## 4 Results and Discussion
### Pressure Fluctuations and Vibration Characteristics Caused by the Slug Flow
#### 4.2.2 Effect on Vibration of Slug Flow Characteristics and Comparative Analysis  
In the present study, 17 slug flow conditions were studied, where the liquid superficial velocity and superficial gas velocity were between 0.5-1.5 m/s and 0.5-2.5 m/s, as shown in Table 4. The characteristics of the slug flow were investigated at various gas-liquid superficial velocities. The effects of the slug flow characteristics quantities, such as the slug velocity and the slug frequency, on the vibration characteristics of the jumper, were investigated by combining the flow pattern characteristics captured by a high-speed camera. The process of slug formation can be described as a consequence of the growth of unsteady waves on the layered film and their interactions with the passing gas. The average number of slugs traveling through a specific segment per unit of time can be used to estimate the slug frequency. The slug formation process variation tended to be more regular and periodic at lower mass fluxes and flow rates with lower liquid superficial velocities. With the increasing liquid superficial velocity, the slugs became gradually blurred and more chaotic. Figure 14 shows the relationship between the gas-liquid mixing velocity and the slug frequency. The figure shows that the frequency of slugs increased with the gas-liquid mixing velocity. In particular, when the two-phase mixing velocity was larger than 2 m/s, the slug frequency increased significantly. As the liquid superficial velocity was fixed, an increase in the gas velocity caused a faster increase in the slug frequency. While in another case, with a fixed gas superficial velocity and an increasing liquid velocity, the slug frequency also became larger, but the trend was slower than in the previous case. This indicates that the gas velocity had a more significant effect on the frequency of the slug. The increase in the gas velocity accelerated the gas-liquid alternation in the pipeline, and the frequency of the slug also increased. The impact of the slug frequency on the vibration amplitude is depicted in Figure 15. The vibration amplitude is expressed as the root mean square of the acceleration of the experimental vibration data. From the figure, it can be observed that the vibration amplitude increased with the increasing slug frequency. Combined with the natural frequency of the jumper given earlier, when the slug frequency was nearly equal to the structural natural frequency, the alternating gas-liquid flow characteristics of the slug caused the jumper to resonate, thus significantly increasing the vibration amplitudes. It can be obtained from the figure that the frequencies of the slug at points A and B were 6.2 Hz and 5.96 Hz respectively. Table 3 gives the natural frequency of the first six orders, and the frequencies of the slug at points A and B were very close to the first-order natural frequency of the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & \(V_{sl}\) & \(V_{sg}\) & \(\beta\) & \(Q_{ml}\) & \(Q_{mg}\) \\
**No. ** & **(m/s)** & **(m/s)** & **(t/h)** & **(kg/h)** \\ \hline
1 & 0.5 & 0.5 & 0.5  
structure. This caused resonance in the pipeline so that the amplitudes at points A and B increased significantly, as marked by the arrow in the figure. Figure 16 shows the relationship between the slug velocity and the vibration amplitude at increasing air velocities of \(V_{sl}\) = 0.5 m/s, 0.75 m/s, 1 m/s, and 1.5 m/s. In the figure, it can be seen that increases in the slug velocity also caused the amplitude to increase. Under low liquid superficial velocity conditions, when the superficial velocity of the mixed gas-liquid increased, while the gas velocity remained unchanged, the superficial velocity of the liquid phase gradually increased. As the liquid phase velocity gradually increased to close to the gas velocity, it combined with the slow-flowing liquid in the liquid film in front of it.