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The investigation of orientation angle effect of random elliptical obstacles on permeability and tortuosity in porous media using Image Processing technique and Lattice Boltzmann Method

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Abstract

In this numerical study, the fluid flow through fluid-saturated porous media with random elliptical obstacles was simulated using the Two Relaxation Times mode and D2Q9 model of second discretization version of Lattice Boltzmann Method. For the generation of porous media and geometrical calculations, the Image Processing technique was applied. The mathematical programs were validated by the calculation of hydrodynamic entrance length for the developing Poiseuille flow between two fixed parallel flat plates. Also, another validation was executed regarding the satisfaction of continuity equation for fluid flow through porous media. The results obtained from these two validations confirmed the existence of very good precision for calculations. Besides, with using Darcy’s law, the dimensionless permeability was calculated and the variation of it with respect to aspect ratio was explored. The effect of orientation angle (θ) and rotation of elliptical obstacles on the properties of porous media such as dimensionless permeability and streamline-based tortuosity was completely investigated. The streamline-based tortuosity as a function of porosity was also surveyed in this work. With the help of a novel algorithm, written in C language, the stream functions were calculated and the streamlines and also the velocity vectors in various porous media were depicted, too.

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Abbreviations

A :

Area of channel cross section (m2)

a :

Large radius of ellipse (m)

A P :

Area of particle (m2)

A.R.:

Aspect ratio of ellipse

b :

Small radius of ellipse (m)

D h :

Hydraulic diameter (m)

H :

Distance between two walls of channel (m)

K :

Permeability (m2)

K′ :

Normalized (dimensionless) permeability

L e :

Entrance length (m)

L e * :

Dimensionless entrance length

L P :

Particle hydraulic diameter (m)

lu:

Lattice unit (LBM unit for length)

M :

Molar mass (kg/mol)

m :

Total number of streaming nodes in channel

Ma:

Mach number

n :

Number of fluid nodes at each cross section of channel

p :

Perimeter of particle (m)

\({\bar{P}}_{{in}}\) :

Fluid mean pressure at inlet cross section of porous medium (Pa)

\({\bar{P}}_{{out}}\) :

Fluid mean pressure at outlet cross section of porous medium (Pa)

R :

Universal gas constant (J/(mol K))

Re:

Reynolds number

ReH :

Reynolds number based on distance H

S P :

Sphericity of particle

\(\bar{S}_{P}\) :

Mean sphericity of particle

T :

Thermodynamic absolute temperature (K)

t :

Time (s)

u :

Fluid velocity (m/s)

\(\bar{u}_{{in}}\) :

Fluid mean velocity at inlet cross section of porous medium (m/s)

\(\bar{u}_{{out}}\) :

Fluid mean velocity at outlet cross section of porous medium (m/s)

u x :

Fluid velocity along x-axis (m/s)

V P :

Volume of particle (m3)

V pore :

Pore volume of porous medium (m3)

V solid :

Solid volume of porous medium (m3)

x :

Coordinate parallel with flow direction (m)

y :

Coordinate perpendicular to flow direction (m)

∆P :

Pressure drop (Pa)

θ :

Orientation angle (degree)

μ :

Fluid dynamic viscosity (Pa s)

ν :

Fluid kinematic viscosity (m2/s)

ρ :

Fluid density (kg/m3)

\(\tau\) :

Velocity-based tortuosity

\(\bar{\tau}\) :

Streamline-based tortuosity

ϕ :

Porosity

in:

Inlet

out:

Outlet

LBM:

Lattice Boltzmann Method

SI:

International System

º:

Degree

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Acknowledgements

Mr. Mohammad Ezzatabadipour expresses his especial gratitude to Mr. Hamid Zahedi for development of an efficient new algorithm for drawing streamlines from velocity vectors by a mathematical program written in the combination of C and MATLAB languages (MEX Function) and also, for utilizing Image Processing technique by MATLAB for LBM simulations.

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Authors and Affiliations

  1. Sirjan Jahan Steel Complex (SJSCO), Sirjan, Iran

    Mohammad Ezzatabadipour

  2. Department of Physical Chemistry, Faculty of Chemistry, Ferdowsi University of Mashhad, Mashhad, Iran

    Hamid Zahedi

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  1. Mohammad Ezzatabadipour
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  2. Hamid Zahedi
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Correspondence to Hamid Zahedi.

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Ezzatabadipour, M., Zahedi, H. The investigation of orientation angle effect of random elliptical obstacles on permeability and tortuosity in porous media using Image Processing technique and Lattice Boltzmann Method. Indian J Phys 96, 4283–4299 (2022). https://doi.org/10.1007/s12648-022-02387-z

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  • DOI: https://doi.org/10.1007/s12648-022-02387-z

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