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arXiv 1507.04504physics.flu-dyn
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垂直逆流层流气液流动的线性和非线性不稳定性

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

Patrick Schmidt, Lennon Ó'Náraigh, Mathieu Lucquiaud, Prashant Valluri

摘要:

我们考虑气液两相流中界面不稳定性的成因和动力学,作为一个模型的二维槽道流的薄降膜剪切逆流气体。该方法是线性稳定性理论(Orr-Sommerfeld分析)与直接数值模拟的两相流的情况下,非线性扰动。我们研究了三个主要流动参数(液体和气体之间的密度对比、膜厚度、驱动气流的压降)对界面动力学的影响。基于Orr-Sommerfeld理论的能量收支分析揭示了在高密度对比度的情况下多种共存的不稳定模式(界面、剪切、内部),这导致模式合并和模式竞争,但对于低密度对比度,只有一种动态相关的不稳定内部模式。相同的线性稳定性方法提供了一个定量预测的开始(部分)液体流动逆转的气体和液体流速。低密度对比度的绝对和对流不稳定性的研究表明,该系统是绝对不稳定的,但两个狭窄的区域的研究参数空间。直接数值模拟相同的系统(低密度对比)表明,线性理论举行了非常好的大振幅波的发病以及弱非线性波的存在。相比之下,高密度对比度对应更密切的空气-水型系统,虽然线性稳定性理论是成功的,在确定最主要的功能,在界面波动力学在早期到中期的时间,由线性理论选择的短波进行二次不稳定性和波列不再是定期的,而是表现出混乱的动力学,并最终,波翻转。

英文摘要:

We consider the genesis and dynamics of interfacial instability in gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of three main flow parameters (density contrast between liquid and gas, film thickness, pressure drop applied to drive the gas stream) on the interfacial dynamics. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable internal mode for low density contrast. The same linear stability approach provides a quantitative prediction for the onset of (partial) liquid flow reversal in terms of the gas and liquid flow rates. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. In comparison, for high density contrasts corresponding more closely to an air-water-type system, although the linear stability theory is successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic dynamics and eventually, wave overturning.

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