# Prediction of Abrasive and Impact Wear Due to Multi-Shaped Particles in a Centrifugal Pump via CFD-DEM Coupling Method

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Geometric Model and Mesh

^{3}/h with a head of 8.3 m, under a 1450 rpm rotation speed. The diameters of the pump inlet, impeller, and pump outlet are 115 mm, 190 mm, and 100 mm, respectively. The polyhedron meshes of the computational domain and five prism layers at the wall boundaries (see Figure 1b) were created. To ensure the slight influence of mesh number on the results, the pump head was employed to test the mesh independence, as shown in Table 1. It is apparent from this table that there is a slight change in the pump head when the mesh number is bigger than 1,255,663. Thus, the mesh number was set as 1,255,663 for subsequent simulations.

#### 2.2. Governing Equations of Solid-Liquid

_{f}, x, u, p, and μ

_{eff}are the time, fluid density, coordinates, fluid velocity, fluid pressure, and fluid effective viscosity, respectively. The vectors

**g**,

**F**

_{drag}

**F**

_{sl}, and

**F**

_{pg}denote the gravity and particles-liquid interaction forces, namely the drag force, Saffman’s lift force, and pressure gradient force. Furthermore, α

_{f}is the fluid volume fraction in each cell, which is also called porosity or void fraction. All the particle centers are assumed to be located in a selected computational cell, and α

_{f}can be estimated through the equation:

_{p}

_{,i}denotes the volume of particle i within the computational cell. V

_{cell}is the cell volume.

**I**denotes the moment of inertia of the particle. The d

**v**/dt and d

**ω**/dt are translational and angular acceleration of the particle. The vector

**F**

_{c}denotes the collisional forces of a particle with other particles or wall boundaries. The vector

**T**

_{c}is the sum of contact torques produced by particle-particle and particle-wall collision, and

**T**

_{f}denotes the particle torque produced by the surrounding liquid.

#### 2.3. Particle and Wear Model

_{e}denotes the equivalent spherical diameter, and ρ

_{p}denotes the particle density. Sphericity is the most commonly used measure accounting for the shape of a non-spherical particle. It can be defined as:

_{s}and S

_{p}, respectively, denote the superficial areas of a sphere and a non-spherical particle. Furthermore, the volume concentration of these particles above is set as 2%, and particles are produced in the vicinity of the pump inlet with arbitrary positions and orientations. The Hertz-Mindlin contact model [13] and a soft-sphere model [14] are applied to model the collisional forces of a particle with other particles or wall boundaries in DEM. Table 3 summarizes the coefficients of interactions included in the applied models. Moreover, the abrasive wear in this work is modeled using the Archard wear model [15], while the erosive wear is modeled using the Oka wear model [16,17], which has been widely adopted.

#### 2.4. Liquid Phase Setup

^{−3}Pa·s and 998 kg/m

^{3}, respectively. Moreover, the pump walls were determined as a no-slip boundary condition, and the two-Layer all y+ wall treatment was adopted as a wall function. The pump inlet was defined as a velocity inlet with a constant profile of 1.829 m/s, and the pump outlet was defined as a pressure outlet. The residual value of each variable for convergence was determined as 10

^{−4}. In addition, the pump head fluctuations as a function of physical time were monitored in Figure 3. It is apparent that pump head fluctuations achieve stability with a regular vibration at about t = 0.24 s, which indicates a spatial convergence.

## 3. Results

#### 3.1. Validation

#### 3.2. Particle Distribution

#### 3.3. Wear of Flow Parts

#### 3.4. Effect of Particle Shape

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Particle DEM and geometrical models: (

**a**) tetrahedron, (

**b**) hexahedron, (

**c**) octahedron, (

**d**) dodecahedron.

**Figure 5.**Trajectory and distribution of different particles: (

**a**) tetrahedron, (

**b**) hexahedron, (

**c**) octahedron, (

**d**) dodecahedron, and (

**e**) sphere.

**Figure 6.**Overall impact wear rate of flow parts as a function of time: (

**a**) tetrahedron, (

**b**) hexahedron, (

**c**) octahedron, (

**d**) dodecahedron, and (

**e**) sphere.

**Figure 7.**Overall abrasive wear rate of flow parts as a function of time: (

**a**) tetrahedron, (

**b**) hexahedron, (

**c**) octahedron, (

**d**) dodecahedron, and (

**e**) sphere.

**Figure 12.**Regression equation for particle sphericity: (

**a**) relative impact wear rate and (

**b**) relative abrasive wear rate.

Mesh Number | Pump Head (m) | Deviation (%) |
---|---|---|

650,584 | 8.47 | |

833,197 | 8.79 | 3.83 |

1,042,510 | 8.87 | 0.92 |

1,255,663 | 8.89 | 0.23 |

1,349,142 | 8.90 | 0.15 |

Tetrahedron | Hexahedron | Octahedron | Dodecahedron | Sphere | |
---|---|---|---|---|---|

ξ | 0.709 | 0.802 | 0.829 | 0.923 | 1 |

D_{e} (mm) | 1 | 1 | 1 | 1 | 1 |

ρ_{p} (kg/m^{3}) | 2600 | 2600 | 2600 | 2600 | 2600 |

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

Restitution | 0.5 | 0.7 |

Static friction | 0.3 | 0.15 |

Rolling friction | 0.01 | 0.01 |

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**MDPI and ACS Style**

Tang, C.; Yang, Y.-C.; Liu, P.-Z.; Kim, Y.-J.
Prediction of Abrasive and Impact Wear Due to Multi-Shaped Particles in a Centrifugal Pump via CFD-DEM Coupling Method. *Energies* **2021**, *14*, 2391.
https://doi.org/10.3390/en14092391

**AMA Style**

Tang C, Yang Y-C, Liu P-Z, Kim Y-J.
Prediction of Abrasive and Impact Wear Due to Multi-Shaped Particles in a Centrifugal Pump via CFD-DEM Coupling Method. *Energies*. 2021; 14(9):2391.
https://doi.org/10.3390/en14092391

**Chicago/Turabian Style**

Tang, Cheng, You-Chao Yang, Peng-Zhan Liu, and Youn-Jea Kim.
2021. "Prediction of Abrasive and Impact Wear Due to Multi-Shaped Particles in a Centrifugal Pump via CFD-DEM Coupling Method" *Energies* 14, no. 9: 2391.
https://doi.org/10.3390/en14092391