On reduced modeling of mass transport in wavy falling films

Abstract

In many industrial units such as packing columns, falling film reactors, etc., the liquid phase is designed as a falling film. It is well known that the mass and heat transfer in laminar wavy film flows is significantly enhanced compared to flat films. The kinetic phenomena underlying the increase in mass and heat transfer are, however, still not fully understood. For an efficient design of falling film units, computational models that account for these enhanced transport mechanisms are of key importance. In this article, we present a reduced modeling approach based on a long-wave approximation to the fluid dynamics of the film. Furthermore, we introduce a new two-dimensional (2D) high-resolution laser-induced luminescence measurement technique. Both in the numerical simulation results and in the high-resolution 2D-concentration measurements obtained in the experiments we observe similar patterns of high concentrations locally, especially in the areas close to the wave hump.Since the species transport is dominated by the liquid side, the key idea toward a reduced model is to reduce the detailed two-phase model to a one-phase model of the liquid film phase only, which is still able to account for the wavy enhancement mechanisms. To this end, the two-phase NSE are replaced byThe colored areas resemble the light collected on the CCD-sensor for the first image (P 1 ) and the second image (P 2 ). [Color figure can be viewed at wileyonlinelibrary.com.]

A numerical study of mass transfer from laminar liquid films

“…There is a considerable body of literature devoted to this topic which has been described in books (Chang & Demekhin 2002; Kalliadasis et al 2012) and in many review articles (see, e.g. Chang 1994; Oron, Davis & Bankoff 1997; Weinstein & Ruschak 2004; Craster & Matar 2009; Bandi et al 2018). It has long been known that the film surface ceases to remain plane as soon as the Reynolds number exceeds a critical value, which is a decreasing function of the inclination angle and vanishes for a vertical surface.…”

“…Some authors (see, e.g. Sisoev et al 2005; Rastaturin et al 2006; Bandi et al 2018) combined the film thickness predicted by such models with a parabolic velocity profile to tackle the diffusion problem. While the actual velocity distribution can be approximately parabolic if the local flow rate is used, an uncertainty remains as to the overall correctness of the approach.…”

Transportmodelle für Flüssigkeitsfilme

“…Allerdings hängt die Totzeit bei Flüssigkeitsfilmen von zeitveränderlichen Größen wie den Liquideigenschaften und dem Massenstrom ab [8], weshalb die Modellierung mit konstanter Totzeit lediglich eine grobe Näherung darstellt. Des Weiteren treten insbesondere bei gravitationsgetriebenen Flüssigkeitsfilmen Oberflächenwellen auf [4,15]. Letztere bestehen aus einem großen Wellenbuckel und kleineren Kapillarwellen davor [2,4].…”

“…Des Weiteren treten insbesondere bei gravitationsgetriebenen Flüssigkeitsfilmen Oberflächenwellen auf [4,15]. Letztere bestehen aus einem großen Wellenbuckel und kleineren Kapillarwellen davor [2,4]. Neben diesen Phänomenen sind zahlreiche weitere Effekte -wie Turbulenz, Druckgradienten, Fouling oder der Marangoni-Effekt -möglich, die das dynamische Flussverhalten beeinflussen können [19].…”

“…Im E/A-Verhalten eines Flüssigkeitsfilm bzgl. des Massenstroms sind sowohl die zeitvariable Totzeit als auch das Überschwingen des Ausgangsmassenstroms auf Grund des großen Wellenbuckels ersichtlich [2,4,34]. Daher sind Modelle erforderlich, welche diese Phänomene abbilden können.…”