Nonlinear Stability Characterization of Thin Newtonian Liquid Films Flowing down a Cylinder Moving in a Vertical Direction

沿垂直方向移動之直立圓柱表面流下的牛頓流體薄膜流的非線性穩定性分析

宋鴻明(Hung-Ming Sung) ； 李宗乙(Zong-Yi Lee) ； 徐仲亭(Chung-Ting Hsu)

《修平學報》 24期 (2012/03) Pp. 69-84

https://doi.org/10.29548/BGYY.201203.0006

摘要

本文針對牛頓流體薄膜流，探討沿垂直方向移動的直立圓柱表面流下的薄膜流之非線性液動穩定性問題。首先使用長波微擾法推導薄膜的自由面方程式，在探討薄膜流場的穩定性問題上，主要分析圓柱的移動效應對系統穩定性的影響。研究結果顯示，在非線性液動穩定性分析中指出亞臨界穩定及超臨界穩定現象的存在；圓柱在垂直方向不同的移動條件，為影響薄膜流穩定性之重要因素。

關鍵字

牛頓流體 ； 薄膜流 ； 長波微擾法

並列摘要

This study presents a nonlinear stability analysis of thin Newtonian liquid films flowing down a cylinder moving in a vertical direction. The long-wave perturbation method is employed to derive the generalized kinematic equations for a free film interface. The current thin liquid film stability analysis provides a valuable input to investigations into the influence of the style of motion of the vertical cylinder on the stability behavior of the thin film flow. The modeling results indicate that both subcritical instability and supercritical stability conditions are possibly to occur in the film flow system. The movement of vertical cylinder significantly affects the stability behaviors of thin film flow. These behaviors can be quantitatively characterized in details by using the proposed approach.

並列關鍵字

Newtonian liquid ； thin film flow ； long-wave perturbation

參考文獻

Lin, C. C. The theory of hydrodynamic stability, （Cambridge : Cambridge University Press, 1955）.

Chandrasekhar,S. Hydrodynamic and hydromagnetic stability, （Oxford : Oxford University Press,1961）.

Stuart, J. T. “On the role of Reynolds stresses in stability theory,” J. Aero. Sci., 23（1956）, pp.86-88.

Benjamin T. B. “Wave formation in laminar flow down an inclined plane,” J. Fluid Mech. 2 （1957） , pp.554-574.

Yih C. S. “Stability of liquid flow down an inclined plane,” Phys. Fluids 6 （1963）, pp.321-334.