Commun. Comput. Phys., 14 (2013), pp. 1058-1072.


Pressure Distribution of the Gaseous Flow in Microchannel: A Lattice Boltzmann Study

Zimian Xu 1, Zhaoli Guo 1*

1 State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.

Received 17 June 2012; Accepted (in revised version) 24 January 2013
Available online 8 May 2013
doi:10.4208/cicp.170612.240113a

Abstract

In this paper the pressure distribution of the gaseous flow in a microchannel is studied via a lattice Boltzmann equation (LBE) method. With effective relaxation times and a generalized second order slip boundary condition, the LBE can be used to simulate rarefied gas flows from slip to transition regimes. The Knudsen minimum phenomena of mass flow rate in the pressure driven flow is also investigated. The effects of Knudsen number (rarefaction effect), pressure ratio and aspect ratio (compression effect) on the pressure distribution are analyzed. It is found the rarefaction effect tends to the curvature of the nonlinear pressure distribution, while the compression effect tends to enhance its nonlinearity. The combined effects lead to a local minimum of the pressure deviation. Furthermore, it is also found that the relationship between the pressure deviation and the aspect ratio follows a pow-law.

AMS subject classifications: 76P05

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Key words: Lattice Boltzmann method, gaseous flows, pressure distribution, microchannel.

*Corresponding author.
Email: xzmmzx@gmail.com (Z. M. Xu), zlguo@mail.hust.edu.cn (Z. L. Guo)
 

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