Solitary waves on falling liquid films in the inertia-dominated regime

Fabian Denner,Berend G M Van Wachem,Serafim Kalliadasis,Christos N Markides,Alexandros Charogiannis,Marc Pradas

doi:10.1017/jfm.2017.867

Fabian Denner, Berend G M Van Wachem + Show 4 more

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https://doi.org/10.1017/jfm.2017.867

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Abstract

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

Highlights

Falling liquid films have been a topic of fundamental and applied research for several decades since the pioneering experiments by Kapitza (1948) and Kapitza & Kapitza (1949)
Despite the significant number of studies focusing on the hydrodynamics of solitary waves on falling liquid films, most of which have been conducted in the region of small-to-moderate Reynolds numbers (Re 20), a number of open questions regarding the hydrodynamics of inertia-dominated solitary waves still remain
Falling liquid films exhibit rich spatiotemporal dynamics governed by a complex interplay between inertia, viscosity, surface tension and gravity

Summary

Introduction

Falling liquid films have been a topic of fundamental and applied research for several decades since the pioneering experiments by Kapitza (1948) and Kapitza & Kapitza (1949). A falling liquid film is a convectively unstable open-flow hydrodynamic system with a rich variety of spatiotemporal structures and a sequence of wave instabilities and transitions that are generic to a large class of hydrodynamic and other nonlinear systems. Despite their apparent complexity one can still identify robust coherent structures, i.e. solitary waves, in what appears to be a randomly disturbed surface. Falling liquid films are typically associated with low flow rates, low pressure drops, small thermal resistances and large contact areas per unit volume Not surprisingly, they play a central role in a wide spectrum of engineering applications. The present study focuses on the hydrodynamic mechanisms that govern solitary waves on inertia-dominated falling films and, in particular, on flow features that have been shown to improve the heat and mass transport characteristics of the films

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