Evolution of flow disturbances in cocurrent gas-liquid flows

Abstract

Studies of interfacial waves in horizontal gas-liquid flows, close to neutral stability, suggest that the rate of evolution of the interface may be linked to nonlinear interactions between the fundamental mode and the subharmonic -- even if the subharmonic is linearly stable. The rate of evolution increases as the subharmonic becomes more unstable. A comparison of linear stability techniques used to predict the initial behavior of waves reveals similar predictions of growth rates and almost identical speeds between a two layer laminar Orr-Sommerfeld theory and an Orr-Sommerfeld theory when the effect of the (turbulent) gas flow enters as boundary conditions on the liquid layer. However, there is disagreement at small wavenumbers as to the point at which the growth curve crosses 0. This is a significant problem because longwave disturbances, in our case roll waves, form by growth of (initially) small amplitude waves that have frequencies which are 0.5 to 1 Hz, which is in the range where the two theories disagree about the sign of the growth rate. While nonlinear effects are probably involved in the formation of the peak (at least while its amplitude is small), the linear growth rate must play an important role when the amplitude is small.