Numerical simulation of wavy falling film flow using VOF method

Surface wave dynamics of vertical falling films under monochromatic-frequency flowrate-forcing perturbations is computed by the direct simulation of Navier–Stokes equations using the Volume of Fluid (VOF) method to track free surfaces and the Continuum Surface Force (CSF) model to account for dynamic boundary conditions at free surfaces. The numerical VOF–CSF model is completely formulated, and more attention is given to understanding instabilities of thin films. At low frequency and high flowrate, the small inlet disturbance develops into large solitary waves preceded by small capillary bow waves. The circulation flow compatible with the solitary wave size is observed in the solitary peak. On the other hand, at high frequency and low Re, small-amplitude waves in nearly sinusoidal shape without fore-running capillary waves are formed on the surface. The quasi-periodic waveforms are found to occur at the nearly sinusoidal wave regime. The slight increase in wave-amplitude and wavelength, and decrease in residual thickness as waves evolves downstream are observed for both solitary waves and sinusoidal types. The variation of velocity and pressure along a wave are strong at the wave trough and capillary wave region, due to the large surface curvature there. The pressure variation perpendicular to the wall is negligible and only a small variation is observed at the solitary wave trough and capillary region.