## 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 this process, the combination of gas and liquid made the fluid inside the pipe become less stable, which also increased the pipe vibration amplitudes, as shown by the increasing RMS values. According to the definition of the process of slug formation  
Figure 14: Slug frequency at the different gas –liquid superficial mixing velocities. Figure 15: Slug frequency at the different gas –liquid superficial mixing velocities. given at the beginning of this section, since the slug frequency is a quantitative indicator of the slugs passing through a pipe section within a given time span, a longer liquid slug led to a lower slug frequency. Under the low-velocity condition, a long slug was formed in the jumper. With the gradually increasing velocity of the two phases, the stability of the long liquid film decreased, and the long liquid film was easy to break up, resulting in the reduction of the slug length, and thus, the frequency of the slug gradually increased. Because of this, the slug length reduced when the superficial liquid velocity increased with the constant superficial gas velocity. A quantitative comparison of the slug frequency and slug velocity obtained through the simulations and the experiments under the flow conditions in Table 4 is shown in Figures 17-20. As can be observed in Figures 17 and 18, the slug frequency predicted by the numerical simulation was within 13.7% of the maximum error of the experimentally obtained slug frequency, and the trend was the same under different flow conditions. When the superficial gas velocity was constant, the increase in the slug frequency was caused by an increase in the liquid superficial velocity. At the inlet, the gas-phase mixing allowed for the accelerated formation of slugs, after which an increase in the liquid superficial velocity enhanced the mixing effect and accelerated the development of slugs. It is worth mentioning that it is obvious from the two figures that the frequencies of the slug for the  
Figure 16: The vibration amplitude vs. the slug velocity at a \(V_{sl}\) of (**a**) 0.5 m/s, (**b**) 0.75 m/s, (**c**) 1 m/s, (**d**) 1.5 m/s. simulations and experiments were very close to each other at low velocities, and as the gas-liquid mixing speed increased, the experimental and simulated values of the slug frequencies began to deviate significantly from each other. This is because the VOF model used in the numerical simulations still tracked the slug flow well at larger velocities, while for the experiments, the pressure loss due to the velocity and position led to large deviations in the experimental results. Moreover, this also led to larger frequencies obtained from the numerical simulations than those obtained from the experiments. Figure 17: Comparison of experimental data and simulation results of the slug frequency at a superficial liquid velocity \(V_{sl}\) = 0.5 m/s. Figure 18: Comparison of experimental data and simulation results of the slug frequency at a superficial gas velocity \(V_{sg}\) = 0.5 m/s. As shown in Figures 19 and 20, the maximum error between the slug velocity obtained by the numerical simulation and the experimentally obtained slug velocity was within 10%. The slug velocity obtained from the simulation was higher than the experimentally obtained slug velocity because the surface tension of the gas-liquid was constant in the numerical simulation, which increased the slug velocity. Furthermore, the incompressible model used in the numerical simulation also influenced the numerical results. Figure 19: Comparison of experimental values and simulation data of the slug velocity at a superficial liquid velocity \(V_{sl}=1\) m/s. Figure 20: Comparison of experimental values and simulation data of the slug velocity at a superficial gas velocity \(V_{sg}=1\) m/s.