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

机译:垂直逆流层流气液流动中的线性和非线性不稳定性

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We consider the genesis and dynamics of interfacial instability in vertical 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 two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. 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 interfacial mode for low density contrast. 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. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes - from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation. (C) 2016 AIP Publishing LLC.
机译:我们使用垂直流-气流动中界面不稳定性的发生和动力学,以逆流气体剪切下的薄降膜的二维通道流为模型。该方法是线性稳定性理论(Orr-Sommerfeld分析),以及在非线性扰动情况下两相流的直接数值模拟。我们研究了两个主要流动参数对界面动力学的影响,即膜厚度和施加以驱动气流的压降。为了与文献中的现有研究联系,还检查了各种密度对比的影响。基于Orr-Sommerfeld理论的能量预算分析显示,在高密度对比的情况下,各种共存的不稳定模式(界面,剪切,内部)会导致模式合并和模式竞争,但对于低密度只有一种动态相关的不稳定界面模式对比。对低密度对比的绝对和对流不稳定性的研究表明,除了所研究参数空间的两个狭窄区域以外,该系统对于所有其他区域都是绝对不稳定的。对同一系统的直接数值模拟(低密度对比)表明,线性理论在大振幅波的出现以及弱非线性波的存在上具有明显的优势。对于高密度对比度(更接近于空气-水型系统),线性稳定性理论还可以成功确定早期到中间时间界面波动力学中最主要的特征。然而,由线性理论选择的短波经历了二次不稳定性,并且波列不再规则,而是呈现出混沌运动。相同的线性稳定性理论可以预测波的传播方向何时发生变化-从向下到向上。我们从负载和洪水的角度概述了这种变化的实际含义。波的传播方向的变化以基于液体和气体流速的流图以图形方式表示,并且预测仅以很小的偏差就可以延续到非线性状态。 (C)2016 AIP出版有限责任公司。

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