|Abstract: ||本文以數值方法探討微流道內之滑動氣體流場, 工作流體為氮氣和氦氣, 假設流體為連體但邊界為可滑動。雖然本文作者在不久前成功地以解非穩態可壓縮之Navier-Stokes方程式來探討此一問題, 但因此方程組之雙曲及拋物線特性使得此一解法非常沒有效率, 本研究結果證實滑動氣體流場可由穩態可壓縮之邊界層方程式來求解。由於穩態邊界層方程式為一組拋物線方程組, 其解可以快速求得, 使得此一解法成為研究滑動氣體流場之高效率精確工具。本文結果也讓我們瞭解滑動流場之有趣特性: (1)驅動此一流場之壓力梯度相當大但由於與壁面之摩擦力很大管內流體速度相當小, 其相對之雷諾數亦相當小, 大約是10/sup -3/到10/sup -2/, 因此本文所探討之流場可假設為層流。(2)在微流道內擴散為動量及能量交換傳遞的主要方式, 滑動邊界是由於氣體分子與管壁動量及能量交換不完全所致, 此一滑動邊界對流場速度及質流率均有決定性的影響。|
The present work studies numerically gaseous flow in micro-channels. The working fluids are nitrogen and helium and their Knudsen numbers at the channel outlet are 0.055 and 0.165, respectively. The proposed model assumes the fluid is a continuum but employs a slip boundary condition on the channel wall. Although slip flows in micro-channels can be investigated by solving the unsteady, compressible Navier-Stokes equations, as was done previously by the author, the hyperbolic-parabolic character of the equations makes it very inefficient. The results of present work show that they 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 flows. The results of present study also reveal some interesting features of micro-channel flows. First, a large pressure gradient is required to drive the flow due to the extraordinarily small channel height, but the velocity remains very small in the cases studied due to the high shear stress at the wall. Since the velocities are small, the corresponding Reynolds numbers are also small, on the order of 10/sup -3/ to 10/sup -2/, the flows simulated can be safely assumed to be laminar. Second, diffusion is the dominant mechanism in momentum and energy transfers inside the channel. The slip boundary condition is the result of rarefaction which is due to the incomplete momentum and energy exchanges between gas molecules and the walls. Our results show that the slip condition has decisive effects on the velocity and mass flow rate of the flow.