# Simulation of Two-Phase Flow of Shotcrete in a Bent Pipe Based on a CFD-DEM Coupling Model
## 1 Introduction  
Significant progress has been made in the theoretical and equipment research fields and the process of improvement and development of shotcrete applications. The wet-concrete spraying technology has been widely promoted and applied to above-ground and underground support structures [1; 2; 3]. Pumping is the most important pipeline transportation method for wet shotcrete in coal mines. The movement of the shotcrete material is characterized by the interactions among the particles and between the particles and pipe wall during pneumatic conveying in the rubber hose after pumping. In addition, determining the shotcrete material motion, material blockage, and wear of the bent pipe in the pipeline transportation process in a field test is difficult [4; 5; 6]. Thus, the pneumatic conveying process in the section of spraying concrete requires further investigation. In the wet-shotcrete support project, the concrete material is usually pumped and pneumatically conveyed to the working face by a wet spraying machine (Figure 1). Pneumatic conveying is affected by many factors such as workability of concrete, environmental conditions, pipe assembly, actual pressure, and pump outlet speed; therefore, the field situation is more complex. Identifying the relevant factors, introducing them into numerical models, and evaluating their impacts on conveying performance are crucial andchallenging. Therefore, the numerical simulations do not focus on the entire wet spraying system; instead, they are limited to the local area of the concrete flow, i.e., the piping units. The continuous spraying of underground concrete causes the bending deformation of the rubber hose. The impact of the shotcrete material on the bent pipe, their collision, and the shotcrete accumulation have adverse effects on the long-term use of the rubber hose and its spraying performance. Therefore, the movement characteristics of shotcrete material in the pipeline during pneumatic conveying must be studied. Owing to the rapid advances in computer technology, numerical simulations have been widely used in the pneumatic conveying field. The discrete element method (DEM) is a numerical method that is used to simulate a great number of mutually interacting particles based on their equation of motion in a system. The DEM is usually coupled with computational fluid dynamics (CFD) in the study of gas-solid two-phase flows [7; 8; 9; 10; 11; 12]. For example, [PERSON] [13] combined the CFD and DEM to simulate numerically the pneumatic conveying process in a horizontal channel and to study the effects of the wall roughness and random effects of turbulence on the particle diffusion. [PERSON] [14] used the CFD-DEM to simulate numerically the flow characteristics of gas-solid two-phase flows in a pneumatic conveying pipe with a bent section. Moreover, [PERSON] [15] established a transport equation for the interface of gas-liquid coupled multiphase flow and used the numerical simulation software Fluent to simulate the velocity and pressure distributions at the interface between slug and gas-liquid two-phase flows. Shotcrete is a mixture of cement slurry and has aggregates with a certain viscosity. [PERSON], [PERSON], and [PERSON] [16; 17; 18] used the DEM to model concrete materials with good accuracy. Moreover, [PERSON] [19] and [PERSON] [20] established DEM models for self-compacting concrete in the filling state of the rock-fill structure and verified the model with experiments; in addition, they studied the workability and feasibility of the self-compacting concrete. [PERSON] [21] developed a hard-core soft-shell model to simulate the concrete flow and determined the relationships among the main parameters of the mechanical model and the macroscopic rheological properties of the concrete numerical model; however, the concrete material was greatly simplified in the simulations.