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Volume 8, Issue 5
Gas Flow Through Square Arrays of Circular Cylinders with Klinkenberg Effect: A Lattice Boltzmann Study

Zhenhua Chai, Baochang Shi, Zhaoli Guo & Jianhua Lu

Commun. Comput. Phys., 8 (2010), pp. 1052-1073.

Published online: 2010-08

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  • Abstract

It is well known that, as non-continuum gas flows through microscale porous media, the gas permeability derived from Darcy law is larger than the absolute permeability, which is caused by the so-called Klinkenberg effect or slippage effect. In this paper, an effective definition of Knudsen number for gas flows through square arrays of circular cylinders and a local boundary condition for non-continuum gas flows are first proposed, and then the multi-relaxation-time lattice Boltzmann equation including discrete effects on boundary condition is used to investigate Klinkenberg effect on gas flow through circular cylinders in square arrays. Numerical results show that the celebrated Klinkenberg equation is only correct for low Knudsen number, and second-order correction to Klinkenberg equation is necessary with the increase of Knudsen number. Finally, the present numerical results are also compared to some available results, and in general an agreement between them is observed.

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@Article{CiCP-8-1052, author = {}, title = {Gas Flow Through Square Arrays of Circular Cylinders with Klinkenberg Effect: A Lattice Boltzmann Study}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {5}, pages = {1052--1073}, abstract = {

It is well known that, as non-continuum gas flows through microscale porous media, the gas permeability derived from Darcy law is larger than the absolute permeability, which is caused by the so-called Klinkenberg effect or slippage effect. In this paper, an effective definition of Knudsen number for gas flows through square arrays of circular cylinders and a local boundary condition for non-continuum gas flows are first proposed, and then the multi-relaxation-time lattice Boltzmann equation including discrete effects on boundary condition is used to investigate Klinkenberg effect on gas flow through circular cylinders in square arrays. Numerical results show that the celebrated Klinkenberg equation is only correct for low Knudsen number, and second-order correction to Klinkenberg equation is necessary with the increase of Knudsen number. Finally, the present numerical results are also compared to some available results, and in general an agreement between them is observed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.010809.081209a}, url = {http://global-sci.org/intro/article_detail/cicp/7608.html} }
TY - JOUR T1 - Gas Flow Through Square Arrays of Circular Cylinders with Klinkenberg Effect: A Lattice Boltzmann Study JO - Communications in Computational Physics VL - 5 SP - 1052 EP - 1073 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.010809.081209a UR - https://global-sci.org/intro/article_detail/cicp/7608.html KW - AB -

It is well known that, as non-continuum gas flows through microscale porous media, the gas permeability derived from Darcy law is larger than the absolute permeability, which is caused by the so-called Klinkenberg effect or slippage effect. In this paper, an effective definition of Knudsen number for gas flows through square arrays of circular cylinders and a local boundary condition for non-continuum gas flows are first proposed, and then the multi-relaxation-time lattice Boltzmann equation including discrete effects on boundary condition is used to investigate Klinkenberg effect on gas flow through circular cylinders in square arrays. Numerical results show that the celebrated Klinkenberg equation is only correct for low Knudsen number, and second-order correction to Klinkenberg equation is necessary with the increase of Knudsen number. Finally, the present numerical results are also compared to some available results, and in general an agreement between them is observed.

Zhenhua Chai, Baochang Shi, Zhaoli Guo & Jianhua Lu. (2020). Gas Flow Through Square Arrays of Circular Cylinders with Klinkenberg Effect: A Lattice Boltzmann Study. Communications in Computational Physics. 8 (5). 1052-1073. doi:10.4208/cicp.010809.081209a
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