# CFD-DEM Simulation of Fast Fluidization of Fine Particles in a Micro Riser

^{1}

^{2}

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*Processes*: Women's Special Issue Series)

## Abstract

**:**

## 1. Introduction

^{3}). Fine particles are rarely used in DEM simulation, but they are widely used in engineering. For example, the catalytic cracking catalyst (FCC) particles, as a typical fine fluidized material, show advantages and characteristics different from other types of particles, such as a high gas–solid mass transfer rate, high bed expansion ratio and high heat transfer rate; they significantly expand before bubbling. Moreover, their cohesion is stronger, and the van der Waals force should not be ignored in many cases.

## 2. Drag Model

## 3. Simulation Method

## 4. Results and Discussion

#### 4.1. Particle Agglomeration

#### 4.2. Gas–Solid Back-Mixing

^{2}·s), and it is much smaller than in the literature [20], which is 90~110 kg/(m

^{2}·s). This significant difference indicates that the overall drag force calculated with the PCDD model is largely reduced in the current simulations.

^{2}·s). The experimental result given by Li and Kwauk [30] and the simulation result presented by Yang et al. [31] are both approximately 14.3 kg/(m

^{2}·s), indicating that the correlation formula has good predictive power. The correlation value at the current gas operating velocity 1.7 m/s is 19.9 kg/(m${G}_{\mathrm{s}}^{\ast}$·S). Therefore, due to the failure to reasonably simulate the back-mixing behavior of particles, the outlet solid flux is overestimated in [20], which is even much higher than the saturation entrainment rate of particles. The currently selected gas–solid properties are basically the same as those in Yang et al. In this work the operating gas velocity is slightly higher, and the particle filling ratio is slightly lower. However, the simulated average outlet solid flux is much lower than the simulated and correlated values in CFB. The authors speculate that the most direct reason might be the geometry effect. In MFB compared with CFB, the bed diameter is very small, and thus for the wall, the relative area of contact with particles significantly enlarges [11]. The strong wall friction force causes the particles near the wall to be unable to be transported upward, which through particle collisions, gradually passed to the surrounding particles and even the central area. And the gas phase needs to consume a lot of energy or pressure drop for suspended particles, which seriously hinders the transport of the particles.

#### 4.3. Axial Structure

#### 4.4. Radial Structure

## 5. Conclusions

- (1)
- The local structure in the MFB satisfies the natural property of fast fluidized particle agglomeration, forming a disperse dilute phase and continuous dense phase;
- (2)
- There is serious gas–solid back-mixing in the MFB, and the dense phase is the main area of gas–solid back-mixing. The wall friction factor aggravates the particle remixing effect, resulting in a relatively low outlet solid flux;
- (3)
- The axial porosity presents an increasing distribution with the bed height but does not strictly satisfy the monotonic exponential distribution. The solid volume fraction at the bottom of the bed is much lower than the correlated results for a CFB;
- (4)
- The radial porosity exhibits a weak core-annulus structure with a higher central region and lower side region. Compared with the correlated results for a CFB, the central region in the MFB is relatively dense, while the side region is relatively dilute;
- (5)
- All distinct variation results of the present simulation can be successfully explained using the relatively strong friction factor. Thus, the present drag model and simulation are both validated and effective, at least in the sense of a qualitative trend.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | area, m^{2} |

Ar | Archimedes number |

C | drag coefficient |

D | bed wide, m |

d | particle diameter or distance between particles, m |

e | unit vector |

F | force on particle, and N |

Fr | Fred number |

G | outlet solid flux, kg·m^{−2}·s^{−1} |

g | gravity acceleration, m·s^{−2} |

h | smooth length, m |

H | height of bed, m |

H_{a} | Hamaker constant, N·m |

H_{0} | Truncation distance, m |

I | inertia moment of particle as spherical, kg·m^{2} |

i, j, k | particle or grid index |

N | number of particles |

p | pressure, Pa |

r | particle position vector |

r | dimensionless radius |

S_{p} | momentum exchange source term |

T | torque, N·m |

t | time, s |

u_{0} | inlet gas velocity, m·s^{−1} |

u | gas velocity, m·s^{−1} |

u_{t} | particle terminal speed |

V | volume, m^{3} |

v | particle velocity, m·s^{−1} |

$\epsilon $ | porosity |

$\overline{\epsilon}$ | cross-sectional porosity |

${\epsilon}_{\mathrm{sd}}$ | solid volume fraction at bottom of bed |

$\kappa $ | stiffness coefficient, N·m^{−1} |

$\lambda $ | solid volume fraction multiplier |

$\mu $ | viscosity, N·s·m^{−2} |

$\rho $ | density, kg·m^{−3} |

$\tau $ | viscous stress tensor, Pa |

$\omega $ | particle angular velocity, s^{−1} |

$\xi $ | restitution coefficient |

subscript | |

2D | two-dimension |

3D | three-dimension |

c | contact |

d | drag |

g | gas |

i, j, k | particle or grid index |

mf | minimal fluidized state |

p | particle |

s | solid |

t | total |

v | van der Waals |

w | bed wall |

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Particle | Gas |
---|---|

Density ρ_{p} = 930 kg·m^{−3} | Viscosity μ_{g} = 1.7 × 10^{−5} N·s·m^{−2} |

Particle diameter d_{p} = 54 μm | Density ρ_{g} = 1.28 kg·m^{−3} |

Porosity at minimum fluidization ε_{mf} = 0.45 | Inlet gas velocity u_{0} = 1.7 m·s^{−1} |

Stiffness Coef. κ = 10 N·m^{−1} | CFD time step Δ t_{g} = 2 × 10^{−6} s |

Restitution Coef. ξ = 0.9 | |

DEM time step Δ t_{p} = 2.5 × 10^{−7} s |

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**MDPI and ACS Style**

Wu, G.; Li, Q.; Zuo, Z.
CFD-DEM Simulation of Fast Fluidization of Fine Particles in a Micro Riser. *Processes* **2023**, *11*, 2417.
https://doi.org/10.3390/pr11082417

**AMA Style**

Wu G, Li Q, Zuo Z.
CFD-DEM Simulation of Fast Fluidization of Fine Particles in a Micro Riser. *Processes*. 2023; 11(8):2417.
https://doi.org/10.3390/pr11082417

**Chicago/Turabian Style**

Wu, Guorong, Qiang Li, and Zhanfei Zuo.
2023. "CFD-DEM Simulation of Fast Fluidization of Fine Particles in a Micro Riser" *Processes* 11, no. 8: 2417.
https://doi.org/10.3390/pr11082417