Numerical Study of the Movement of Single Fine Particles in Porous Media Based on LBM-DEM
Abstract
:1. Introduction
2. Mathematic Model
2.1. Model of LBM
2.2. Solid–Solid Coupled Model
2.3. Liquid–Solid Coupled Model
2.4. Dynamics Model of Discrete Particle
3. Physical Model and Numerical Simulation Conditions
4. Model Validation
5. Numerical Simulation Results and Analysis
5.1. Migrations and Sedimentations of Fine Particles in Porous Media under Different Particle Densities
5.2. Migration and Sedimentation of a Fine Particle in Porous Media under Different Diameters
5.3. Effect of Fine Particles on the Flow Field in Porous Media
5.4. Migration and Sedimentation of Two Fine Particles in Porous Media
5.5. Migration and Sedimentation of Three Fine Particles in Porous Media
6. Summary and Conclusions
- (1)
- A fine particle with a density of 2.1–2.5 g/cm3 can travel longer distance under fluid drag, gravity and collision force, although it is more likely to deviate from the channel and collide with the internal wall of porous media; however, a fine particle with a density of 3.0 g/cm3 will be deposited on an internal wall after a shorter route because of its greater gravity.
- (2)
- The migration distance of a fine particle is not linearly correlated with its density. A fine particle with a density less than 2.0 g/cm3 is liable to stagnate in a low-infiltration area in porous media.
- (3)
- A fine particle with a smaller diameter is also likely to be stranded in a low-infiltration area even though its Stokes number is small.
- (4)
- A fine particle blocking the pore throat in porous media results in an evident pressure fluctuation of the flow field, intensifying the momentum transfer between the flow field and fine particles. An increase in diameter of a fine particle causes a greater increase in the pressure drop of the liquid–solid flow compared to an increase in the fine particle’s density.
- (5)
- If the horizontal distance between two non-contact fine particles is less than 0.25 cm, the presence of one fine particle may improve the migration of the other, and the other will travel a longer distance in the flow field in porous media.
- (6)
- When the pressure drop of the liquid–solid flow approaches a stable state, the values of the pressure drop of the liquid–solid flow containing two or three fine particles in porous media are slightly greater than that of the liquid–solid flow containing only one fine particle.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
distribution function | |
equilibrium distribution function | |
velocity vector | |
external force term | |
transition function | |
lattice sound speed | |
lattice spacing | |
time step | |
pressure of the fluid | |
macroscopic fluid velocity | |
normal contact force (N) | |
tangential contact force (N) | |
normal stiffness coefficient | |
unit vector from particle i to particle j | |
restitution coefficient determined by experiment | |
tangential stiffness coefficient | |
slip velocity of contact point (m/s) | |
, | radii of particles i and j (m) |
tangential unit vector | |
contact force (N) | |
contact torque (N m) | |
local force acting on fluid | |
Lagrange force density | |
velocity of the particle boundary discrete point | |
velocity pre-collision | |
matrix with interpolation items | |
matrix with extensions | |
, | fluid Euler coordinates |
, | solid Lagrange coordinates |
dr | thickness of the solid forcing shell |
ds | distance between two adjacent Lagrangian points on the solid boundary |
velocity of the Euler point of the fluid | |
fluid force of particle | |
fluid torque of particle | |
number of Lagrange points on the particle boundary | |
number of local Euler meshes around the particle | |
Lagrange point coordinate | |
center coordinate of the particle mass | |
mass of solid particles (kg) | |
rotational inertia of solid particles (kg·m2) | |
gravity (N) | |
υ | kinematic viscosity (m2/s) |
Cd | resistance coefficient |
Fd | resistance of the particle (N) |
pressure drop (Pa) | |
t | time (s) |
k | permeability |
L | length of the porous media |
W | width of the porous media |
ki | initial permeability of porous media. |
Greek Symbols | |
discrete velocity direction | |
dimensionless relaxation time | |
fluid density | |
, , | model parameters |
normal overlap of the contact particles | |
, | normal and tangential damping coefficients |
tangential displacement | |
tangential friction coefficient of the particles | |
weight coefficient | |
, | angular velocities of particle i and j (rad/s) |
Dirac function | |
porosity | |
µ | viscosity of fluid |
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Physical Property Parameter | Values |
---|---|
Normal elastic coefficient of particles (g/s2) | 8 × 105 |
Coefficient of restitution of particles | 0.9 |
Friction coefficient of particles | 0.3 |
Time step (s) | 0.0000012963 |
Parameter | Value |
---|---|
Density of fluid (g/cm3) | 1.0 |
Inlet velocity of fluid Vin (cm/s) | −2.0 |
Length in X-axis L (cm) | 2 |
Height in Y-axis W (cm) | 4 |
Diameter of large particles (cm) | 0.16 |
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Zhou, Y.; Fo, B.; Xu, R.; Xi, J.; Cai, J. Numerical Study of the Movement of Single Fine Particles in Porous Media Based on LBM-DEM. Sustainability 2024, 16, 7346. https://doi.org/10.3390/su16177346
Zhou Y, Fo B, Xu R, Xi J, Cai J. Numerical Study of the Movement of Single Fine Particles in Porous Media Based on LBM-DEM. Sustainability. 2024; 16(17):7346. https://doi.org/10.3390/su16177346
Chicago/Turabian StyleZhou, Yinggui, Bin Fo, Ruifu Xu, Jianfei Xi, and Jie Cai. 2024. "Numerical Study of the Movement of Single Fine Particles in Porous Media Based on LBM-DEM" Sustainability 16, no. 17: 7346. https://doi.org/10.3390/su16177346