Hydrodynamic stability of a sheared liquid film
Hydrodynamic stability of a sheared liquid film
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剪切液膜的流体动力学稳定性
DOI：
10.1017/s0022112095003855
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发表时间：
1995
影响因子：
3.7
通讯作者：
B. Boersma
中科院分区：
文献类型：
--
作者：
R. Miesen;B. Boersma
我们研究了被气体剪切的液体薄层的流体动力学稳定性。首先，讨论了自由面近似问题的界面条件。然后，我们研究的相速度小于最大速度在液膜，即内部模式，扩展以前的结果和解决一些明显的矛盾的干扰流的稳定性。通过放弃自由表面近似，求解气体和液体的Orr-Sommerfeld方程，研究了气体的动力学效应。对液膜稳定性的影响非常大，这可以用波速的虚部（决定膜的稳定性）非常小来解释。因此，自由面近似法一般是不正确的。然后，我们研究的韦伯数上的临界雷诺数的依赖性，液体速度分布的曲率和气体的性质。与气体包括在内，第二种模式的不稳定性被发现具有相速度，这是，在一般情况下，大于最大液体速度，并对应于毛细重力波。我们比较结果与文献中的实验，良好的协议被发现。最后，本研究的相关性，以产生“滚波”，这是重要的，从实用的角度来看，给出了一个建议。
We study the hydrodynamic stability of a thin layer of liquid that is sheared by a gas. First, the interface conditions for the free surface approximation of the problem are discussed. We then study the stability of the flow to disturbances with phase speeds smaller than the maximum velocity in the liquid film, i.e. the internal mode, extending previous results and resolving some apparent contradictions. The dynamic effect of the gas is studied by dropping the free surface approximation and solving the Orr-Sommerfeld equation for the gas together with that for the liquid. The effect on the stability of the liquid film is very large, which is explained by the fact that the imaginary part of the wave speed (which determines the stability of the film) is very small. Consequently the free surface approximation is, in general, not correct. We then study the dependence of the critical Reynolds number on the Weber number, on the curvature of the liquid velocity profile and on the properties of the gas. With the gas included, a second mode of instability is found which has a phase velocity that is, in general, larger than the maximum liquid velocity and corresponds to capillary-gravity waves. We compare results with experiments from the literature; good agreement is found. Finally, a suggestion on the relevance of this study to the generation of ‘roll waves’, which are important from a practical point of view, is given.