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Recent Advances and Perspectives of CFD–DEM Simulation in Fluidized Bed

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Abstract

The coupling of computational fluid dynamics (CFD) and discrete element method (DEM) has become an important method for studying dense fluidized beds. Since DEM can track the motion behavior of each particle individually and CFD can qualitatively and quantitatively describe the fluid evolution process, the discussion of fluidized beds using CFD–DEM method has been realized from small scale to laboratory scale and even extended to large engineering scale. This work presents a comprehensive review of the application of coupled CFD–DEM methods in fluidized beds and identifies the issues that need to be addressed. The detailed analysis is summarized mainly from the definition of particle flow system, DEM modeling theory (particle–fluid interaction and integration scheme of particle motion information, etc.), CFD modeling theory (discussion of turbulence model) and CFD–DEM coupled mapping methods (including Unresolved CFD–DEM and Resolved CFD–DEM). Existing studies have verified from multi-scales that the coupled CFD–DEM approach is reliable for predicting particle motion in fluidized beds. The findings are summarized and discussed, and future developments and challenges are highlighted. This work will provide theoretical guidance for subsequent researchers using the coupled CFD–DEM method.

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Abbreviations

\(A^{\prime}\) :

Projected area of particles

\({\varvec{a}}_{n}\) :

Acceleration of current time

\({\varvec{a}}_{r}\) :

Relative acceleration

\(B\) :

Magnetic field intensity

\(C_{D}\) :

Drag coefficient

\(\hat{C}_{H}\) :

Damping coefficient

\(C_{n}\) :

Normal damping coefficient

\(E\) :

Electric field intensity

\(E_{n}\) :

Young's modulus

\({\varvec{F}}_{Vol}\) :

Body force

\({\varvec{F}}_{Sur}\) :

Surface force

\({\varvec{F}}_{gra}\) :

Gravitational force

\({\varvec{F}}_{mag}\) :

Magnetic force

\({\varvec{F}}_{bou}\) :

Buoyancy force

\({\varvec{F}}_{ele}\) :

Electrical charge force

\({\varvec{F}}_{ij}^{n}\) :

Normal contact force

\({\varvec{F}}_{ij}^{t}\) :

Tangential contact force

\({\varvec{F}}_{Van}\) :

Van der waals

\({\varvec{F}}_{Saf}\) :

Saffman force

\({\varvec{F}}_{Cap}\) :

Capillary liquid bridge force

\({\varvec{F}}_{Lap}\) :

Laplace term

\({\varvec{F}}_{Ten}\) :

Surface tension term

\(f_{grid}^{i}\) :

Volume fraction of particle i

\(H_{1}\) :

Stokes' shape factor

\(H_{2}\) :

Newton's shape factor

\(K_{nl}\) :

Normal contact stiffness

\(K_{\tau }\) :

Loading normal stiffness

\(\hat{K}_{H}\) :

Stiffness coefficient

\(m_{i}\) :

Mass of particle i

\(m_{pw}\) :

Mass of particles in contact with wall

\(m_{pi}\) :

Mass of contact particles

\({\varvec{n}}\) :

Unit normal vector

\(p\) :

Fluid pressure

\(q\) :

Electric charge force

\(Re\) :

Reynolds number

\(Re_{\Omega }\) :

Eddy Reynolds number

\(r^{ * }\) :

Effective radius

\(r_{ij}\) :

Relative radius

\(r_{con}\) :

Contact radius

\(s_{\tau }\) :

Relative movement of contact points

\(s_{n}\) :

Normal overlap volume

\({\varvec{u}}_{f}\) :

Fluid velocity

\(V_{grid}\) :

Grid volume

\(V_{pi}\) :

Volume of the particle

\({\varvec{v}}_{n}\) :

Particle velocity of current time

\(W\) :

Adsorption power per unit area

\({\varvec{x}}_{n}\) :

Position of current time

\(\Delta t\) :

Time step

\(\nabla p\) :

Local pressure gradient

\(\Delta L\) :

Grid size

\(\Delta {\varvec{s}}_{\tau }\) :

Tangential relative movement in unit time step

\(\Delta V_{j}\) :

Lumped volume associated with point j

\(\alpha_{f}\) :

Fluid volume fraction

\(\alpha_{i}\) :

Volume fraction of particles

\(\delta_{ij}\) :

Kronecker function

\(\varepsilon\) :

Restitution coefficient of the material

\(\eta_{\tau }\) :

Tangential damping ratio

\(\tau\) :

Stokes relaxation time

\(\tau_{f}\) :

Viscous stress tensor

\(\tilde{\boldsymbol{\tau }}_{ij}\) :

Viscous stress tensor

\(\tilde{\boldsymbol{\tau }}_{ij}^{SGS}\) :

Subgrid stress term

\(\nu_{n}\) :

Poisson's ratio

\(\mu_{f}\) :

Fluid shear viscosity

\(\vartheta\) :

Friction coefficient

\(\rho_{f}\) :

Fluid density

\(\sigma_{k}\) :

Turbulent Prandtl number

\({\varvec{\omega}}\) :

Angular velocity

CFD:

Computational fluid dynamics

DEM:

Discrete element method

TFM:

Two fluid model

DNS:

Direct numerical simulation

TPM:

Two phase model

LES:

Large eddy simulation

RANS:

Reynold average Navier–Stokes equations

PCM:

Particle center method

DPVM:

Dividing particle volume method

SPM:

Satellite point method

MCM:

Monte Carlo methods

SKM:

Statistical kernel method

DGM:

Dual grid method

PM:

Porous method

DM:

Diffusion method

SPH:

Smooth particle dynamics

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos. 52079058 and 52209113), Natural Science Foundation of Jiangsu Province (Grant no. BK20220544), China Postdoctoral Science Foundation (Grant no. 2023M731367) and Jiangsu Excellent Postdoctoral Funding Program (Grant no. 2022ZB641).

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Authors and Affiliations

  1. Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, 212013, China

    Zhenjiang Zhao, Ling Zhou, Ling Bai & Bo Wang

  2. CFD Lab, Washington University in St. Louis, St. Louis, 63130, USA

    Ramesh Agarwal

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  1. Zhenjiang Zhao
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Correspondence to Ling Zhou.

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Appendix A

Appendix A

See Tables 7 and 8.

Table 7 Relationship between coarsening ratio and computational efficiency in the literature a
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Table 8 Scale laws used for CG CFD–DEM models in the literature a
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Zhao, Z., Zhou, L., Bai, L. et al. Recent Advances and Perspectives of CFD–DEM Simulation in Fluidized Bed. Arch Computat Methods Eng 31, 871–918 (2024). https://doi.org/10.1007/s11831-023-10001-6

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