# Simulation of Two-Phase Flow of Shotcrete in a Bent Pipe Based on a CFD-DEM Coupling Model
## 3 Geometric Model and Meshes  
Rubber hoses provide flexibility to the pneumatic conveying process of concrete materials. However, bent pipe structures with different angles suffer from internal wear and unstable particle movement. The geometric model in Figure 3 consists of the horizontal pipes L\({}_{1}\) and L\({}_{2}\) and the bent-pipe structure \(R\). The definite mass flow rate can be obtained based on the horizontal pipe L\({}_{1}\). The bend angles were set to 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), and 150\({}^{\circ}\). For the particle phase, the self-developed DEM code is merged into CFD, a coupling scheme is used between the CFD and DEM, and the explicit time integration method is used to calculate the motions of particles in the DEM. A compromise between efficiency and accuracy is made: spherical particles with diameters of 5 and 8 mm were used to represent the coarse aggregate covered with cement slurry. Based on field tests and related reports in the literature [37; 38], the gas flow velocity was set to 64 m/s, and the initial particle velocity was 1.5m/s; subsequently, the particle was accelerated to a stable velocity for relatively stable flow. The applied particle parameters and operating conditions are listed in Table 1 [39; 40; 41; 42].  
The number of meshes has a great influence on the accuracy of the transient simulation results of the airflow field. Therefore, mesh independence studies are necessary to ensure that both discretization and rounding errors are within acceptable limits and that the mesh used does not significantly affect the simulation results. Three discrete grids with different densities are generated by ICEM, which are denoted as fine meshes, better meshes, and medium meshes, respectively. In all three cases, the mesh quality is above 0.5.  
Using these three meshing cases as shown in Figure 3 (A--A section), the air velocities were compared and analyzed. Figure 4 shows the comparison results of velocity at cross  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Index** & **Unit** & **Value** \\ \hline \multirow{8}{*}{DEM} & Pipe diameter D & m & 0.06 \\  & Horizontal tube length L\({}_{1}\) & m & 5 \\  & Horizontal tube length L\({}_{2}\) & m & 2.5 \\  & Curvature radius of bent pipe R & m & 0.2 \\  & Coefficient of static friction & - & 0.68 \\  & Coefficient of rolling friction & - & 0.15 \\  & Coefficient of restitution & - & 0.55 \\  & Density (particles) & kg/m\({}^{3}\) & 2300 \\  & JKR surface energy & J & 16 \\  & Poisson ratio & - & 0.25 \\  & Time step & s & \(2\times 10^{-5}\) \\  & Density (air) & kg/m\({}^{3}\) & 1.225 \\  & Viscosity & kg/(m\(\cdot\)s) & 1.7894 \(\times 10^{-5}\) \\ CFD & Pressure outlet & Pa & 101325 \\  & Time step & s & \(2\times 10^{-3}\) \\  & Viscous model & - & k-epsilon model \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic parameters.  
Figure 3: Geometric model and grids of a longitudinal section of bent pipe (bend angle of 90\({}^{\circ}\)).  
sections of the roadway. It can be observed that the simulation results of airflow velocity using three different kinds of grids show similar variation trends. The velocities using better meshes were very close to the values using fine meshes, but the results using medium meshes were quite different from the results using the other two different meshes. Therefore, it can be considered that better meshes have already met the requirement of meshing independence.