# Validation of a Discrete Element Method (DEM) Model of the Grinding Media Dynamics within an Attritor Mill Using Positron Emission Particle Tracking (PEPT) Measurements

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Experimental Setup: Attritor Mill HD01 and Positron Emission Particle Tracking (PEPT)

^{3}. Information on the mill dimensions and grinding media are summarised in Table 1. During the experiments, the temperature inside the mill was controlled by circulating water at a constant temperature of 10 °C through a cooling jacket.

#### 2.2. Positron Emission Particle Tracking (PEPT)

#### Data Processing: Tracer Location Reconstruction

#### 2.3. DEM and Simulation Conditions

^{6}Pa are used, rather than realistic values in the order of 10

^{10}–10

^{11}Pa, with little effect on the simulation results. Since, a wide range of velocities exists in the attritor an average value of the coefficient of restitution equal to 0.7 was selected. This fairly high value is justified assuming that the collisions between the grinding media are not expected to be very dissipative in absence of powder. The same value for the coefficient of restitution is used for both media-media and media-wall contacts. The static friction was considered as a parameter to adjust against PEPT data to obtain the correct representation of the media flow field. Three values of static friction coefficient were used (0.15, 0.3 and 0.5) and the same coefficient was used for both media-media and media-wall contacts. The rolling friction coefficient of the grinding media was set equal to zero. The latter parameter always acts to oppose rolling, however, its effect can be neglected when the motion of spherical particles, such as the grinding media, is considered [3,22,45,46,47]. During the PEPT experiments the tracer location was measured on average every 30 milliseconds (approximately 35 measurements per second) therefore, the same characteristic time was used in the DEM simulations to sample the particle data.

#### DEM Data Postprocessing Using the Coarse Graining Method

## 3. Results and Discussion

#### 3.1. Effect of Impeller Speed Evaluated from PEPT Experiments

#### 3.2. Effect of the Impeller Clearance Evaluated from PEPT Experiments

#### 3.3. Effect of the Media Loading Evaluated from PEPT Experiments

## 4. Validation of a Static Friction Adjusted-DEM Model by Using Positron Emission Particle Tracking (PEPT) Measurements

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Experimental rig: (

**a**) attritor mill HD1 (Union Process, Akron, OH, USA) with a schematic of the vessel showing the pin positions for the clearance of 12.7 mm (1/2 inch) and (

**b**) PEPT scanner (University of Birmingham, Birmingham, UK).

**Figure 2.**Example for a PEPT raw dataset representing the tracer particle position along the Z direction (vertical axis) over time for the impeller speed of 300 rpm.

**Figure 4.**PEPT dimensionless velocity magnitude (v/v

_{tip}) at the different impeller speeds of 300 rpm, 450 rpm and 600 rpm. Test case using the bead loading of 2.4 kg and the bottom clearance of 12.7 mm.

**Figure 5.**PEPT velocity vector maps for the impeller speed of 300 rpm, 450 rpm and 600 rpm highlighting the recirculation patterns within the attritor. Test case using the bead loading of 2.4 kg and the bottom clearance of 12.7 mm.

**Figure 6.**PEPT normalised tracer occupancy plot at the impeller speed of 300 rpm, 450 rpm and 600 rpm. Test case using the bead loading of 2.4 kg and the bottom clearance of 12.7 mm.

**Figure 7.**PEPT dimensionless velocity magnitude (v/v

_{tip}) for two values of clearance: 12.7 mm and 19 mm. Test case using the bead loading of 2.4 kg and the impeller speed of 300 rpm.

**Figure 8.**PEPT velocity vector maps for two values of clearance: 12.7 mm and 19 mm. Test case using the bead loading of 2.4 kg and the impeller speed of 300 rpm.

**Figure 9.**PEPT normalised tracer occupancy plot for two values of clearance: 12.7 mm and 19 mm. Test case using the bead loading of 2.4 kg and the impeller speed of 300 rpm.

**Figure 10.**Axial tracer position (Z) as function of the time of the PEPT experiments for two impeller clearance values: (

**a**) 12.7 mm and (

**b**) 19 mm. The impeller position is represented by the red straight line.

**Figure 11.**PEPT dimensionless velocity magnitude (v/v

_{tip}) for two bead loading: 2.4 kg and 3.0 kg of media. Test case using the clearance of 19 mm and the impeller speed of 600 rpm.

**Figure 12.**PEPT normalised tracer occupancy plot for two bead loading: 2.4 kg and 3.0 kg of media. Test case using the clearance of 19 mm and the impeller speed of 600 rpm.

**Figure 13.**Histogram of the velocity magnitude for the attritor mill and for three sub-domains of the mill: top region, middle region and bottom region. PEPT test case using the bead loading of 2.4 kg, the impeller clearance of 19 mm and the impeller speed of 300 rpm.

**Figure 14.**Probability density functions (pdf) of the velocity magnitude calculated for the top, middle and bottom regions. Comparison between PEPT data and DEM simulations as function of the static friction coefficient for the impeller speed of (

**a**) 300 rpm and (

**b**) 600 rpm.

**Figure 15.**Comparison of the velocity flow field for DEM simulations and PEPT data at the impeller speed of (

**a**) 300 rpm and (

**b**) 600 rpm.

**Figure 16.**Velocity magnitude along the dimensionless attritor height (Z/H) for three dimensionless radial positions (r/D: 0.2, 0.3, 0.4). Comparison between DEM results and PEPT data at the impeller speed of (

**a**) 300 rpm and (

**b**) at 600 rpm.

Dimensions (mm) | Material | |
---|---|---|

Mill chamber | Yttria-stabilised zirconia | |

Height | 164 | |

Diameter | 90 | |

Impeller arms | Yttria-stabilised zirconia | |

Diameter | 66 | |

Grinding media | Yttria-stabilised zirconia | |

Diameter | 5 |

N | Impeller Speed (rpm) | Bead Loading (kg) | % Chamber Filling (volumetric) | Bottom Clearance (mm) |
---|---|---|---|---|

1 | 600 | 3.0 | 77 | 12.7 |

2 | 300 | 3.0 | 77 | 12.7 |

3 | 300 | 3.0 | 77 | 15.9 |

4 | 300 | 2.4 | 61 | 19 |

5 | 600 | 2.4 | 61 | 19 |

6 | 600 | 3.0 | 77 | 19 |

7 | 300 | 3.0 | 77 | 19 |

8 | 450 | 2.7 | 69 | 19 |

9 | 300 | 2.4 | 61 | 12.7 |

10 | 450 | 2.4 | 61 | 12.7 |

11 | 600 | 2.4 | 61 | 12.7 |

12 | 300 | 2.7 | 69 | 15.9 |

Material Parameters | Symbols | Values |
---|---|---|

Media ball radius (mm) | r | 2.5 |

Media ball density (Kg/m^{3}) | ρ | 5950 |

Young modulus (Pa) | E | 2.1 × ${10}^{7}$ |

Poisson’s ratio (-) | ν | 0.3 |

Coefficient of restitution (-) | ε | 0.7 |

Static friction coefficient (-) | μ_{s} | 0.15, 0.35, 0.50 |

Rolling friction coefficient (-) | μ_{r} | 0 |

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**MDPI and ACS Style**

Daraio, D.; Villoria, J.; Ingram, A.; Alexiadis, A.; Hugh Stitt, E.; Marigo, M. Validation of a Discrete Element Method (DEM) Model of the Grinding Media Dynamics within an Attritor Mill Using Positron Emission Particle Tracking (PEPT) Measurements. *Appl. Sci.* **2019**, *9*, 4816.
https://doi.org/10.3390/app9224816

**AMA Style**

Daraio D, Villoria J, Ingram A, Alexiadis A, Hugh Stitt E, Marigo M. Validation of a Discrete Element Method (DEM) Model of the Grinding Media Dynamics within an Attritor Mill Using Positron Emission Particle Tracking (PEPT) Measurements. *Applied Sciences*. 2019; 9(22):4816.
https://doi.org/10.3390/app9224816

**Chicago/Turabian Style**

Daraio, Domenico, Jose Villoria, Andrew Ingram, Alessio Alexiadis, E. Hugh Stitt, and Michele Marigo. 2019. "Validation of a Discrete Element Method (DEM) Model of the Grinding Media Dynamics within an Attritor Mill Using Positron Emission Particle Tracking (PEPT) Measurements" *Applied Sciences* 9, no. 22: 4816.
https://doi.org/10.3390/app9224816