Absolute and convective instabilities in counter-current gas–liquid film flows
Journal of Fluid Mechanics
Absolute and convective instabilities in counter-current gas-liquid film flows. We consider a thin liquid film flowing down an inclined plate in the presence of a countercurrent turbulent gas. By making appropriate assumptions, Tseluiko & Kalliadasis (2011) developed low-dimensional non-local models for the liquid problem, namely a long-wave model and a weighted integral-boundary-layer model, that incorporate the effect of the turbulent gas. By utilising these models, along with the
... ith the Orr-Sommerfeld problem formulated using the full governing equations for the liquid phase and associated boundary conditions, we explore the linear stability of the gas-liquid system. In addition, we devise a generalised methodology to investigate absolute and convective instabilities in the nonlocal equations describing the gas-liquid flow. We observe that at low gas flow rates, the system is convectively unstable with the localised disturbances being convected downwards. As the gas flow rate is increased, the instability becomes absolute and localised disturbances spread across the whole domain. As the gas flow rate is further increased, the system again becomes convectively unstable with the localised disturbances propagating upwards. We find that the upper limit of the absolute instability region is close to the 'flooding' point associated with the appearance of large-amplitude standing waves, as obtained in Tseluiko & Kalliadasis (2011) , and our analysis can therefore be used to predict the onset of flooding. We also find that an increase in the angle of inclination of the channel requires an increased gas flow rate for the onset of absolute instability. We generally find good agreement between the results obtained using the full equations and the reduced models. Moreover, we find that the weighted integral-boundary-layer model generally provides better agreement with the results for the full equations than the longwave model. Such an analysis is important for understanding the ranges of validity of the reduced model equations. In addition, a comparison of our theoretical predictions with the experiments of Zapke & Kröger (2000a) shows a fairly good agreement. We supplement our stability analysis with time-dependent computations of the linearised weighted integral-boundary-layer model. To provide some insight into the mechanisms of instability, we perform an energy budget analysis.