Detailed hydrodynamic characterization of harmonically excited falling-film flows: A combined experimental and computational study

Abstract

We present results from the simultaneous application of planar laser-induced fluorescence (PLIF), particle image velocimetry (PIV) and particle tracking velocimetry (PTV), complemented by direct numerical simulations, aimed at the detailed hydrodynamic characterization of harmonically excited liquid-film flows falling under the action of gravity. The experimental campaign comprises four different aqueous-glycerol solutions corresponding to four Kapitza numbers (Ka = 14, 85, 350, 1800), spanning the Reynolds number range Re = 2.3-320, and with forcing frequencies f w = 7 and 10 Hz. PLIF was employed to generate spatiotemporally resolved film-height measurements, and PIV and PTV to generate two-dimensional velocity-vector maps of the flow field underneath the wavy film interface. The latter allows for instantaneous, highly localized velocity-profile, bulk-velocity, and flow-rate data to be retrieved, based on which the effect of local film topology on the flow field underneath the waves is studied in detail. Temporal sequences of instantaneous and local film height and bulk velocity are generated and combined into bulk flow-rate time series. The time-mean flow rates are then decomposed into steady and unsteady components, the former represented by the product of the mean film height and mean bulk velocity and the latter by the covariance of the film-height and bulk-velocity fluctuations. The steady terms are found to vary linearly with the flow Re, with the best-fit gradients approximated closely by the kinematic viscosities of the three examined liquids. The unsteady terms, typically amounting to 5%-10% of the mean and peaking at approximately 20%, are found to scale linearly with the film-height variance. And, interestingly, the instantaneous flow rate is found to vary linearly with the instantaneous film height. Both experimental and numerical flow-rate data are closely approximated by a simple analytical relationship with only minor deviations. This relationship includes terms such as the wave speed c and mean flow rate Q, which can be obtained by relatively simple and inexpensive methods, thus allowing for spatiotemporally resolved flow-rate predictions to be made without requiring explicit knowledge of the full flow-field information underneath the wavy interface.

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

“…The agreement between experimental measurements and DNS results is in general very good, especially for the small Reynolds numbers, cases A1 (Re = 5.1) and B1 (Re = 7.5). At larger Reynolds numbers the flow field is strongly dependent on the local wave shape and can vary rapidly in space, as shown by the experimental measurements of Charogiannis et al (2017) for instance. Hence, in particular at the front of the solitary wave (see figure 12c), small differences in local film height and measurement position can lead to noticeable differences in the velocity profile.…”

“…The experimental apparatus and methodologies developed to generate the film thickness and velocity data have been described extensively in our previous publications (Charogiannis et al , 2017, and therefore only a summary is presented here for the sake of clarity and completeness. A schematic of the experimental arrangement, itself an evolution of a previously developed set-up (Mathie et al 2013;Markides et al 2015), is depicted in figure 2.…”

“…The flow rate and the maximum velocity in the film exhibit their highest values at (approximately) the same Reynolds number at which the film height reaches its maximum. With respect to the link between film height and flow rate, this is to be expected based on the recent study of Charogiannis et al (2017), reporting a linear relationship between film height and flow rate. However, the connection of the film height (and flow rate) with the maximum flow velocity and the recirculation in the moving frame of reference has not been reported before.…”

“…Note that for the flow conditions studied in figure 15, a theoretical criterion derived by Rohlfs & Scheid (2015) predicts the onset of flow recirculation for Re circ ≈ 20, which is in reasonable agreement with the observed onset of flow recirculation at Re circ ≈ 25. A possible explanation for this difference in Re circ is the reduced bulk velocity compared to the Nusselt solution for increasing wave height reported by Charogiannis et al (2017), that shifts the critical local flow rate for the onset of flow recirculation to a higher Reynolds number. Aside from the reduction of (streamwise) translational kinetic energy, the onset of flow recirculation in the moving frame of reference also leads to a downward motion (in the wall direction) of the flow in the main wave hump.…”

Direct Effect of Solvent Viscosity on the Physical Mass Transfer for Wavy Film Flow in a Packed Column

“…A slightly discrepancy in the velocity profile is observed at higher Reynolds number (=77). As shown by Charogiannis et al 54 , flow field inside the film strongly depends on the local wave shape that quickly vary in space at higher Re value. Subsequently, a small difference in the measuring location can results in a noticeable change in the velocity profile.…”