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Stability of stratified two-phase flows in horizontal channels

机译：水平通道中分层两相流的稳定性

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Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems, the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength. (C) 2016 AIP Publishing LLC.
机译：研究了水平通道内分层两相流对任意波数扰动的线性稳定性。对于每个子层中定义的流函数扰动，该问题都简化为Orr-Sommerfeld方程，并通过边界条件耦合，边界条件也考虑了可能的界面变形和毛细作用力。应用切比雪夫搭配方法，将方程和界面边界条件简化为利用特征值线性代数的标准方法针对整个特征值谱和相关特征向量求解的广义特征值问题。关于不稳定性质的一些其他结论是从最不稳定的扰动模式得出的。结果以稳定性图的形式汇总，显示了分层光滑流动模式稳定的运行条件。发现对于气-液和液-液系统，具有光滑界面的分层流仅在相对较低流速的密闭区域中是稳定的，这与实验一致，但是不能通过长波分析来预测。取决于流动条件，临界扰动可以主要起源于界面（所谓的“不稳定性的界面模式”）或大部分的相之一（即“剪切模式”）。目前的分析表明，不稳定的类型与扰动波长之间没有明确的相关性。 （C）2016 AIP出版有限责任公司。

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