# A Numerical Approach to Characterize the Efficiency of Cyclone Separator

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Governing Equations of the Multiphase CFD Model

#### 2.1. Navier Stokes Equation

#### 2.2. Turbulence Model

#### 2.3. Discrete Phase Model

## 3. Numerical Approach to Multiphase Flow Cyclone

#### 3.1. Cyclone CFD Model

#### 3.2. Grid Generation

#### 3.3. Boundary Conditions and Numerical Settings

^{3}) was used as the injection fluid (density: 998.2 kg/m

^{3}, viscosity: 2.7 cSt). For the boundary conditions, the inlet velocity of the fluid was 2.15 m/s and the outlet pressure in the atmospheric conditions was 1 atm, which was applied equally to each model. The Reynolds number of the continuous phase used in the simulation was 5.9 × 10

^{4}. To confirm the performance of the cyclone filter according to particle size, particles of various sizes (10, 15, 20, and 25 µm) were mixed and then injected. The volume fraction of the dispersed phase was considered to be 5% (case 1), and 0.5% (case 2) of the total. Case 1 verified the numerical method of the liquid–solid cyclones and Case 2 compared the cyclone performance according to the change in shape. As the wall roughness directly influences the filter efficiency, an equal value of 3.2 µm was used in the experiment. Table 3 lists the boundary conditions used for the analysis.

^{−3}and the main variables (inlet pressure and outlet flow rate) had a constant value for a period of time. While solving, as the first step, the initial conditions were considered only for the fluid flow. As the second step, particle tracking of various sizes was performed based on the fluid flow.

## 4. Results and Validation

#### 4.1. Experiment Set Up

#### 4.2. Simulation Results and Discussion

#### 4.3. Comparison of CFD and Experiment

## 5. Analysis of Comparative Study Results

#### 5.1. Tangential Velocity

#### 5.2. Axial Velocity

#### 5.3. Cyclone Performance

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$u$ | Instantaneous velocity of fluid. |

$\stackrel{-}{{u}_{i}}$ | Average velocity of fluid. |

${{u}_{i}}^{\prime}$ | Fluctuating component of velocity. |

${x}_{i}$ | Spatial position. |

$\stackrel{-}{p}$ | Average pressure of fluid. |

$\rho $ | Fluid density. |

$\mu $ | Fluid absolute dynamic viscosity. |

$-\rho \stackrel{-}{{{u}_{i}}^{\prime}}\stackrel{-}{{{u}_{j}}^{\prime}}$ | Reynolds stress tensor. |

${D}_{T,ij}$ | Turbulence diffusion. |

${P}_{ij}$ | Stress production. |

${\varphi}_{ij}$ | Pressure strain. |

${\epsilon}_{ij}$ | Dissipation term. |

${F}_{ij}$ | Rotation production. |

${u}_{p}$ | Velocity of particles. |

${F}_{D}$ | Drag force. |

${\rho}_{p}$ | Density of particles. |

${g}_{i}$ | Gravitational acceleration |

${F}_{s}$ | Corresponds to the additional forces. |

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**Figure 2.**Schematic diagram of cyclone models; (

**a**) Model 1 (basic), (

**b**) Model 2 (added socket 1), and (

**c**) Model 3 (added socket 2).

**Figure 3.**Meshing of the cyclone models; (

**a**) Model 1 (basic), (

**b**) Model 2 (added socket 1), and (

**c**) Model 3 (added socket 2).

**Figure 5.**Contour of Model 1 injected with 5 percent particles; (

**a**) Total pressure, (

**b**) Velocity magnitude, and (

**c**) Vortices distribution.

**Figure 6.**Distribution profile of Model 1 injected with 5 percent particles; (

**a**) Total pressure and (

**b**) Velocity magnitude.

**Figure 7.**Comparison of calculated and measured results; (

**a**) inlet static pressure and (

**b**) upper outlet flow rate.

**Figure 9.**Tangential velocity profile y1 (cylindrical center) and y2 (conical center); (

**a**) Tangential velocity at y1 and (

**b**) Tangential velocity at y2.

**Figure 11.**Comparison of cyclone filter performance; (

**a**) Separation efficiency and (

**b**) Number of particles contained in discharge fluid (100 mL).

Geometry | Symbol | Dimensions (mm) | ||
---|---|---|---|---|

Model 1 | Model 2 | Model 3 | ||

Cylindrical length | $\mathrm{h}$ | 112 | ||

Conical length | $\mathrm{H}$ | 187 | ||

Inlet diameter | ${\mathrm{D}}_{\mathrm{i}}$ | $\varphi $ 38.5 | ||

Cylindrical diameter | $\mathrm{D}$ | $\varphi $ 74 | ||

Vortex finder diameter | ${\mathrm{D}}_{\mathrm{e}}$ | $\varphi $ 36.75 | ||

Conical under diameter | $\mathrm{B}$ | $\varphi $ 18.5 | ||

Socket 1 diameter | $\mathrm{a}$ | - | $\varphi $ 21.5 | - |

Socket 1 length | $\mathrm{b}$ | - | 70 | - |

Socket 2 diameter | $\mathrm{c}$ | - | - | $\varphi $ 30.26 |

Socket 2 middle diameter | $\mathrm{d}$ | - | - | $\varphi $ 6 |

Socket 2 diameter | $\mathrm{e}$ | - | - | 70 |

Cyclone models | Model 1 | Model 2 | Model 3 | ||||||
---|---|---|---|---|---|---|---|---|---|

Number of Elements | 178,578 | 189,306 | 205,476 | ||||||

Mesh quality | AR | OQ | S | AR | OQ | S | AR | OQ | S |

9.75 | 0.99 | 0.81 | 14.88 | 0.99 | 0.85 | 12.49 | 0.99 | 0.82 |

Section | Boundary Conditions | |
---|---|---|

Category | DPM | |

Inlet | Velocity inlet | Reflect |

Upper outlet | Pressure outlet | Escape |

Under outlet | Pressure outlet | Trapped |

Wall | - | Reflect |

Comparison | Inlet Static Pressure (bar) | Upper Outlet Flow Rate (L/min) |
---|---|---|

Measured | 1.85 (±0.5) | 111.27 (±6.18) |

Calculated | 1.89 (±0.08) | 98.27 (±3.74) |

Comparison | Upper Outlet Flow Rate (L/min) | (Inlet/Upper Outlet) × 100 (%) |
---|---|---|

Model 1 | 100.93 | 67.29 |

Model 2 | 101.30 | 67.53 |

Model 3 | 137.93 | 91.95 |

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**MDPI and ACS Style**

Kang, Y.R.; Kwak, J.B. A Numerical Approach to Characterize the Efficiency of Cyclone Separator. *Machines* **2023**, *11*, 440.
https://doi.org/10.3390/machines11040440

**AMA Style**

Kang YR, Kwak JB. A Numerical Approach to Characterize the Efficiency of Cyclone Separator. *Machines*. 2023; 11(4):440.
https://doi.org/10.3390/machines11040440

**Chicago/Turabian Style**

Kang, Yu Rim, and Jae B. Kwak. 2023. "A Numerical Approach to Characterize the Efficiency of Cyclone Separator" *Machines* 11, no. 4: 440.
https://doi.org/10.3390/machines11040440