## 1 Introduction
### Experimental Results and Analysis  
The overpressures at different monitoring points in five different pipe configurations and with three distinct gas volumes were measured in the experiments. The focus of the subsequent analysis was the influence of initial peak overpressure and the ratio of abrupt cross-section areas on the pipe attenuation coefficient. Taking the monitoring data of a middle pipeline with a 0.36 m diameter when the volume of methane air was 0.18 m\({}^{3}\) as an example, the variation law of gas explosion shock wave overpressure at abrupt cross-section area change was analyzed. Figure 3 shows the overpressure changes at each measurement point in the pipe for the case of 0.18 m\({}^{3}\) combustible gas and the 0.36 m diameter of the middle pipe. The overpressure change curves at measuring points 1, 2, and 3 were basically the same, and two clear peak overpressures occurred. The first peak overpressure was formed by shock wave attenuation from explosive source, while the second peak overpressure was formed by reflection wave from the large cross-section pipe to the small cross-section pipe. At measuring points 4-6, the first peak overpressure measured 0.4646 MPa, 0.4687 MPa, and 0.4475 MPa, respectively, suggesting an increasing and then decreasing trend. However, the second peak overpressure increased from 0.4254 MPa at measuring point 4 to 0.902 MPa at measuring point 6, showing a gradually increasing trend. This indicates that reflected waves appeared at the location where the cross-section area decreases from the large pipe to the small pipe, and these were superimposed onto the incident waves, resulting in the overpressure of reflected waves exceeding that of the incident waves. When the shock wave propagated from the small cross-section pipe to the large cross-section pipe (measuring points 6 and 7), the overpressure changed from 0.7638 MPa to 0.4646 MPa, a decrease of 39.17%. This is mainly because the diffraction intensity of shock wave decreases in this region. However, when the shock wave propagated from the large cross-section pipe to the small cross-section pipe, the peak overpressure changed from 0.4475 MPa to 0.5299 MPa, an increase of 18.41%. It can be concluded that, when the cross-section area of a pipeline changes abruptly from small to large, the peak overpressure decreases. In contrast, when the cross-section area of a pipeline changes abruptly from large to small, the shock wave overpressure increases. The curves of overpressure at measuring points 7-10 were basically the same because they were not disturbed by abrupt change in a cross-section area of the pipeline. Figure 4 shows the change in peak overpressure with respect to distance for different pipes with fuel volumes of 0.18 m\({}^{3}\), 0.23 m\({}^{3}\), and 0.28 m\({}^{3}\). When the diameter of the middle section of the pipeline is no greater than 0.24 m, the peak overpressure tends to decrease first, then increase, and finally decrease again. However, when the diameter of middle section of the pipeline is greater than 0.24 m, peak overpressure again decreases, increases, and decreases before finally increasing and decreasing once more. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Measurement Point** & **P1** & **P2** & **P3** & **P4** & **P5** & **P6** & **P7** & **P8** & **P9** & **P10** \\ \hline Distance & 10.25 & 11 & 11.75 & 12.25 & 13 & 13.75 & 14.25 & 15 & 16 & 17 \\ \hline \end{tabular} Note: P represents pressure sensor.  
\end{table} 
Table 1: Distance of each measurement point from explosion source (m). To characterize the variation laws of maximum explosion overpressure in the pipes with abrupt cross-section area change, three concepts are proposed: attenuation coefficient,  
Figure 4: Maximum explosion overpressure versus propagation distance. Figure 3: Overpressure change of each point in the pipe with an abrupt cross\(-\)section change (\(V=0.18\) m\({}^{3}\), \(d=0.36\) m). increase coefficient, and reflection coefficient.