# Analysis of Feed Inlet and Optimal Feeding Amount of Waste Ground Film Impurity Removal Equipment

^{1}

^{2}

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^{*}

^{†}

*Appl. Sci.*

**2023**,

*13*(17), 9905; https://doi.org/10.3390/app13179905 (registering DOI)

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overall Structure and Working Principle of the Film Miscellaneous Wind Separator

#### 2.1.1. Overall Structure

#### 2.1.2. Working Principle

#### 2.2. CFD-DEM Fluid-Solid Coupling Simulation Analysis

#### 2.2.1. Principle of Agglomeration and Depolymerization of Membrane Hybrids

_{c}

_{max}, was greater than the maximum viscous force, F

_{vn}, the agglomerates were broken. The relationship between them was given using Equation (1):

_{1}and d

_{2}are particle sizes (m); when d

_{2}was much larger than d

_{1}, it was considered to be a collision between the agglomerate and wall; k is the elastic deformation coefficient of the particle (Pa); ρ

_{p}is the density of the agglomerate (kg/m

^{3}); v is the relative collision velocity of the agglomerate and wall of the drum sieve (m/s); ν is Poisson’s ratio; and E is Young’s modulus of elasticity (Pa).

^{2}); v

_{n}is the normal relative motion velocity of the agglomerate and the wall (m/s); h is the distance from the surface of the agglomerate to the surface of the trommel screen (m); and R* is the folding radius, where $\frac{1}{{R}^{*}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}$; R

_{1}and R

_{2}are the equivalent radii of the agglomerate and the wall of the trommel screen, respectively, and R

_{2}can be increased to infinity.

#### 2.2.2. Fluid-Solid Coupling Simulation

#### Pre-Processing of Fluid-Solid Coupling Simulation

#### Particle Model Authenticity Verification Test

_{f}is the material suspension position circular cross-section radius (mm); r

_{m}is the thermal anemometer position circular cross-section radius (mm); v

_{f}is the material suspension speed (m/s); and v

_{m}is the thermal anemometer reading.

#### Analysis of Simulation Results

#### 2.3. Optimal Structural Form and Feeding Volume Determination

#### 2.3.1. Force Analysis of Residual Film–Impurity Mixtures

_{N}) during stage Ⅰ. The direction of displacement of the residual film–impurity mixture was along the inlet slope and downward. There was an acute angle between the direction of gravity and the direction of motion, which resulted in positive work; the direction of friction was opposite to the direction of motion, which resulted in negative work. The direction of the support force was perpendicular to the direction of motion, resulting in zero work. The law of conservation of energy was represented using Equation (6).

_{1}, and the direction was the same as the inlet slope, that is, β = 45°. The residual film–impurity mixture was subjected to vertical downward gravity (mg) and airflow resistance (F

_{t}) relative to the direction of material velocity, γ, during stage II; the direction of airflow resistance was the same as the direction of movement of the material relative to the airflow, and the airflow resistance, F

_{t}, was calculated using Equation (7):

^{2}); and ρ

_{s}is the air density (kg/m

^{3}).

#### 2.3.2. Inlet Structure Design

^{2}, respectively.

#### 2.3.3. Optimal Structural Form and Feeding Volume Determination

^{−4}, b = 0.1453, c = −12.46171, and R

^{2}was 0.99436. The fitted curve equation was given using Equation (8):

#### 2.4. Test Equipment

#### 2.5. Test Program and Evaluation Index

#### 2.5.1. Test Program

#### 2.5.2. Evaluation Indicators

_{1}is the ratio of impurities in the residual film (%); m

_{2}is the mass of residual film in the film collection box (kg); and m

_{1}is the mass of impurities in the film collection box (kg).

## 3. Results

## 4. Discussion

## 5. Conclusions

- (1)
- In this study, we addressed the problem that a large amount of residual film–impurity mixture is not efficiently depolymerized during the operation of a residual film–impurity mixture separator. Based on the principle of residual film–impurity mixture depolymerization and the flow-solid coupling simulation method, the maximum collision force between the residual film–impurity mixture and the inside of the device was determined as the key factor affecting the mixture depolymerization.
- (2)
- Analysis of the whole feeding process revealed that when the residual film–impurity mixture separation device was in stable operation, the factors influencing the magnitude of the collision force between the residual film–impurity mixture and the device interior originated from the feed inlet position. The optimal conditions were a square inlet port and a feeding rate of 202 kg/h.
- (3)
- The above-mentioned inlet structure and feeding rate were used as standards, and machine tests were conducted. The test results showed that the average value of the ratio of impurities in the residual film was 6.966%, which was 5.004% lower than the value of 11.97% before optimization. Based on all statistical data, the coefficient of variation was calculated to be 7.38% with a variance of 0.36453. The dispersion of the statistical results was small, and the ratio of impurities in the residual film remained unchanged during the continuous operation of the film–impurity wind separator.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Types of residual film recovery machinery. (

**a**) straw-returning residual film recycling baler; (

**b**) standing pole-type residual film recycling machine.

**Figure 4.**Tumbler sieve-type film trash wind separator: (1) centrifugal fan; (2) duct; (3) inlet; (4) upper seal cover; (5) pipe support frame; (6) centrifugal blower; (7) tumbler screen; (8) spiral blade; (9) screen hole clearing device; (10) film collection box; (11) support roller; (12) frame; (13) lower seal cover; (14) controller; (15) motor; (16) conveying device; (17) spacer conveyor.

**Figure 7.**Model of residual film particles. (

**a**) Arrangement pattern of residual film particles; (

**b**) deformation effect after force; (

**c**) soil particles; (

**d**) straw pellets.

**Figure 8.**Experimental validation of discrete element models. (

**a**) stacking angle simulation test; (

**b**) suspension speed verification test.

**Figure 9.**Simulation test: (

**a**) schematic diagram of fluid-solid coupling test; (

**b**) force diagram of different positions of tumbler screen at different moments.

**Figure 10.**Force analysis of residual film–impurity mixtures. Note: l is the length of the inclined section of the inlet (m); v

_{1}is the instantaneous speed of the residual film–impurity mixture into the trommel screen (m/s); and v

_{1}’ is the speed of the residual film–impurity mixture fed into the inlet (m/s).

Materials | Intrinsic Parameters | Value |
---|---|---|

Residual film | Dimensions (length × width × thickness)/mm × mm × mm | 100 × 30 × 0.1 |

Poisson’s ratio | 0.23 | |

Shear modulus/Pa | 1.2 × 10^{6} | |

Density/kg/m^{3} | 104 | |

Straw | Dimensions (diameter × length)/mm × mm | 8 × 80 |

Poisson’s ratio | 0.35 | |

Shear modulus/Pa | 1.37 × 10^{8} | |

Density/kg/m^{3} | 257.8 | |

Soil | Equivalent particle size/mm | 2 |

Poisson’s ratio | 0.4 | |

Shear modulus/Pa | 1.6 × 10^{8} | |

Density/kg/m^{3} | 1430 |

Number of Test Groups | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|

Evaluation Index | ||||||

Ratio of impurities in the residual film/% | 7.27 | 7.56 | 6.77 | 6.21 | 7.02 | |

Coefficient of variation/% | 7.38 | |||||

Variance | 0.36453 |

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## Share and Cite

**MDPI and ACS Style**

Kang, J.; Xie, C.; Peng, Q.; Wang, N.; Wang, X.; Zhang, Y.
Analysis of Feed Inlet and Optimal Feeding Amount of Waste Ground Film Impurity Removal Equipment. *Appl. Sci.* **2023**, *13*, 9905.
https://doi.org/10.3390/app13179905

**AMA Style**

Kang J, Xie C, Peng Q, Wang N, Wang X, Zhang Y.
Analysis of Feed Inlet and Optimal Feeding Amount of Waste Ground Film Impurity Removal Equipment. *Applied Sciences*. 2023; 13(17):9905.
https://doi.org/10.3390/app13179905

**Chicago/Turabian Style**

Kang, Jianming, Chenshuo Xie, Qiangji Peng, Nannan Wang, Xiaoyu Wang, and Yaoli Zhang.
2023. "Analysis of Feed Inlet and Optimal Feeding Amount of Waste Ground Film Impurity Removal Equipment" *Applied Sciences* 13, no. 17: 9905.
https://doi.org/10.3390/app13179905