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Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 3, pp 1931–1942 | Cite as

Pore-scale modeling of rarefied gas flow in fractal micro-porous media, using lattice Boltzmann method (LBM)

  • H. Rostamzadeh
  • M. R. SalimiEmail author
  • M. Taeibi-Rahni
Article

Abstract

Due to the widespread use of rarefied gas flow in micro-porous media in industrial and engineering problems, a pore-scale modeling of rarefied gas flow through two micro-porous media with fractal geometries is presented, using lattice Boltzmann method. For this purpose, square- and circular-based Sierpinski carpets with fractal geometries are selected due to their inherent behavior for real porous media. Diffusive reflection slip model is used and developed for these porous media through this study. With this respect, the planar Poiseuille flow is selected as a benchmark and validated with the literature. The effect of Knudsen number (Kn) on the permeability is investigated and compared in each geometry. It is shown that as Knudsen number increases, the permeability will increase due to the gas slippage effect on the solid blocks. In addition, it is observed that the permeability is more sensitive to the gaseous flow behavior at the slip and beginning of transition flow regimes. At last, the permeability relationship with Knudsen number is presented with a higher coefficient of determination for both fractal geometries, showing that this relation is logarithmic.

Keywords

Fractal micro-porous media Sierpinski carpet Rarefied gas flow Lattice Boltzmann method (LBM) Pore-scale simulation Diffusion reflection 

List of symbols

Symbols

Ap

Total pores area (m2)

At

Total area (m2)

ci

Discrete velocity (m s−1)

cs

Sonic velocity (m s−1)

Df

Fractal dimension

Fi

Distribution function

\( f_{\alpha }^{\text{eq}} \)

Equilibrium distribution function

Fx

Body force in x-direction (Pa m−1)

H

Height (m)

K

Permeability coefficient (m2)

Kn

Knudsen number

L

Length (m)

Lch

Characteristics length (m)

LBM

Lattice Boltzmann method

N

Cumulative number of capillary tubes

Ny

Number of nodes at y-direction

P

Pressure (Pa)

u

Velocity (m s−1)

wi

Weight coefficient

xb

Boundary node location

xf

Fluid node location

Greek Symbols

α

Fractal coefficient factor

λ

Mean free path (m)

λmax

Upper limit self-similar region

λmin

Lower limit self-similar region

τ

Relaxation time (s)

ϕ

Porosity coefficient

ρ

Density (kg m−3)

μ

Dynamic viscosity (Pa s)

υ

Kinematic viscosity (m2 s−1)

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • H. Rostamzadeh
    • 1
  • M. R. Salimi
    • 2
    Email author
  • M. Taeibi-Rahni
    • 1
  1. 1.Department of Aerospace EngineeringSharif University of TechnologyTehranIran
  2. 2.Aerospace Research Institute, Ministry of Science, Research and TechnologyTehranIran

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