Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows
- School of Engineering, The University of Edinburgh, Edinburgh EH9 3JL (United Kingdom)
- School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4 (Ireland)
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.
- OSTI ID:
- 22599000
- Journal Information:
- Physics of Fluids, Vol. 28, Issue 4; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-6631
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
42 ENGINEERING
AIR
CHAOS THEORY
COMPUTERIZED SIMULATION
CONVECTIVE INSTABILITIES
COUNTER CURRENT
DENSITY
FLOW RATE
GAS FLOW
LIQUID FLOW
LIQUIDS
NONLINEAR PROBLEMS
PRESSURE DROP
STABILITY
STREAMS
TWO-DIMENSIONAL CALCULATIONS
TWO-PHASE FLOW
WAVE PROPAGATION