Research Papers: Fundamental Issues and Canonical Flows

An Efficient Method of Generating and Characterizing Filter Substrates for Lattice Boltzmann Analysis

[+] Author and Article Information
John Ryan Murdock

Department of Mechanical
Engineering–Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: jrmurdoc@mtu.edu

Aamir Ibrahim

Department of Mechanical
Engineering–Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: aamiri@mtu.edu

Song-Lin Yang

Fellow ASME
Department of Mechanical
Engineering–Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: slyang@mtu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 9, 2017; final manuscript received September 28, 2017; published online November 23, 2017. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 140(4), 041203 (Nov 23, 2017) (11 pages) Paper No: FE-17-1216; doi: 10.1115/1.4038167 History: Received April 09, 2017; Revised September 28, 2017

To provide porous media substrates that are quick to generate and characterize for lattice Boltzmann analysis, we propose a straightforward algorithm. The method leverages the benefits of the lattice Boltzmann method (LBM), and is extensible to multiphysics flows. Several parameters allow for simple customization. The generation algorithm and LBM are reviewed, and suggested implementation covered. Additionally, results are discussed and interpreted to evaluate the approach. Several verification tools are employed such as Darcy's law, the Ergun equation, the Koponen correlation, a newly proposed correlation, and experimental data. Agreement and repeatability are found to be excellent, suggesting this relatively simple method is a good option for engineering studies.

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Fig. 1

Sample generated substrate geometry: φ = 50%

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Fig. 2

Sample generated substrate geometry: φ = 80%

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Fig. 3

D2Q9 lattice structure

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Fig. 4

Blending functions, W1 (ϕ) and W2 (ϕ) versus porosity (ϕ)

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Fig. 5

Computational filter domain and boundaries

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Fig. 6

Velocity field at 50% porosity (Re 2.6)

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Fig. 7

Velocity field at 80% porosity (Re 49)

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Fig. 8

Porosity versus permeability at multiple velocities

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Fig. 9

Re versus friction factor at multiple velocities and porosities, compared to Ergun equation

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Fig. 10

Nondimensional permeability, K/Dp2 versus ϕ, fit to the Koponen model

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Fig. 11

Semilog plot: Nondimensional permeability, K/Dp2 versus ϕ, fit to the Koponen model

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Fig. 12

Nondimensional permeability, K/Dp2 versus ϕ, fit to the GB model

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Fig. 13

Semilog plot: Nondimensional permeability, K/Dp2 versus ϕ, fit to the GB model

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Fig. 14

Nondimensional permeability, K/Dp2 versus ϕ, fit to the GK model

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Fig. 15

Semilog plot: Nondimensional permeability, K/Dp2 versus ϕ, fit to the GK model

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Fig. 16

Semilog plot: Nondimensional permeability, K/Dp2 versus porosity, ϕ compared with experimental data




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