# Pressure Study on Pipe Transportation Associated with Cement Coal Gangue Fly-Ash Backfill Slurry
## 2 Materials and Methods
\[Re=\frac{vD\rho}{\mu} \tag{1}\]  
where \(Re\) is the Reynolds number, \(v\) is the conveying velocity, m/s; \(D\) is the diameter of the pipeline, m; \(\mu\) is the slurry relative viscosity, Pa-s and \(\rho\) is the slurry density, kg/m\({}^{3}\). Figure 3: This relation of the shear stress to shear rate on the various solid concentration among 76.05%, 78.05% and 80.05%. Figure 2: The instruments that uses in the slurry rheological tests: (**a**) and the RheoWin software Rotational rheometer Rheolab QC and RheoWin software (Anton Paar Company Ltd., Ostfidern, Germany); (**b**) six bladed vane rotors. The CGFB slurry workable test show the density of the CGFB ranges between 1920 to 2100 kg/m\({}^{3}\) and the relative viscosity ranges from 1.64 to 1.78 Pa-s. Thus, the average density of 2000 kg/m\({}^{3}\) and the average relative viscosity of 1.71 pa-s were employed to calculate the Reynolds number. The average value of the density and the CGFB slurry relative viscosity were obtained from the experimental study:  
\[Re=\frac{vD2000}{1.71}<2100 \tag{2}\]  
\[D<\frac{1.8}{v} \tag{3}\]  
Referring to Equation (3), awe assume the slurry pipeline diameter is 150 mm; under this condition, the CGFB slurry transportation sustains the laminar flow when the conveying velocity is up to 12 m/s, which means that most cases of CGFB slurry transportation belong to the category of the laminar layer. Based on the coal mine backfilling currently, the slurry conveying velocity ranges 1.6-2.0 m/s in site-practice. Thus, the study was made with the assumption that the CGFB conveying velocity ranges from 1.4 to 2.2 m/s. Within this range, the slurry definitely belongs to the laminar state. A simulation method was used to investigate the CGFB slurry conveying velocity impacts in a straight pipe and 90\({}^{\circ}\) elbow pipe based on the different inlet velocities. The CGFB flow characteristics in the pipe transportation of both the straight pipe and the bend were obtained at the various velocity ranges from 1.4 m/s to 2.2 m/s with increments of 0.2 m/s. The structuration grids of the straight pipe and elbow pipe were established in the ICEM CFD (Ansys Corporation, Canonsburg, PA, USA) and then the finished mesh file was loaded into the ANASYS R15.0 software (Ansys corporation, Canonsburg, PA, USA). The CGFB slurry pipe transportation laboratory experimental test requires the minimum interval distance between the two monitors is 15,000 mm. The minimum distance is essential to reduce the data distribution because of the slurry movement. Thus, in the CFD simulation, the straight pipe was model with a length of 17,000 mm. I think the length is enough for the flow fully developed. The length and diameter of the straight pipe were considered as 17,000 mm and 150 mm, respectively. On the 90\({}^{\circ}\) elbow pipe construction, the radius was set as 600 mm and an extension for a length of 1,600 mm was developed on both the inlet and outlet parts. Figure 4 shows the geometry of the constructed straight pipeline and elbow pipeline. The material of pipeline was considered to be mild steel [17]. The validation of the model was obtained by simulating the steady laminar forced convection of water in a horizontal tube. The mesh independence was examined with different mesh sizes obtained by refining a coarser size until the results were unchanged.