现代物理  >> Vol. 2 No. 2 (May 2012)

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

DOI: 10.12677/mp.2012.22004, PDF, HTML, 下载: 3,069  浏览: 10,394  国家自然科学基金支持

作者: 樊小朝*:新疆大学电气工程学院

关键词: 特殊饱和液膜流动稳定性摄动法Orr-Sommerfeld方程
Special Saturated Liquid Film; Flow Stability; Perturbation Method; Orr-Sommerfeld Equation

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.

文章引用: 樊小朝. 特殊饱和液膜流动稳定性Orr-Sommerfeld方程求解及分析[J]. 现代物理, 2012, 2(2): 21-24. http://dx.doi.org/10.12677/mp.2012.22004

参考文献

[1] 李欣. 波动液膜流动传热特性及稳定性研究[D]. 华北电力大学, 2006.
[2] 田英. 分层液膜流动传热特性及影响因素分析[D]. 华北电力大学, 2008.
[3] Y. L. Cheng, X. C. Fan. Effect of Stratification on stability of flow and heat transfer in the liquid film flowing down an inclined heated plate. Modern Physics Letters B, 2010, 24(13): 1461-1465.
[4] 叶学民, 阎维平, 蒋章焰, 王军. 自由降膜表面波流动和传热特性的研究[J]. 华北电力大学学报, 1999, 26(1): 7-12.
[5] 杨世铭, 陶文铨编著. 传热学[M]. 北京: 高等教育出版社, 2006: 211.
[6] S. G. Bankoff. Dynamics and stability of thin heated liquid films. Journal of Heat Transfer, 1990, 112(3): 538-546.
[7] 程友良, 叶学民. 非线性表面张力对饱和液膜传热稳定性的影响[J]. 华北电力大学学报, 2002, 29(2): 50-54.
[8] 师晋生, 施明恒. 饱和下降液膜的稳定性研究[J]. 应用力学学报, 1999, 16(4): 27-34.