## 4 Results and Discussion
As with the angle of \(5^{\circ}\), at the gas velocity of 9.89 m/s, the liquid accumulation of 50 mL in the pipe does not cause slug flow. Slug flow in \(t_{1}\) to \(t_{3}\), \(t_{3}\) to \(t_{4}\) completed a periodic movement, from slug entering the inclined pipe to slug discharging, and then to a new slug entering. Figure 8: Slug flow pipeline pressure distribution \(5^{\circ}\): (**a**) flow image in the pipeline at point A and \(P_{4}\) at time \(t_{1}\); (**b**) flow image in the pipeline at point A and \(P_{4}\) at time \(t_{2}\); (**c**) flow image in the pipeline at point A and \(P_{4}\) at time \(t_{3}\); (**d**) flow image in the pipeline at point A and \(P_{4}\) at time \(t_{4}\). When the gas velocity is 9.89 m/s, the slug flow image with the liquid accumulation of 300 mL is shown in Figure 10. At \(t_{1}\), the liquid at point A gathers to form a liquid bridge, making preparations for the slug head to enter the pipeline, as displayed in Figure 10a. At \(t_{2}\), the head of the slug entered the upward inclined pipe, as with the model of \(t_{2}\) established in Section 3. The liquid film area of the slug is at point A, while the upper liquid slug in the inclined pipe begins to dissipate, as presented in Figure 10b. At \(t_{3}\), part of the liquid flows out of the inclined pipe, and the remaining liquid flows back along the pipe, as shown in Figure 10c. The liquid re-aggregates at point A in \(t_{4}\), as exhibited in Figure 10d. In addition, due to the direction of the liquid backflow being opposite to the gas in the inclined pipe, a small liquid slug appears in the convective extrusion. Figure 10: _Cont._  
Figure 9: Verification of slug flow pressure model with an inclination of 10\({}^{\circ}\). When the angle is 15\({}^{\circ}\) and the gas velocity is 9.89 m/s, the liquid accumulation volume in the pipe are 50 mL and 80 mL without slugging flow, and the deviation between the experiment and the model is within \(\pm\)20%, as displayed in Figure 11. Compared with 5\({}^{\circ}\) and 10\({}^{\circ}\), the pressure difference line slope of different liquid accumulation volume in 15\({}^{\circ}\) pipe is larger, indicating that the pressure change at point A and \(P_{4}\) are more violent due to the increase in the angle. As with the above two angles, the pressure difference of slug flow in the pipe decreases first and then increases, which corresponds to the slug flow cycle of enter, discharge, and re-enter. Figure 12a-d are the slug flow images in a liquid accumulation of 300 mL pipe with an inclination angle of 15\({}^{\circ}\) and a gas velocity of 9.89 m/s. From \(t_{1}\) to \(t_{4}\), the liquid accumulates twice at point A and flows out once in the inclined pipe. The movement form is consistent with the pressure model established in Section 3. The variation in the pressure difference at an inclination of 20\({}^{\circ}\) in Figure 13 can be divided into descending and ascending processes. Moreover, the occurrence of these two processes is associated with the outflow of slug in the inclined pipe. It can be seen from the experiment that when the liquid volume is 50 mL, 80 mL, and 100 mL, slug flow does not occur in the pipe with an inclination of 20\({}^{\circ}\). Comparing the experiment and model calculation results at this angle, the error range is within \(\pm\)20%, as shown in Figure 7.0 During the descent, part of the liquid slug is discharged from the pipeline, which reduces the blockage in the inclined pipeline and makes the pressure difference smaller. In the ascending process, due to the inclination of the pipeline, some liquid slugs flow back under gravity and collide with the gas. This increases the pressure at \(P_{4}\) and then the pressure difference is less than that at \(t_{1}\). Figure 7.1 Verification of slug flow pressure model with an inclination of 15\({}^{\circ}\).