Nonlinear waves on liquid film surfaces—I. Flooding in a vertical tube

Abstract The recently available data on flooding in two-phase annular flow are examined via a simplified version of the Navier-Stokes equation. Instantaneous stress exerted on the interface by the gas phase is described by validated empirical correlations. Analysis of the equation then explains why the flat-film thickness is found to be in agreement with time-averaged values under total downflow and total upflow conditions. Wave celerity obtained from the equation is also found to be in excellent quantitative agreement with experimental data. More importantly, the simplicity of the equation allows analysis on the growth of nonlinear, finite-amplitude waves from the surface. A mechanism explaining the observed irregular wave behaviour near flooding is suggested.

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