Abstract
In this study investigated the deposition of micro-scaled particles using the lattice Boltzmann (LBM) and finite volume (FVM). A real-time data transfer is used to transfer data between LBM and FVM, while a special grid generation algorithm is used to generate a boundary grid around the micro-particles. In order to track particle information such as velocity, direction, and concentration over time, an adaptive interface is developed between FVM and LBM zones. The pore-scale porous media approach is assumed to further improve the results’ quality and reliability. Pores have an average diameter of two mm, while micro-particles have an average diameter of 0.2 mm. The results showed that the deposition layer’s formation directly affected the fluid’s flux rate at the inlet. Heat transfer coefficients of the fluid change in response to the density of the fluid as the deposition layer thickness increases. The thermal conductivity coefficient of the wall decreases as the deposition layer increases, which is variable over time and along the path. Furthermore, we found that heat transfer and pressure drop are affected by the deposition process in the porous medium. Porous media with an increasing pressure drop are also subject to an increasing pressure drop due to the deposition process. In addition, the particles’ thermal conductivity can affect the porous medium’s net heat transfer rate. The heat transfer coefficient has been evaluated, and the results showed that 8.43% exists between the numerical analysis and the results of the empirical test at the highest error value. Existing particles’ density bank in the porous medium beats, such particles exhibit little change due to their extremely small size, resulting in a 0.4 percent and 0.5 percent increase in pressure drop due to deposition at 100. It showed that the suggested method of grid generation based on the cell birth–death algorithm, which serves as the foundation for the particle’s transfer tracking algorithm, the porous medium abled track 70 million particles.
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Abbreviations
- \(\widehat{\mathrm{f}}\mathrm{i}\) :
-
Dimensionless function
- \({\mathrm{U}}^{\mathrm{m}}\) :
-
Mixture velocity (x direction), [m.s−1]
- \({\mathrm{e}}_{\mathrm{i}}\) :
-
Collision velocity
- \({\mathrm{T}}_{\mathrm{particle}}\) :
-
Particle temperature [k]
- f:
-
Lattice distribution function
- \({\mathrm{k}}_{\mathrm{s}}\) :
-
\(conduction \, coefficient\) For solid [W.m−1.K−1]
- \(\widehat{\mathrm{x}}\) :
-
Dimensionless point
- \(\mathrm{x},\mathrm{y},\mathrm{z}\) :
-
Coordinates
- \({\widehat{\mathrm{c}}}_{\mathrm{i}}\) :
-
Dimensionless discrete particle of speed
- \(\widehat{\mathrm{f}}\) :
-
Dimensionless of function
- \({\Omega }_{\mathrm{i}}\) :
-
The collision operator
- \(\widehat{\mathrm{t}}\) :
-
Dimensionless of time
- \(\widehat{\Delta }\mathrm{t}\) :
-
Dimensionless of time
- \({\mathrm{f}}_{\mathrm{i}}\) :
-
Fluid velocity distribution function
- \({\upomega }_{\mathrm{i}}\) :
-
Equilibrium distribution function facto
- \({\mathrm{f}}_{\mathrm{i}}^{\left(\mathrm{eq}\right)}\) :
-
Equilibrium distribution function
- \({\uptau }^{{\mathrm{m}}^{*}}\) :
-
Stress of mth phase, [n.m−2]
- \({\mathrm{C}}_{\mathrm{x}}={\mathrm{C}}_{\mathrm{y}}={\mathrm{C}}_{\mathrm{z}}\) :
-
Volume fraction [kg.m−1]
- \(\upzeta\) :
-
Friction coefficient
- \({\mathrm{c}}_{\mathrm{i}}\) :
-
Yields of results
- \({\Delta \mathrm{T}}^{\mathrm{m}}\) :
-
Temperature gradient, [K]
- \({\mathrm{T}}_{\mathrm{fliud}}\) :
-
Fluid temperature [k]
- \({\nabla \mathrm{T}}_{\mathrm{solid}}\) :
-
Temperature gradient for solid
- \({\mathrm{h}}_{\mathrm{nf}}\) :
-
Convection coefficient for nanofluid [W.m−1.K−1]
- \({\uplambda }_{\mathrm{sediment \, layer}}\) :
-
Ratio of the dynamic viscosity for sediment
- \({\mathrm{U}}_{\mathrm{x}}\cdot {\mathrm{U}}_{\mathrm{y}}\cdot {\mathrm{U}}_{\mathrm{z}}\) :
-
Velocity in xyz-direction for liquid phase, [m.s−1]
- \({\uplambda }_{\mathrm{particle}}\) :
-
Ratio of the dynamic viscosity for particle
- \({\mathrm{v}}^{{\mathrm{m}}^{*}}\) :
-
Velocity of mth phase, [m.s−1]
- \({\mathrm{\alpha }}^{{\mathrm{m}}^{*}}\) :
-
Volume fraction for mth fluid phase
- \({\mathrm{x}}^{{\mathrm{m}}^{*}}\) :
-
Passion of mth phase, [\(\mathrm{m}]\)
- \(\upmu\) :
-
Dynamic viscosity, [kg.m−1.s−1]
- \({\mathrm{H}}^{\mathrm{m}}\) :
-
Multiphase energy, [w]
- \({\uplambda }^{\mathrm{m}}\) :
-
Mixture thermal conductivity, [W.m−1.K−1]
- \(\mathrm{p}\) :
-
Total pressure, [Pa]
- \(\uprho\) :
-
Density, [kg.m−3]
- \({\mathrm{q}}_{\mathrm{H}}^{\mathrm{m}}\) :
-
Heat flux for mth fluid, [W.m−2]
- \({\uprho }^{{\mathrm{m}}^{*}}\) :
-
Density of mth phase, [kg.m−3]
- \({\mathrm{U}}^{{\mathrm{drm}}^{*}}\) :
-
Mixture velocity, [m.s−1]
- \({\uprho }^{\mathrm{m}}\) :
-
Mixture density, [kg.m−3]
- \({\mathrm{H}}^{{\mathrm{m}}^{*}}\) :
-
Energy of mth phase, \([w]\)
- \({\uplambda }^{{\mathrm{m}}^{*}}\) :
-
Thermal conductivity for mth fluid phase, [W.m−2.K−1]
- \({\mathrm{q}}_{\mathrm{f}}^{\mathrm{^{\prime}}\mathrm{^{\prime}}}\) :
-
Heat flux for fluid, [W.m−2]
- \({\Delta }_{\mathrm{t}}\) :
-
Time step, [s]
- \(\mathrm{T}\) :
-
Temperature, [K]
- \({\Delta }_{\mathrm{x}}\) :
-
Lattice spacing, [m]
- t:
-
Times, [s]
- \({\uplambda }_{\mathrm{tube}}\) :
-
Ratio of the dynamic viscosity for tube
- m:
-
Mixture
- eq:
-
Equilibrium
- ^:
-
Dimensionless
- m*:
-
Mth
- “:
-
Flux
- LBM:
-
Lattice Boltzmann method
- FVM:
-
Finite volume method
- DEM:
-
distinct element method
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Ashouri, H., Mohammadiun, H., Mohammadiun, M. et al. An innovative method for calculating the deposition of micro-scale particles in pore-scale porous media. J Therm Anal Calorim 148, 8627–8640 (2023). https://doi.org/10.1007/s10973-023-12043-1
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DOI: https://doi.org/10.1007/s10973-023-12043-1