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Nonlinear waves in counter-current gas-liquid film flow

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journal contribution
posted on 11.08.2014 by Dmitri Tseluiko, Serafim Kalliadasis
We investigate the dynamics of a thin laminar liquid film flowing under gravity down the lower wall of an inclined channel when turbulent gas flows above the film. The solution of the full system of equations describing the gas–liquid flow faces serious technical difficulties. However, a number of assumptions allow isolating the gas problem and solving it independently by treating the interface as a solid wall. This permits finding the perturbations to pressure and tangential stresses at the interface imposed by the turbulent gas in closed form. We then analyse the liquid film flow under the influence of these perturbations and derive a hierarchy of model equations describing the dynamics of the interface, i.e. boundary-layer equations, a long-wave model and a weakly nonlinear model, which turns out to be the Kuramoto– Sivashinsky equation with an additional term due to the presence of the turbulent gas. This additional term is dispersive and destabilising (for the counter-current case; stabilizing in the co-current case). We also combine the long-wave approximation with a weighted-residual technique to obtain an integral-boundary-layer approximation that is valid for moderately large values of the Reynolds number. This model is then used for a systematic investigation of the flooding phenomenon observed in various experiments: as the gas flow rate is increased, the initially downward-falling film starts to travel upwards while just before the wave reversal the amplitude of the waves grows rapidly. We confirm the existence of large-amplitude stationary waves by computing periodic travelling waves for the integral-boundary-layer approximation and we corroborate our travelling-wave results by time-dependent computations.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

JOURNAL OF FLUID MECHANICS

Volume

673

Pages

19 - 59 (41)

Citation

TSELUIKO, D. and KALLIADASIS, S., 2011. Nonlinear waves in counter-current gas-liquid film flow. Journal of Fluid Mechanics, 673, pp. 19-59.

Publisher

© Cambridge University Press

Version

VoR (Version of Record)

Publication date

2011

ISSN

0022-1120

eISSN

1469-7645

Language

en

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