## 4 Results and Discussion
### Pressure Fluctuations and Vibration Characteristics Caused by the Slug Flow  
#### 4.2.1 Pressure Fluctuations and Comparisons  
The internal pressure fluctuation across the jumper caused by the slug flow was analyzed by selecting a typical slug flow condition of V\({}_{\rm sl}\) = 0.5 m/s and V\({}_{\rm sg}\) = 0.5 m/s. The temporal evolutions of the pressure measured by the pressure sensors P1, P2, P3, P6, P7, and P8 in the experiment are shown in Figure 11. P1, P2, and P3 represent the pressure  
Figure 10: Flow visualization of each section of the slug flows under three flow velocities in the experimental jumper: (**a**) S1, (**b**) S2, (**c**) S3, (**d**) S4, (**e**) S5, (**f**) S6, and (**g**) S7 at \(V_{sl}\) = 0.5 m/s and \(V_{\rm sg}\) = 0.5 m/s (left); \(V_{sl}\) = 0.5 m/s and \(V_{sg}\) = 1 m/s (middle); \(V_{sl}\) = 1 m/s and \(V_{sg}\) = 0.5 m/s (right). fluctuations across the three sections of jumper S1, S2, and S3. The time-averaged flow pressure of the fluid gradually decreased after the gas-liquid two-phase entered from the inlet and flowed through several elbows as a result of the pressure loss caused by the friction between the gas-liquid flow and the pipe wall, as well as by the local pressure loss through the elbow. The figure shows strong spikes in the time histories of the pressure at P1, P2, and P3, indicating a clear phase separation of the two-phase flow. The gas phase in section S1 merged in the form of a large gas bubble. When it flowed through the pressure measurement point, a gradual pressure drop was detected, followed by a gradual rise in the pressure when the liquid plug passed through, showing an obvious periodic change. At P6-P8, a bimodal structure with obvious pressure fluctuations was observed (denoted by the red dashed circles in Figure 11) because there was more gas-liquid mixture in this section of flow. As in section S6, the flow pattern was similar to the wavy flow of the segment plugs, and the flow in section S5 led to less gas phase buildup at the elbow, causing a relatively large disturbance to the liquid phase. Thus, inside the red dashed circles in Figure 11, a secondary fluctuation in the pressure extremum was observed in a short period of time. The PSDs of the pressure in the frequency domain were obtained by using fast Fourier transformation for the pressure fluctuations, as illustrated in Figure 12. It can be seen that the dominant frequency of the pressure variation was 0.15 Hz. The overall dominant pressure fluctuation frequency was low. The alternating gas-liquid flow mainly caused the pressure fluctuation. The M-shaped jumper used in the experiment was a symmetrical structure; the first and second halves were composed of a rising section, a horizontal section, and a falling section. From the pressure time domain fluctuations, it can be seen that the first half of the pressure measurement points (P1, P2, P3) and the second half of the pressure measurement points (P6, P7, P8) show generally similar spectra distributions, which was due to the similarity of the flow trend caused by the structural similarity of the first and second sections. However, the second half of the section was influenced by the flow of the first half and exhibited different pressure variation characteristics from the first section. There was an obvious second harmonic frequency at 0.3 Hz in addition to the primary frequencies at P6, P7, and P8. Figure 11: Pressure fluctuations in the time domain. In the one-way fluid-structure coupling analysis, the pressure measured in Fluent needed to be transferred to the structural response model. Therefore, the pressure data obtained from the numerical simulations using Fluent needed to be compared with the pressure data obtained from the experiments to validate the numerical model and to ensure the accuracy of the structural calculation model.