A Dynamic Coarse Grain Discrete Element Method for Gas-Solid Fluidized Beds by Considering Particle-Group Crushing and Polymerization
Abstract
:1. Introduction
2. Mathematical Model
2.1. Coarse Grain DEM Model for Solid Phase
2.1.1. Drag Force
2.1.2. Contact Force
2.1.3. Coarse Graining
2.2. CFD Model for Gas Phase
2.3. Particle-Group Crushing and Polymerization Model
3. Numerical Method
- (1)
- Calculate the pseudo velocity from Equation (51) by substituting the initial velocity .
- (2)
- Solve Equation (54) to obtain the pressure .
- (3)
- Employing the pressure , solve Equation (48) to obtain the velocity .
- (4)
- Solve Equation (56) to obtain .
- (5)
- Correct the velocity to get by use of equations in form of Equation (55).
- (6)
- Return to step 1 and repeat until convergence.
- (7)
- After convergence, calculate the pressure .
4. Simulation Results
5. Conclusions
- A dynamic particle-group crushing and polymerization procedure is considered in the coarse grain DEM-CFD model.
- The dynamically coarse graining is based on an EMMS type model.
- Heterogeneities are considered in the coarse graining systems by using the EMMS drag force model.
- The method is validated by comparing the simulation results with the experimental ones.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
particle mass, [] | |
particle volume, [] | |
particle velocity, [] | |
gas pressure, [] | |
drag force, [] | |
gravitational force, [] | |
contact force, [] | |
void fraction, [—] | |
interphase momentum exchange coefficient, [] | |
gas velocity, [] | |
particle diameter, [] | |
gas density, [] | |
drag coefficient, [—] | |
heterogeneity index, [—] | |
particle Reynolds number, [—] | |
gas viscosity, [] | |
normal spring constant, [] | |
tangential spring constant, [] | |
normal damping coefficient, [] | |
tangential damping coefficient, [] | |
normal overlap between particles, [] | |
tangential overlap between particles, [] | |
unit normal vector, [—] | |
unit tangential vector, [—] | |
friction coefficient, [—] | |
particle radius, [] | |
angular velocity, [] | |
elasticity modulus, [] | |
Poisson ratio, [—] | |
inertial moment, [] | |
coarse grain ratio, [—] | |
gravitational acceleration, [] | |
viscous stress tensor, [] | |
volume of the computational cell, [] |
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Physical Quantities | Units | Data set |
---|---|---|
Particle Density | kg/m3 | 1150 |
Particle diameter | mm | 1.5 |
Stiffness | N/m | 800 |
Coefficient of friction | — | 0.3 |
Coefficient of restitution | — | 0.9 |
Gas density | kg/m3 | 1.28 |
Gas viscosity | N × s/m2 | 1.7 × 10−5 |
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Wang, X.; Chen, K.; Kang, T.; Ouyang, J. A Dynamic Coarse Grain Discrete Element Method for Gas-Solid Fluidized Beds by Considering Particle-Group Crushing and Polymerization. Appl. Sci. 2020, 10, 1943. https://doi.org/10.3390/app10061943
Wang X, Chen K, Kang T, Ouyang J. A Dynamic Coarse Grain Discrete Element Method for Gas-Solid Fluidized Beds by Considering Particle-Group Crushing and Polymerization. Applied Sciences. 2020; 10(6):1943. https://doi.org/10.3390/app10061943
Chicago/Turabian StyleWang, Xiaodong, Kai Chen, Ting Kang, and Jie Ouyang. 2020. "A Dynamic Coarse Grain Discrete Element Method for Gas-Solid Fluidized Beds by Considering Particle-Group Crushing and Polymerization" Applied Sciences 10, no. 6: 1943. https://doi.org/10.3390/app10061943