Numerical Simulations of Gaseous Slip Flow in Micro-channels

• Main Authors: Fu-Chih Yu, 余福治
• Other Authors: Ching-Shung Chen
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/34524599447675280574

碩士 === 淡江大學 === 航空太空工程學系 === 87 === The objective of present work is to investigate gaseous flow in micro-channels analytically as well as numerically and compare the results with experiment data. Gaseous flow is typically classified into one of four flow regions according to its Knudsen number. These regions are continuum flow, slip flow, transition flow, and free molecular flow. The proposed model assumes the flow is a continuum but employs a slip condition on the channel wall. Although numerical methods for solving the compressible Navior-Stokes equations can be used to study this problem, they are inefficient due to their hyperbolic-parabolic character. The results of present work show that slip flow can be predicted accurately by solving the compressible boundary-layer equations. The parabolic character of the boundary-layer equations renders the present method a very efficient and accurate tool in studying slip flow. The results of present work reveal some interesting features of slip micro-channel flows. First, due to the extraordinarily small dimensions, a large pressure gradient is required to drive the flow. Although the pressure gradient is large, the velocity remains very small due to the high shear stress on the wall, and the corresponding Reynolds number is also relatively small, so that the flow can be safely assumed to be laminar. Second, diffusion is the dominant momentum and energy transfer mechanism in micro-channel. The results also show that the slip boundary condition, which is the result of incomplete momentum and energy exchanges between the impinging gas molecules and the walls, has decisive effects on velocity and therefore mass flow rate of the flow. The computed results are compared with experimental data and theoretical solution. The agreement is quite good. It indicates that the slip model of this study is indeed able to predict micro-channel flows in the slip region, but further study is needed for flows in the transition or free molecular regions.