# Design of Cyclone Separator Critical Diameter Model Based on Machine Learning and CFD

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## Abstract

**:**

## 1. Introduction

## 2. Research Methods

#### 2.1. Governing Equation for Numerical Simulation

^{+}< 11. The Table 1 shows the boundary conditions for numerical analysis applied in this study. The simulation time is set as 1.5 second considering the physic time. For CFD simulation, the SIMPLE algorithm, PRESTO! alogorithm. Second order upwind scheme were used for pressure term, pressure–velocity term, and turbulence kinetic and dissipation and momentum term, respectively. The criteria of residual values of the turbulence equation and other equation for assessing CFD convergence were set as ${10}^{-6}$ and ${10}^{-4}$.

#### 2.2. Machine Learning Algorithm

## 3. Results

#### 3.1. CFD Simulation Result for Validation

^{4}. The particle density is 2770 kg/m

^{3}. The particle size distribution is divided to 10 class based on the Rosin–Rammler theory as Equation (6).

^{+}< 11. The growth from the wall is at a ratio of 1.5. The CFD results by three grid types were compared with the experimental data as Table 4. As the mesh size decreases, the numerical values converged. The error between the CFD results and the referenced experimental results was within 2%. The grid size of fine type mesh was 6.5 mm. The fine type mesh was selected due to the numeric accuracy and computational cost in this study. Furthermore, the mesh quality check for the fine type mesh was performed as shown the Table 5. The quality checking results show that the averaged skewness is 0.177 which represents the reasonable accuracy of mesh shape and the averaged aspect ratio of the fine mesh is about 1.814. Therefore, the fine type mesh is acceptable. The selected grid size is used as an input condition of CFD analysis for neural network modeling.

#### 3.2. CFD Simulation for the Dependent Variable of Cyclone

#### 3.3. Cyclone Performance Prediction Model Development Using Neural Network Algorithm

## 4. Conclusions

- (1)
- The particle behavior characteristics in the cyclone were analyzed from the Lagrangian perspective. It was demonstrated that the centrifugal force and the drag force are similar in the diameter with the 50% separation efficiency. This indicates that the critical diameter is important dependent variable for cyclone design based on particle separation theory. Therefore, the critical diameter was applied to the neural network as the design dependent variable.
- (2)
- The neural network model was developed by using CFD combinations that considered various design space based on the DoE. The learning parameters of developed model showed sufficient distribution in the design space, and the neural network prediction model can accurately predict the critical diameter obtained by CFD. Furthermore, the neural network prediction results showed superior performance compared to the traditional multi linear regression results. Therefore, the CFD methodology combined with the neural network method can be applied for efficient and fast design of the cyclone.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Comparison results of the velocity distribution experiment and the prediction results according to the turbulence model.

**Figure 7.**The force analysis acting on particle; (

**a**) 1 μm behavior, (

**b**) 1.5 μm behavior, (

**c**) 5 μm behavior.

**Figure 8.**The averaged force results acting during the separation time with the separation efficiency curve.

**Figure 10.**The result of comparing the prediction performance of the MLR model and the neural network model.

**Figure 11.**The training results and prediction results by the NN and MLR; (

**a**) Neural network results; (

**b**) Multi linear regression.

Boundary Condition | Values |
---|---|

Inlet velocity | 800 (m^{3}/h) |

Pressure drop | 1 atm |

Time step size | 0.001 s |

Number of time step | 1500 |

Boundary Condition | Min (x/D^{1}) | Max (x/D^{1}) |
---|---|---|

Outlet diameter | 0.275 | 0.475 |

Inlet width | 0.15 | 0.35 |

Inlet height | 0.3375 | 0.5375 |

Cone length | 0.5 | 1.95 |

^{1}is 0.4 m.

Factors | Values (x/D^{1}) |
---|---|

Outlet diameter | 0.375 |

Inlet width | 0.25 |

Inlet height | 0.4375 |

Cone length | 1.225 |

Cylinder length | 1.25 |

Vortex finder length | 0.45 |

Tube | 0.74 |

Con-tip-diameter | 0.375 |

Collector Length | 0.745 |

Collector diameter | 0.735 |

^{1}is 0.4 m.

Mesh Type | Coarse | Fine | Finest | Exp. [19] |
---|---|---|---|---|

Separation efficiency | 52.21% | 84.42% | 84.35% | 83.5% |

Error with Exp. [19] | 37.4% | 1.101% | 1.017% | - |

Mesh Type | Values |
---|---|

Skewness average | 0.177 |

Aspect ratio average | 1.814 |

Optimized Parameters | Values |
---|---|

Epoch | 5200 |

Learning rate | 0.00054 |

Batch size | 2 |

Number of layer | 5 |

Node | 8/16/24/16/8 |

Metric | MLR | NN | Improvement |
---|---|---|---|

Mean normalized error | 6.73 | 1.86 | −27.6% |

R^{2} | 0.735 | 0.972 | +32.2% |

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Park, D.; Go, J.S. Design of Cyclone Separator Critical Diameter Model Based on Machine Learning and CFD. *Processes* **2020**, *8*, 1521.
https://doi.org/10.3390/pr8111521

**AMA Style**

Park D, Go JS. Design of Cyclone Separator Critical Diameter Model Based on Machine Learning and CFD. *Processes*. 2020; 8(11):1521.
https://doi.org/10.3390/pr8111521

**Chicago/Turabian Style**

Park, Donggeun, and Jeung Sang Go. 2020. "Design of Cyclone Separator Critical Diameter Model Based on Machine Learning and CFD" *Processes* 8, no. 11: 1521.
https://doi.org/10.3390/pr8111521