# Simulation of Two-Phase Flow of Shotcrete in a Bent Pipe Based on a CFD-DEM Coupling Model
## 4 Calculation Results and Analysis
### Flow Field of Particle Phase  
Figure 10 presents the particle velocity and particle distribution within the pipe under the action of a high-pressure gas flow. The particles within the horizontal pipe flow in a suspension state, and the particle packing density is not uniform. Under the action of a high-pressure gas flow, the particles have a higher density when they are just picked up by the gas flow. With the continuous generation of particles in the inlet, the pipe cross-section decreases, and the windward side of the particles increases. In addition, the packing density decreases continuously as the particles move forward. After entering the bent pipe, the particles accumulate near the midline of the outside area of the bent pipe; they form a rope-like structure (particularly in the 30\({}^{\circ}\) and 90\({}^{\circ}\) bent pipes), which is usually called \"the particle rope\" [43]; this typical phenomenon in gas-solid two-phase flows in bent pipes is mainly due to the inertia among particles and the inelastic collisions between the particles and wall surface. Under the actions of the subsequent turbulence and secondary flows, the particle rope starts to disperse gradually. The comparison of the particle flow characteristics in the three bent pipes shows that when passing through the 150\({}^{\circ}\) bent pipe, the particles disperse under the action of turbulence before forming the particle rope; this indicates the strong effect of the different angles of the bent pipes on the dispersion of the particle rope. Furthermore, after the particles pass through the bent pipe structure, their velocities recover at different times. The particles accumulate significantly later for a bend angle of 30\({}^{\circ}\) than for the other bend angles. Hence, the greater resistances among the particles and between the particles and pipe wall causes the particle velocities to recover more slowly. In addition, the particle accumulation at a bend angle of 30\({}^{\circ}\) is more severe and may block the pipe. Figure 7: Global distribution of static pressure in pipelines with different bend angles. Figure 8: Distribution of static pressure in bent pipes with different bend angles. (**a**) \(z=0\) distribution cloud map of global static pressure in bent pipes with different bend angles. (**b**) Line chart of the global distribution of static pressure with respect to distance. Figure 11a-c shows the variations in the velocities of individual concrete particles of different sizes in pipes with different bend angles over time. The particles comprise coarse  
Figure 10: Distributions of moving concrete particles in 30\({}^{\circ}\), 90\({}^{\circ}\), and 150\({}^{\circ}\) bent pipes. Figure 9: Distribution of gas phase velocities in 30\({}^{\circ}\) and 45\({}^{\circ}\) bent pipes. aggregates with diameters of 5 and 8 mm (their surfaces are covered with cement slurry) and agglomerates of particles of different sizes. The values of 10 particles of each type were averaged to eliminate the accidental effect of particle sizes. According to Figure 11a-c, the particle velocity suddenly changes behind the bent pipe, and the 5 mm particles exhibit a greater acceleration than the other two particle types; hence, they enter the bent pipe section first. This is because although the particle with a large particle size has a larger area under the action of air, it can obtain more acceleration, but the resistance of air to particles is relatively high. Obviously, the resistance has a greater impact on the particle at an air velocity of 64 m/s. The different bent pipe structures have great effects on particle velocity. The particle velocity decreases by approximately 73% behind the 30\({}^{\circ}\) bent pipe and by approximately 15-35% behind the 90\({}^{\circ}\) and 150\({}^{\circ}\) bent pipes. This is because the particle in the 30\({}^{\circ}\) bent pipe is not affected by the gas phase, and its velocity continues to decrease.