修正后的N-S方程研究微流动的稳定性

Modified N-S equations to study the stability of micro-flow

研究了克努森数不是特别大的微流动的稳定性,这种流动处于N-S方程适用的临界处。考虑到壁面对流体的作用力,修正流体的黏性系数,然后用修正后的N-S方程研究微流动的稳定性。类比于势能的幂函数衰减形式,本文也定义了一个黏性系数的幂次衰减模型并讨论了模型参数对稳定性的影响。用切比雪夫配置点法解模型中的微分方程,用QR法分析流动的稳定性。在所研究的流动尺度内,受壁面的影响,失稳雷诺数减小。从速度分布图上看,出现了拐点,这种拐点越明显,流动越容易失稳。

Modified N-S equations have been used to study the stability of microflow with a not-too-large Knudsen number. This paper presents a new model considering the wall actions to express the viscosity in microflow. Chebyshev collocation method and the QR matrix eigenvalue algorithm have been employed to solve the Orr-Sommerfeld equation. The effects of the parameters of the model on the flow stability were also studied. The flow becomes less stable with modified viscosity,and the probable reason is that there is inflexion in average flow.