Counter‐current gas‐liquid wavy film flow between the vertical plates analyzed using the Navier‐Stokes equations

Abstract

in Wiley InterScience (www.interscience.wiley.com).The article is devoted to a theoretical analysis of counter-current gas-liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier-Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier-Stokes system and (2) the simplified Benjamin-Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u-velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative uvelocities take place in the neighbourhood of the film thickness minimumHere, Re ¼ 20 and k neut /L ¼ 0.25; (a) and (e) correspond to U GS ¼ 2.5 m/s; (b) and (f), U GS ¼ 7.0 m/s; (c) and (g) U GS ¼ 8.5 m/s; (d) and (h) U GS ¼ 9.07 m/s. Lines 1-3 correspond to water at k neut /L ¼ 0.25, 0.2, 0.15, respectively. Lines 4-6 correspond to 2.5% butanol at k neut /L ¼ 0.25, 0.2, 0.15, respectively.

Nonlinear waves in counter-current gas–liquid film flow

“…It should be noted that the results are sensitive to the period. This is to be expected and was also found by Trifonov (2010). It suggests that the flooding velocity is sensitive to the typical wave-separation length.…”

“…The approach adopted in the present paper is similar to that of Demekhin (1981) and a recent study by Trifonov (2010), namely the gas problem is solved independently under appropriate assumptions. However, instead of solving the full Navier-Stokes equations for the liquid problem, as in Trifonov (2010), we derive various lowdimensional models, i.e.…”

“…However, instead of solving the full Navier-Stokes equations for the liquid problem, as in Trifonov (2010), we derive various lowdimensional models, i.e. a long-wave model, a weakly nonlinear model and an IBL approximation based on weighted residual techniques.…”

“…Compared with the studies by Demekhin (1981) and Trifonov (2010), we use a more accurate model to obtain the perturbations to the shear stress and to the pressure at the interface imposed by the turbulent gas, namely we choose to work in curvilinear boundary-layer coordinates and make use of the quasi-laminarity assumption of Miles (1957) and Benjamin (1959) (Demekhin 1981 andTrifonov 2010 also used the Miles-Benjamin quasi-laminarity assumption but worked in Cartesian coordinates). However, in the works by Miles (1957) and Benjamin (1959), the influence of turbulence comes only through the turbulent mean velocity profile and the usual Navier-Stokes equations are used.…”

“…computations, unlike Trifonov (2010) who focused on travelling waves only. Moreover, the IBL model has certain advantages over full Navier-Stokes especially for moderate Reynolds numbers: it is a low-dimensional model expressed in terms of interfacial and average quantities which makes it attractive for both mathematical and numerical scrutiny.…”