Abstract
Numerical simulations using CFD-DEM (Computational Fluid Dynamics—Discrete Elements Method) are used to investigate the hydrodynamic behavior of the phases in solid–liquid fluidized beds. However, some challenges are posed to the prediction of energy dissipation and bed expansion on these systems—little knowledge on the collision effects on the solid phase and the high computational cost of assessing the dissipative effects of the lubrication force resulting from the liquid phase. In this context, the present study assessed the collision effects based on the coefficient of restitution, the main parameter of contact between the particles, and the influence of the lubrication force on the dynamics of a fluidized bed. For this, a lubrication force model was implemented in an open-source software CFDEM®project. The model was tested for collisions with fluids of different viscosities and showed good agreement with experimental data. Furthermore, the model was applied to the simulation of a fluidized bed using a high viscosity liquid and dense particles and the results indicated that the lubrication force had a significant impact on the bed dynamics, influencing the fraction of voids, porosity and particle velocity.
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The data presented in the article are available in the public repository of the Federal University of São Carlos, at the website https://repositorio.ufscar.br/handle/ufscar/13677.
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Abbreviations
- d p :
-
Particle diameter [m]
- e :
-
Coefficient of restitution [-]
- e eff :
-
Effective coefficient of restitution [-]
- e fit :
-
Fitted coefficient of restitution [-]
- E :
-
Young’s modulus [Pa]
- E’:
-
Effective Young’s modulus [Pa]
- f a :
-
Adhesion force [N]
- f D :
-
Drag force [N]
- f c , j :
-
Elastic force [N]
- f d , j :
-
Viscous damping force [N]
- f l :
-
Lubrication force [N]
- f ∇ P :
-
Pressure gradient force [N]
- f ∇ ·τ :
-
Viscous force due to shear stress [N]
- F pf :
-
Volumetric fluid-particle forces [N m−3]
- g :
-
Gravitational acceleration [m s−2]
- G :
-
Shear stress module [Pa]
- G’ :
-
Effective shear stress module [Pa]
- h :
-
Relative particle distance [m]
- k c :
-
Particle amount [-]
- m i :
-
Particle mass [kg]
- M t , j :
-
Tangential torque [N m]
- p :
-
Fluid phase pressure [Pa]
- r eff :
-
Effective radius [m]
- r p :
-
Particle radius [m]
- Re p :
-
Particle Reynolds number [-]
- u f :
-
Fluid velocity [m s−1]
- u p :
-
Particle velocity [m s−1]
- v 1 :
-
Normal impact velocity [m s−1]
- v 2 :
-
Normal rebound velocity [m s−1]
- ΔV :
-
Cell volume [m3]
- v i :
-
Linear velocity [m s−1]
- β :
-
Friction coefficient [kg m−3 s−1]
- δ :
-
Minimum distance [µm]
- δ n :
-
Normal displacement [m]
- δ t :
-
Tangential displacement [m]
- ε :
-
Volume fraction of fluid phase (void fraction) [-]
- μ f :
-
Fluid viscosity [Pa s]
- μr , j :
-
Rolling friction coefficient [-]
- ω i :
-
Angular velocity [rad s−1]
- ρf :
-
Fluid density [kg m−3]
- ρp :
-
Particle density [kg m−3]
- τ :
-
Stress tensor [Pa
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Funding
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES)—Finance Code 001, and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, processes n° 2018/16036-8 and 2018/20711-2).
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All authors contributed to the manuscript conception. All steps were supervised by GCL, the project coordinator. All authors commented and contributed to previous versions of the article. All authors read and approved the final manuscript.
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Campos, J.P.F., Melo, K.R.B. & Lopes, G.C. Implementation, validation and application of a lubrication force model in CFD-DEM simulations. Braz. J. Chem. Eng. 39, 429–440 (2022). https://doi.org/10.1007/s43153-021-00134-1
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DOI: https://doi.org/10.1007/s43153-021-00134-1