhazmat.2018.09.059 Received 12 June 2018; Received in revised form 21 September 2018; Accepted 22 September 2018 Available online 26 September 2018 0304-3894/ © 2018 Elsevier B.V. All rights reserved.
Journal of Hazardous Materials 363 (2019) 16–25
Y. Song, Q. Zhang
Nomenclature
a ap Ad B c pg c pd d dd D Ed FD Fx G h hfg Hlat Hpyrol k∞ md • md md, in md, out Oh r r0 Red
Δt T Ta Td Td, in Td, init Td, out Tref T∞ u u′ u ud v
Absorption coefficient (m−1) Equivalent absorption coefficient (m−1) Surface area of the droplet (m2) Breakup time constant Heat capacity of gas product species (J/kg K) Heat capacity of the droplet (J/kg K) Orifice diameter of obstacle (m) Droplet diameter (m) Inner diameter of pipeline (m) Equivalent emission of the droplets Drag force (N) Additional forces (N) Incident radiation (rad) Convective heat transfer coefficient (W/m2 K) Latent heat (J/kg) Latent heat at reference conditions (J/kg) Heat of pyrolysis as volatiles are evolved (J/kg) Thermal conductivity of the gas (W/m K) Mass of the droplet (kg) Mass flow rate of the droplets (kg/s) Mass of the droplet on cell entry (kg) Mass of the droplet on cell exit (kg) Ohnesorge number Newly-formed droplet radius (m) Undisturbed droplet radius (m) Reynolds number based on the droplet diameter and the
relative velocity(W/m2 K4) Time step (s) Local temperature (K) Taylor number Droplet temperature (K) Temperature of the droplet on cell entry (K) Droplet initial temperature (K) Temperature of the droplet on cell exit (K) Reference temperature for enthalpy (K) Local temperature of the continuous phase (K) Gas phase velocity (m/s) A Gaussian distributed random velocity fluctuation (m/s) Mean fluid phase velocity (m/s) Droplet velocity (m/s) Relative velocity between the droplet and the gas phase (m/s)
Greek letters Droplet emissivity Radiation temperature (K) The maximum growth rate or the most unstable wave Fluid density (kg/m3) Droplet density (kg/m3) Stefan-Boltamann constant (5.67 × 108 W/m2 K4) Droplet surface tension Scattering coefficient (m2/kg) Corresponding wavelength of Λ
εd θR Λ ρ ρd σ σd σs Ω
The droplet will absorb heat, when the droplet temperature is lower than its evaporation temperature. The heat balance equation is used to establish the relationship between droplet temperature and convection and radiation heat transfer to the droplet surface.
explosion suppression by water mist were mostly under the condition that water mist had been mixed uniformly with premixed gas before the explosion [19–21]. But this condition is inconsistent with the explosion suppression by water mist in practical engineering. In mine production, the invalid or inadequate effects of explosion suppression by water mist are especially prominent, which is due to the limits of the triggering technology and the poor property of suppressant. Researches into the influence of water mist characteristics on the suppression effects are important to practical engineering. Therefore, the action mechanism between water mist and the explosion flame based on the practical engineering process is urgent to be studied. In view of the high risk and input of explosive experimental research, and the interaction between water mist and explosive flame is difficult to observe, in this study, the CFD code was adopted which has been proven to be one of the most widely used tools to build fire models [22–24]. A two dimensional turbulent explosion mathematical model for combustible gas in pipeline was built in this study. The explosion flame propagation and the interaction between the water mist and the explosion flame was obtained in this study. The numerical simulation study of the transient process of gas explosion inhibition by water mist has been carried out to obtain the regulation of explosion suppression by water mist in the purpose of providing theoretical basis for the suppression technology in gas pipeline and the key parameters of engineering calculation.
md c pd
dTd = hAd (T∞ − Td ) + εd Ad σ (θR4−Td4 ) dt
(1)
When the temperature of the droplet reaches the vaporization temperature, the evaporation occurs, and continues until the droplet reaches the boiling point. The droplet temperature is updated according to a heat balance that relates the sensible heat change in the droplet to the convective and latent heat transfer between the droplet and the continuous phase
md c pd
dTd dmd = hAd (T∞ − Td ) + hfg + εd Ad σ (θR4−Td4 ) dt dt
(2)
When the droplet temperature reaches the boiling point, boiling rate equation is applied as
d (dd ) 2 ⎛ 2k∞ (1 + 0.23 Red ) (T∞ − Td ) + εd Ad σ (θR4−Td4 ) ⎞⎟ = ⎜ dt ρd hfg ⎝ dd ⎠
(3)
While the continuous phase always impacts the discrete phase, the effect of the discrete phase trajectories can also be incorporated on the continuum. This two-way coupling was accomplished by alternately solving the discrete and continuous phase equations. The interphase exchanges of heat, mass, and momentum between the particle and the continuous phase are given by
2. Computational method A finite element computational code for fluid dynamics was adopted to calculate the explosion inhibition propagation. The code solved the gas phase as a continuum by means of the time-averaged Navier-Stokes equations, while the dispersed phase was solved by tracking a large number of droplets through the calculated flow field. The turbulence flow was characterized by standard k-ε model. The finite-rate/eddy dissipation model was used to compute the chemical reactions. The detailed formulas of these models are listed in the Ref [25].
Mass exchange m =
Δmd • md,0 md,0
Momentum exchange M = Thermal exchange 17
(4) •
∑ FD (ud − u) mdΔt
(5)
Journal of Hazardous Materials 363 (2019) 16–25
Y. Song, Q. Zhang
Q = (md, in − md, out ) ⎜⎛−⎛Hlat − ⎝ ⎝ ⎜
− md, out
∫T
Td, out
ref
∫T
Td, init
ref
c pd dT + md, in
∫T
c pg dT + Td, in
ref
∫T
Td, init
ref
c pd dT ⎞ + Hpyrol⎞⎟ ⎠ ⎠
c pd dT
⎟
(6)
Radiation absorption by droplets is enabled by used the P-1 model. The P-1 radiation model is based on the expansion of the radiation intensity into an orthogonal series of spherical harmonics. The transport equation for incident radiation is
1 ∇G ⎞ − aG + 4aσT 4 = 0 ∇⎛ 3( a + σs ) ⎠ ⎝ ⎜
⎟
⎜
(7)
⎟
(8)
The dispersion of droplets due to turbulence in the fluid phase can be predicted using the stochastic tracking model [26]. The trajectory of a discrete phase droplet is predicted by integrating the force balance on the particle, which is written in a Lagrangian reference frame. This force balance equates the droplet inertia with the forces acting on the particle, and can be written (for the x direction in Cartesian coordinates) as
g (ρd − ρ) dud = FD (u − ud ) + + Fx dt ρd
(9)
ρg v 2r0 σ
(10)
At higher Weber number, the thin sheet is continuously drawn from the periphery of the deforming drop. The sheet disintegrates a short distance downstream from the drop. These breakup types which have continuing shearing and entraining action are all governed by the Kelvin-Helmholtz instability. These breakup types can be named as shear-induced entrainment [27–29]. Consider the breakup of the droplets to be induced by the relative velocity between the gas and liquid phases. The model assumes that the time of breakup and the resulting droplet size are related to the fastestgrowing Kelvin-Helmholtz instability. The rate of change of droplet radius in the parent parcel is given by [30]
dr r − 0.61Λ =− dt 3.726Br ΛΩ
(13)
(1) Water droplets were spherical in shape with uniform sizes. The initial mist size was uniform that all the droplets had the same diameters. The simulation neglected the drop breakup during the process of droplet sprayed and diffusing for the drag acting to the droplets was small. The drop breakup was mainly induced by the shock of gas explosion, so the drop breakup occurred when the shock wave arrived to the water mist region. (2) Collisions and coalescence were ignored. O'Rourke's algorithm assumes that two droplets may collide only if they are in the same continuous-phase cell [32]. For the configurations considered, this probability was small enough for particle–particle interactions, such as collisions and coalescence, to be disregarded to simplify the model. Some water droplets are broken after colliding with the wall, but the number of droplets occurring droplet-wall collisions are few for most droplets moved to the open end of the pipe driven by the turbulence. So the interaction between the wall and water droplets was neglected. (3) The wall of the pipe was adiabatic. The collisions between droplets and wall and phase transformation near the wall were not considered. Since the primary interest of the current work was to study the interaction between flame and water mist, the interaction between the wall surface and water droplet was not considered, as it would add further complications to the problem.
To predict the turbulent dispersion of particles by integrating the trajectory equations for individual particles, using the instantaneous fluid velocity u = u + u′ (t ) , along the particle path during the integration. The mechanism of droplet fragmentation depends on the Weber number of the parent droplet.
We =
ρr 3 0.34 + 0.38We1.5 Ω ⎛⎜ 0 ⎟⎞ = (1 + Oh)(1 + 1.4Ta0.6) ⎝ σ ⎠
Most of mine explosion accidents are combustible gas explosions, namely the flame propagating at a subsonic speed while the pressure wave at a supersonic speed. The two-wave and three-zone structure of leading shock wave and the flame wave is formed due to this explosion model [31]. To reconstruct this process, a long cylindrical pipeline was modeled. The pipe was 8.9 m long with 0.108 m diameter. It had closed left end and open right end, as shown in Fig. 1(a). There were symmetric obstacles located inside the first 1.5 m of the pipe from the closed end, and the area blockage ratio (BR), where BR = 1-(d/D)2, was 0.36. On the side of the left closed end, a 2.5 m long section of the pipe was assumed to be filled with premixed stoichiometric methane-air mixture. The spraying zone is 1 m long located in the range of 3–4 m from the left end. The 2-D axisymmetrical model was adapted to simply the pipe, and a higher grid density was used near the wall, as shown in Fig. 1(b). The model was based on the following simplifying assumptions:
For a gray, absorbing, emitting, and scattering medium containing absorbing, emitting, and scattering particles, the transport equation for the incident radiation can be written as ⎜
(12)
3. Model
⎟
1 σT 4 ∇G ⎞ + 4π ⎛a + Ed⎞ − (a + ap ) G = 0 ∇⎛ ⎝ π ⎠ ⎠ ⎝ 3(a + σs )
Λ (1 + 0.45Oh0.5)(1 + 0.4Ta0.7) 9.02 r0 (1 + 0.87We1.67)0.6
(11)
Fig. 1. Pipeline schematic view and mesh. 18
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Y. Song, Q. Zhang
process lasted 20 ms that was shorter than the time of shock wave reaching the water mist zone.
3.1. Model validation In order to regulate the parameters of methane explosion and water droplets, the experiments to study the inhibition effects of water mists on 9.5% methane explosions were simulated [33]. The pressure histories and the flame structures of 9.5% methane explosion and inhibition experiment by 224 g /m3 spraying concentration were simulated based on the numerical methods. The explosive gas and inhibitor in Cao et al’ explosion were same with our simulation. The governing equations and models to simulate Cao et al’ explosion were same with those of our simulation. Therefore, simulating Cao et al’ explosion to perform the model validation was equivalent to the simulating of the real lab experiment. The simulative and experimental results are shown in Fig. 2. The simulated pressure curves are agreed well with the experimental results under the two conditions by adjusting the parameters. Meanwhile, the simulated flame propagations are consistent with the experimental flame front structures. Therefore, it is considered that the numerical model methods are accurate and the parameters of the explosive gas and inhibitor are appropriate.
4. Results and discussion 4.1. Effect of initial water mist concentration on the process of explosion suppression The 0.3 kg/m3, 0.6 kg/m3, 0.9 kg/m3, 1.2 kg/m3 and 1.5 kg/m3 initial spraying concentrations were simulated. In this section, the initial droplet size was fixed as 50 μm. 4.1.1. Pressure propagation process under inhibition by water mist The premixed gas was sparked and then the leading shock wave traveled the obstacles zone. The overpressure increased to 0.37 MPa with the speed of 700 m/s before the shock reached to the water mist zone. The drop breakup occurred induced by the shock with high speed and high pressure. At the same time, the droplets moved to the right end of the pipe under the drive of turbulent shock wave [35,36]. The droplet size reduced from 50 μm to 0.05 μm (minimum) after the shock wave passed the water mist zone. As shown in Fig. 4, the droplets had the following drift regulation: droplets of smaller size were more likely to be disturbed by the turbulence and moved closer to the open end of pipeline (at 0.0471 s); at 0.0521 s, the distribution of water droplets was changed. The larger droplets were located closer to the open end for the momentum of the droplet is proportional to the diameter of the droplet. Fig. 5 shows the effect of initial spraying concentrations on peak overpressure along the pipeline axis. The curve of 9.5% methane explosion peak overpressure appeared to rise to a maximum and then fell to a low value, and finally went up again due to pressure relieving when arriving at the open end. This behavior is in agreement with the experimental data of Li et al. [34] and Ma et al. [37]. The curves of explosion inhibition by water mist under different initial spraying concentrations exhibited a same behavior: all curves increased first and decreased afterwards. A consistent trend reflected in Fig. 5 is that the peak overpressure decreases with the increase of initial mist concentration. The shock provides energy to break up droplets. A higher mist concentration means more energy loss of the shock wave. It is found that at 7 m of the pipe, the peak overpressures of inhibition by water mist are larger than that of gas explosion. This is because that the flame arrived at the water mist zone at that time to make water mist vaporize with the volume expansion of 1700 times. The vaporization expansion of the water mist led to the pressure rise. The peak
3.2. Mesh validation A test on mesh independence was carried out to determine the reasonable mesh density. The premixed 9.5% methane combustion experiment [34] was simulated under three different mesh sizes. Table 1 shows the comparison between the peak overpressure along the test pipe and simulation results. It can be seen that when the grids increased to 618 103, the agreement is achieved between simulated and experimental values. And a higher number of grids (980 338) does not yet any significant improvement. As such, the mesh with 618 103 grids was used for all simulation cases presented in the following sections. 3.3. Formation process of initial water mist zone In engineering, the water spray occurs when the alarm inducting explosion. In this paper, that was simplified as the process that the droplets started to be injected into the pipe when the premixed gas was sparked. Fig. 3 shows the process of droplets dispersion. The water mist dispersion process contained the following steps: (1) The boundary condition in the range of 3–4 m was first set as the pressure-inlet; (2) The droplets was injected from the pressure-inlet boundary; (3) The boundary condition was set as the wall after the initial droplets all injected in the pipeline; (4) During the static progress, the droplets were uniformly located in the range of 3–4 m. It is to be noted that the whole
Fig. 2. Comparison between simulated and experimental results. 19
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Table 1 Comparison between experimental peak overpressure and simulation results. Locations of pressure monitoring points along the axis of the test pipe (m)
Peak overpressure (MPa) and relative errors of 250 550 grids
Peak overpressure (MPa) and relative errors of 618 103 grids
Peak overpressure (MPa) and relative errors of 980 338 grids
Peak overpressure of the experiment (MPa) [34]
0.375 1.625 2.875 3.875 5.125 6.525 7.525 8.275
0.0363/ 0.2883/ 0.3664/ 0.4188/ 0.3535/ 0.2833/ 0.1527/ 0.2025/
0.0330/ 0.2592/ 0.3176/ 0.3987/ 0.3103/ 0.2588/ 0.1309/ 0.2338/
0.0329/ 0.2589/ 0.3175/ 0.3957/ 0.3085/ 0.2513/ 0.1312/ 0.2339/
0.0323 0.2583 0.3165 0.3885 0.3045 0.2583 0.1227 0.2325
12.38% 11.61% 15.77% 7.80% 16.09% 9.68% 24.4% 12.90%
2.16% 0.35% 0.35% 2.63% 1.90% 0.19% 6.68% 0.56%
1.86% 0.23% 0.32% 1.85% 1.31% 2.71% 6.93% 0.60%
4.1.3. Effect pattern of explosion inhibition by water mist The histories of water mist vaporization rate and temperature of each monitoring point under 0.3 kg/m3 and 1.2 kg/m3 spraying concentrations are presented in Fig. 8(a) and (b) respectively. Fig. 8(c) is the temperature history of premixed methane explosion. Compare Fig. 8(a)–(c), the temperature curve of premixed methane explosion reached the peak value rapidly; the temperature curve of each monitoring point fluctuated for a long time under the effect of inhibition by water mist, that is, the flame delay phenomenon occurred. Compared with the vaporization rate history of the water mist, it is found that the flame temperature fluctuation is caused by the heat absorption of droplets vaporization. The flame and the water mist produce the energy exchange during this process, which makes the peak temperature decrease obviously. The peak values of the water mist vaporization rates under different spraying concentrations are obtained and shown in Fig. 8(d). It can be seen that the greater the spraying concentration was, the greater the peak vaporization rate appeared along the pipeline axis. When the concentration of initial spraying decreased, the distance of the droplet drift downstream became farther, so the maximum peak of the curve appeared later. Fig. 9(a) shows the CH4 concentration histories at each monitoring point for CH4-Air explosion. It is known that the leading shock wave of the explosion can make the turbulence in the unburned gas region, which causes the unburned fuel to spread out of the premixed zone. The expansion production with high temperature and pressure in the upstream can also push the unburned fuel to the open end. As a result the gas concentration is getting lower from the ignition end to the open end. Fig. 9(b) and (c) show the concentration of CH4 varying with time under the spraying concentrations of 0.6 kg/m3 and 1.5 kg/m3 respectively. Compared them with Fig. 9(a), the reduction of methane
overpressure did not rise again near the open end, which was indicated that the explosion flame had been inhibited by the water mist and could not provide energy for the propagation of shock wave.
4.1.2. Effect of water mist on flame propagation process Fig.6 shows the changes of the flame front structure during the process of explosion inhibition by water mist. The premixed gas was located in the range of 0–2.5 m before explosion. Hemispherical flame was formed when the flame inside the original premixed region (at 0.0448 s). The flame stretch appeared beyond the original methane accumulation region (at 0.0471 s). At 0.0532 s, the flame reached the water mist region, and then the volumetric expansion of water mist vaporization caused the flame instabilities, as a result the flame front began to be obviously wrinkled. It is shown in Fig. 7 that, with the increase of initial spraying concentrations, the faster the peak temperature decreased along the pipe axis. When the initial spraying concentration increased from 1.2 kg/m3 to 1.5 kg/m3, the two curves were almost coincided. It is deduced that the capability to inhibit explosion temperature approached the limit when the initial concentration was 1.5 kg/m3. The flame front generated more wrinkles with the increase of water mist concentration. When the wrinkles developed to enough surfaces, they could divide into several small units. The curvature of each small unit increased to absorb more heat, so that the inhibition effect of water mist cannot be further enhanced [38]. The temperature to predict the extinction of hydrocarbon fuels combustion is 1600 K [39]. As shown in Fig. 7, the flame spread was completely inhibited at 6.5 m of the pipe when the spraying concentration was 1.5 kg/m3.
Fig. 3. Formation process of initial water mist zone. 20
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Fig. 4. The interaction between explosion shock wave and water mist and the mist size distribution with time.
Fig. 5. Peak overpressures along the pipe axis for different initial spraying concentrations.
Fig. 7. Peak temperature along the pipe axis for different initial water mist concentrations.
concentration was more obvious, that is, the water mist causes the heat absorbing, the oxygen separating and the unburned gas diluting. Fig. 9(d) is the distribution of peak CH4 concentration along the
pipeline axis during the explosion inhibition of water mist for different spraying concentrations. It is known that the lower limit of methane concentration of CH4-Air explosion is 4.65% [40]. It is shown in
Fig. 6. Effect of water mist on flame structure. 21
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Fig. 8. Water mist vaporization for different spraying concentrations and explosion temperature histories. 1—(0.8, 0), 2—(1.5, 0), 3—(2.8, 0), 4—(3.2, 0), 5—(3.6, 0), 6—(4, 0), 7—(4.5, 0), 8—(5.5, 0), 9—(6.5, 0), 10—(7, 0), 11—(7.5, 0), 12—(8, 0), 13—(8.5, 0).
Fig. 9. CH4 concentration histories for different spraying concentrations. 1—(0.8, 0), 2—(1.5, 0), 3—(2.8, 0), 4—(3.2, 0), 5—(3.6, 0), 6—(4, 0), 7—(4.5, 0), 8—(5.5, 0), 9—(6.5, 0), 10—(7, 0), 11—(7.5, 0), 12—(8, 0), 13—(8.5, 0). 22
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Fig. 9(d) that the range in which the fuel concentration was lower than the limit concentration expanded as the concentration of water mist increased. When the concentration of spraying increased to 1.5 kg/m3, the methane concentration in the section behind 6.5 m was lower than the limit concentration, that is, the explosion at 6.5 m had been completely inhibited. 4.2. Effect of initial droplet size on the process of explosion inhibition In order to study the effect of droplet size on the explosion inhibition, the initial spraying concentration was fixed as 1.5 kg/m3. The initial droplet sizes were set as 20 μm, 50 μm, 100 μm, 150 μm and 200 μm. Fig. 10 shows the flame velocity at various locations along the pipe axis for different initial droplet sizes. It can be seen that the water mist can effectively reduce the flame velocity of gas explosion. However, the reduction rate of flame velocity is not linearly related to the initial droplet size. When the initial droplet size increased from 20 μm to 100 μm, the inhibition effect on flame velocity was gradually enhanced; however, when the initial droplet size increased to 150 μm, the of flame velocity did not change significantly compared with the initial droplet size of 100 μm; when the initial particle size was increased to 200 μm, the inhibition effect to flame wave velocity was weaker than that of 50 μm. Due to the analysis of 4.1.1., it is known that the leading shock wave generated by the gas explosion causes droplets breakup and drift downstream; the initial droplet size was different, the size and number of droplets after breakup were different; in this case, when the flame propagated into the water mist zone, the vaporization amount of the water mist was different. Fig.10 shows the vaporization rate of droplets for initial sizes of 20 μm and 200 μm when the flame wave propagated to 5 m of the pipe. Although the smaller the size of a single droplet is, the faster the vaporization rate is, the instantaneous distribution of the water mist with different initial droplet sizes were different as the droplets migrated to the open end. When the flame propagated at 5 m, the evaporation rate of 200 μm was faster than that of 20 μm, and the energy exchange of 200 μm produced between the flame and the droplet was greater than that of 20 μm, so the effect of the flame velocity inhibition also exhibited that the former was stronger than the latter. Fig. 11 presents the peak temperature along the axial direction for different initial droplet sizes. The process of inhibition to flame temperature by water mist was divided into three periods. At the beginning, when the droplet size increased from 50 μm to 150 μm, the smaller the droplet size, the better the inhibition effect on flame temperature (at the range of 3–4.5 m). This is because the smaller the initial droplet size is, the smaller the droplet size after breakup is. The faster the vaporization rate of the water mist is, the more obvious the explosion
Fig. 11. Peak temperature along axial distance for different initial droplet sizes.
inhibition effect is. In the middle stage of inhibition, the inhibition effect on flame temperature by different initial droplet sizes is the same as that of flame velocity. In the later stage, the peak temperature reduced rapidly near the open end of the pipeline due to the effective suppression on the methane combustion. Fig. 12 shows the effects of initial droplet sizes on combustion rate. It can be seen that the combustion rate of each monitoring point decreased obviously after the inhibition by water mist. The moment corresponding to the maximum combustion rate is taken as the arrival time of the flame [41], that is, it is considered that the flame does not propagate to this position when the peak value of combustion rate is 0, which is used to obtain the flame length. Fig. 12(d) shows the peak combustion rate along axial direction for different initial droplet sizes. It can be seen that when the initial particle size was 150 μm, the flame length was shortest and the explosion flame was effectively inhibited at 6 m. 5. Conclusion A numerical study on gas explosion inhibition by water mist was undertaken. The transient propagation of premixed gas explosion inhibited by a range of water mist (1 m) in a pipeline was modeled with the standard k-ε model and the discrete phase model. Under the initial spraying concentrations of 0.3 kg/m3, 0.6 kg/m3, 0.9 kg/m3, 1.2 kg/m3 and 1.5 kg/m3 fixed with 50 μm initial droplet size and the initial droplet sizes of 20 μm, 50 μm, 100 μm, 150 μm and 200 μm fixed with 1.5 kg/m3 spraying concentration, the conclusions can be drawn from
Fig. 10. Effects of initial droplet sizes on flame velocity. 23
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Fig. 12. Effects of initial droplet sizes on combustion rate. 1—(1, 0), 2—(2, 0), 3—(3, 0), 4—(4, 0), 5—(4.5, 0), 6—(5, 0), 7—(5.5, 0), 8—(6, 0), 9—(6.5, 0), 10—(7, 0), 11—(7.5, 0), 12—(8, 0).
the simulation results as follows. The water mist occurred transversely flowing driven by the leading shock wave of methane explosion. The drop breakup induced by leading shock wave and the droplet sizes were reduced rapidly. When the water mist flowed to the open end, the flow velocities of the droplets with different sizes were different, which made the water mist concentration at the same position always in the dynamic state. The inhibition effect of spraying concentration in the range of ∼1.5 kg/m3 on the explosion overpressure was not significant. The inhibition effect of water mist was mainly reflected in the suppression of the flame temperature. Water mist could absorb the combustion heat and evaporate rapidly, resulting in the great reduction of the flame front temperature. When the initial spraying concentration was 1.5 kg/ m3 and the initial droplet size was 150 μm, the explosion temperature can be reduced by 52.2%. When the initial droplet sizes of water mist were in the range of 50–150 μm, the effect of the water mist on the methane explosion was effective, the flame length was obviously reduced. But the water mist with too large or too small droplet sizes had no obvious inhibition effect on the gas explosion.
[4] M. Gieras, R. Klemens, R. Klemens, B. Szatan, M. Gieras, P. Wolański, A. Maranda, J. Nowaczewski, J. Paszula, Suppression of dust explosions by means of different explosive charges, J. Loss Prev. Process Ind. 13 (2000) 265–275. [5] G. Grant, J. Brenton, D. Drysdale, Fire suppression by water sprays, Prog. Energy Combust. Sci. 26 (2000) 79–130. [6] A. Yoshida, T. Okawa, W. Ebina, H. Naito, Experimental and numerical investigation of flame speed retardation by water mist, Combust. Flame 162 (5) (2015) 1772–1777. [7] R. Ananth, H.D. Willauer, J.P. Farley, F.W. Williams, Effects of fine water mist on a confined blast, Fire Technol. 46 (2010) 641–675. [8] H. Shimiz, M. Tsuzuki, Y. Yamazaki, A.K. Hayashi, Experiments and numerical simulation on methane flame quenching by water mist, J. Loss Prev. Process Ind. 14 (2001) 603–608. [9] G. Grant, J. Brenton, D. Drysdale , Fire suppression by water sprays, Prog. Energy Combust. Sci. 26 (2000) 79–130. [10] Y.T. Liang, W. Zeng, Numerical study of the effect of water addition on gas explosion, J. Hazard. Mater. 174 (1–3) (2010) 386–392. [11] D.M. Zhu, D. Liang, J.Y. Liu, Numerical simulation of ultrafine water mist extinguishing mechanism, Procedia Eng. 71 (2014) 28–33. [12] A. Yoshida, T. Okawa, W. Ebina, H. Naito , Experimental and numerical investigation of flame speed retardation by water mist, Combust. Flame 162 (5) (2015) 1772–1777. [13] Y.L. Xu, L.Y. Wang, M.G. Yu, S.J. Wan, Z.P. Song, S.K. Wang, Study on the characteristics of gas explosion affected by induction charged water mist in confined space, J. Loss Prev. Process Ind. 40 (2016) 227–233. [14] B. Pei, M.G. Yu, L.W. Chen, X.N. Zhu, Y. Yong, Experimental study on the synergistic inhibition effect of nitrogen and ultrafine water mist on gas explosion in a vented duct, J. Loss Prev. Process Ind. 40 (2016) 546–553. [15] Z. Liu, A.K. Kim, A review of water mist fire suppression technology: part II – application studies, J. Fire Prot. Eng. 11 (2001) 16–42. [16] B.T. Fisher, A.R. Awtry, R.S. Sheinson, J.W. Fleming, Flow behavior impact on the suppression effectiveness of sub-10-μm water drops in propane/air co-flow nonpremixed flames, Proc. Combust. Inst. 31 (2007) 2731–2739. [17] K.C. Adiga, F.H. Robert, R.S. Sheinson, F.W. Williams, S. Ayers, A computational and experimental study of ultra fine water mist as a total flooding agent, Fire Saf. J. 42 (2007) 150–160. [18] M. Hurley, SFPE Handbook of Fire Protection Engineering, fifth ed., Springer, New York, 2015. [19] P.P. Zhang, Y.H. Zhou, X.Y. Cao, X.L. Gao, M.S. Bi, Mitigation of methane/air explosion in a closed vessel by ultrafine water fog, Saf. Sci. 62 (2014) 1–7. [20] F.H. Wang, M.G. Yu, X.P. Wen, H.X. Deng, B. Pei, Suppression of methane/air explosion in pipeline by water mist, J. Loss Prev. Process Ind. 49 (Part B) (2017) 791–796.
Acknowledgments The research presents in this paper was supported by the National Science Foundation of China (11772057). References [1] J.W. Zhang, D. Lei, W.X. Feng, An approach for estimating toxic releases of H2Scontaining natural gas, J. Hazard. Mater. 264 (2014) 350–362. [2] K. Lebecki, J. Śliż, K. Cybulski, Z. Dyduch, Efficiency of triggered barriers in dust explosion suppression in galleries, J. Loss Prev. Process Ind. 14 (2001) 489–494. [3] J.J.L.D. Plessis, Active explosion barrier performance against methane and coal dust explosions, Int. J. Coal Sci. Technol. 2 (2015) 261–268.
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an open-space chamber, Fuel 113 (2013) 86–96. [32] P.J. O’Rourke. Collective Drop Effects on Vaporizing Liquid Sprays, Princeton University, Princeton, New Jersey, 1981 PhD thesis. [33] X.Y. Cao, J.J. Ren, M.S. Bi, Y.H. Zhou, Y.M. Li, Experimental research on the characteristics of methane/air explosion affected by ultrafine water mist, J. Hazard. Mater. 324 (2017) 489–497. [34] D. Li, Q. Zhang, Q.J. Ma, S.L. Shen, Comparison of explosion characteristics between hydrogen/air and methane/air at the stoichiometric concentrations, Int. J. Hydrogen Energy 40 (2015) 8761–8768. [35] L.P. Hsiang, G.M. Faeth, Drop deformation and breakup due to shock wave and steady distances, Int. J. Multiphas. Flow 21 (1995) 545–560. [36] D.R. Guildenbecher, C. López-Rivera, P.E. Sojka, Secondary atomization, Exp. Fluids 46 (3) (2009) 371–402. [37] Q.J. Ma, Q. Zhang, D. Li, J.C. Chen, S.Y. Ren, S.L. Shen, Effects of premixed methane concentration on distribution of flame region and hazard effects in a tube and a tunnel gas explosion, J. Loss Prev. Process Ind. 34 (2015) 30–38. [38] J.M. Ingram, A.F. Auerill, P.N. Battersby, P.G. Holborn, P.F. Nolan, Suppression of hydrogen-oxygen-nitrogen explosions by fine water mist: part 1. Burning velocity, Int. J. Hydrogen Energy 37 (24) (2012) 19250–19257. [39] D. Drysdale, An Introduction to Fire Dynamics [M], John Wiley and Sons Inc, New York, 1985. [40] M. Gieras, R. Klemens, G. Rarata, P. Wolan´ski, Determination of explosion parameters of methane-air mixtures in the chamber of 40 dm3 at normal and elevated temperature, J. Loss Prev. Process Ind. 19 (2006) 263–270. [41] Q.J. Ma, Q. Zhang, L. Pang, Hazard effects of high-speed flow from methane-hydrogen premixed explosions, Process Saf. Prog. 33 (2014) 85–93.
[21] X.Y. Cao, J.J. Ren, M.S. Bi, Y.H. Zhou, Q.J. Wang, Experimental research on methane/air explosion inhibition using ultrafine water mist containing additive, J. Loss Prev. Process Ind. 43 (2016) 352–360. [22] S. Vilfayeau, T. Myers, A.W. Marshall, A. Trouvé, Large eddy simulation of suppression of turbulent line fires by base-injected water mist, Proc. Combust. Inst. 36 (2017) 3287–3295. [23] W. Xie, P.E. DesJardin, An embedded upward flame spread model using 2D direct numerical simulations, Combust. Flame 156 (2009) 522–530. [24] W. Yang, T. Parker, H.D. Ladouceur, R.J. Kee, The interaction of thermal radiation and water mist in fire suppression, Fire Saf. J. 39 (2004) 41–66. [25] Y.F. Song, Q. Zhang, The quantitative studies on gas explosion suppression by an inert rock dust deposit, J. Hazard. Mater. 353 (2018) 62–69. [26] H. Ounis, G. Ahmadi, J.B. McLaughlin, Brownian diffusion of submicrometer particles in the viscous sublayer, J. Colloid Interf. Sci. 143 (1) (1991) 266–277. [27] H. Zhao, Z.W. Wu, W.F. Li, J.L. Xu, H.F. Liu, Transition Weber number between surfactant-laden drop bag breakup and shear breakup of secondary atomization, Fuel 221 (2018) 138–143. [28] K.C. Adiga, H.D. Willauer, R. Ananth, F.W. Williams, Implications of droplet breakup and formation of ultra fine mist in blast mitigation, Fire Safety J. 44 (3) (2009) 363–369. [29] M. Pilch, C.A. Erdman, Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop, Int. J. Multiphase Flow 13 (1987) 741–757. [30] R.D. Reitz, Mechanisms of atomization processes in high-pressure vaporizing sprays, Atomization Spray Technol. 3 (1987) 309–337. [31] W. Gao, T. Mogi, J.H. Sun, R. Dobashi, Effects of particle thermal characteristics on flame structures during dust explosions of three long-chain monobasic alcohols in
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Contents lists available at ScienceDirect
Journal of Hazardous Materials journal homepage: www.elsevier.com/locate/jhazmat
Quantitative research on gas explosion inhibition by water mist Yifan Song, Qi Zhang
⁎
T
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Explosion inhibition Spraying concentration Droplet size Flame temperature Numerical simulation
Water mist as an effective explosion inhibitor has wide application prospect to prevent and reduce gas explosion hazard. The quantitative study of gas explosion inhibition with water mist provides the groundwork for the design of gas explosion suppression system. In this paper, the influence of the initial droplet sizes and spraying concentrations on explosion inhibition were numerically studied in a 2D numerical model. Under the initial spraying concentrations in the range of ∼1.5 kg/m3, the inhibition effect of water mist on the explosion overpressure was not significant. The inhibition effect of water mist was mainly reflected in the suppression of the explosion flame temperature. When the initial droplet sizes were in the range of 50–150 μm, the flame length was obviously reduced. But when the initial droplet sizes were less than 50 μm or more than 150 μm, the inhibition to reduce flame length begin to weaken. The results of this study provide the theoretical basis of the suppression technology for gas explosion.
1. Introduction Gas explosion accidents result in large directly and indirectly economic loss every year in China, which seriously limits the development of coal industry [1]. The key to solve this problem is to find a material which can control the gas explosion efficiently combining with suppressing explosion techniques to prevent the disaster occurrence. The active explosion suppression as one effective technology has been widely used in coal mine and other industry concourses [2–4]. Active suppression technologies are mainly by means of spraying inhibitor to suppress the scope and intensity of explosion to avoid excess pressure and temperature in limited spaces. The detectors are used to induct the initial explosion in order to inhibit the process of explosion and eliminate or weaken the harmful factors of explosion, that is, high temperature flame, shock wave and harmful gas. However, coal mine production system is usually too huge to make the explosion suppression device spread in all over the corner. The effective use range of each device is limited, which makes the explosion suppression to be greatly limited resulting in vicious gas explosion occasionally happening. Due to the fine dispersity, high heat capacity and ease of evaporation, water mist has got widely used in building fire, ship fires and other fire types [5,6]. A number of researches have been conducted to develop the theory and technology of explosion suppression by water mist [7–9]. Liang and Zeng [10] used the SENKIN code of chemical kinetics package to analyze the mole fraction profiles of reactants, free radicals and catastrophic gases in the process of gas explosion suppression by
⁎
water mist. Zhu et al. [11] developed an Eulerian–Lagrange model to study the extinguishing effect of ultra-fine water mist in total flooding experiment in confined space. The cooling and suffocation effects and the smaller average diameter of ultra-water mist were the main factors to extinguish fire. The effects of fine water mist on laminar flame speeds of propane-air mixtures are investigated both experimentally and numerically by Yoshida et al. [12]. The results showed that the large radial acceleration of the flow induced the mist droplet accumulation around the stagnation stream line, leading to the negative dependence of flame speed on stretch rate. Compared with the normal water mist, the gas explosion could be more effectively suppressed by the positively charged water mist [13]; the inhibition effect became stable with the increase of the nitrogen fraction in the ultrafine water mist [14]. However, the influence of spraying concentration on the changes in explosion flame structure and the relationship between the pressure rising and flame propagation have not been mentioned in the open literatures. Feasibility study of explosion suppression by ultra fine water mist (diameter＜10 μm) has been discussed in literatures [15]. Sub-10-μm water drops were found to be an effective flame suppressant in a coflow cup burner flame [16]. The ultra fine water mist was able to successfully extinguish all pool fires [17]. The water mist (20 μm＜ diameter＜200 μm) having strong engineering application background, however, has been fewer studies made on its fire suppression mechanism [18]. Moreover, the secondary breakup process of water mist is researched insufficiently. In literatures, researches on premixed gas
Corresponding author. E-mail address: [email protected] (Q. Zhang).
https://doi.org/10.1016/j.jhazmat.2018.09.059 Received 12 June 2018; Received in revised form 21 September 2018; Accepted 22 September 2018 Available online 26 September 2018 0304-3894/ © 2018 Elsevier B.V. All rights reserved.
Journal of Hazardous Materials 363 (2019) 16–25
Y. Song, Q. Zhang
Nomenclature
a ap Ad B c pg c pd d dd D Ed FD Fx G h hfg Hlat Hpyrol k∞ md • md md, in md, out Oh r r0 Red
Δt T Ta Td Td, in Td, init Td, out Tref T∞ u u′ u ud v
Absorption coefficient (m−1) Equivalent absorption coefficient (m−1) Surface area of the droplet (m2) Breakup time constant Heat capacity of gas product species (J/kg K) Heat capacity of the droplet (J/kg K) Orifice diameter of obstacle (m) Droplet diameter (m) Inner diameter of pipeline (m) Equivalent emission of the droplets Drag force (N) Additional forces (N) Incident radiation (rad) Convective heat transfer coefficient (W/m2 K) Latent heat (J/kg) Latent heat at reference conditions (J/kg) Heat of pyrolysis as volatiles are evolved (J/kg) Thermal conductivity of the gas (W/m K) Mass of the droplet (kg) Mass flow rate of the droplets (kg/s) Mass of the droplet on cell entry (kg) Mass of the droplet on cell exit (kg) Ohnesorge number Newly-formed droplet radius (m) Undisturbed droplet radius (m) Reynolds number based on the droplet diameter and the
relative velocity(W/m2 K4) Time step (s) Local temperature (K) Taylor number Droplet temperature (K) Temperature of the droplet on cell entry (K) Droplet initial temperature (K) Temperature of the droplet on cell exit (K) Reference temperature for enthalpy (K) Local temperature of the continuous phase (K) Gas phase velocity (m/s) A Gaussian distributed random velocity fluctuation (m/s) Mean fluid phase velocity (m/s) Droplet velocity (m/s) Relative velocity between the droplet and the gas phase (m/s)
Greek letters Droplet emissivity Radiation temperature (K) The maximum growth rate or the most unstable wave Fluid density (kg/m3) Droplet density (kg/m3) Stefan-Boltamann constant (5.67 × 108 W/m2 K4) Droplet surface tension Scattering coefficient (m2/kg) Corresponding wavelength of Λ
εd θR Λ ρ ρd σ σd σs Ω
The droplet will absorb heat, when the droplet temperature is lower than its evaporation temperature. The heat balance equation is used to establish the relationship between droplet temperature and convection and radiation heat transfer to the droplet surface.
explosion suppression by water mist were mostly under the condition that water mist had been mixed uniformly with premixed gas before the explosion [19–21]. But this condition is inconsistent with the explosion suppression by water mist in practical engineering. In mine production, the invalid or inadequate effects of explosion suppression by water mist are especially prominent, which is due to the limits of the triggering technology and the poor property of suppressant. Researches into the influence of water mist characteristics on the suppression effects are important to practical engineering. Therefore, the action mechanism between water mist and the explosion flame based on the practical engineering process is urgent to be studied. In view of the high risk and input of explosive experimental research, and the interaction between water mist and explosive flame is difficult to observe, in this study, the CFD code was adopted which has been proven to be one of the most widely used tools to build fire models [22–24]. A two dimensional turbulent explosion mathematical model for combustible gas in pipeline was built in this study. The explosion flame propagation and the interaction between the water mist and the explosion flame was obtained in this study. The numerical simulation study of the transient process of gas explosion inhibition by water mist has been carried out to obtain the regulation of explosion suppression by water mist in the purpose of providing theoretical basis for the suppression technology in gas pipeline and the key parameters of engineering calculation.
md c pd
dTd = hAd (T∞ − Td ) + εd Ad σ (θR4−Td4 ) dt
(1)
When the temperature of the droplet reaches the vaporization temperature, the evaporation occurs, and continues until the droplet reaches the boiling point. The droplet temperature is updated according to a heat balance that relates the sensible heat change in the droplet to the convective and latent heat transfer between the droplet and the continuous phase
md c pd
dTd dmd = hAd (T∞ − Td ) + hfg + εd Ad σ (θR4−Td4 ) dt dt
(2)
When the droplet temperature reaches the boiling point, boiling rate equation is applied as
d (dd ) 2 ⎛ 2k∞ (1 + 0.23 Red ) (T∞ − Td ) + εd Ad σ (θR4−Td4 ) ⎞⎟ = ⎜ dt ρd hfg ⎝ dd ⎠
(3)
While the continuous phase always impacts the discrete phase, the effect of the discrete phase trajectories can also be incorporated on the continuum. This two-way coupling was accomplished by alternately solving the discrete and continuous phase equations. The interphase exchanges of heat, mass, and momentum between the particle and the continuous phase are given by
2. Computational method A finite element computational code for fluid dynamics was adopted to calculate the explosion inhibition propagation. The code solved the gas phase as a continuum by means of the time-averaged Navier-Stokes equations, while the dispersed phase was solved by tracking a large number of droplets through the calculated flow field. The turbulence flow was characterized by standard k-ε model. The finite-rate/eddy dissipation model was used to compute the chemical reactions. The detailed formulas of these models are listed in the Ref [25].
Mass exchange m =
Δmd • md,0 md,0
Momentum exchange M = Thermal exchange 17
(4) •
∑ FD (ud − u) mdΔt
(5)
Journal of Hazardous Materials 363 (2019) 16–25
Y. Song, Q. Zhang
Q = (md, in − md, out ) ⎜⎛−⎛Hlat − ⎝ ⎝ ⎜
− md, out
∫T
Td, out
ref
∫T
Td, init
ref
c pd dT + md, in
∫T
c pg dT + Td, in
ref
∫T
Td, init
ref
c pd dT ⎞ + Hpyrol⎞⎟ ⎠ ⎠
c pd dT
⎟
(6)
Radiation absorption by droplets is enabled by used the P-1 model. The P-1 radiation model is based on the expansion of the radiation intensity into an orthogonal series of spherical harmonics. The transport equation for incident radiation is
1 ∇G ⎞ − aG + 4aσT 4 = 0 ∇⎛ 3( a + σs ) ⎠ ⎝ ⎜
⎟
⎜
(7)
⎟
(8)
The dispersion of droplets due to turbulence in the fluid phase can be predicted using the stochastic tracking model [26]. The trajectory of a discrete phase droplet is predicted by integrating the force balance on the particle, which is written in a Lagrangian reference frame. This force balance equates the droplet inertia with the forces acting on the particle, and can be written (for the x direction in Cartesian coordinates) as
g (ρd − ρ) dud = FD (u − ud ) + + Fx dt ρd
(9)
ρg v 2r0 σ
(10)
At higher Weber number, the thin sheet is continuously drawn from the periphery of the deforming drop. The sheet disintegrates a short distance downstream from the drop. These breakup types which have continuing shearing and entraining action are all governed by the Kelvin-Helmholtz instability. These breakup types can be named as shear-induced entrainment [27–29]. Consider the breakup of the droplets to be induced by the relative velocity between the gas and liquid phases. The model assumes that the time of breakup and the resulting droplet size are related to the fastestgrowing Kelvin-Helmholtz instability. The rate of change of droplet radius in the parent parcel is given by [30]
dr r − 0.61Λ =− dt 3.726Br ΛΩ
(13)
(1) Water droplets were spherical in shape with uniform sizes. The initial mist size was uniform that all the droplets had the same diameters. The simulation neglected the drop breakup during the process of droplet sprayed and diffusing for the drag acting to the droplets was small. The drop breakup was mainly induced by the shock of gas explosion, so the drop breakup occurred when the shock wave arrived to the water mist region. (2) Collisions and coalescence were ignored. O'Rourke's algorithm assumes that two droplets may collide only if they are in the same continuous-phase cell [32]. For the configurations considered, this probability was small enough for particle–particle interactions, such as collisions and coalescence, to be disregarded to simplify the model. Some water droplets are broken after colliding with the wall, but the number of droplets occurring droplet-wall collisions are few for most droplets moved to the open end of the pipe driven by the turbulence. So the interaction between the wall and water droplets was neglected. (3) The wall of the pipe was adiabatic. The collisions between droplets and wall and phase transformation near the wall were not considered. Since the primary interest of the current work was to study the interaction between flame and water mist, the interaction between the wall surface and water droplet was not considered, as it would add further complications to the problem.
To predict the turbulent dispersion of particles by integrating the trajectory equations for individual particles, using the instantaneous fluid velocity u = u + u′ (t ) , along the particle path during the integration. The mechanism of droplet fragmentation depends on the Weber number of the parent droplet.
We =
ρr 3 0.34 + 0.38We1.5 Ω ⎛⎜ 0 ⎟⎞ = (1 + Oh)(1 + 1.4Ta0.6) ⎝ σ ⎠
Most of mine explosion accidents are combustible gas explosions, namely the flame propagating at a subsonic speed while the pressure wave at a supersonic speed. The two-wave and three-zone structure of leading shock wave and the flame wave is formed due to this explosion model [31]. To reconstruct this process, a long cylindrical pipeline was modeled. The pipe was 8.9 m long with 0.108 m diameter. It had closed left end and open right end, as shown in Fig. 1(a). There were symmetric obstacles located inside the first 1.5 m of the pipe from the closed end, and the area blockage ratio (BR), where BR = 1-(d/D)2, was 0.36. On the side of the left closed end, a 2.5 m long section of the pipe was assumed to be filled with premixed stoichiometric methane-air mixture. The spraying zone is 1 m long located in the range of 3–4 m from the left end. The 2-D axisymmetrical model was adapted to simply the pipe, and a higher grid density was used near the wall, as shown in Fig. 1(b). The model was based on the following simplifying assumptions:
For a gray, absorbing, emitting, and scattering medium containing absorbing, emitting, and scattering particles, the transport equation for the incident radiation can be written as ⎜
(12)
3. Model
⎟
1 σT 4 ∇G ⎞ + 4π ⎛a + Ed⎞ − (a + ap ) G = 0 ∇⎛ ⎝ π ⎠ ⎠ ⎝ 3(a + σs )
Λ (1 + 0.45Oh0.5)(1 + 0.4Ta0.7) 9.02 r0 (1 + 0.87We1.67)0.6
(11)
Fig. 1. Pipeline schematic view and mesh. 18
Journal of Hazardous Materials 363 (2019) 16–25
Y. Song, Q. Zhang
process lasted 20 ms that was shorter than the time of shock wave reaching the water mist zone.
3.1. Model validation In order to regulate the parameters of methane explosion and water droplets, the experiments to study the inhibition effects of water mists on 9.5% methane explosions were simulated [33]. The pressure histories and the flame structures of 9.5% methane explosion and inhibition experiment by 224 g /m3 spraying concentration were simulated based on the numerical methods. The explosive gas and inhibitor in Cao et al’ explosion were same with our simulation. The governing equations and models to simulate Cao et al’ explosion were same with those of our simulation. Therefore, simulating Cao et al’ explosion to perform the model validation was equivalent to the simulating of the real lab experiment. The simulative and experimental results are shown in Fig. 2. The simulated pressure curves are agreed well with the experimental results under the two conditions by adjusting the parameters. Meanwhile, the simulated flame propagations are consistent with the experimental flame front structures. Therefore, it is considered that the numerical model methods are accurate and the parameters of the explosive gas and inhibitor are appropriate.
4. Results and discussion 4.1. Effect of initial water mist concentration on the process of explosion suppression The 0.3 kg/m3, 0.6 kg/m3, 0.9 kg/m3, 1.2 kg/m3 and 1.5 kg/m3 initial spraying concentrations were simulated. In this section, the initial droplet size was fixed as 50 μm. 4.1.1. Pressure propagation process under inhibition by water mist The premixed gas was sparked and then the leading shock wave traveled the obstacles zone. The overpressure increased to 0.37 MPa with the speed of 700 m/s before the shock reached to the water mist zone. The drop breakup occurred induced by the shock with high speed and high pressure. At the same time, the droplets moved to the right end of the pipe under the drive of turbulent shock wave [35,36]. The droplet size reduced from 50 μm to 0.05 μm (minimum) after the shock wave passed the water mist zone. As shown in Fig. 4, the droplets had the following drift regulation: droplets of smaller size were more likely to be disturbed by the turbulence and moved closer to the open end of pipeline (at 0.0471 s); at 0.0521 s, the distribution of water droplets was changed. The larger droplets were located closer to the open end for the momentum of the droplet is proportional to the diameter of the droplet. Fig. 5 shows the effect of initial spraying concentrations on peak overpressure along the pipeline axis. The curve of 9.5% methane explosion peak overpressure appeared to rise to a maximum and then fell to a low value, and finally went up again due to pressure relieving when arriving at the open end. This behavior is in agreement with the experimental data of Li et al. [34] and Ma et al. [37]. The curves of explosion inhibition by water mist under different initial spraying concentrations exhibited a same behavior: all curves increased first and decreased afterwards. A consistent trend reflected in Fig. 5 is that the peak overpressure decreases with the increase of initial mist concentration. The shock provides energy to break up droplets. A higher mist concentration means more energy loss of the shock wave. It is found that at 7 m of the pipe, the peak overpressures of inhibition by water mist are larger than that of gas explosion. This is because that the flame arrived at the water mist zone at that time to make water mist vaporize with the volume expansion of 1700 times. The vaporization expansion of the water mist led to the pressure rise. The peak
3.2. Mesh validation A test on mesh independence was carried out to determine the reasonable mesh density. The premixed 9.5% methane combustion experiment [34] was simulated under three different mesh sizes. Table 1 shows the comparison between the peak overpressure along the test pipe and simulation results. It can be seen that when the grids increased to 618 103, the agreement is achieved between simulated and experimental values. And a higher number of grids (980 338) does not yet any significant improvement. As such, the mesh with 618 103 grids was used for all simulation cases presented in the following sections. 3.3. Formation process of initial water mist zone In engineering, the water spray occurs when the alarm inducting explosion. In this paper, that was simplified as the process that the droplets started to be injected into the pipe when the premixed gas was sparked. Fig. 3 shows the process of droplets dispersion. The water mist dispersion process contained the following steps: (1) The boundary condition in the range of 3–4 m was first set as the pressure-inlet; (2) The droplets was injected from the pressure-inlet boundary; (3) The boundary condition was set as the wall after the initial droplets all injected in the pipeline; (4) During the static progress, the droplets were uniformly located in the range of 3–4 m. It is to be noted that the whole
Fig. 2. Comparison between simulated and experimental results. 19
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Table 1 Comparison between experimental peak overpressure and simulation results. Locations of pressure monitoring points along the axis of the test pipe (m)
Peak overpressure (MPa) and relative errors of 250 550 grids
Peak overpressure (MPa) and relative errors of 618 103 grids
Peak overpressure (MPa) and relative errors of 980 338 grids
Peak overpressure of the experiment (MPa) [34]
0.375 1.625 2.875 3.875 5.125 6.525 7.525 8.275
0.0363/ 0.2883/ 0.3664/ 0.4188/ 0.3535/ 0.2833/ 0.1527/ 0.2025/
0.0330/ 0.2592/ 0.3176/ 0.3987/ 0.3103/ 0.2588/ 0.1309/ 0.2338/
0.0329/ 0.2589/ 0.3175/ 0.3957/ 0.3085/ 0.2513/ 0.1312/ 0.2339/
0.0323 0.2583 0.3165 0.3885 0.3045 0.2583 0.1227 0.2325
12.38% 11.61% 15.77% 7.80% 16.09% 9.68% 24.4% 12.90%
2.16% 0.35% 0.35% 2.63% 1.90% 0.19% 6.68% 0.56%
1.86% 0.23% 0.32% 1.85% 1.31% 2.71% 6.93% 0.60%
4.1.3. Effect pattern of explosion inhibition by water mist The histories of water mist vaporization rate and temperature of each monitoring point under 0.3 kg/m3 and 1.2 kg/m3 spraying concentrations are presented in Fig. 8(a) and (b) respectively. Fig. 8(c) is the temperature history of premixed methane explosion. Compare Fig. 8(a)–(c), the temperature curve of premixed methane explosion reached the peak value rapidly; the temperature curve of each monitoring point fluctuated for a long time under the effect of inhibition by water mist, that is, the flame delay phenomenon occurred. Compared with the vaporization rate history of the water mist, it is found that the flame temperature fluctuation is caused by the heat absorption of droplets vaporization. The flame and the water mist produce the energy exchange during this process, which makes the peak temperature decrease obviously. The peak values of the water mist vaporization rates under different spraying concentrations are obtained and shown in Fig. 8(d). It can be seen that the greater the spraying concentration was, the greater the peak vaporization rate appeared along the pipeline axis. When the concentration of initial spraying decreased, the distance of the droplet drift downstream became farther, so the maximum peak of the curve appeared later. Fig. 9(a) shows the CH4 concentration histories at each monitoring point for CH4-Air explosion. It is known that the leading shock wave of the explosion can make the turbulence in the unburned gas region, which causes the unburned fuel to spread out of the premixed zone. The expansion production with high temperature and pressure in the upstream can also push the unburned fuel to the open end. As a result the gas concentration is getting lower from the ignition end to the open end. Fig. 9(b) and (c) show the concentration of CH4 varying with time under the spraying concentrations of 0.6 kg/m3 and 1.5 kg/m3 respectively. Compared them with Fig. 9(a), the reduction of methane
overpressure did not rise again near the open end, which was indicated that the explosion flame had been inhibited by the water mist and could not provide energy for the propagation of shock wave.
4.1.2. Effect of water mist on flame propagation process Fig.6 shows the changes of the flame front structure during the process of explosion inhibition by water mist. The premixed gas was located in the range of 0–2.5 m before explosion. Hemispherical flame was formed when the flame inside the original premixed region (at 0.0448 s). The flame stretch appeared beyond the original methane accumulation region (at 0.0471 s). At 0.0532 s, the flame reached the water mist region, and then the volumetric expansion of water mist vaporization caused the flame instabilities, as a result the flame front began to be obviously wrinkled. It is shown in Fig. 7 that, with the increase of initial spraying concentrations, the faster the peak temperature decreased along the pipe axis. When the initial spraying concentration increased from 1.2 kg/m3 to 1.5 kg/m3, the two curves were almost coincided. It is deduced that the capability to inhibit explosion temperature approached the limit when the initial concentration was 1.5 kg/m3. The flame front generated more wrinkles with the increase of water mist concentration. When the wrinkles developed to enough surfaces, they could divide into several small units. The curvature of each small unit increased to absorb more heat, so that the inhibition effect of water mist cannot be further enhanced [38]. The temperature to predict the extinction of hydrocarbon fuels combustion is 1600 K [39]. As shown in Fig. 7, the flame spread was completely inhibited at 6.5 m of the pipe when the spraying concentration was 1.5 kg/m3.
Fig. 3. Formation process of initial water mist zone. 20
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Fig. 4. The interaction between explosion shock wave and water mist and the mist size distribution with time.
Fig. 5. Peak overpressures along the pipe axis for different initial spraying concentrations.
Fig. 7. Peak temperature along the pipe axis for different initial water mist concentrations.
concentration was more obvious, that is, the water mist causes the heat absorbing, the oxygen separating and the unburned gas diluting. Fig. 9(d) is the distribution of peak CH4 concentration along the
pipeline axis during the explosion inhibition of water mist for different spraying concentrations. It is known that the lower limit of methane concentration of CH4-Air explosion is 4.65% [40]. It is shown in
Fig. 6. Effect of water mist on flame structure. 21
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Fig. 8. Water mist vaporization for different spraying concentrations and explosion temperature histories. 1—(0.8, 0), 2—(1.5, 0), 3—(2.8, 0), 4—(3.2, 0), 5—(3.6, 0), 6—(4, 0), 7—(4.5, 0), 8—(5.5, 0), 9—(6.5, 0), 10—(7, 0), 11—(7.5, 0), 12—(8, 0), 13—(8.5, 0).
Fig. 9. CH4 concentration histories for different spraying concentrations. 1—(0.8, 0), 2—(1.5, 0), 3—(2.8, 0), 4—(3.2, 0), 5—(3.6, 0), 6—(4, 0), 7—(4.5, 0), 8—(5.5, 0), 9—(6.5, 0), 10—(7, 0), 11—(7.5, 0), 12—(8, 0), 13—(8.5, 0). 22
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Fig. 9(d) that the range in which the fuel concentration was lower than the limit concentration expanded as the concentration of water mist increased. When the concentration of spraying increased to 1.5 kg/m3, the methane concentration in the section behind 6.5 m was lower than the limit concentration, that is, the explosion at 6.5 m had been completely inhibited. 4.2. Effect of initial droplet size on the process of explosion inhibition In order to study the effect of droplet size on the explosion inhibition, the initial spraying concentration was fixed as 1.5 kg/m3. The initial droplet sizes were set as 20 μm, 50 μm, 100 μm, 150 μm and 200 μm. Fig. 10 shows the flame velocity at various locations along the pipe axis for different initial droplet sizes. It can be seen that the water mist can effectively reduce the flame velocity of gas explosion. However, the reduction rate of flame velocity is not linearly related to the initial droplet size. When the initial droplet size increased from 20 μm to 100 μm, the inhibition effect on flame velocity was gradually enhanced; however, when the initial droplet size increased to 150 μm, the of flame velocity did not change significantly compared with the initial droplet size of 100 μm; when the initial particle size was increased to 200 μm, the inhibition effect to flame wave velocity was weaker than that of 50 μm. Due to the analysis of 4.1.1., it is known that the leading shock wave generated by the gas explosion causes droplets breakup and drift downstream; the initial droplet size was different, the size and number of droplets after breakup were different; in this case, when the flame propagated into the water mist zone, the vaporization amount of the water mist was different. Fig.10 shows the vaporization rate of droplets for initial sizes of 20 μm and 200 μm when the flame wave propagated to 5 m of the pipe. Although the smaller the size of a single droplet is, the faster the vaporization rate is, the instantaneous distribution of the water mist with different initial droplet sizes were different as the droplets migrated to the open end. When the flame propagated at 5 m, the evaporation rate of 200 μm was faster than that of 20 μm, and the energy exchange of 200 μm produced between the flame and the droplet was greater than that of 20 μm, so the effect of the flame velocity inhibition also exhibited that the former was stronger than the latter. Fig. 11 presents the peak temperature along the axial direction for different initial droplet sizes. The process of inhibition to flame temperature by water mist was divided into three periods. At the beginning, when the droplet size increased from 50 μm to 150 μm, the smaller the droplet size, the better the inhibition effect on flame temperature (at the range of 3–4.5 m). This is because the smaller the initial droplet size is, the smaller the droplet size after breakup is. The faster the vaporization rate of the water mist is, the more obvious the explosion
Fig. 11. Peak temperature along axial distance for different initial droplet sizes.
inhibition effect is. In the middle stage of inhibition, the inhibition effect on flame temperature by different initial droplet sizes is the same as that of flame velocity. In the later stage, the peak temperature reduced rapidly near the open end of the pipeline due to the effective suppression on the methane combustion. Fig. 12 shows the effects of initial droplet sizes on combustion rate. It can be seen that the combustion rate of each monitoring point decreased obviously after the inhibition by water mist. The moment corresponding to the maximum combustion rate is taken as the arrival time of the flame [41], that is, it is considered that the flame does not propagate to this position when the peak value of combustion rate is 0, which is used to obtain the flame length. Fig. 12(d) shows the peak combustion rate along axial direction for different initial droplet sizes. It can be seen that when the initial particle size was 150 μm, the flame length was shortest and the explosion flame was effectively inhibited at 6 m. 5. Conclusion A numerical study on gas explosion inhibition by water mist was undertaken. The transient propagation of premixed gas explosion inhibited by a range of water mist (1 m) in a pipeline was modeled with the standard k-ε model and the discrete phase model. Under the initial spraying concentrations of 0.3 kg/m3, 0.6 kg/m3, 0.9 kg/m3, 1.2 kg/m3 and 1.5 kg/m3 fixed with 50 μm initial droplet size and the initial droplet sizes of 20 μm, 50 μm, 100 μm, 150 μm and 200 μm fixed with 1.5 kg/m3 spraying concentration, the conclusions can be drawn from
Fig. 10. Effects of initial droplet sizes on flame velocity. 23
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Fig. 12. Effects of initial droplet sizes on combustion rate. 1—(1, 0), 2—(2, 0), 3—(3, 0), 4—(4, 0), 5—(4.5, 0), 6—(5, 0), 7—(5.5, 0), 8—(6, 0), 9—(6.5, 0), 10—(7, 0), 11—(7.5, 0), 12—(8, 0).
the simulation results as follows. The water mist occurred transversely flowing driven by the leading shock wave of methane explosion. The drop breakup induced by leading shock wave and the droplet sizes were reduced rapidly. When the water mist flowed to the open end, the flow velocities of the droplets with different sizes were different, which made the water mist concentration at the same position always in the dynamic state. The inhibition effect of spraying concentration in the range of ∼1.5 kg/m3 on the explosion overpressure was not significant. The inhibition effect of water mist was mainly reflected in the suppression of the flame temperature. Water mist could absorb the combustion heat and evaporate rapidly, resulting in the great reduction of the flame front temperature. When the initial spraying concentration was 1.5 kg/ m3 and the initial droplet size was 150 μm, the explosion temperature can be reduced by 52.2%. When the initial droplet sizes of water mist were in the range of 50–150 μm, the effect of the water mist on the methane explosion was effective, the flame length was obviously reduced. But the water mist with too large or too small droplet sizes had no obvious inhibition effect on the gas explosion.
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