HAL : hal-00533000, version 2

DOI : 10.1016/j.physd.2011.07.007

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Physica D: Nonlinear Phenomena 240, 21 (2011) 1714-1723

Versions disponibles :

v1 (05-11-2010)

v2 (02-04-2012)

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

Alexandre Ern 1, Rémi Joubaud 1, Tony Lelievre 1, 2

(15/10/2011)

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.

1 :	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech
2 :	MICMAC (INRIA Paris - Rocquencourt)
	Ecole des Ponts ParisTech – INRIA

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : Free-surface Navier-Stokes – Thin liquid film – Surface wave instability – Critical Reynolds number – Direct numerical simulation – ALE formulation

hal-00533000, version 2

http://hal.archives-ouvertes.fr/hal-00533000

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Contributeur : Alexandre Ern <>

Soumis le : Lundi 2 Avril 2012, 16:48:56

Dernière modification le : Lundi 2 Avril 2012, 16:59:58