Abstracts - KTH Mechanics

120
Experimental study of inclined film flow along periodic
corrugations: The effect of wall steepness
K. Argyriadi a, M. Vlachogiannis a and V. Bontozoglou a
Major questions arising in connection to film flow along corrugated walls are: (1)
What is the morphology and structure of steady flow? (2) Under which conditions is
the steady flow stable? (3) What are the characteristics of wavy, fully-developed flow
under unstable conditions? The geometric characteristics of the corrugations are main
input parameters, and the flat wall evidently serves as reference point for all other
cases.
The present work considers flow of a film of water along rectangular corrugations
of constant wavelength (L=12 mm) and varying height, B. Thus, main goal is the
study of the effect of corrugation steepness, B/L (which dictates the extent of
deviation from the flat wall) on the various flow phenomena outlined by the
aforementioned questions. The conditions investigated correspond to the laminar,
inertia-dominated regime, and include inclination angles 1º-15º and Re~10-450.
Steady flow leads to a static deformation of the free surface, of the same
wavelength as the wall, which is interpreted in terms of a resonance interaction with
maximum deformation at a peak Re 1. The deformation is characterized by the
steepness of the free surface and by its harmonic content (deviation from sinusoidal
shape), of which the former is found independent of corrugation steepness and the
latter strongly dependent on it.
Transition to a three-dimensional flow regime (consisting of transverse arrays of
depressions along corrugation valleys) occurs beyond the peak Re, i.e. at the maximum
steady, two-dimensional deformation, which notably is the same for all corrugation
steepnesses and inclination angles tested. At lower Re, the steady two-dimensional
flow becomes convectively unstable to streamwise disturbances that evolve into
travelling waves. An interesting experimental finding is that the critical Re for stability
increases drastically with corrugation steepness. This result, which was anticipated
theoretically 2, proves that steep corrugations have a strong stabilizing effect on the
steady flow.
Moving to fully-developed wavy flow under unsteady conditions, we find that the
shape of travelling waves is dictated by a combination of near-solitary humps (steep
front/gentle tail) with the small-scale deformation of steady flow. Steep wall
corrugations appear to significantly regularize the frequency and increase the size of
these travelling waves, in comparison to their counterparts along a flat wall. The
difference is attributed to the continuous interaction of travelling pulses with the
steadily deformed substrate.
a Dept. of Mechanical & Industrial Engineering, University of Thessaly, GR-38334 Volos, Greece.
1 Bontozoglou, CMES 1, 129 (2000).
2 Wierschem and Aksel, Physica D 186, 221 (2003).