# CFD Modeling of Gas–Solid Cyclone Separators at Ambient and Elevated Temperatures

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## Abstract

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## 1. Introduction

## 2. Fundamentals of Gas–Solid Cyclone Separators

#### 2.1. Performance Parameters of Cyclones

#### 2.1.1. Separation Efficiency

#### 2.1.2. Pressure Loss

- Pressure loss at the inlet;
- Pressure loss in the separation zone;
- Pressure loss associated with the vortex finder.

#### 2.2. Effect of Solids Loading on Cyclone Performance

^{−3}to 2.6 × 10

^{−2}kg${}_{s}$/kg${}_{g}$. However, they have stated that the separation efficiency at high mass loading of particles is somewhat dependent on the inlet gas velocity of the cyclone, i.e., the swirl strength [28]. The overall separation efficiency versus inlet solids loading of selected experimental studies is presented in Figure 2. In this figure, the improvement of separation efficiency with the cyclone Reynolds number can be observed from the experimental data of [19] for a fixed value of kinematic response time of particles of ${\tau}_{p}=\frac{{\rho}_{p}{d}_{p}^{2}}{18\phantom{\rule{3.33333pt}{0ex}}{\mathsf{\mu}}_{g}}=0.1$ milliseconds. The improvement is more noticeable for lower mass loadings, i.e., below 0.01 kg${}_{s}$/kg${}_{g}$. The kinematic response time of particles used in the study of Fassani and Goldstein [29] is somewhat higher compared to the particles of other studies presented in Figure 2, leading to a very high efficiency of separation. For the rest of the studies, no conclusive argument can be stated regarding the effect of this parameter.

#### 2.3. Effect of Operating Temperature on Cyclone Performance

## 3. Approaches for the Numerical Modeling of Gas–Solid Systems

## 4. CFD Simulation Studies of Gas–Solid Cyclones at Ambient Temperature

#### 4.1. Group I: Single-Phase Flow CFD Simulations

#### 4.2. Group II: One-Way Coupled Gas–Solid Flow Simulations

#### 4.3. Group III: Two- and Four-Way Coupled Gas–Solid Flow Simulations

#### 4.3.1. E–L and Hybrid Model Simulations

#### Effect of Solids Loading

#### Agglomeration of Particles

#### 4.3.2. E–E Simulations

#### 4.4. Summary

## 5. CFD Simulation Studies of Gas–Solid Cyclones at Elevated Temperatures

#### 5.1. Group I: Single-Phase Flow CFD Simulations

#### 5.2. Group II: One-Way Coupled Gas–Solid Flow Simulations

#### 5.3. Group III: Two- and Four-Way Coupled Gas–Solid Flow Simulations

#### 5.3.1. Cyclone Heat Exchangers

#### 5.3.2. CFD Simulation of Cyclones as a Part of a Bigger System

#### 5.4. Summary

## 6. Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CFB | Circulating fluidized bed |

CFD | Computational fluid dynamics |

DDPM | Dense discrete phase model |

DEM | Discrete element method |

DRW | Discrete random walk |

E–E | Eulerian–Eulerian |

E–L | Eulerian–Lagrangian |

LES | Large eddy simulation |

LRR | Launder, Reece, and Rodi model [73] (variation of the RSTM) |

KTGF | Kinetic theory of granular flows |

PBM | Population balance model |

PVC | Precessing vortex core |

RSTM | Reynolds stress transport model |

SGS | Subgrid-scale |

SSG | Speziale, Sarkar, and Gatski model [74] (variation of the RSTM) |

UDF | User-defined function |

URANS | Unsteady Reynolds-averaged Navier–Stokes |

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**Figure 1.**(

**a**) Schematic drawing of a conical reverse-flow cyclone separator illustrating the basic operating principle and the presence of a double vortex inside the cyclone [21], reproduced with permission from G. Towler and R. Sinnott, Specification and design of solids-handling equipment, published by Elsevier, 2013. (

**b**) Qualitative patterns of axial, tangential, and radial velocity components of the gas-flow field in cyclones (right) [22], reproduced with permission from M. Trefz and E. Muschelknautz, Extended cyclone theory for gas flows with high solids concentrations, published by John Wiley and Sons, 1993. (

**c**) The secondary flow pattern caused by the swirl and pressure gradients in the cyclone [19], reproduced with permission from A. Hoffmann and L. Stein, Gas Cyclones and Swirl Tubes: Principles, Design and Operation; published by Springer Nature, 2007.

**Figure 3.**Experimental data of pressure drop (normalized with the pressure drop of a particle-free cyclone, $\Delta {P}_{0}$) versus mass loading of pilot-scale cyclones from selected studies [7,8,9,29,31,32,37]. The lines are numerical fits to each set of experimental data. The Reynolds number is calculated based on the inlet velocity and the cyclone body diameter.

**Figure 4.**Map of gas–solid interaction regimes of particle-laden turbulent flows. ${\tau}_{p}$ and ${\tau}_{e}$ are the particle kinetic response time and time-scale of large eddies in a turbulent flow, respectively. Reproduced with permission from S. Elghobashi, On predicting particle-laden turbulent flows; published by Springer Nature, 1994 [61].

**Figure 5.**Comparison of predicted mean velocity profiles (

**a**,

**b**), rms velocities (

**c**,

**d**), and grade efficiencies (

**e**) using the Reynolds stress transport model (RSTM) and large eddy simulation (LES) for a cyclone with a body diameter of 0.29 m and operating at ambient temperature and pressure [96]. The experimental data on separation efficiency are from [97]. Reproduced with permission from S. Shukla et al., The effect of modeling of velocity fluctuations on prediction of collection efficiency of cyclone separators; published by Elsevier, 2013.

**Figure 6.**The predicted time-averaged values of axial and tangential velocities as well as the resolved turbulent kinetic energy of the gas for a pilot-scale cyclone with a body diameter of 0.29 m and operating with different mass loadings of particles using two-way coupled LES at 0.75D (top) and 2D (bottom) below the cyclone roof [116]. Reproduced with permission from J.J. Derksen, Simulation of mass-loading effects in gas-solid cyclone separators; published by Elsevier, 2006.

**Figure 7.**Grade efficiency predicted by the CFD simulation of Sgrott and Sommerfeld [108] for a pilot-scale cyclone loaded with particles with a diameter of 0.5–60 microns and a mass loading of 0.1 kg${}_{s}$/kg${}_{g}$. 1 W-C, 2 W-C, and 4 W-C refer to one-way coupling, two-way coupling, and four-way coupling methods (using CFD–DEM without agglomeration), respectively. Sphere and history models are volume-equivalent and inertia-equivalent approaches for agglomeration, respectively. Reproduced with permission from O.L. Sgrott and M. Sommerfeld, Influence of inter-particle collisions and agglomeration on cyclone performance and collection efficiency; published by John Wiley and Sons, 2018.

**Figure 8.**Predicted trajectories of particles of different diameters in an industrial-scale cyclone with a body diameter of 3.45 m. The trajectories are colored with particle temperature. The inlet gas and particle temperatures are 634 K and 611 K, respectively, and inlet solids mass loading is around 0.8 kg${}_{s}$/kg${}_{g}$ [145]. Reproduced with permission from M. Wasilewski, Analysis of the effects of temperature and the share of solid and gas phases on the process of separation in a cyclone suspension preheater; published by Elsevier, 2016.

**Table 1.**Summary of the available approaches for computational fluid dynamics (CFD) simulation of gas–solid flows with the inclusion of closure models to be considered in each approach. The table is inspired from [60].

**Table 2.**Details of the selected CFD studies of gas–solid flow in cyclones operating at ambient temperature with the four-way coupling method, in chronological order.

Author(s) | Cyclone Dimensions, D × H (m ${}^{2}$) | Cyclone Re Number ${}^{\left(\mathit{a}\right)}$ | Particle Diameter ( $\mathsf{\mu}$m) | Inlet Mass Loading (kg ${}_{\mathit{s}}$/kg ${}_{\mathit{g}}$) | CFD Solver | Turbulence Model/Turbulent Dispersion | Drag Model | Validation/Comments |
---|---|---|---|---|---|---|---|---|

Chu et al. [109] | 0.2×0.8 | 272,000 | 2000 (mono-sized) | up to 2.5 | ANSYS FLUENT (computational fluid dynamics–discrete element model, CFD–DEM, + user–defined functions, UDF) | Reynolds stress turbulent model, RSTM/not mentioned | friction and pressure gradient drags + particle rotation | Pressure drop is compared with the experiments for particle-free and particle-laden flows with solids loadings in the range of 0–2.5 kg${}_{s}$/kg${}_{g}$ |

Schneiderbauer et al. [110] | 2.5×6.0 | 817,000 | 0.6–400 (size range) | 0.22 | ANSYS FLUENT 16 (hybrid Eulerian–Eulerian, E–E, and Eulerian–Lagrangian, E–L) | RSTM/not mentioned | heterogeneous model of [111] | Predicted grade and overall efficiencies are compared with the measurements. The implemented agglomeration model is reported to be crucial for proper prediction of grade efficiency, while the predicted overall efficiency is not influenced by presence of the agglomeration model. |

Wei et al. [112] | 0.3×1.1 | 113,000–263,000 | 2000 (mono-sized) | 0.72–8.64 | ANSYS FLUENT 15.0 coupled with EDEM 2.7 (CFD–DEM) | RSTM/not mentioned | Gidaspow [50] | Predicted pressure drops are compared with the experimental data for solids loadings of 0.72–8.64 kg${}_{s}$/kg${}_{g}$. Presence of solid strands and an ash top ring are reported. |

Kozolub et al. [106] | 0.2×0.78 | 75,300–130,000 | 2000 (size range) | 0.61–2.9 | ANSYS FLUENT 13.0 (dense discrete phase model, DDPM, based on kinetic theory of granular flow, KTGF) | RSTM/not mentioned | Wen–Yu [113] | Pressure drop is compared with the experimental data for particle-free and particle-laden flows with solids loadings in the range of 0–2.9 kg${}_{s}$/kg${}_{g}$. For the particle-laden flow, the trend of pressure drop change is well predicted while the values are somewhat overpredicted. |

Sgrott and Sommerfeld [108] | 0.29×1.16 | 280,000 | 0.5–60 (size range) | 0.1 | [C3.0cm]OpenFOAM 2.3.1 (CFD–DEM + agglomeration) | [C2.0cm]Large eddy simulation, LES/isotropic Langevin model | not mentioned particle rotation | For a particle-free flow, the predicted velocity profiles are compared with the experimental data of [114]. No validation is given for the particle-laden simulation case. |

Zhou et al. [107] | 0.29×1.16 | 30,000–188,000 | 2000–2800 (size range) | 0.07–0.46 | ANSYS FLUENT 6.3 (CFD–DEM) | RSTM/not mentioned | Gidaspow [50] particle rotation lift force | The predicted velocity profiles of a particle-free flow are compared with the experimental data of [114]. The pressure drop of the particle-free and particle-laden cases is compared with the measurements, while the difference between the particle-free and particle-laden pressure drops is not significant. |

Hwang et al. [35] | 0.2×0.8 | 272,000 | 2000 (mono-sized) | up to 20 | ANSYS FLUENT 16.2 (DDPM–KTGF) | RSTM/discrete random walk, DRW | Wen–Yu [113] | The predicted pressure loss is compared with the experimental and numerical data of [109] for solid mass loadings up to 2.5. |

^{(a)}The Reynolds number is calculated based on the inlet velocity and the cyclone body diameter.

**Table 3.**Selected CFD studies of industrial-scale cyclones operating at elevated temperatures, in chronological order.

Author(s) | Scale of Simulation | CFD Solver | Gas–Solid Model | Turbulence/Drag Models |
---|---|---|---|---|

Cristea and Conti [143] | Preheater system (≈ 58 m height) | ANSYS FLUENT 18.1 | hybrid (DDPM–KTGF) | RSTM/Schiller and Naumann [146] |

Mikulčić et al. [144] | Industrial cyclone (≈ 13 m height and 6 m diameter) | FIRE commercial solver | E–L (two–way coupled) | LES/not mentioned |

Wasilewski [145] | Industrial cyclone (≈ 9 m height and 3.5 m diameter) | ANSYS FLUENT 14 | E–L (two–way coupled) | RSTM/Schiller and Naumann [146] |

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**MDPI and ACS Style**

Nakhaei, M.; Lu, B.; Tian, Y.; Wang, W.; Dam-Johansen, K.; Wu, H.
CFD Modeling of Gas–Solid Cyclone Separators at Ambient and Elevated Temperatures. *Processes* **2020**, *8*, 228.
https://doi.org/10.3390/pr8020228

**AMA Style**

Nakhaei M, Lu B, Tian Y, Wang W, Dam-Johansen K, Wu H.
CFD Modeling of Gas–Solid Cyclone Separators at Ambient and Elevated Temperatures. *Processes*. 2020; 8(2):228.
https://doi.org/10.3390/pr8020228

**Chicago/Turabian Style**

Nakhaei, Mohammadhadi, Bona Lu, Yujie Tian, Wei Wang, Kim Dam-Johansen, and Hao Wu.
2020. "CFD Modeling of Gas–Solid Cyclone Separators at Ambient and Elevated Temperatures" *Processes* 8, no. 2: 228.
https://doi.org/10.3390/pr8020228