倒置平面基底上液膜流动的演化特性研究  

Study on evolution characteristics of liquid film flowing down inverted substrates

作　　者：邵明玉 张忠伟 马驰骋[1] 荆栋[1] 华珍[1] SHAO Mingyu;ZHANG Zhongwei;MA Chicheng;JING Dong;HUA Zhen(School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, China)

机构地区：[1]山东理工大学交通与车辆工程学院,山东淄博255000

出　　处：《西北大学学报（自然科学版）》2022年第3期452-458,共7页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金青年项目(11702162);山东省自然科学基金(ZR2018LE014,ZR2019BA001,ZR2016EEM12)。

摘　　要：薄膜流动作为工程中常用的传热/传质手段,广泛应用于换热器和聚合物成形等设备中。该文重点分析了倒置基底上的薄膜流动问题,从Navier-Stokes方程出发,利用润滑近似理论建立自由液面的运动控制方程,推导其变分形式;在开源有限元程序Freefem++中建立了有限元模型,并开展了二维数值模拟和三维数值模拟。通过数值模拟发现,倒置角度越大,流动形态演化的越快,当倒置角度较小时,流动呈现一种稳定的行波态,倒置角度较大时,液膜会在短期内演化为强衰减形态和孤立波并存的形式,经过足够长的时间后,液膜会完全演化成多个孤立波的形式。该文的工作可以方便地拓展到类似问题的研究中,为薄膜流动的数值模拟提供了一种新的思路。As a commonly used heat/mass transfer method in engineering,thin film flows are widely encountered in heat exchangers and polymer forming equipment.This paper mainly focuses on the dynamic problem of liquid film flowing down inverted substrates.Based on Navier-Stokes equation and lubrication approximation theory,the governing equation for the free liquid surface is established.Then the variational form of the governing equation is derived.Finite element model is set up in Freefem++,and two-dimensional and three-dimensional numerical simulation are given for different conditions.Numerical simulations show that with a larger inverted angle,the films also evolve faster.When the inverted angle is small,the flow presents a stable traveling wave state.When the inversion angle is large,the liquid film will evolve into coexistence form of strong damped oscillations and solitary waves.With enough time,the liquid film will completely evolve into multiple solitary waves.This work can be conveniently extended to the study of similar problems,which provides a new technology for the numerical simulation of thin film flow.

关 键 词：倒置基底 润滑理论 薄膜流动 有限单元法 Freefe m++ 

分 类 号：TU311[建筑科学—结构工程] P315.9[天文地球—地震学]