Hydromagnetic Instability of a Thin Condensate (Evaporating) Fluid Film Under Rotating Centrifugal Force

旋轉離心力於凝結（蒸發）液膜之磁液穩定性分析

鄭博仁(Po-Jen Cheng) ； 林銘哲(Ming-Che Lin)

《中國機械工程學刊》 37卷6期 (2016/12) Pp. 577-586

摘要

As a condensate (evaporating) film flow is formed, the propagating waves at the film surface produce the interfacial transfers of mass and heat. The consequence of the coupling energy equation of heat transfer is considered, while the vapor-liquid phase change processes also play a decisive role in the flow field. The macroscopic instabilities can cause the enhancement of mass and heat transfer to fluid flow. In magnetohydrodynamic flows, the conducting magnetic field and the fluid intensely interact and create complex magnetic and dynamic phenomena. Both the Naviere-Stokes equations of hydrodynamics and the Maxwell's equations of magnetic dynamic effects must be considered in MHD. The study investigates the stability on surface waves of the thin electrically-conductive and gravity-driven condensate (evaporating) liquid film flows with phase change under the effects of the magnetohydrodynamic field and centrifugal force using a long-wave perturbation method to solve for generalized kinematic equations with free film interface. The condensate (evaporating) effect, the Hartmann number, and the Rossby number of a gravity-driven liquid film are explored by employing stability analysis theories. The results point out the flow stability is enhanced as the film condenses, while the evaporating property has a destabilizing effect. Moreover, it is revealed that by increasing the Hartmann number and decreasing Rossby number tends to intensify the stability as traveling down along the rotating vertical cylinder.

關鍵字

phase change ； Hydromagnetic instability ； liquid film

並列摘要

當接觸面上形成凝結(蒸發)薄膜流時，薄膜表面傳遞的波在交界面產生質傳與熱傳現象，此時，液－汽相變化的影響將扮演重要角色，因此熱傳特性的能量方程式需加入流場模型中，而此流場的不穩定性將增加交界面的質傳與熱傳效應。磁液動流中，流體流動方程式和電磁場方程式交互效應是高度複雜的，因為它涉及同時求解流體流動之納米爾－史脫克斯方程式和描述磁場的麥克斯威爾方程式。本文利用長波微擾解所得到之廣義自由面運動方程式，探討磁液動力場和離心力作用於具相變化電導性凝結(蒸發)液膜之表面波，所表現的磁液動穩定性，分析凝結(蒸發)效應、漢特曼數及羅斯比數等參數，對重力作用下相變流體薄膜系統的影響。結果指出凝結流比蒸發流較具穩定作用，再者，增加漢特曼數及減少羅斯比數，旋轉圓柱液膜磁液動穩定性提高。