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Theories and Applications of CFD–DEM Coupling Approach for Granular Flow: A Review

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Abstract

Bio-particulate matter includes grains, cereal crops, and biomass that are considered discrete materials with irregular size and shape. Although the flow of these particles can behave like a continuum fluid at times, their discontinuous behavior cannot be simulated with traditional continuum-based modeling. The Discrete Element Method (DEM), coupled with Computational Fluid Dynamics (CFD), is considered a promising numerical method that can model discrete particles by tracking the motion of each particle in fluid flow. DEM has been extensively used in the field of engineering, where its application is starting to achieve the popularity in agricultural processing. While CFD has been able to simulate the complex fluid flows with a quantitative and qualitative description of the temporal and spatial change of the flow field. This paper reviews the recent strategies and the existing applications of the CFD–DEM coupling approach in aerodynamic systems of bio-particles. It mainly represents four principal aspects: the definition of aerodynamic systems with its principals, modeling of particle motion including interaction forces of particle–particle and particle–fluid in the system, CFD–DEM coupling methodologies, and drag correlation models with theoretical developments, and the applications of aerodynamic systems related to the agricultural field. The existing published literature indicates that CFD–DEM is a promising approach to study the bio-particulate matter behavior immersed in fluid flow, and it could be benefiting from developing and optimizing the device's geometry and the operations. The main findings are discussed and summarized as a part of the review, where future developments and challenges are highlighted.

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Abbreviations

\(A_{i}\) :

Projected area of particle

\(a\) :

Separation radius between particles

\(C_{d}\) :

Drag coefficient

\(C_{ij}\) :

Convection

\(D_{T,ij}\) :

Turbulent diffusion

\(D_{L,ij}\) :

Molecular diffusion

\(D\) :

Domain diameter

\(d\) :

Normal distance to the wall

\(d_{i}\) :

Particle diameter

\(d_{{i_{vol} }}\) :

Particle diameter with the same volume of the actual one

\(E_{i}\) :

Young’s modulus of particle

\(E_{w}\) :

Young’s modulus of wall boundary

\(F_{net}\) :

Net force acting on a particle

\(F_{ij}^{C}\) :

Total contact force acting on a particle

\(F_{i}^{f}\) :

Fluid-particle interaction force

\(F_{ij}^{n}\) :

Normal contact force on a particle

\(F_{ij}^{t}\) :

Tangential contact force on a particle

\(F_{i}^{t,T}\) :

Tangential contact force at current time

\(F_{i}^{{t,\left( {T - \Delta T} \right)}}\) :

Tangential contact force at previous time

\(F_{i}^{n,T}\) :

Normal contact force at current time

\(F_{i}^{{n,\left( {T - \Delta T} \right)}}\) :

Normal contact force at previous time

\(F_{{i_{adh} }}^{n,T}\) :

Normal adhesive force at current time

\(F_{ij}\) :

Force production by system rotation

\(F_{i}^{f}\) :

Interaction force of the fluid on particle

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

Gravity force

\(f_{adh}\) :

Adhesive force fraction

\(G_{k}\) :

Kinetic energy generation due to the velocity

\(G_{b}\) :

Kinetic energy generation due to buoyancy

\(G_{ij}\) :

Buoyancy production rate of \(\overline{{u_{i}^{\prime } u_{j}^{\prime } }}\)

\(g\) :

Gravity acceleration

\(T_{K}\) :

Kolmogorov time scale

\(T_{e}\) :

Turnover time of large eddy

\(T\) :

Time

\(u\) :

Root mean square of fluid velocity

\(u_{f}\) :

Average velocity component of fluid

\(V_{a}\) :

Air velocity

\(V_{T}\) :

Terminal velocity

\(V_{f}\) :

Average velocity of the fluid

\(V_{i}\) and \(V_{j}\) :

Particles velocity before interaction

\(V_{i}^{^{\prime}}\) and \(V_{j}^{^{\prime}}\) :

Particles velocity after interaction

\(Vol_{i}\) :

Particle volume

\(Vol\) :

Volume occupied by particles and fluid

\(Y_{M}\) :

Dilatation contribution over dissipation rate

\(Z\) :

Particle size or geometry

\(\phi_{ij,1}\) :

Slow pressure-strain

\(\phi_{ij,2}\) :

Rapid pressure-strain

\(\phi_{ij,3}\) :

Wall-reflection term

\(\phi_{ij}\) :

Pressure strain

\(\emptyset_{i}\) :

Particle sphericity

\(\eta\) :

Damping ratio

\(\eta^{t}\) :

Tangential damping ratio

\(K_{1}\) :

Stokes’ shape factor

\(K_{2}\) :

Newton’s shape factor

\(k_{a}\) :

Coefficient of aerodynamic resistance

\(K_{u}^{n}\) :

Unloading contact stiffnesses

\(K_{l}^{n}\) :

Loading contact stiffnesses

\(l\) :

Length scale of the energy-containing eddies

\(m^{*}\) :

Equivalent mass of particles

\(m_{i} \,\,{\text{and}}\,\, m_{j}\) :

Mass of particles \(i\,\, {\text{and}}\,\, j\)

\(N\) :

Number of particles

\(n_{k}\) :

Component of \(x_{k}\) normal to the wall

\(\widehat{{n_{c} }}\) :

Unit vector in the normal direction

\(n\,\,{\text{and}} \,\, t\) :

Normal and tangential coordinates

\(p\) :

Pressure shared by two phases

\(P_{max}\) :

Maximum liquid bridge tensile force

\(P_{ij}\) :

Stress production rate of \(\overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }}\)

\(R_{{e_{i} }}\) :

Particle Reynolds number

\(R_{\epsilon }\) :

Dissipation of swirl and rotational effect

\(R_{e}\) :

Reynolds number

\(R_{i}\,\, {\text{and}}\,\, R_{j}\) :

Radii of particles \(i\,\, {\text{and}}\,\, j\)

\(s_{max}^{t}\) :

Maximum relative tangential displacement

\(s^{t}\) :

Tangential relative displacement at contact

\(S^{n}\) :

Normal overlapping

\(\Delta S^{n}\) :

Change in the normal overlapping

\(\Delta S^{t}\) :

Change in the tangential overlapping

\(S^{n,T}\) :

Normal overlap value at the current time

\(S^{n,T - \Delta T }\) :

Normal overlap value at the previous time

\(S_{k}\) and \(S_{\epsilon }\) :

Constant source terms for user-defined

\(S_{user}\) :

Constant source term for user-defined

\(\Delta T\) :

Timestep

\(T_{i}\) :

Response time of particle

\(\rho_{f}\) :

Fluid density

\(\rho_{f} \overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }}\) :

Reynolds stress tensor

\(\rho_{a}\) :

Air density

\(\rho_{i}\) :

Particle density

\(\mu_{f}\) :

Fluid turbulent viscosity

\(\mu_{t}\) :

Turbulent viscosity

\(\mu\) :

Friction coefficient

\(\mu_{a}\) :

Dynamic viscosity of the air

\(\mu_{{f_{eff} }}\) :

Effective turbulent viscosity of a fluid

\(\alpha_{f}\) :

Fluid volume fraction

\(\alpha_{k}\) and \(\alpha_{\epsilon }\) :

Inverse effective Prandtl number for \(k\) and \(\epsilon\)

\(\alpha_{i}\) :

Particle volume fraction of

\(\varepsilon\) :

Coefficient of restitution

\(\sigma_{k}\) and \(\sigma_{\epsilon }\) :

Turbulent Prandtl numbers for \(k\) and \(\epsilon\)

\({\Gamma }\) :

Surface energy

\(\epsilon_{ij}\) :

Dissipation

\(\delta_{adh}\) :

Adhesive distance

\(\tau_{f }\) :

Viscous stress tensor

\(\upsilon_{f}\) :

Kinematic viscosity of the fluid

\(\frac{d}{dT}S^{t}\) :

Relative tangential velocity at the contact

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52079058 and 51979138), Nature Science Foundation for Excellent Young Scholars of Jiangsu Province (Grant No. BK20190101), National Key Research and Development Project (Grant No. 2020YFC1512404).

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Authors and Affiliations

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

    Mahmoud A. El-Emam, Ling Zhou, Chen Han & Ling Bai

  2. Department of Agricultural and Biosystems Engineering, Alexandria University, Shatby, 21526, Egypt

    Mahmoud A. El-Emam

  3. School of Mechanical Engineering, Nantong University, Nantong, 226019, China

    Weidong Shi

  4. Department of Mechanical Engineering and Materials Science, Washington University in Saint Louis, St. Louis, 63130, USA

    Ramesh Agarwal

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El-Emam, M.A., Zhou, L., Shi, W. et al. Theories and Applications of CFD–DEM Coupling Approach for Granular Flow: A Review. Arch Computat Methods Eng 28, 4979–5020 (2021). https://doi.org/10.1007/s11831-021-09568-9

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