Influences of Wall Topography on Unsteady Free Surface Waves in Film Flow

Two-dimensional unsteady failing film flows,with periodic perturbations at inlet。along a substrate with rectangular corrugations are studied numerically by using VOF method.It indicates that imposed periodic perturbations with different frequencies induce traveling surface waves with different wavelengths.As wavelength of structured wall is relatively short,it is found that the static deformed waves due to corrugations ride on the progressive wave resulted from imposed external perturbations.If these two wavelengths become close to each other.nonlinear effect promotes coalescence between neighboring surface waves.At a dimensionless film height 0.26,wavelength of wall equals to that of progressive wave at a perturbed frequency f=7 Hz,resonant phenomenon is observed in film flow.Additionally,we discuss effect of corrugations on structure of film flow field,and find that the phase velocity decreases as the trough depth of wall increased.