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

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Ern, Alexandre¹  Joubaud, Remi¹  Lelievre, Tony¹ 

[1] Univ Paris Est, CERMICS, Ecole Ponts, F-77455 Marne La Vallee 2, France

关键词: Free-surface Navier-Stokes;    Thin liquid film;    Surface wave instability;    Critical Reynolds number;    Direct numerical simulation;    ALE formulation;   

DOI  :  10.1016/j.physd.2011.07.007

来源: Elsevier

【 摘 要 】

We 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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free