Vibration-induced instability of a fluid film flowing down a vertical plane: Experimental and numerical comparison

Abstract

This paper constitutes the latest part of an investigation into the vibration-induced instability of a fluid flowing down an inclined plane. Paper I [H. Garih et al., “Detailed analysis of the vibration induced instability of a liquid film flow,” Phys. Fluids 25(1), 014101 (2013)] involved an in-depth look at the development and characteristics of the vibration-induced instabilities via bespoke linear stability analysis via spectral methods in the case of a fluid flowing down an inclined plane. Paper II [H. Garih, J. L. Estivalezes, and G. Casalis, “On the transient phase of the Faraday instability,” Phys. Fluids 25(12), 124104 (2013)] involved solution of the problem numerically via 3-D direct numerical simulation (DNS) simulations and a study of the effect of initial conditions on the transient phase of instability development in the case of a flat horizontal receptacle with no fluid flow. Paper III [H. Garih et al., “Vibration-induced instability of a fluid film flowing down a vertically inclined plane: Experimental and theoretical comparison,” Phys. Fluids 29(10), 104103 (2017)] involved validating the theory of linear stability as applied to a fluid flowing down a vertically inclined plane via an experimental comparison. In this latest part, a two-dimensional direct numerical simulation is carried out for the case with air flow at the fluid interface. The numerical solver was compared to the experiment by evaluating the frequency spectra at specific forcing amplitudes where mode 2 and 3 instabilities become dominant. The simulation reproduced the principal features of the frequency spectra in all cases to a high degree of accuracy and demonstrates that a consideration of a two-dimensional case is sufficient to accurately resolve the onset and growth of higher mode nonlinear instabilities without the need to account for three-dimensional effects.