**4. Error Analysis**

The simulation results and experimental data were compared for two different structures, which were the big vessel connected to the small vessel with the 4.45-m pipe and the 6.45-m pipe. The peak pressure values at different ignition positions from the simulation and experiment are shown in Figure 14.

In Figure 14a, "A1" to "A7" correspond to the adopted ignition positions: the sidewall of the big vessel, the center of the big vessel, location 1, location 2, location 4, the center of small vessel, and the sidewall of the small vessel. Similarly, in Figure 14b, "B1" to "B8" represent the adopted ignition positions: the sidewall of the big vessel, the center of the big vessel, location 1, location 2, location 4, location 6, the center of the small vessel, and the sidewall of the small vessel.

Figure 14 shows that the variation that depended with the ignition positions of the peak pressure in the simulation and experiment were analogous. From Figure 14a, the average error between the simulation and experimental data is 7.7% in the big vessel with the 4.45-m pipe connected to it. The average error is shown in Figure 14b is 8.04%. Overall, 70% of the simulation data were marginally larger than those of the experimental data in all the compared points, in which the average difference was 6.97%. Generally, an experiment was controlled by more factors in comparison with a simulation. Even though the radiation model was employed, with the aim of improving simulated accuracy, some degree of discrepancy still could be observed. The increase of the temperature in the wall of the pipes was limited in the physical experiment. A considerable temperature difference existed between the combustion products and the wall of the pipe. The energy was dissipated on account of thermal convection, thermal conduction, and thermal radiation. As a result, the simulation data had higher values than the experimental data [34]. Consequently, on the one hand, the simulation effectively reproduced the development of the gas explosion in linked vessel. On the other hand, it correctly predicted the variations of pressure, temperature, and the changing concentration of products with different factors.

**Figure 14.** Comparison between the simulation data and experimental data of the natural gas explosion pressure versus time in the linked vessels.
