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Effect of wall corrugations on scalar transfer to a wavy falling liquid film

Published online by Cambridge University Press:  28 November 2018

Georg F. Dietze Open the ORCID record for Georg F. Dietze [Opens in a new window]
Georg F. Dietze*
Affiliation:
Laboratoire FAST, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France
*
†Email address for correspondence: dietze@fast.u-psud.fr
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Abstract

Direct numerical simulation is employed to study the effect of small-scale wall corrugations on scalar transfer through the wavy surface of a vertically falling liquid film in interaction with a strongly confined counter-current gas flow. Three wall geometries are considered: (i) a flat wall for reference; (ii) a sinusoidal corrugation typically found on structured packings in chemical engineering devices; and (iii) a heuristic design consisting of isolated semicircular bumps distanced by the wavelength of the surface waves. We consider the limiting case of a Dirichlet condition for the transported scalar (temperature or mass fraction) at the liquid–gas interface and focus on liquid-side transport. We consider convection-dominated regimes at moderate and large Péclet numbers, representative of heat and mass transfer respectively, and confront forced and noise-driven wave regimes. Our results show that sinusoidal wall corrugations increase transfer by up to 30 per cent in terms of the exchange length required to transfer a fixed amount of the transported quantity. A slightly greater intensification is achieved through the bump-shaped corrugations, which intermittently disrupt the moving-frame vortex forming within the large-amplitude solitary waves, allowing these to replenish with unsaturated liquid. However, when the velocity of the strongly confined gas flow is increased above a certain threshold, the bumps can trigger the flooding of the channel.

JFM classification

Mixing: Mixing Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 1098 - 1128
Copyright
© 2018 Cambridge University Press 

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Dietze supplementary movie 1

Repeated extrusion of scalar plumes from the interfacial scalar boundary layer (figure 5). Case 4 (table 1): periodically-forced waves, long sinusoidal wall corrugation, strongly-dominant convection (Pe=4590).

Download Dietze supplementary movie 1(Video)
Video 2.3 MB

Dietze supplementary movie 2

Repeated de- and acceleration of the leading front of surface waves moving over the long sinusoidal corrugation. Case 4 (table 1): periodically-forced waves.

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Video 1.7 MB

Dietze supplementary movie 3

Redistribution of liquid within a wave hump as it moves over a bump-shaped corrugation (figures 7 and 8). Case 5 (table 1): periodically-forced waves, strongly-dominant convection (Pe=4590).

Download Dietze supplementary movie 3(Video)
Video 2 MB

Dietze supplementary movie 4

Cascade of flooding events at successive bump-shaped corrugations after increasing the gas flow (figure 12). Case 5 (table 1) with additional stepwise increase of counter-current gas flow rate (figure 11a).

Download Dietze supplementary movie 4(Video)
Video 1.4 MB

Dietze supplementary movie 5

Flooding at the third bump-shaped corrugation after increasing the gas flow rate (figure 12b). Case 5 (table 1) with additional stepwise increase of counter-current gas flow rate (figure 11a). Contours show the streamwise velocity component (blue: upward flow; red: downward flow).

Download Dietze supplementary movie 5(Video)
Video 1.2 MB