A simultaneous planar laser-induced fluorescence, particle image velocimetry and particle tracking velocimetry technique for the investigation of thin liquid-film flows

Abstract

A simultaneous measurement technique based on planar laser-induced fluorescence imaging (PLIF) and particle image/tracking velocimetry (PIV/PTV) is described for the investigation of the hydrodynamic characteristics of harmonically excited liquid thin-film flows. The technique is applied as part of an extensive experimental campaign that covers four different Kapitza (Ka) number liquids, Reynolds (Re) numbers spanning the range 2.3 -320, and inlet-forced/wave frequencies in the range 1 -10 Hz. Film thicknesses (from PLIF) for flat (viscous and unforced) films are compared to micrometer stage measurements and analytical predictions (Nusselt solution), with a resulting mean deviation being lower than the nominal resolution of the imaging setup (around 20 μm). Relative deviations are calculated between PTV-derived interfacial and bulk velocities and analytical results, with mean values amounting to no more than 3.2% for both test cases. In addition, flow rates recovered using LIF/PTV (film thickness and velocity profile) data are compared to direct flowmeter readings. The mean relative deviation is found to be 1.6% for a total of six flat and nine wavy flows. The practice of wave/phase locked flow-field averaging is also implemented, allowing the generation of highly localized velocity profile, bulk velocity and flow rate data along the wave topology. Based on this data, velocity profiles are extracted from 20 locations along the wave topology and compared to analytically derived ones based on local film thickness measurements and the Nusselt solution. Increasing the waviness by modulating the forcing frequency is found to result in lower absolute deviations between experiments and theoretical predictions ahead of the wave crests, and higher deviations behind the wave crests. At the wave crests, experimentally derived interfacial velocities are overestimated by nearly 100%. Finally, locally non-parabolic velocity profiles are identified ahead of the wave crests; a phenomenon potentially linked to the cross-stream velocity field.

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

“…Note that the velocity profile is parabolic in the tail and underneath the crest of the solitary wave, even for the case with the highest Reynolds number (case C6, Re = 77). This agrees with previously reported numerical results (Malamataris et al 2002;Gao et al 2003;Malamataris & Balakotaiah 2008) and experimental measurements (Adomeit & Renz 2000;Moran et al 2002;Charogiannis et al 2015). Interestingly, the self-similarity of the velocity profile in the laboratory frame of reference is unaffected by the onset of a recirculation region in the moving frame when the maximum flow velocity exceeds the wave speed (for instance, in case C6).…”

Self-similarity of solitary waves on inertia-dominated falling liquid films

“…In a previous study on the dynamics of solitary waves on inertia-dominated falling liquid film of Denner et al [37], the results obtained with the DNS framework [47][48][49] used in this study showed excellent agreement with experimental measurements [6]. We propose a novel scaling for solitary waves, which we derive from the Nusselt flat film solution based on the physical mechanisms that underpin the growth and dispersion of solitary waves.…”

“…This leads to a strongly non-parabolic velocity profile at the front of the solitary wave [6,36,37], including flow reversal underneath the trough preceding the solitary wave under certain conditions [4,5,38,39]. Furthermore, if inertia is sufficiently high, the maximum flow velocity of the film exceeds the phase velocity of the solitary waves, leading to a recirculation zone in the main wave hump with respect to the reference frame moving with the wave [39][40][41][42].…”

“…Falling liquid films have been an active research topic for several decades, starting with the pioneering experiments by the father-son team of the Kapitza family [1,2], and extending to more recent work in both planar [3][4][5][6] and annular flow geometries [7,8]. A falling liquid film is an open-flow hydrodynamic system that is convectively unstable to long-wave disturbances at small flow rates.…”

“…A falling liquid film is an open-flow hydrodynamic system that is convectively unstable to long-wave disturbances at small flow rates. It can be studied with the simplest experimental apparatus (e.g., [6]) while at the same time the theoretical analysis of a falling liquid film is facilitated by the substantial reduction of the complexity of the governing equations offered by the long-wave nature of the instability. The simplicity of the resulting model equations, single evolution equations or coupled averaged evolution equations, makes them useful prototypes for mathematical and numerical scrutiny.…”