Simulation of High Knudsen Number Gas Flows in Nanochannels via the Lattice Boltzmann Method A.H. Meghdadi Isfahani 1,a , A. Soleimani 1,b , A. Homayoon 1 1 Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Isfahan, Iran a amir_meghdadi@pmc.iaun.ac.ir, b soleimani@pmc.iaun.ac.ir Keywords: lattice Boltzmann method, micro and nano flows, Knudsen minimum effect, rarefaction Abstract. Using a modified Lattice Boltzmann Method (LBM), pressure driven flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen number, Kn, covering the slip, transition and to some extend the free molecular regimes. The results agree very well with exiting empirical and numerical data. Introduction Fluid flow plays a major role in micro and nano devices therefore; it has attracted the interests of the computational fluid dynamic researchers significantly. To categorize flow regimes, a nondimensional number known as the Knudsen number (Kn) is defined. It is the ratio of the molecular mean free path to a flow geometric characteristics length. For 0.01 < Kn < 0.1, flow can be assumed continuous, but slip velocities appear on solid walls. For the transition regime (Kn > 0.1), the continuity assumption and consequently the validity of the Navier Stokes Equations, NSE, is questionable as the size is reduced significantly. In such cases, because of the solid walls effect, the fluid flow behavior depends strongly on the geometry dimensions [1]. the Lattice Boltzmann Method (LBM) is an approach for the flow simulation in small scales. The Lattice Boltzmann Equation (LBE) is a more fundamental equation compared to the NSE, which is valid for all ranges of Knudsen number [5]. Therefore, the LBM can be used to simulate fluid flows in all regimes upon appropriate adjustments [6]. Recently there have been attempts to use the LBM for gaseous flows in slip flow regime but only a few papers can be mentioned for the use of LBM in transition regime [7-13]. To this end, two methods are proposed based on the use of higher order LBM [7-10] and the modification of the mean free path [11-13]. The multi-speed or higher order LBM has been developed to increase the order of accuracy in the discretization of velocity phase space. Although Ansumali, et al. [9] have demonstrated that the high order LBMs have improved current capability but Kim, et al. [10] showed that this method can predict the rarefaction effects only for ) 1 . 0 ( O Kn = and at large Kn, the mass flow rate can not be predicted properly by these methods. Additionally, the high-order LBMs with large numbers of discrete velocities are not numerically stable [14]. On the other hand, the models based on the local mean free path are complicated and can not be used for complex geometries such as porous media. In this article, by relating the viscosity to the local Kn, a generalized diffusion coefficient is obtained in such a way that wide range of Kn regimes of flow can be simulated more accurately. The LBM The continuum Boltzmann equation is a fundamental model for rarefied gases in the kinetic theory [15,16]. Due the complicated nature of the Boltzmann equation [17] Bhatnagar, Gross and Krook [18] proposed a simplified model for LBM known as the BGK-LBM: (1) [ ] ) , ( ) , ( 1 ) , ( ) , ( t x f t x f t x f t t t c x f eq i i i i i      − − = − ∆ + ∆ + τ Advanced Materials Research Vols. 403-408 (2012) pp 5318-5323 Online available since 2011/Nov/29 at www.scientific.net © (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.403-408.5318 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 212.50.232.226-07/01/12,05:49:58)