特殊饱和液膜流动稳定性Orr-Sommerfeld方程求解及分析

Solution and Analysis of Orr-Sommerfeld Equation of Flow Stability on Special Saturated Liquid Film

摘要: 利用Navier-Stokes方程和边界条件对沿加热壁面倾斜下降的特殊饱和液膜的流动和传热问题进行了描述，并建立其数学模型，再根据温度的非线性函数表达表面张力与波动之间的关系，利用摄动法导出了描述液膜流动稳定性的Orr-Sommerfeld方程。最后对方程进行了求解，分析得到了惯性力、热毛细力、蒸汽压力以及毛细压力对流动稳定性的影响。

Abstract: The flow and heat transfer of the special saturated liquid film falling down an inclined heated plate were described by the N-S equation and the reasonable boundary condition. And the corresponding mathematical model was established, the relation between the surface tension and the fluctuation by nonlinear function on temperature was expressed. Then the Orr-Sommerfeld equation describing the flow stability of liquid film was obtained. Finally, the inertia force, heat capillary force, steam pressure and capillary pressure were analyzed about the influence on the flow stability.