Numerical study of a thin liquid film flowing down an inclined wavy plane

Abstract

To cite this version:Alexandre Ern, Rémi Joubaud, Tony Lelievre. Numerical study of a thin liquid film flowing down an inclined wavy plane. Physica D: Nonlinear Phenomena, Elsevier, 2011, 240 (21) AbstractWe investigate the stability of a thin liquid film flowing down an inclined wavy plane using a direct numerical solver based on a finite element/arbitrary Lagrangian Eulerian approximation of the free-surface Navier-Stokes equations. We study the dependence of the critical Reynolds number for the onset of surface wave instabilities on the inclination angle, the waviness parameter, and the wavelength parameter, focusing in particular on mild inclinations and relatively large waviness so that the bottom does not fall monotonously.In the present parameter range, shorter wavelengths and higher amplitude for the bottom undulation stabilize the flow. The dependence of the critical Reynolds number evaluated with the Nusselt flow rate on the inclination angle is more complex than the classical relation (5/6 times the cotangent of the inclination angle), but this dependence can be recovered if the actual flow rate at critical conditions is used instead.

Numerical Simulation of the Effect of the Uneven Wall on the Liquid Film Flow

“…Over decades, plenty of theoretical and experimental research in the field of film has been done [1,2,3,4]. Alexandre [5] studied the stability of liquid film flowing down an inclined wavy plane based on the finite element method. The liquid film flow in engineering fields often accompanied with heating, surfactant, electric field or vibration.…”