Reference EPFL-ARTICLE-147393doi:10.1115/1.2955990View record in Web of Science Record created on 2010-03-19, modified on 2017-05-10

Two-Phase Flow Patterns and Flow-Pattern Maps: Fundamentals and Applications

Countercurrent gas–liquid flow in inclined and vertical ducts — I: Flow patterns, pressure drop characteristics and flooding

A low-dimensional model capturing the fully coupled dynamics of a wavy liquid film in interaction with a strongly confined laminar gas flow is introduced. It is based on the weighted residual integral boundary layer approach of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369) and accounts for viscous diffusion up to second order in the film parameter. The model is applied to study two scenarios: a horizontal pressure-driven water film/air flow and a gravity-driven liquid film interacting with a co- or counter-current air flow. In the horizontal case, interfacial viscous drag is weak and interfacial waves are primarily driven by pressure variations induced by the velocity difference between the two layers. This produces an extremely thin interfacial shear layer which is pinched at the main and capillary wave humps, creating several elongated vortices in the wave-fixed reference frame. In the capillary wave region preceding a large wave hump, flow separation occurs in the liquid in the form of a vortex transcending the liquid–gas interface. For the gravity-driven film, a twin vortex (in the wave-fixed reference frame) linked to the occurrence of rolling waves has been identified. It consists of the known liquid-side vortex within the wave hump and a previously unknown counter-rotating gas-side vortex, which are connected by the same interfacial stagnation points. At large counter-current gas velocities, interfacial waves on the falling liquid film are amplified and cause flooding of the channel in a noise-driven scenario, while this can be delayed by forcing regular waves at the most amplified linear wave frequency. Our model is shown to exactly capture the long-wave linear stability threshold for the general case of two-phase channel flow. Further, for the two considered scenarios, it predicts growth rates and celerity of linear waves in convincing agreement with Orr–Sommerfeld calculations. Finally, model calculations of nonlinear interfacial waves are in good agreement with film thickness and velocity measurements as well as streamline patterns in both phases obtained from direct numerical simulations.

Wavy liquid films in interaction with a confined laminar gas flow

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.

/pdf/nonlinear-waves-in-counter-current-gas-liquid-film-flow-1a12xtio4h.pdf

Nonlinear waves in counter-current gas-liquid film flow

https://philon.cheng.auth.gr/philon/site/sdocs/s36.pdf

D.G. Kröger

Papers

Countercurrent gas–liquid flow in inclined and vertical ducts — I: Flow patterns, pressure drop characteristics and flooding

The influence of fluid properties and inlet geometry on flooding in vertical and inclined tubes

Countercurrent gas–liquid flow in inclined and vertical ducts — II: The validity of the Froude–Ohnesorge number correlation for flooding