## 1 Introduction
Later scholars mostly studied slug flow in pipes under general conditions. However, it also provides theoretical guidance for the pressure study of slug flow under ZNLF. S slug flow is the most common flow pattern in pipeline transmission [30]. Numerous studies have attempted to predict the slug flow in the two-phase flow pipes. [PERSON] and [PERSON] [31] proposed a slug flow prediction model of gas-liquid flow based on the observation. The slug body velocity, the slug head velocity, the liquid film velocity, the slug length, the liquid film area behind the slug, and the surface shape of the mixing area can be predicted. It was matched with the experimental data of [PERSON] and [PERSON] [32]. [PERSON] [33] established the slug flow cell model of and predicted the phase fraction and pressure gradient. However, that model depends on some key assumptions and the choice of four closure rules. Then, [PERSON] [34] discussed these basic issues and emphasized their limitations by comparing them with the existing data. On this basis, the flow assumption of the model was explored and improved. [PERSON] and [PERSON] [35] established a unified  
Figure 1: Formation of slug flow in transmission pipeline. model of slug length and slug body liquid holdup as a function of inclination angle. In contrast to experimental data, this model can be used to predict slug flow behavior in upward pipelines. The above slug flow models are all established based on steady-state conditions. [PERSON] et al. [36] presented a transient slug flow prediction model. The model combined the single-cell slug flow model and the numerical transient two-fluid models and applied the closure law to the description of the physical characteristics of slug flow. Following that, many studies focused on the establishment of the hydrodynamic model of slug flow. [PERSON] et al. [37] placed a hydrodynamic prediction model of slug flow in a horizontal pipe. PDVSA INTEVEP experimental data were used to evaluate the model and the absolute average relative error of the model in predicting the pressure drop of slug flow was less than 6%. [PERSON] et al. [38] established a unified hydrodynamic model based on slug flow hydrodynamics to predict the flow pattern transition, pressure gradient, liquid holdup, and slug characteristics of gas-liquid two-phase pipe flow at different angles. The model made significant inroads in eliminating discontinuities in closed relationships. [PERSON] et al. [39; 40] established a hydrodynamic model of slug flow by a slug element. On this basis, a heat transfer model was deduced. The model was verified by experimental data of different void fraction, pressure drop, and two-phase heat transfer coefficient. In some recent studies, the experimental and visual study of slug flow has played a prominent role. [PERSON] et al. [41] conducted a non-invasive measurement of slug flow vibration of a curved flexible riser. The vibration displacement and gas-liquid flow in the pipe were observed. They found that the vibration caused by the slug flow mainly occurred on the curvature surface of the flexible riser. The fluctuation of the slug flow pressure in the pipeline participated in the dynamic response of the riser, and the vibration frequency was also observed in the pressure fluctuation, which was reflective of the fluid-structure interaction. [PERSON] and [PERSON] [42] investigated the pressure drop characteristics of slug flow, using air and low-viscosity mineral oil in a pipe with an inner diameter of 4 cm. Combined with the visual image and pressure drop oscillation time, the relevant flow parameters related to slug flow were measured, and the theoretical slug flow model for predicting the total pressure gradient of slug unit was established by using the empirical correlation of slug flow parameters. [PERSON] et al. [43] visualized the characteristic parameters (velocity, length, and liquid film thickness) and pressure drop of slug flow in a narrow rectangular channel.