# CFD-DEM Simulation for the Distribution and Motion Feature of Solid Particles in Single-Channel Pump

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Computational Domain and Meshing

^{3}/h, head H = 20 m, rotational speed n = 1800 rpm, inlet diameter D

_{1}= 50 mm, impeller diameter D

_{2}= 138 mm, pump outlet diameter D

_{3}= 110 mm. The polyhedron meshes are generated in the entire computational domain, as shown in Figure 1a. In addition, for the turbulent flow simulation, an appropriate resolution of the near-wall region is needed, and 5 prism layers are created next to all the wall surfaces (see Figure 1b) to improve the accuracy of the flow solution. Table 1 shows the results of the mesh dependency test for the head of the pump. It shows that the pump head remains steady when the grid number exceeds 535,665. Given the great amount of CFD-DEM coupling calculations, relatively few meshes are significant for simulation efficiency in the subsequent optimization process. Hence, the optimal number of mesh cells was determined as 535,665. As a kind of real-mass particle, the acceleration of gravity (g = 9.81 m/s

^{2}) is also taken into consideration, with its direction opposite to the y-axis.

#### 2.2. Governing Equations

_{f}is the fluid density, u is the fluid velocity, p is the pressure of the fluid, μ

_{eff}is the effective viscosity, x is the coordinates,

**g**is the acceleration of gravity, and

**F**

_{s}is the drag force between the particles and the liquid. ${\alpha}_{f}$ represents the porosity around the particle, which can be calculated as:

_{p,i}represents the volume of particle i in a CFD cell, n represents the number of particles inside the cell, V

_{cell}represents the volume of the cell.

**F**

_{c}represents the contact force,

**F**

_{drag}represents fluid drag force, m is the particle mass, and

**I**is the moment of inertia of the particle. d

**v**/dt is the translational acceleration of the particle, d

**ω**/dt is the angular acceleration of the particle,

**T**

_{c}is the contact torque, and

**T**

_{f}is the torque caused by the fluid.

#### 2.3. CFD-DEM Coupling

#### 2.4. Particle Model

^{3}, and the particles were selected in a diameter of 3.0 mm, while the particle flow rate was set to 4000 particles/s at the pump inlet. When the particles contact each other or solid boundaries, their momentum and energy are exchanged. This necessitates a DEM phase interaction model to describe the particle–particle and particle–wall interactions. In this model, the Hertz–Mindlin contact model [17] was adopted to solve the contact forces of particles, which were described by a soft-sphere model [18]. The Hertz–Mindlin contact model is the standard model that was used for describing the particle–particle and particle–wall interactions. The collision parameters used in the models are summarized in Table 2.

#### 2.5. Fluid Phase Setup

^{−3}Pa·s, ρ = 998 kg/m

^{3}). The pump walls as well as particle surfaces were defined as no-slip walls, and the pump outlet was defined as a pressure outlet with p = 1.0bar. At the velocity inlet, a constant profile was specified. The absolute convergence criterion for the calculated residuals was set as 10

^{−4}by default, together with monitoring the variations in average pressure at the pump inlet during the computations, as shown in Figure 4.

## 3. Results and Discussion

#### 3.1. Validation

#### 3.2. Mixed-Sized Particle

#### 3.2.1. Particle Trajectory and Distribution

#### 3.2.2. Particle Velocity Distribution

#### 3.2.3. Particle Contact Force Distribution

#### 3.3. Different-Shaped Particles

#### 3.3.1. Particle Trajectory and Distribution

#### 3.3.2. Velocity Field of Liquid Phase

#### 3.3.3. Collision Between Particle and Wall

## 4. Conclusions

- Particles tended to maintain a steady trajectory towards the volute that corresponds with the shape of the impeller blade. The smaller particles had a much more uniform distribution in the passages of the impeller and volute than the larger ones.
- The smaller-sized particles possessed a greater velocity distribution range and velocity peak but a smaller contact force compared with the larger particles. Besides this, there were apparent slip velocities between the liquid and solid-phase flows inside the pump.
- The trajectories of the cylindrical and pie-shaped particles in the impeller were close to the pressure side. However, the spherical particles were dispersed more uniformly in the impeller and volute than the other two cases.
- The pie-shaped particles had the most severe collisions, and the spherical particles had the least in total. The hub and shroud wall suffered a minor contact force, but the blade and volute wall both sustained a considerable contact force.
- In order to reduce wear, the blades and volute can be designed to have more wear resistance than other parts. Moreover, before entering the pump, the particles or foreign bodies can be made as round as possible to reduce wear.
- According to the limited particle model and flow parameters in this research, the other shapes and rigidity of particles with different fluid viscosities and other fluid properties could be factored into the CFD-DEM coupling method for future research.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Particle shape models: (

**a**) cylinder particle, (

**b**) pie-shaped particle, (

**c**) spherical particle.

**Figure 5.**Comparison of the total head between the present simulation and the experimental data [12].

**Figure 10.**Trajectory and distribution of three distinct-shaped particles (

**a**) cylinder practice; (

**b**) pie-shaped particle; (

**c**) spherical particle.

**Figure 11.**Relative velocity field of the liquid phase at the mid-span of the impeller for the three shape cases: (

**a**) cylinder particle, (

**b**) pie-shaped particle, (

**c**) spherical particle.

Grid Number | Head [m] | Deviation [%] |
---|---|---|

250,493 | 18.09 | |

331,976 | 18.26 | 0.93 |

427,510 | 18.37 | 0.60 |

535,665 | 18.41 | 0.22 |

689,142 | 18.43 | 0.11 |

Collision Coefficient | Particle-Particle | Particle-Wall |
---|---|---|

Restitution | 0.5 | 0.5 |

Static friction | 0.61 | 0.8 |

Rolling friction | 0.01 | 0.01 |

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**MDPI and ACS Style**

Tang, C.; Kim, Y.-J.
CFD-DEM Simulation for the Distribution and Motion Feature of Solid Particles in Single-Channel Pump. *Energies* **2020**, *13*, 4988.
https://doi.org/10.3390/en13194988

**AMA Style**

Tang C, Kim Y-J.
CFD-DEM Simulation for the Distribution and Motion Feature of Solid Particles in Single-Channel Pump. *Energies*. 2020; 13(19):4988.
https://doi.org/10.3390/en13194988

**Chicago/Turabian Style**

Tang, Cheng, and Youn-Jea Kim.
2020. "CFD-DEM Simulation for the Distribution and Motion Feature of Solid Particles in Single-Channel Pump" *Energies* 13, no. 19: 4988.
https://doi.org/10.3390/en13194988