RESEARCH PAPER International Journal of Recent Trends in Engineering, Vol. 1, No. 5, May 2009 15 Numerical Simulation of Gaseous Microflows by Lattice Boltzmann Method D. Arumuga Perumal 1 , Vamsi Krishna 2 , G. Sarvesh 3 and Anoop K. Dass 4* Mechanical Engineering Department, Indian Institute of Technology Guwahati, North Guwahati, India 1 Email: d.perumal@iitg.ernet.in 4* Email: anoop@iitg.ernet.in Abstract— This work is concerned with application of the Lattice Boltzmznn Method (LBM) to compute flows in micro-geometries. The choice of using LBM for microflow simulation is a good one owing to the fact that it is based on the Boltzmann equation which is valid for the whole range of the Knudsen number. In this work LBM is applied to simulate the pressure driven microchannel flows and micro lid-driven cavity flows. First, the microchannel flow is studied in some details with the effects of varying the Knudsen number, pressure ratio and Tangential Momemtum Accomodation Coefficient (TMAC). The pressure distribution and other parameters are compared with available experimental and analytical data with good agreement. After having thus established the credibility of the code and the method including boundary conditions, LBM is then used to investigate the micro lid-driven cavity flow. The computations are carried out mainly for the slip regime and the threshold of the transition regime. Index Terms— Microchannel, micro lid-driven cavity, LBM, TMAC, MEMS I. INTRODUCTION Development of Micro-electro-mechanical systems (MEMS) in the recent years has motivated and necessitated the study of flows in micro-scale geometries such as micro lid-driven cavity and micro-channel. Both experimental and computational efforts have been undertaken to understand the specific features of the microscale flows [1-5]. Micro-devices have attracted increasing attention due to their applications in various of fields, such as DNA analysis, cell separation, cell manipulation, biological and chemical analysis [6]. Flows through microchannels are the most common configuration in all of the biomedical applications [7]. Traditional numerical simulations relying on continuum approach and the Navier-Stokes equations break down at higher values of the Knudsen number Kn which equals the ratio of the mean free path of the gas molecules λ to the characteristic length H of the flow system. In the micro-scale geometries Kn is generally high and the Navier-Stokes equation loses validity. It is generally accepted that the Navier-Stokes equations with no-slip boundary conditions are only appropriate when < 0.001. Kn For > 10 Kn the system can be considered as a free molecular flow. The gas flow for 0.001 < < 0.1 Kn is termed slip regime and 0.1 < < 10 Kn is termed transition regime. In the above four regimes, particle based methods such as Molecular Dynamics (MD) and the Direct Simulation Monte Carlo (DSMC) made some progress in simulation of micro-geometries. However, the computational cost of these methods is usually very large. In the last one and a half decade or so, Lattice Boltzmann method (LBM) has emerged as a new and effective numerical approach of Computational Fluid Dynamics (CFD) and it has achieved considerable success in simulating fluid flows and heat transfer. As opposed to convectional numerical methods based on the discretization of the macroscopic continuum equations, LBM is based on constructing simplified kinetic models containing the physics of microscopic and mesoscopic processes so that averaging can recover macroscopic properties that obeys the continuum equations. The choice of using LBM for microflow simulation is a good one owing to the fact that it is based on the Boltzmann equation which is valid for the whole range of the Knudsen number. In particular, LBM is now being applied to micro-flows in the slip and low-transition regimes. Lattice Boltzmann Methods have earlier been used extensively to simulate incompressible fluid flows with no-slip boundary conditions; but application of LBM to compute gaseous microflows is still an emerging area with some unanswered questions. A few researchers have carried out simulations of the gaseous microflows using Lattice Boltzmann Method. First, Nie et al. [8] used the LBM with bounce-back boundary condition to simulate two-dimensional micro- channel and micro lid-driven cavity flow. They employed the LBM in the no-slip and slip regime, but it is known that the no-slip boundary conditions are generally unrealistic for slip and transition flows and it cannot capture the real microflow characteristics. Tang et al. [10, 11] applied kinetic theory based boundary condition to study gaseous slip flow in micro-scale geometries. Zhang et al. [12] used the tangential momentum accommodation coefficient (TMAC) to describe the gas-surface interactions. Shirani and Jafari [13] applied a combination of bounce-back and specular boundary © 2009 ACADEMY PUBLISHER