# Use of Precise Area Fraction Model for Fine Grid DEM Simulation of ICFB with Large Particles

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## Abstract

**:**

## 1. Introduction

## 2. Precise Area Fraction Model

## 3. Extension to Three-Dimensional Simulation

_{sphere}and V

_{segment}can be easily and precisely calculated. In fact, one can also directly calculate V

_{quasi semi-segment}and V

_{quasi quarter-segment}by use of a single mathematical formula, employing the double definite integral and compound numerical integral. See [13] for more details.

## 4. Simulation Methods

## 5. Results and Discussion

#### 5.1. Big Bubble

#### 5.2. Solid Volume Fraction

#### 5.3. Relative Pressure

#### 5.4. Bed Layer Height

## 6. Conclusions

- (1)
- The PAF model is given to precisely calculate the solid or gas area fraction, and theoretically to more properly calculate the grid porosity.
- (2)
- The simulated big bubble is generally consistent with the experiment results in shape and size. The present simulation works well enough to model the basic bubbling phenomenon of an ICFB.
- (3)
- The simulated fluctuation time scales and amplitudes of solid volume fraction, relative pressure and bed layer height are close to the experimental results, showing that DEM can perform well in modelling time-varying waveforms for the physical quantities in a bubbling fluidized bed by use of the PAF model.
- (4)
- Although the present two-dimensional simulations are in better agreement with the experiments, to model the gas-solid fluidization hydrodynamics more precisely, one should prefer to apply three-dimensional simulations.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$C$ | standard drag coefficient for particle |

$d$ | particle diameter, m |

$dx,dy$ | grid width and height, m |

$F$ | force on particle, N |

$f$ | grid area occupied by particle, s^{2} |

$g$ | gravity acceleration, m s^{−2} |

$H$ | bed layer height, m |

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

$h$ | smoothing length, m |

$i,j,k$ | particle or grid indexes |

$N$ | particle number |

$p$ | pressure, Pa |

$r$ | location vector of particle, m |

$r$ | particle radius, m |

$R\hspace{0.17em}e$ | Reynolds number of particle |

$T$ | torque, N m |

$t$ | time, s |

$u$ | gas velocity, m s^{−1} |

$V$ | particle volume, m^{3} |

$v$ | particle velocity, m s^{−1} |

$X,Y$ | horizontal and vertical coordinate of particle center, m |

$x,y$ | horizontal and vertical coordinate of grid center, m |

Greek letters | |

$\beta $ | momentum exchange coefficient, kg m^{−3} s^{−1} |

$\epsilon $ | porosity |

$\lambda $ | amplification factor |

$\mu $ | gas viscosity, N s m^{−2} |

$\pi $ | ratio of circumference |

$\rho $ | density, kg m^{−3} |

$\tau $ | viscous stress tensor, Pa |

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

Subscripts/superscripts | |

2D | two-dimensional |

3D | three-dimensional |

$\mathrm{C}$ | collision |

$\mathrm{D}$ | drag |

$\mathrm{g}$ | gas |

$i,j,k$ | particle or grid indexes |

$\mathrm{p}$ | particle |

1 | lower-left vertex of grid |

## References

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**Figure 8.**Particle distributions of present simulation and experiment [18].

Parameter | Value |
---|---|

Particle density ρ_{p} | 1150 kg·m^{−3} |

Particle diameter d_{p} | 1.545 mm |

Real particle number | 4080 |

Minimum porosity | 0.475 |

Spring constant | 200 N·m^{−1} |

Friction Coef. | 0.3 |

Restitution Coef. | 0.9 |

Smoothing length h | 3.8625 mm |

Superficial gas velocity | 0.9 m·s^{−1} |

Gas viscosity μ_{g} | 1.8 × 10^{−5} N·s·m^{−2} |

Gas density ρ_{g} | 1.28 kg·m^{−3} |

Bed height | 0.5 m |

Bed width | 0.09 m |

Grid number | 27 × 150 |

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**MDPI and ACS Style**

Wu, G.; Ouyang, J.
Use of Precise Area Fraction Model for Fine Grid DEM Simulation of ICFB with Large Particles. *Symmetry* **2020**, *12*, 399.
https://doi.org/10.3390/sym12030399

**AMA Style**

Wu G, Ouyang J.
Use of Precise Area Fraction Model for Fine Grid DEM Simulation of ICFB with Large Particles. *Symmetry*. 2020; 12(3):399.
https://doi.org/10.3390/sym12030399

**Chicago/Turabian Style**

Wu, Gruorong, and Jie Ouyang.
2020. "Use of Precise Area Fraction Model for Fine Grid DEM Simulation of ICFB with Large Particles" *Symmetry* 12, no. 3: 399.
https://doi.org/10.3390/sym12030399