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Prediction of hydrodynamic characteristics of a 3D liquid-solid tapered fluidized bed using kinetic theory of rough spheres

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Abstract

The fluidized bed bioreactor is an economical and efficient method for wastewater treatment. In the fluidized bed bioreactor, fluidized particles carrying microorganisms consume the organic pollutants in wastewater. The collision and friction between carrier particles in the fluidized bed can affect the efficiency of wastewater treatment. Therefore, understanding the hydrodynamics of fluidized bed bioreactors is crucial. In this study, the particle collision velocity depending on particle volume fraction and granular temperature, as well as considering the influence of particle surface roughness and elasticity through the critical Stokes number, a dynamic restitution coefficient model for wet rough particles is developed to provide a more accurate description of the collision behavior between wet rough particles. The model is incorporated into the kinetic theory of rough spheres to perform numerical simulations on the hydrodynamic characteristics of a three-dimensional liquid-solid tapered fluidized bed using the two-fluid model. The simulation results exhibit better agreement with experimental data by Wu et al. compared to prior studies. Furthermore, sensitivity analyses are conducted on drag force, virtual mass force, and lift force. It is observed that the Koch-Hill drag model predicts the bed expansion heights closest to the measured results. Additionally, the impacts of static bed height and particle density on the fluidized bed hydrodynamics are investigated. Simulation results indicate that an increase in static bed height initially leads to an increase and then a decrease in particle collision velocity. Within the current study scope, particle collision velocity exhibits a monotonic increase with increasing particle density.

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Data availability

Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

Abbreviations

Ar:

Archimedes number

a :

Dimensionless coefficient

a ct :

Dimensionless coefficient

a kt :

Dimensionless coefficient

b :

Dimensionless coefficient

C 1 :

Dimensionless coefficient

C 2 :

Dimensionless coefficient

d s :

Solid particle diameter; m

E :

Young’s modulus; Pa

e dry :

Dry restitution coefficient

e wet :

Wet restitution coefficient

g :

Acceleration due to gravity; m·s-2

g 0 :

Radial distribution function

K s :

Nondimensional moment of inertia

k s :

Solid conductivity; J/m·K·s

p l :

Liquid pressure; Pa

p s :

Solid pressure; Pa

Re :

Reynolds number

St :

Stokes number

St c :

Critical Stokes number

u l :

Liquid velocity; m·s-1

u s :

Particles velocity; m·s-1

v impact :

Particles impact velocity; m·s-1

α r :

Dimensionless coefficient

α t :

Dimensionless coefficient

β :

Tangential restitution coefficient

β ls :

Drag coefficient between liquid and solid phases; kg·m-3·s-1

γ s :

Energy exchange between liquid and solid phases; kg·m-1·s-3

δ :

Moment of inertia; kg·m²

δ l :

Liquid film thickness; m

ε l :

Liquid volume fraction

ε s :

Solid volume fraction

ε s,max :

Maximum solid volume fraction at the packed state

η 1 :

Dimensionless coefficient

η 2 :

Dimensionless coefficient

θ o :

Total granular temperature; m2·s−2

λ :

Dimensionless coefficient

μ b :

Solid bulk viscosity; kg·m-1·s-1

μ l :

Liquid viscosity; kg/m·s

μ s :

Solid shear viscosity; kg·m-1·s-1

ξ r :

Solid rotational viscosity; kg/m·s

ρ l :

Liquid density; kg·m-3

ρ s :

Solid density; kg·m-3

τ l :

Liquid stress tensor; Pa

τ s :

Solid stress tensor; Pa

χ :

Dimensionless coefficient

χ c :

Dimensionless coefficient

χ k :

Dimensionless coefficient

χ s :

Collisional dissipation rate of the granular fluctuating energy; kg·m-1·s-3

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Acknowledgements

This work was supported by the Scientific Starting Fund from Changzhou University (Grant No. ZMF22020063), the National Natural Science Foundation of China (Grant No. 51876032) and the Open Project of Jiangsu Key Laboratory of Oil-Gas Storage and Transportation Technology (Grant No. CDYQCY202203).

Funding

This work was supported by the Scientific Starting Fund from Changzhou University (Grant No. ZMF22020063), the National Natural Science Foundation of China (Grant No. 51876032) and the Open Project of Jiangsu Key Laboratory of Oil-Gas Storage and Transportation Technology (Grant No. CDYQCY202203).

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Oil-Gas Storage and Transportation Technology, Changzhou University, Changzhou, 213164, China

    Ruichao Tian, Jianlin **e, Yueming Guo, **aoxue Jiang & Chaoxu Shen

  2. School of Petroleum Engineering, Northeast Petroleum University, Daqing, 163318, China

    Shuyan Wang

  3. Tazhong Oil and Gas Development Department, Tarim Oilfield Company, Korla, 841000, China

    Konghang Yang

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  1. Ruichao Tian
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Contributions

R.T. and S.W. conceived of the presented idea, developed the theory, performed the computations and wrote the main manuscript text, J.X. conducted preliminary research and performed the computations. All authors discussed the results and contributed to the final manuscript.

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Correspondence to Shuyan Wang.

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Tian, R., **e, J., Wang, S. et al. Prediction of hydrodynamic characteristics of a 3D liquid-solid tapered fluidized bed using kinetic theory of rough spheres. Granular Matter 26, 75 (2024). https://doi.org/10.1007/s10035-024-01445-z

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