摘要
分别从分子运动论及连续流理论出发,对体积力驱动的微尺度平面泊肃叶(Poiseuille)流的横向分布特征进行了分析.分子水平模拟采用直接模拟蒙特卡罗(direct simulation Monte Carlo,DSMC)方法;连续流理论则主要考察了伯内特(Burnett)及超伯内特(Super--Burnett)等高阶连续模型,在平行流假设下,获得一组高阶非线性常微分方程,补充完整的边界条件,并应用龙格--库塔(Runge--Kutta)方法求解.结果表明,即使对于过渡领域流动,高阶连续模型可以给出与DSMC结果完全相符的压力分布,而速度分布当努森(Knudsen)数约为0.2时即在壁面开始出现偏差;对于温度的横向分布,伯内特模型回复到纳维--斯托克斯(Navier--Stokes)水平,不能得到与DSMC一致的双峰结构,而超伯内特模型在滑移流动领域与DSMC定性相符,在过渡领域却仅能正确预测主流区温度分布,壁面附近差异明显;横向热流与纳维--斯托克斯模型预测接近,但机理上存在本质区别.本文结果提示选用连续模型时,不仅要根据流动参数来判断,还可以根据所关注的物理量来进行调整,适度扩大连续模型的适用范围.但即使采用高阶本构关系,连续模型仍然不能完全描述壁面附近区域的非平衡效应(如努森层效应),这是试图扩大连续模型适用范围时必然会遇到的困难.
In this paper, the planar microchannel force-driven Poiseuille flow was analyzed by using the gas kinetic theory and the macroscopic continuous flow theory, respectively. In the kinetic theory, the direct simulation Monte Carlo （DSMC） method was used where the body force was a substitute for the pressure gradient in order to ignore the length effect of the channel. In the continuous flow theory, the Burnett and super-Burnett constitutive relations were adopted and nonlinear ordinary differential equations of higher-orders were obtained by the hypothesis of parallel flow. Then, the equations were solved by Runge-Kutta method with the necessary boundary conditions. It was shown that the pressure distribution predicted by the high order continuous model could agree very well with that by DSMC even when the flow was in the transition region. And deviation of the velocity would exist near the wall when the Knudsen number is larger than 0.2. The temperature dip can not be obtained by Burnett model what will revert to the Navier-Stokes model for temperature distribution. The super-Burnett model can capture the temperature dip, similar to the DSMC result, while the temperature profile near the wall is quite different from the DSMC result. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model.
出处
《力学学报》
EI
CSCD
北大核心
2013年第3期314-322,共9页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金委员会与中国工程物理研究院联合基金资助项目(10976029)
The project was supported by the National Natural Science Foundation of China-NSAF(10976029)
