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