# A Mixing Behavior Study of Biomass Particles and Sands in Fluidized Bed Based on CFD-DEM Simulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Particle Model

**is the particle mass,**

_{p}**u**is the particle velocity,

_{p}**f**is the contact force,

_{c}**f**is the gas-solid drag force,

_{d}**f**is pressure gradient force,

_{pg}**G**is the particle gravity. I

_{p}_{s}and

**T**are particle momentum of rotation inertia and torque.

_{s}_{d}represents the fluid effects on particles:

_{p}is the particle volume,

**u**

_{f}is the gas velocity, β is the interphase momentum transfer coefficient expressed by the classical drag force model, Ergun [32] or Wen & Yu equations [33]:

_{f}is gas dynamic viscosity, d

_{p}is the particle diameter. C

_{D}is the drag force coefficient of a singe particle [34]:

#### 2.2. Governing Equations of Fluid Phase

_{f}is the gas phase density,

**u**is the gas velocity, p is the gas phase pressure,

_{f}**g**is the acceleration of gravity,

**κ**is the tensor of stress, which is given by:

_{ij}is the Kronecker delta function:

_{ij}is strain tensor:

_{p,i}is the volume of particle i, V

_{cell}is the volume of cell, α is the gas volume fraction in each cell, u

_{p,i}is the velocity of particle i.

#### 2.3. Particle Mixing Index

## 3. Experiment and Simulation Conditions

#### 3.1. Experiment Details

#### 3.2. Simulation Conditions

^{−6}s and the DEM time step is 10 × 10

^{−7}s in the calculation. 20 processors are assigned for each case to conduct parallel calculations on a high performance computer. The actual calculation time of each case is around 4 weeks.

## 4. Results and Discussion

#### 4.1. Validity of Simulation Results

#### 4.2. Particle Mixing Characteristics at Different Gas Velocities

#### 4.2.1. Instantaneous Particle Height

_{biomass}is the number of biomass and N

_{sand}is the number of sand.

#### 4.2.2. Particle Averaged Kinetic Energy

#### 4.2.3. Particle Mixing Index

#### 4.2.4. Time Averaged Biomass Distribution

#### 4.3. Particle Mixing Characteristics with Different Biomass Particle Sizes

#### 4.3.1. Instantaneous Particle Mixing Behavior

#### 4.3.2. Particle Averaged Kinetic Energy

#### 4.3.3. Time Averaged Biomass Distribution

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${C}_{d}$ | drag force coefficient of singe particle |

$\overline{C}$ | mean of sampled concentration |

c_{i} | local concentration |

D_{b} | biomass particle distribution |

D_{ij} | strain tensor |

d_{p} | diameter of particle p |

f_{c} | contact force |

f_{d} | gas-solid drag force |

f_{pg} | pressure gradient force |

G | acceleration of gravity |

G_{p} | particle gravity |

H_{b} | instantaneous height of biomass particles |

H_{s} | instantaneous height of sand |

I_{s} | particle momentum of rotation inertia |

M | number of sand |

m_{p} | particle mass |

N_{biomass} | total number of biomass particles in the case |

N_{sand} | total number of sand in the case |

P | gas phase pressure |

Re | Reynolds number |

T_{s} | particle torque |

u_{f} | fluid velocity |

u_{p} | particle velocity |

u_{p,i} | velocity of particle i |

v_{cell} | volume of cell |

V_{p} | volume of particle p |

v_{p,i} | volume of particle i |

ρ_{f} | gas phase density |

µ_{f} | gas dynamic viscosity |

α | void fraction |

β | interphase momentum transfer coefficient |

δ_{ij} | Kronecker delta function |

κ | tensor of stress |

σ_{0}^{2} | variance of complete separated particles in statistical grids |

σ_{r}^{2} | concentration variation of particles when fully mixed |

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**Figure 2.**Void fraction in the near wall area. (Simulation case: Biomass diameter is 2 mm; Sand diameter is 0.8 mm; gas velocity is 2.0 m/s.).

**Figure 3.**Gas velocity in the near wall area. (Simulation case: Biomass diameter is 2 mm; Sand diameter is 0.8 mm; gas velocity is 2.0 m/s.).

**Figure 4.**Snapshots of the instantaneous fluidized process. (Simulation case: Biomass diameter is 2 mm; Sand diameter is 0.8 mm; gas velocity is 1.0 m/s. Experiment case: Millet is the biomass particles used in experiments; gas velocity is 1.0 m/s. Biomass mass fraction is 6 % in both simulation and experiments.).

**Figure 5.**Pressure drop comparison of experiment and simulation. (Simulation case: Biomass diameter is 2 mm; Sand diameter is 0.8 mm; gas velocity is 1.0 m/s. Experiment case: Millet is the biomass particles used in experiments; gas velocity is 1.0 m/s. Biomass mass fraction is 6% in both simulation and experiments.).

**Figure 6.**The instantaneous average height of particles (Biomass diameter is 2 mm). (

**a**) is a period of 10 s and (

**b**) is the details of the first second.

**Figure 10.**Time averaged biomass concentration by height. Time range is from 8 s to 10 s. Biomass particle diameter is 2 mm.

**Figure 11.**Snapshots of particles instantaneous movements. (

**a**) biomass particle size is 1.5 mm; (

**b**) biomass particle size is 2.0 mm; (

**c**) biomass particle size is 3.0 mm; sand diameter is 0.8 mm and gas velocity is 1.5 m/s in all three cases).

Force | Equation |
---|---|

Normal elastic force | ${\mathbf{F}}_{en}=-{\scriptscriptstyle \frac{4}{3}}{E}^{\ast}\sqrt{{r}^{\ast}}{\delta}_{n}^{{\scriptscriptstyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\mathbf{n}$ |

Normal damping force | ${\mathbf{F}}_{dn}=-\alpha {\left({\scriptscriptstyle \frac{4}{3}}{E}^{\ast}{m}^{\ast}\sqrt{{r}^{\ast}{\delta}_{n}}\right)}^{0.5}{v}_{rn}\mathbf{n}$ |

Tangential elastic force | ${\mathbf{F}}_{dt}=-{\scriptscriptstyle \frac{{\mu}_{i+}{\mu}_{j}}{2}}{\left(8{G}^{\ast}{m}^{\ast}\right)}^{0.5}{\left({r}^{\ast}{\delta}_{n}{\delta}_{t}\right)}^{0.25}{\mathbf{u}}_{slip}$ |

Tangential damping force | ${\mathbf{F}}_{et}=\{\begin{array}{l}-8{G}^{\ast}\sqrt{{r}^{\ast}{\delta}_{n}}{\mathbf{u}}_{slip}\Delta t\text{}\mathrm{if}\text{}\left|{\mathbf{F}}_{t}\right|\le \left|{\mathbf{F}}_{n}\right|{\mu}_{ij}\\ \left(\left|{\mathbf{F}}_{t}+{\mathbf{F}}_{n}\right|\right){\scriptscriptstyle \frac{{\mu}_{i+}{\mu}_{j}}{2}}{\scriptscriptstyle \frac{{\mathsf{\delta}}_{\mathbf{t}}}{{\delta}_{t}}}\text{}\mathrm{if}\text{}\left|{\mathbf{F}}_{t}\right|\left|{\mathbf{F}}_{n}\right|{\mu}_{ij}\end{array}$ |

*where, ${\scriptscriptstyle \frac{1}{{E}^{\ast}}}={\scriptscriptstyle \frac{1-{v}_{i}^{2}}{{E}_{i}}}+{\scriptscriptstyle \frac{1-{v}_{i}^{2}}{{E}_{j}}}$, ${\scriptscriptstyle \frac{1}{{G}^{\ast}}}={\scriptscriptstyle \frac{2-{v}_{i}}{{G}_{i}}}+{\scriptscriptstyle \frac{2-{v}_{j}}{{G}_{j}}}$, ${G}_{i}={\scriptscriptstyle \frac{{E}_{i}}{2\left(1+{v}_{i}\right)}}$, ${G}_{j}={\scriptscriptstyle \frac{{E}_{j}}{2\left(1+{v}_{j}\right)}}$, ${\scriptscriptstyle \frac{1}{{r}^{\ast}}}={\scriptscriptstyle \frac{1}{{r}_{i}}}+{\scriptscriptstyle \frac{1}{{r}_{j}}}$ in which, E* is the reduced elastic modulus, E _{i} and E_{j} is the Elastic modulus of particle i and j; r* is the reduced radius, r_{i} and r_{j} is the radius of particle i and j; G_{i} and G_{j} is the shear modulus of particle i and j, v_{i} and v_{j} is poisson ratio of particle i and j [37]. |

Parameters | Unit | Value |
---|---|---|

Diameter of sand | mm | 0.8 |

Diameter of biomass particle | mm | 1.5, 2, 3 |

Density of sand | kg/m^{3} | 2650 |

Density of biomass | kg/m^{3} | 1300 |

Density of gas | kg/m^{3} | 1.28 |

Velocity of gas | m/s | 1.0 m/s, 1.5 m/s, 2.5 m/s |

Viscosity of gas | Pa∙s | 1.75 × 10^{−5} |

Wall young’s modulus | MPa | 1 × 10^{6} |

Wall friction coefficient | 0.35 | |

Wall restitution coefficient | 0.9 | |

Biomass Young’s modulus | Mpa | 1.6 × 10^{3} |

Biomass Possion ratio | 0.4 | |

Biomass friction coefficient | 0.34 | |

Biomass restitution coefficient | 0.59 | |

Biomass mass fraction | 2%, 4%, 6% | |

Sand Young’s modulus | Mpa | 1 × 10^{6} |

Sand Possion ratio | 0.33 | |

Sand friction coefficient | 0.35 | |

Sand restitution coefficient | 0.9 | |

CFD Mesh size | mm | 6 × 6 × 6 |

v_{mf} | m/s | 0.36, 0.4, 0.54 |

Biomass Diameter | Mass Ratio | ||
---|---|---|---|

2% | 4% | 6% | |

1.5 mm | 903 | 1806 | 2708 |

2 mm | 381 | 762 | 1143 |

3 mm | 113 | 226 | 339 |

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## Share and Cite

**MDPI and ACS Style**

Wang, H.; Zhong, Z. A Mixing Behavior Study of Biomass Particles and Sands in Fluidized Bed Based on CFD-DEM Simulation. *Energies* **2019**, *12*, 1801.
https://doi.org/10.3390/en12091801

**AMA Style**

Wang H, Zhong Z. A Mixing Behavior Study of Biomass Particles and Sands in Fluidized Bed Based on CFD-DEM Simulation. *Energies*. 2019; 12(9):1801.
https://doi.org/10.3390/en12091801

**Chicago/Turabian Style**

Wang, Heng, and Zhaoping Zhong. 2019. "A Mixing Behavior Study of Biomass Particles and Sands in Fluidized Bed Based on CFD-DEM Simulation" *Energies* 12, no. 9: 1801.
https://doi.org/10.3390/en12091801