Interfacial dynamics in counter-current gas-liquid flows
This dissertation considers the genesis and dynamics of interfacial instability in vertical laminar 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 by means of Orr-Sommerfeld analysis together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. The influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream, is investigated. To make contact with existing studies in the literature, the effect of various density and viscosity contrasts as well as surface tension 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 and intermediate density contrast. Furthermore, high viscosity contrast and increases in surface tension lead to some amount of mode competition for thin film. 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. These regions are extended at intermediate density contrast and exhibit only small changes with increased viscosity contrast or surface tension. Direct numerical simulations of the system with 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. Furthermore, linear stability theory also predicts when the direction of travel of the waves changes - from downwards to upwards. The practical implications of this change in terms of loading and flooding is discussed. The change in direction of the wave propagation is represented graphically for each investigated system 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. Besides the semi-analytical and numerical analyses, experiments with an practically relevant setup and flow system have been carried out to benchmark and validate the models developed in this work.
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