# CFD Modeling and Simulation of the Hydrodynamics Characteristics of Coarse Coal Particles in a 3D Liquid-Solid Fluidized Bed

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. CFD Mathematical Model Development

#### 2.1. CFD-KTGF Model

#### 2.2. Turbulent Model

#### 2.3. Interphase Force Models

#### 2.3.1. Gidaspow Drag Force Model

#### 2.3.2. Moraga Lift Force Model

## 3. Simulation Details

_{0}(100 mm), the coal particles were initially patched. The boundary conditions can be classified into velocity inlet (small holes at the bottom of the bed), pressure outlet, and wall in the fluidized bed reactor; the rest of the bottom plate which is not velocity inlet uses a wall BC.

## 4. Results and Discussion

#### 4.1. Grid Dependence Analysis

_{l}= 0.0125 m/s, ρ

_{s}= 1.4–1.5 kg/m

^{3}and d

_{s}= 0.85 ± 0.15 mm, whereas the Gidaspow equations [31] were used as the drag model.

#### 4.2. Model Validation

^{3}and size of 0.6 ± 0.1 mm; the other was a large and heavy particle with a density of 1700–1800 kg/m

^{3}and size of 1.75 ± 0.25 mm. The comparisons of the expansion degree were performed at different velocities.

^{3}) and fine (0.6 ± 0.1 mm) coal particles, the bed expansion degree increased from 15% to 75%. However, as presented in Figure 4B, the bed expansion degree increased from 11% to 24% for the high-density (1600–1700 kg/m

^{3}) and coarse particles (1.75 ± 0.25 mm) when the superficial liquid velocity increased from 0.0167 to 0.0236 m/s. A higher critical fluidization velocity was observed for high-density coarse particles. In addition, the growth rate of the bed expansion height with the increase in liquid velocity was dependent on the particle properties. The predicted bed height is also presented in Figure 4. As can be seen from the figure, the CFD simulation results are in good agreement with the experimental data.

#### 4.3. Model Application

#### 4.3.1. Effect of Coal Particles Size

^{3}. As presented in Figure 5A, when the size of the solid coal particles is within the range of 0.6 ± 0.1 mm, the consistent color in the figure indicates that the local volume fraction of the particles is homogeneous throughout the column. Generally, when the particle size is relatively low, the liquid flow along the fluidized bed is stable and very regular and the particle flow is small and symmetric, which is conducive to the realization of homogeneous flow. However, as the coal particle size increases, the bed expansion height experiences a significant decrease (see Figure 5A–C). The resistance of the fluid to the particles increases as the particle size increases, which results in heterogeneous fluidization in the bed. Moreover, in the radial direction of the bed, the volume fraction of the central solid phase is low, whereas the volume fraction of the near-wall solid phase is high. This is because the particles rise in the central region and fall near the wall at a lower speed. From Figure 5D, it can also be seen that the expansion height of the bed decreases as the diameter of the solid particles increases. Especially in the range of 1.75 ± 0.25 mm, the bed homogeneity worsens, thus disturbing the regularity of the flow state.

#### 4.3.2. Effect of Coal Particle Densities

^{3}) on the fluidization characteristics of coal particles. Figure 7 presents the time evolution of solid-phase holdup. As can be seen from the figure, the bed expansion height decreased from 0.13 to 0.115 m when the coal particle density increased from 1400–1500 to 1800–1900 kg/m

^{3}. From Figure 7A,B, it can be seen that the fluidized bed reached a stable fluidized state after 40 s. In the radial direction of the bed, the volume fraction of the central solid phase was low, whereas the volume fraction of the near-wall solid phase was high. This is because the particles rise in the central region and fall near the wall at a lower speed, which results in the tendency of the particles to stay near the wall for a longer time. When the coal particle density increases to 1700−1800 and 1800−1900 kg/m

^{3}, heterogeneous fluidization can be observed (see Figure 7C,D).

^{3}, the particles were practically unfluidized, despite the presence of many voids in the bed.

## 5. Conclusions

^{3}, the bed expansion height decreased from 0.13 to 0.115 m. It was observed that the bed expansion height fluctuated with flow time due to the formation and movement of vacuoles. The simulation results indicated that the small and light particles are easily fluidized, thus exhibiting a certain range of homogeneous expansion behaviors. For the large and heavy particles, inhomogeneity may occur throughout the bed, including water voids and velocity fluctuations caused by vacuoles.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${C}_{D}$ | Drag coefficient |

${C}_{\mathrm{l}}$ | Lift force coefficient |

${d}_{s}$ | Diameter of particles, m |

$e$ | Particle–particle restitution coefficient |

D | Diffusion coefficient, m^{2}·s^{−} |

$\overrightarrow{F}$ | The liquid-solid interphase force, N·m^{−3} |

$\overrightarrow{\mathrm{g}}$ | Gravitational acceleration, m·s^{−2} |

${\mathrm{g}}_{0}$ | Radial distribution function |

${G}_{i}$ | The product term in turbulence model |

$H$ | Bed expansion height, m |

$I$ | Unit tensor |

$k$ | Turbulence kinetic energy, m^{2}·s^{−2} |

${k}_{\mathsf{\Theta}}$ | Diffusion coefficient, m^{2}·s^{−1} |

${K}_{sl}$ | Interphase exchange coefficient, kg·m^{2}·s^{−1} |

${N}_{c}$ | Courant number |

$p$ | Pressure, Pa |

$\mathrm{Re}$ | Reynolds number |

${S}_{i}$ | Source term in the turbulence model |

$t$ | Time, s |

$v$ | Velocity, m·s^{−1} |

${Y}_{i}$ | Dissipation terms in the turbulence model |

$\alpha $ | Volume fraction |

$\rho $ | Density, kg·m^{−3} |

$\overline{\overline{\tau}}$ | Stress tensor, Pa |

$\mu $ | Viscosity, Pa·s |

$\epsilon $ | Voidage |

$\mathsf{\Theta}$ | Granular temperature, m^{2}·s^{−2} |

${\lambda}_{s}$ | Solid bulk viscosity, Pa·s |

$\omega $ | Specific dissipation rate, s^{−1} |

$\kappa $ | Thermal conductivity, W·m^{−1} K^{−1} |

$\eta $ | Efficiency of energy transfer from the liquid phase to the solid phase, % |

$\gamma $ | The collisional dissipation energy, kg·m^{−1} s^{−3} |

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**Figure 2.**Grid sensitivity analysis: the contours of the solid volume fraction at the time of 50 s at different resolutions.

**Figure 3.**Grid sensitivity analysis: (

**A**) comparison of time-averaged solid volume fractions along bed-height at four grid sizes, (

**B**) comparison of overall bed height as a function of time at four grid sizes.

**Figure 4.**Comparisons between the computational fluid dynamics (CFD) simulation results and experimental data in terms of the degree of expansion under the condition of different superficial liquid velocities: (

**A**) superficial liquid velocity increased from 0.0056 to 0.0111 m/s; (

**B**) superficial liquid velocity increased from 0.0167 to 0.0236 m/s.

**Figure 5.**Time evolutions of the volume fraction of the solid phase under the conditions of different coal particle sizes: (

**A**) 0.6 ± 0.1 mm; (

**B**) 0.85 ± 0.15 mm; (

**C**) 1.25 ± 0.25 mm; (

**D**) 1.75 ± 0.25 mm.

**Figure 6.**Time evolutions of the bed expansion height under the condition of different coal particle sizes.

**Figure 7.**Time evolutions of the volume fraction of the solid phase under the condition of different coal particle densities: (

**A**) 1400–1500 kg/m

^{3}; (

**B**) 1600–1700 kg/m

^{3}; (

**C**) 1700–1800 kg/m

^{3}; (

**D**) 1800–1900 kg/m

^{3}.

**Figure 8.**Time evolutions of the bed expansion height under the conditions of different coal particle densities.

**Table 1.**Parameters of the experimental conditions and experimental results [46].

Parameters | Liquid-Phase Density (kg/m ^{3}) | Liquid-Phase Viscosity (kg/(m·s)) | Particle Density (kg/m ^{3}) | Particle Diameter (mm) | Superficial Liquid Velocity (cm/s) | CFD Degree of Expansion (%) | Experimental Degree of Expansion (%) | Evaluation of Deviation (%) |
---|---|---|---|---|---|---|---|---|

1 | 998.20 | 0.001003 | 1400–1500 | 0.6 ± 0.1 | 0.56 | 15.03 | 17.00 | 1.97 |

2 | 998.20 | 0.001003 | 1400–1500 | 0.6 ± 0.1 | 0.69 | 29.99 | 29.00 | 0.99 |

3 | 998.20 | 0.001003 | 1400–1500 | 0.6 ± 0.1 | 0.83 | 45.16 | 42.00 | 3.16 |

4 | 998.20 | 0.001003 | 1400–1500 | 0.6 ± 0.1 | 0.97 | 60.11 | 55.00 | 5.11 |

5 | 998.20 | 0.001003 | 1400–1500 | 0.6 ± 0.1 | 1.11 | 75.06 | 70.00 | 5.06 |

6 | 998.20 | 0.001003 | 1700–1800 | 1.75 ± 0.25 | 1.67 | 11.02 | 9.00 | 2.02 |

7 | 998.20 | 0.001003 | 1700–1800 | 1.75 ± 0.25 | 1.81 | 13.05 | 11.00 | 2.05 |

8 | 998.20 | 0.001003 | 1700–1800 | 1.75 ± 0.25 | 2.08 | 16.95 | 15.00 | 1.95 |

9 | 998.20 | 0.001003 | 1700–1800 | 1.75 ± 0.25 | 2.22 | 19.99 | 18.00 | 1.99 |

10 | 998.20 | 0.001003 | 1700–1800 | 1.75 ± 0.25 | 2.36 | 24.04 | 22.00 | 2.04 |

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**MDPI and ACS Style**

Peng, J.; Sun, W.; Han, H.; Xie, L.
CFD Modeling and Simulation of the Hydrodynamics Characteristics of Coarse Coal Particles in a 3D Liquid-Solid Fluidized Bed. *Minerals* **2021**, *11*, 569.
https://doi.org/10.3390/min11060569

**AMA Style**

Peng J, Sun W, Han H, Xie L.
CFD Modeling and Simulation of the Hydrodynamics Characteristics of Coarse Coal Particles in a 3D Liquid-Solid Fluidized Bed. *Minerals*. 2021; 11(6):569.
https://doi.org/10.3390/min11060569

**Chicago/Turabian Style**

Peng, Jian, Wei Sun, Haisheng Han, and Le Xie.
2021. "CFD Modeling and Simulation of the Hydrodynamics Characteristics of Coarse Coal Particles in a 3D Liquid-Solid Fluidized Bed" *Minerals* 11, no. 6: 569.
https://doi.org/10.3390/min11060569