微尺度库埃特流动系统数值模拟研究

Research on Numerical Simulation of Micro-scale Couette Flow System

随着微电子机械系统(MEMS)的迅速发展,其工程实际问题:比如微型马达、微型轴承中的流动与传热,已经成为研究的热点。探讨了一种在微电子机械系统中常见的流动系统库埃特流(Couette Flow)。从N-S方程、傅立叶导热定律、理想气体状态方程出发,建立起相应的数学模型。并采用广义微分积分方法(GDQ)来进行数值模拟。最后用蒙特卡洛直接模拟方法(DSMC)来验证,并将两者的数值结果加以分析和比较,新建理论模型的模拟结果与DSMC模拟结果基本吻合。该理论模型能用来模拟滑移区和过渡流动区的气体流动,采用的GDQ方法程序比DSMC程序简单,计算成本也低很多。低速流动时,该理论模型只能预测Kn<1.2时的流动特性。

With the rapid development of the micro electro-mechanical system（ MEMS）, the research on the flow and heat transfer is becoming more and more popular in micro motor and micro bearing often met in MEMS. In this paper, Couette flow which is a sort of flow system simplified in MEMS is mainly explored. The corresponding mathematical model has been built based on N-S Equation, Fourier＇s Law and idea gas state equation. Applying the generalized differential quadrature method （GDQ）, the numerical simulation is made. Finally using the direct simulation of Monte Carlo approach, the new model is verified. The solutions of the two different approaches are analyzed and compared. This model can been used to simulate the gas flow in the slip and transition region. The program of GDQ is more simple than DSMC＇s and its running cost is much lower. The theoretical model is only able to predict the low speed flowing characteristic with Kn〈1. 2.