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Linear and nonlinear instabilities of a co-current gas-liquid flow between two inclined plates analyzed using the Navier-Stokes equations
International Journal of Multiphase Flow ( IF 3.8 ) Pub Date : 2020-01-01 , DOI: 10.1016/j.ijmultiphaseflow.2019.103159
Yu.Ya. Trifonov

Abstract The paper is devoted to a theoretical analysis of a co-current gas-liquid flow between two inclined plates. As a first step, we linearized the Navier-Stokes equations in both phases and carried out a linear stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. We obtained two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral and the fastest growing disturbances varying the liquid and gas Reynolds number. The first mode corresponds to the Kapitza's waves at small values of the gas superficial velocity. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase. We found that the co-current gas velocity destabilize the film flow at all values of the inclination angle and distance between the plates considered in the paper. The range of the wavelength of the unstable disturbances essentially increases with the gas velocity increasing. As a second step, we have performed the systematic study of nonlinear wave regimes. We found that the gas flow affects significantly the wave characteristics decreasing the amplitude and increasing the phase velocity. The complex multi-fold and multi-sheet surface, found on the plane of parameters (wavelength and the liquid Reynolds number) for the gravitational film flow, exists at all velocities of the co-current gas flow. We carried out investigation of the “optimal” waves for several folders and presented comparison with the regimes observed in experiments. Using of the strict equations without any additional assumptions is an important feature of this paper.

中文翻译:

使用 Navier-Stokes 方程分析的两个倾斜板之间并流气液流动的线性和非线性不稳定性

摘要 本文致力于对两斜板之间并流气液流动的理论分析。作为第一步,我们对两个阶段的 Navier-Stokes 方程进行线性化,并对基本稳态解在液体雷诺数和气体表观速度的广泛变化下进行线性稳定性分析。我们获得了不稳定扰动的两种模式,并计算了它们的中性和增长最快的扰动的波长和相速度,这些扰动会随着液体和气体雷诺数的变化而变化。第一种模式对应于气体表观速度值较小时的卡皮察波。不稳定扰动的第二种模式对应于气相中向湍流的转变。我们发现,在论文中考虑的板之间的所有倾角和距离值下,并流气体速度都会使薄膜流动不稳定。不稳定扰动的波长范围基本上随着气体速度的增加而增加。第二步,我们对非线性波状态进行了系统研究。我们发现气流显着影响波特性,降低振幅并增加相速度。在重力薄膜流的参数(波长和液体雷诺数)平面上发现的复杂的多褶和多片表面,在并流气流的所有速度下都存在。我们对几个文件夹的“最佳”波进行了调查,并与实验中观察到的机制进行了比较。
更新日期:2020-01-01
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