Abstract
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.
Highlights
Interface becomes unstable, leading to the development of waves
Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes 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
One of the first to investigate a channel flow with two superimposed fluid layers from a theoretical point was Yih,[1] who used asymptotic expansion to solve the Orr-Sommerfeld (OS) eigenvalue problem associated with the temporal linear stability in the long wavelength limit for equal densities and layer thicknesses. He found that viscosity stratification alone can cause interfacial instability at arbitrarily small Reynolds numbers, which is referred to as Yih mechanism
Summary
Further classification of parallel flow instability is made by way of the absolute/connective dichotomy,[4] which we pursue in the present context of counter-current vertical flows In this way, linear stability analysis is shown to be an effective technique to understand the genesis of interfacial instability. A large number of studies on the nonlinear dynamics of interfacial flows are based on these kind of models.[6,7,8,9] given that their range of applicability is generally not known in advance, they may at times produce incorrect results (e.g., the erroneous prediction of absolute instability in a falling film, as highlighted by Brevdo et al.[10]) This is especially the case for flow regimes involving large pressure fluctuations and potentially large-amplitude waves, for which there is a major necessity to gain fundamental understanding.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
