VI-4

V. Bontozoglou

University of Thessaly

Abstract

Gravity driven flow of a liquid down an inclined wall with periodic corrugations is investigated. Based on a linear analysis, a synchronous resonance between the wall and the free surface is predicted for corrugations with wavelength around 0.002 m. The physical origin of the resonance is sought by lubrication analysis.

A spectral, Fourier-Chebyshev, discretization scheme is cast in the streamfunction formulation and is used to compute the steady flow over large-amplitude waves. The nonlinear resonance cure-including a triple-valued range is computed and the free surface profile is knwon to be highly disturbed around resonance an to change in phase when switching from subcritical to supercritical flow.

Flow separation, resulting in the formation of a recirculation zone inside the wall trough, is computed for high enough corrugations. Separation is shown to occur easier and be more extensive at subcritical flows. The minimum corrugation height for separation to occur generally decreases with Re number, but attains larger values around the resonance conditions.

Shear stress distribution at the wall is shown to deviate significantly from the flat film flow, a result with implications for various wall-to-fluid transport processes. The spacial distribution of velocity gradient normal to the free surface is computed, and regions of inflow (from free surface to the bulk) and outflow are identified. These results are of interest in determining heat and mass transfer rates in process equipment involving gas-liquid flow.