Studies of wavy films in vertical gas-liquid annular flows

Annular gas-liquid flow is encountered in many industrial applications such as wetted-wall absorbers, falling-film reactors, condensers and evaporators and transport of oil and gas mixtures from offshore pipelines. Experimental observations show that the presence of waves on the liquid film increases the transport rates of momentum, heat and mass by 100 to 300% over those expected from the flat film. Previous modeling efforts to predict this transport enhancement have largely been unsuccessful as they were limited to very low Reynolds numbers. This work presents a new model for describing the evolution of large amplitude waves on laminar falling wavy films at high Reynolds numbers (Re {dollar}>{dollar} 100). The model is based on second-order boundary layer theory and includes the pressure variation across the film as well as higher order viscous terms. The consistency and accuracy of the model is verified by comparing the linear stability results with the classical Kapitza's boundary layer model and Orr-Sommerfeld studies of the two-dimensional Navier-Stokes equations. The asymptotic behavior of the model is investigated by transforming it to a traveling wave coordinate. Numerical integration of the traveling wave simplification of the model predicts the existence of chaotic large amplitude, non-periodic waves as observed in the experiments. The computed wave statistics such as wave celerities, rms values of film thickness, probability density functions and film thickness power spectra using the model are in good agreement with those measured on naturally excited fully developed flows at Re {dollar}>{dollar} 100. The present model also overcomes the main deficiency of the classical boundary layer models (namely, negative wall shear stress) predicts large amplitude waves (with peak to substrate ratios of 3 to 4) and better agreement with data.; The model developed for free falling film is also extended to countercurrent gas-liquid flow and it is shown that an increase in the gas flow rate increases the average film thickness, peak to substrate ratio and wave velocities. The model also predicts the existence of recirculation regions within the large waves which are responsible for the observed enhancement in the transport rates.