Three-dimensional wave regimes on vertically falling liquid films: Downstream evolution of statistical characteristics.
to 3D waves for liquid films falling down a vertical plate was conducted. The LIF method was
used to obtain instant shapes of waves. During 2D-3D wave transition, a strong transverse
redistribution of liquid leading to the formation of rivulets on the surface of liquid film takes
place. Obtained data were used to calculate various statistical characteristics such as dispersion,
PDF and PSD.
Three-dimensional (3D) wave regimes are considered to be the last stage of the film flow
evolution at moderate Reynolds numbers. In such regimes surface of the film is covered with
numerous 3D waves. Therefore statistical approaches are often involved in order to describe
these wave regimes.
Results of experimental study of 3D wave characteristics as well as study of transition process
from two-dimensional (2D) to 3D waves for liquid films falling down a vertical plate are
presented. Experiments were carried out in the range of Reynolds numbers 5 < Re < 100. Liquids
with various physical properties were used as working fluids. The whole flow structure was
registered using shadowgraph method. It was found that rivulets formation takes place during the
process of transition from 2D to 3D wave motion. Size of the forming rivulets is weakly affected
by Re, however rivulets’ evolution depends on flow parameters. Detailed structures of the waves
were studied by means of the high speed laser induced fluorescence (LIF) method, which makes
it possible to obtain instantaneous forms of 3D waves. Obtained film thickness data were used to
calculate various statistical characteristics such as dispersion values, probability density
functions (PDF), spectral power densities of film thickness fluctuations, mean film thickness
distribution etc. Extensive statistical analysis showed that rivulets’ behavior is depending on
prior characteristics of 2D waves in the upper part of film flow. Immovable or randomly shifting
in transverse direction rivulets can be observed. On time-averaged (t=0.7s) cross sections
different amount of rivulets can be observed for different moments in time. The statistical
analysis also allows us to suggest that stabilization of 3D wave motion occurs at relatively short
distances from liquid inflow for the flow regimes with high Reynolds numbers whereas at lower
Re continuous downstream evolution of the wave characteristics with gradual damping of the
waves is observed.