Safety evaluations of a large-scale facility under blast loading

2.1. Test apparatus and results

The methane-air mixed explosion experimental system of the tunnel model is shown in Figs. 5 and 6. This system is mainly composed of a 6 m long explosion pipeline with a cross section area of 0.11 m×0.11 m, air distribution system, ignition device, synchronous control system, high-speed camera and data acquisition system. The configuration for the high speed camera is: a shooting frequency of 200 frames per second. During the experiment, appropriate amount of methane-air premixed materials was supplied into the pipeline and one end was ignited under the control of the control system. The produced high-temperature and high-pressure materials expands toward the other end. In the same time, the measurement system records the overpressure output data at the measuring point.

Fig. 5The test system of horizontal square pipeline: 1 – horizontal square pipeline; 2 – air distribution system; 3 – synthronous controller; 4 – data acquisition units; M1 and M2-pressure sensors which are measuring point 1 and measuring point 2; 6 – high-speed camera; 7 – image displayer; 8 – opening area; 9 – inlet/outlet; 10 – ignition device; 11 – control switch; 12 – vacuum unit; 13, 14, 15 – switching valve; 16 – vacuum meter

The pressure sensor applies the high-frequency water-cooled pressure transmitter (Fig. 7). The model of the pressure sensor is CYG1409F (0-1MPa) JAS13C1Q and the frequency response is 100 kHz. The power supply voltage equivalent resistances by the integrated circuit technology, which forms a new Huygens bridge. uses ±15VDC power. This sensor is diffused into four the bridge loses balance after the pressure sensor is stressed, and one signal (0-5 V) proportional to pressure is out.

Fig. 6Experimental system of methane-air mixed explosion

Fig. 7The sensor used for the high-frequency water-cooled pressure transmitter

This study is to discuss the methane-air mixed explosion pressure characteristics under different concentrations. Since the explosion concentration of methane ranges between 5 %-15 %, the methane concentration is determined 6.5 %, 7.5 %, 8.5 %, 9.5 %, 10.5 %, 11.5 %, 12.5 %, and 13.5 % in this experiment, respectively.

The ignition is at one end of the pipeline. Experimental results are shown in Fig. 8, in which the black solid line reflects overpressure data at measuring point 1 (middle point of the pipeline) and the red dotted line reflects overpressure data at measuring point 2 (end point of the pipeline). The ignition energy is 5 J.

Fig. 8Overpressure time curves with the methane concentration

a)$c=$6.5 %

b)$c=$7.5 %

c)$c=$8.5 %

d)$c=$9.5 %

e)$c=$10.5 %

f)$c=$11.5 %

g)$c=$12.5 %

h)$c=$13.5 %

i)$c=$14.5 %

It can be seen from Fig. 8 that experimental results at point 1 and point 2 are different under a certain concentration. Specifically, experimental results at point 1 are higher than those at point 2. This is caused by the certain pressure relief as a result of the poor sealing of experimental apparatus. In the experiment, the explosion phenomenon was the most obvious when methane concentration reached 10.5 %, manifested by the maximum peak overpressure (Table 1) and the brightest flame from the glass window (Fig. 9). When methane concentration reached 9.5 % and 11.5 %, the explosion phenomena were very similar. For that methane concentration, the pressure rise rates were the same, and the peak of the overpressure was very close. There was a loud explosion sound and orange flame from the glass window. However, the explosion sound was weaker than that when methane concentration reached 9.5 %, and the flame was weaker. The explosion sound and flame were further weakened when methane concentration reached 8.5 %. Here it is noted that the audio data are more convincing to show the extent of sound. Nevertheless, for our explosion test of mixed materials, it is difficult to extract the audio signals from the high speed camera.

Fig. 9 shows the integral curve of overpressure versus time. One can see that the impulse increases with time. Until the overpressure drops to zero, the impulse curve tends to be flat.

Fig. 9Curves of impulse versus time

Fig. 10Flame propagation process (electrode ignition) to show the bright orange flame

2.2. Validation of numerical analysis model

FLACS is a three-dimensional computational fluid dynamics software for calculating leakage and explosion (Gexcon 2018). For the FLACS software, the standard $k$-$\epsilon$ turbulence model (Xu et. al 2016)is used to describe the flame development, combustion and explosion behavior, and further to investigate changes in local reactions with various physical parameters such as concentration, temperature, pressure, and turbulence. In this paper, the shock wave characteristics of explosion in a facility are studied using the Flacs. The size of the model was set up based on the dimension of the experimental pipe. The inner diameter of the pipe was 11 cm×11 cm, the length was 6 m, and the thickness of the pipe wall was 1 cm in the model, as shown in Fig. 11. The simulation space was 6.07 m×0.23 m×0.18 m ($X$-axis, $Y$-axis, $Z$-axis), and the grid was divided into cubes with a side length of 1 cm, as shown in Fig. 12. Two pressure measuring points were set at $x=$ 3 m (measuring point 1), and $x=$ 0.25 m (measuring point 2), respectively. We assume that the interior of the model was filled with the methane-air mixture and the ignition position was at the center of the model where $x=$ 5.85 m.

Fig. 11Dimensions of the used pipeline model

Fig. 12Simulations for the space model

The main parameter settings are as follows: The $Z$-axis positive direction is upward, the gravity acceleration direction is the $Z$-axis negative direction, the temperature is 20 ℃, the atmospheric pressure is 1.01 MPa, the air composition is oxygen and nitrogen, and the volume fractions of the oxygen and the nitrogen are 20.95 percent and 79.05 percent respectively. Except that ZL0 ($Z$-axis lower boundary) is the EULER boundary, the other five boundaries are assumed to be the PLANE_WAVE boundary adapted to the explosion scene, CFLC and CFLV are 5 and 0.5, respectively, DTPLOT is 0.01 s, assuming that there is a radiant heat transition. For most explosion simulations, EULER boundary, which is zero-pressure, can be used. The CFLC is the time step restriction of speed of sound, and the CFLV is the time step restriction of flow velocity. In the explosion simulations, a default value of 5 for CFLC, and 0.5 for CFLV is kept. The DTPLOT is the time interval (in seconds) for the field output.

Fig. 13Comparison of test and simulation results (overpressure)

a)$c=$6.5 %

b)$c=$7.5 %

c)$c=$8.5 %

d)$c=$9.5 %

e)$c=$10.5 %

f)$c=$11.5 %

g)$c=$12.5 %

h)$c=$13.5 %

The compassion of test and simulation is shown in Fig. 13. When the ignition energy is 5 J and the concentration of mixed materials is 6.5 % and 7.5 %, the peak of overpressure calculated by numerical simulation differs greatly from the experimental results. In the numerical simulations of FLACS, the hindrance of the conduit wall on the pressure wave is ignored, which can lead to a high overpressure peak than that for the experimental results. When the concentration of mixed materials reaches 10.5 %, methane is fully combusted and the error between experimental and simulation is the least. When the concentration is between 8.5 % and 13.5 %, the error between numerical simulations and the experimental observations can meet the research needs. Table 2 shows a comparison of overpressure calculated by numerical simulations and experimental results under different concentrations.

3.1. Numerical analysis model

In order to study the characteristics of explosion load in a facility, the typical section of a facility in a city is chosen as the research object, as shown in Fig. 14. The facility access line has a feed water (DN600), reclaimed water (DN300), electricity (10 KV), communications, heating (DN300), natural materials (DN300), and a sewer conduit (DN600) with a four-compartment rectangular cross section. The simplified facility model is a rectangular with a size of 2 m×3 m ×200 m, regardless of the role between the materials and the adjacent chamber, as shown in Fig. 15. To make the model more accurate, the opening facilities, such as a personnel entrance and exit, access hole, air vent and the like, which are connected with the external environment, is arranged at two ends of the facility. The facility is composed of the conventional facilities, such as two pipes, a pipe frame, and a personnel climbing ladder. The measuring points of the explosion model are transversely arranged. One measuring point is arranged every 5 m at $z=$ 1.5 m until the end (M1-M20). Within $x=$ (5, 100 m), 24 measuring points (M21-M24) are arranged at the end part at intervals of 1 m. The coordinate values from measuring point 1 to measuring point 24 are shown in Table 3. Additionally, measuring points at positions such as personnel entrance and exit (M25), air vent (M26-M28). And the measuring point position is shown in Fig. 16.

Fig. 14Schematic diagram of tank (mm)

Fig. 15Simulation analysis model of a facility

Fig. 16Measuring point placement within the facility model

3.2. Effects of various parameters

It can be seen from the experimental results that the main parameters influencing the explosion load in the facility are mixed concentration, mixed volume and ignition position. By changing the mixed concentration, the mixed volume and the ignition position, the law of its influence on explosion load in a facility is studied. A typical explosion within facility occurs as shown in Fig. 17 for the propagation of the blast wave.

Fig. 17The propagation process of blast waves in a facility

3.2.1. Influence of mixed concentrations

To study the influence of mixed concentration on explosion load in a facility, the propagation and distribution of explosion wave in the facility were analyzed, with mixed concentration of 6.5 %, 9.5 % and 12.5 %, respectively. We assume that the mixed materials is filled with the facility, and the ignition position is in the middle position. Because of the limitation of the content of the text, it is impossible to give the pressure time history curve of all points. In this paper, the maximum of the pressure peak point in the calculation results and point 24 are selected to study the influence of the mixed concentration on the explosion load, which is shown in Fig. 18. When the concentration of mixed materials is 6.5 %, the peak of overpressure at point 24 is 120.1 kPa. When the concentration of the mixed materials is 9.5 %, the peak of the overpressure at point 24 is 1050.3 kPa. When the concentration of mixed materials is 12.5 %, the peak of the overpressure at point 24 is 388.8 kPa. With the increase of mixed concentration, the peak of overpressure increases first and then decreases. When the concentration of the mixed materials is 9.5 %, the combustion reaction of the methane-air mixed materials is the most adequate, which is in accordance with the experimental results.

Fig. 18Relationship between pressure time history curve and mixed concentration c (point 24)

a)$c=$6.5 %

b)$c=$9.5 %

c)$c=$12.5 %

3.2.3. Influence of ignition position

In order to study the influence of ignition position on the explosion load in a facility, the propagation and distribution of explosion waves in a facility at ignition position ($I_g$) of 100 m, 150 m and 200 m in a facility are analyzed. When the concentration of the mixed materials was 9.5 %, the volume of the mixed materials was filled inside the facility.

Fig. 19The relationship of pressure time history curve with the volume V (point 24)

a)$V=\mathrm{}$2×10×3 m³, $P_{max}=$ 118.4 kPa

b)$V=\mathrm{}$2×50×3 m³, $P_{max}=\mathrm{}$698.2 kPa

c)$V=\mathrm{}$2×100×3 m³, $P_{max}=\mathrm{}$977.0 kPa

d)$V=\mathrm{}$2×200×3 m³, $P_{max}=\mathrm{}$1050.3 kPa

Fig. 20The relationship between the pressure time history curve and the ignition position Ig (point 24)

a)$I_g=$ 100 m

b)$I_g=$150 m

c)$I_g=$200 m

Fig. 20 shows the comparison of the different ignition positions, which is the result of the maximum value of the overpressure peak in the calculation result, that is, the point 24. When the ignition position is at the center of cloud ($I_g=$100 m), the peak of overpressure at point 24 is 1050.3 kPa. When the ignition position is 3/4 of the cloud ($I_g=$150 m), the peak of the overpressure at point 24 is 2627.4 kPa. When the ignition position is at one end of the cloud ($I_g=$ 200 m), the peak of the overpressure at point 24 is 1426.98 kPa. As the ignition position moves toward end within the cloud, the overpressure peak increases first and then decreases.

Table 4Comparison of the peak of overpressure

Volume of the cloud / m3	2×10×3	2×50×3	2×100×3	2×200×3
Overpressure peak /kPa	118.4	698.2	977.0	1050.3

3.3. Calculation formula for the blast loadings

3.3.2. Pressure relief vent

To consider the influence of the pressure relief vent, different parameters of the pressure relief vent are selected in this paper. As shown in Table 5, the explosion concentration is set to be $c=$ 9.5 %, and the volume of the mixed materials is calculated according to the internal space filled with the facility ($V=$ 2 m×3 m×200 m = 1200 m³).

As can be seen from the Eq. (1), under the condition that the distance from the ignition source $L$ and the concentration of the mixed materials $c$ are constant, the blast peak of overpressure $\mathrm{\Delta }P$ related to the pressure relief vent $S_v$ and the distance $L$ from the ignition source, that is:

2

$\mathrm{\Delta }P=f_1\left(\frac{S_v}{L^2}\right)\cdot P_0.$

Table 5Parameter for calculation of pressure relief vent Sv

Parameter	Value
$S_v$ / m2	1 m×1 m = 1 m2	1.5 m×1.5 m = 2.25 m2	2 m×2 m = 4 m2	2 m×3 m = 6 m2	2 m×4 m = 8 m2
$c$ / %	9.5 %
$V$ / m3	1200 m3

By using the results of numerical analysis, the results of $L=$ 25 m, 50m, 75 m, 95 m and 99 m are calculated by fitting formula. According to the Eq. (2), we can obtain a fitting formula which is as follows:

3

$\mathrm{\Delta }P=1.91\cdot {\left(\frac{S_v}{L^2}\right)}^{-0.526}\mathrm{k}\mathrm{P}\mathrm{a},R^2=0.7568.$

The fitting curve is shown in Fig. 21.

Fig. 21The fitting curve of ΔP/P0 and Sv/L2

3.3.3. Volume $\mathit{V}$ of mixed materials

To consider the influence of mixed volume, different mixed volumes were chosen as parameters in this paper. As shown in Table 6, explosion concentration was set to be $c=$ 9.5 % and the pressure relief vent $S_v=$ 4 m².

Table 6Parameters for calculating mixed volume

Parameter	Value
$S_v$ / m2	2 m×2 m = 4 m2
$c$ / %	9.5%
$V$ / m3	2 m×3 m×10 m = 60 m3	2 m×3 m×50 m = 300 m3	2 m×3 m×100 m = 600 m3	2 m×3 m×200 m = 1200 m3

The results of points at $L=$ 25 m, 50 m, 75 m, 95 m and 99 m are calculated by formula fitting, as shown in Fig. 22. It can be seen from the Eq. (3) that in the case of the mixed concentration $c=$ 9.5 % and the pressure relief vent $S_v=$4 m², the peak of overpressure $\mathrm{\Delta }P$ is related to mixed volume $V$ and the distance $L$, that is:

4

$\mathrm{\Delta }P={\left(\frac{S_v}{L^2}\right)}^{-0.526}\cdot f_2\left(\frac{V}{L^3}\right)\cdot P_0.$

According to the Eq. (4), the peak of the overpressure is fitted as shown in Fig. 23, and the fitting formula can be obtained as follows:

5

$\mathrm{\Delta }P=7.26\cdot {\left(\frac{S_v}{L^2}\right)}^{-0.526}{\left(\frac{V}{L^3}\right)}^{0.2115}\mathrm{k}\mathrm{P}\mathrm{a},R^2=0.8112.$

Fig. 22Overpressure time curves of several measuring points

a)$V=$ 60 m³

b)$V=$300 m³

c)$V=$600 m³

d)$V=$ 1200 m³

Fig. 23The fitting curve of ΔP/P0Sv/L2-0.526and V/L3

3.3.4. Concentrations

In order to take into account, the influence of the concentration of mixed materials, different concentrations of the mixed materials were selected as parameters. The concentration of methane was in the range of 6.5 % to 12.5 %. As shown in Table 7, the pressure relief vent $S_v=$4 m², and the volume of the mixed materials was calculated filled with the facility ($V=$1200 m³).

Table 7Parameters for calculating volume of mixed materials

Parameter	Value
$S_v$ / m2	2 m×2 m = 4 m2
$c$ / %	7.5 %	8.5 %	9.5 %	10.5 %	11.5 %	12.5 %
$V$ / m3	1200 m3

Fig. 24 shows the time history curve of the overpressure at $L=$ 1 m (P1), 25 m (P6), 50 m (P11), 75 m (P16), 95 m (P20), 99 m (P21) at different concentrations. The peak of overpressure of P20 and P21 is significantly greater than that of other points, while the overpressure curve of P1, P6, P11, P16 are not significantly different.

Fig. 24Overpressure time curves of several points

a)$c=\mathrm{}$7.5 %

b)$c=\mathrm{}$8.5 %

c)$c=\mathrm{}$9.5 %

d)$c=\mathrm{}$10.5 %

e)$c=\mathrm{}$11.5 %

f)$c=\mathrm{}$12.5 %

The relationship between peak of overpressure and concentration is given in Fig. 25. With the concentration between 7.5 % and 12.5 %, the peak of overpressure at each position tends to increase first and then decrease, and reaches the maximum at about 10 %.

Fig. 25The fitting curve of ΔP/P0Sv/L2-0.526/VL30.2115 and c

As seen from the Eq. (5), under the condition that $L$, $S_v$, $V$ are constant, the peak overpressure $\mathrm{\Delta }P$ is only related to the concentration $c$, that is:

6

$\mathrm{\Delta }P={\left(\frac{S_v}{L^2}\right)}^{-0.526}\cdot {\left(\frac{V}{L^3}\right)}^{0.2115}\cdot P_0\cdot f_3.$

And fitting the data of Fig. 23 according to the Eq. (6) to obtain a curve shown in the figure, wherein the fitting formula is as follows:

7

$\mathrm{\Delta }P=\left[-0.61{\left(c-10.24\right)}^2+6.524\right]\cdot {\left(\frac{S_v}{L^2}\right)}^{-0.526}\cdot {\left(\frac{V}{L^3}\right)}^{0.2115}\mathrm{k}\mathrm{P}\mathrm{a},R^2=0.8202.$

It can be seen from this formula that the peak of overpressure $\mathrm{\Delta }P$ reaches the maximum value at $c=$ 10.5 %, which is 1.07 times higher than the explosive equivalent concentration of 9.5 % methane.

Finally, it is noted that for Figs. 21 and 23, power curve fitting is used, whereas for Fig. 25, polynomial is used.