An explosion test was conducted by FDC Co., Ltd. using an explosive test equipment of FDC Co., Ltd., and the analysis was performed based on the test data of FDC Co., Ltd.

Figure 1 shows the model of the standard container used for the explosion experiment. The model was made of steel, with a volume of 3.07 m³. The container was designed to be sufficiently thick to contain strong explosions. When an explosion occurred during the experiment, the exhaust was discharged through an exhaust port located at the top of the container and covered by a rupture disc. A rupture disc is designed to rupture at a specific pressure; for this experiment, the rupture disc was designed to break at 0.5 bar. Once ruptured, the gases and pressure would be discharged outward.

Figure 1: 
Shape of experimental chamber

Figure 2 shows the layout of the experiment and the equipment used. Pressure sensors were installed near the top of the container. As propane is denser than air, igniting the gas in the chamber will cause residue to remain at the bottom of the container. The propane and air was distributed uniformly by circulating the gas in the chamber by injecting the propane/air gas mixture through a pipe installed at the bottom of the container.

Figure 2: 
Layout of the experiment test facility used for the propane gas experiment

Table 1 lists the size and parameters of the chamber and the diameter of the exit diameter where the rupture disc was installed. The ignition point was located approximately 0.7 m from the bottom of the container. Table 2 lists the conditions of the gas and before ignition in the experimental chamber. The propane/air mixture was injected into the container at a rate of 42 L/min for 60 min. The turbulent mixing of the gases allowed the gases to be uniformly distributed. To match the internal gas’s explosive concentration [3], the internal pressure was set to 0.2 bar for the experiment.

Figure 3 shows the photographs captured during the experiment at different times after the ignition as the flames exited the container. The experiment was conducted in the night to aid the visual confirmation of the ignition and combustion by the naked eye. Figure 3 (a) shows the picture captured 1.11 s after ignition; bright exiting flames are shown expanding wider than the diameter of the chamber’s exit. However, 1.42 s after ignition, as shown in Figure 3 (b), the width of the out-going flame pillar matched the diameter of the chamber exit diameter; 1.61 s after ignition, as shown in Figure 3 (c), the size of the flames reduced significantly until 3.66 s (Figure 3 (d)), where the flames were combusting the remaining gases that were exiting the chamber.

Figure 3: 
Flame profile after explosion

The chemical equation related to the explosion analysis is given by the following Equation (1):

In the numerical analysis, to reduce the calculation time, the piping for the propane/air mixture was not added; instead, an airtight container that contained a uniformly mixed propane/air gas mixture was modeled. The conditions for the experiment were specified for the analysis, and the flame speed closure model [4] was used for the turbulence model. The governing equations are shown in Equation (2):

ωc¯ is the chemical source term;
Sc¯is the source term;
c~is the averaged reaction progress variable;
ρu¯is the density of the unburnt mixture; and
S_T is the turbulent burning velocity.

The governing equation above, Equation (2), affects the resulting turbulence burning velocity. This equation has several advantages compared with the basic molecular reaction rate modeler. First, it is simpler than the basic molecular reaction rate model and the difference in the results of the overall combustion analysis is small. Next, results from the experiments can be entered into the numerical analysis. Therefore, for these reasons and the reduced time for numerical calculation, this method was preferable.

To obtain explosion and fluid characteristics similar to those of the experiment, once the internal pressure of the container reached 0.5 bar, the rupture disc would open. A transient analysis was specified with a total time of 4.8 s. The domain, shown in Figure 4, was used for the analysis and a tetra-element mesh was used for the domain. To further minimize the calculation, only a section of the container was modeled and the symmetry boundary condition was applied. Several points inside the container (near the bottom, center, side walls, and neck) were monitored for temperature.

Figure 4: 
Schematic of symmetry shape

Figure 5 shows the internal mesh of the container, where; the mesh is refined near the ignition point. In addition, the mesh near the walls of the container are refined to measure the temperature variation. The area outside the container was modeled using hexa elements, as shown in Figure 6. The rupture disc was located in the area between the container exit and the external area, and it has been refined to adequately capture the fluid flow and sudden changes that occur after rupture. For the simulation, the total numbers of nodes and elements were 244,220 and 599,256, respectively. The finite-volume-based solver ANSYS CFX was used to perform the numerical analysis of the explosion [5].

Figure 5: 
Vessel part mesh

Figure 6: 
Outer area mesh

Generally, the shear–stress transport (SST) model or the k–epsilon (k–ε) model is utilized in turbulence modeling. For the refined mesh utilized in this analysis, the difference in results was not large, but as the k–ε model required less time than the SST model to complete, it was selected for this analysis. The total energy was applied in the heat transfer equation. The combustion model used the burning velocity model (BVM), which used the Zimont method in a combustion acceleration simulation used in the RUT facility [6]. In the BVM model, the combustion and flame speed was determined by the burning velocity; the burning velocity equation is given in Table 3.

The time step interval for the analysis was initially selected as 1 ms but owing to the sudden change caused by the rupture disc, the interval was changed to 0.2 ms to capture the results adequately.

J. K. Paik et al. [7] performed an experimental analysis on explosions, and the data obtained were compared with the numerical analysis, as shown in Figure 7 and Figure 8. K. Hu and Y. Zhao [8], who analyzed temperature changes as the calculation time and temperature of the explosion as investigated by Q. Liu et al. [9], who used a gas mixture of propane and air for an explosion analysis, was considered in the paper as well. Figure 7 shows the variation in temperature at different points inside the container. The ignition point was located 0.7 m below the center point (MP3) and as the explosion rose upward, a large temperature increase occurred at point MP3 at approximately 0.5 s. At approximately 0.7 s, the rupture disc broke owing the sudden increase in internal pressure and the exit of hot gases from the container. Once the gases exited, the temperature at the center decreased. Simultaneously the points at the neck (MP5) and high wall (MP4), the temperature increased to approximately 2200 K before decreasing to 1000 K subsequently. At the center point, MP3, the gas temperatures varied from 500 to 1500 K. Following that, the pressure stabilized and the combustion expanded fully in the container. After 3 s, the temperature near the bottom wall increased gradually. However, at the bottom end of the container, because combustion did not occur, the temperature did not increase. In addition, during the explosion, the temperature was measured at the neck at approximately 2,237 K and at that instant, the temperature of the nearby upper walls indicated 1,987 K.

Figure 7: 
Internal temperature changes of the chamber after the explosion by specifying the main points

Figure 8: 
Pressure comparison of explosion experiment versus CFX simulation

Figure 8 shows a graph comparing between the pressures obtained in the experiment and the numerical analysis at point MP4. A difference is shown where the numerical result showed an instant where the pressure dropped slightly after the rupture disc ruptured. However, in the experiment, the same pressure drop was not observed. Generally, the conditions before and after the rupture show a general agreement in results. Furthermore, it was observed that leading up to the rupture at approximately 0.7 s, the internal pressure increased in a parabolic shape up to 0.5 bar. After the rupture, the pressure returned to normal air pressure within 2 s. Subsequently, the fluctuated around the air room pressure as the remaining hot air gases exited the container. In this interval, the pressure fluctuated between the maximum of 0.1 bar and the minimum of -0.19 bar.

In Figure 9, several cross sections of the numerical domain show the calculated temperature of the gases at six different time instants. As the flame expanded at 0.73 s, it reached approximately 1500 K as it began to breach the container exit. As flames continued to exit from the container, temperatures as high as 2000 K were recorded as the hot gases began to expand into the surroundings. The diffused gases remained at a temperature of 1700–1800 K. After the initial explosion, some uncombusted propane gas remained inside the container owing to the outside pressure difference and density. After approximately 1 s, the remaining gas was burnt.

Figure 9: 
Result of CFD analysis (temperature)

Figure 10 shows the pressure of the gas at the same instants as shown in Figure 9. As the rupture occurred, the pressure decreased from 0.5 bar until the room pressure.

Figure 10: 
Result of CFD analysis (pressure)

The contours in Figure 11 show the velocity of the gas at the time of the rupture. As shown, the exit velocity of the gas reached 400 m/s and within 1–2 s after the rupture, air entered the container at a velocity of approximately 10–20 m/s.

Figure 11: 
Velocity contour according to the time step

Figure 12 shows the comparison of flames produced in the experiment and numerical analysis. However, a slight 0.3 s time difference occurred between combustions in the experimental and numerical analysis. This difference could be due to the non-occurrence of combustion at the initial ignition but rather at the subsequent ignition attempts. Figure 12 (a) compares the instant where the rupture disc was ruptured and a thick flame column appeared in the experiment. Figure 12 shows the first stages of a strong exiting flame expanding outward in the numerical analysis. In both instants, the flame column width is significantly wider than the exit width. Figure 12 (b) and Figure 12 (b-1) show that the intensity and width of the flames decreased. Subsequently, Figure 12 (c) and Figure 12 (c-1) show that the flames decreased significantly in size. Figure 12 (d) and Figure 12 (d-1) show that the final flames remained.

Figure 12: 
Flame shape comparison of experimental and simulation results after rupture disc opened