Comptes Rendus
Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section
Comptes Rendus. Mécanique, Volume 337 (2009) no. 1, pp. 40-47.

This study is devoted to the three-dimensional numerical simulation of developing secondary flows of Newtonian and viscoelastic fluids through a curved duct of square cross-section. The Phan-Thien–Tanner (PTT) model is used to represent viscoelastic effects. The numerical method uses a finite volume discretization with a staggered grid, and the equations are written in general orthogonal coordinates. The numerical simulations produced for 3 different Dean numbers (125, 137 and 150) show clearly the presence of two steady Dean cells and the upstream development of a four-cell pattern when the centrifugal forces become significant. The comparison between Newtonian and PTT flows shows that the transition from twin-cells to four-cells is anticipated for the viscoelastic fluid.

Cette étude est consacrée à la simulation numérique tridimensionnelle des écoulements secondaires de Dean au sein d'un fluide Newtonien et d'un fluide viscoélastique de Phan-Thien–Tanner s'écoulant dans une conduite courbe de section carrée. La méthode des volumes finis avec un maillage décalé est utilisée pour résoudre les équations de conservation de masse, de quantité de mouvement et l'équation constitutive de PTT écrites en coordonnées orthogonales généralisées. Les calculs faits pour des nombres de Dean de 125, 137 et 150 montrent clairement la présence de deux cellules de Dean et le développement de quatre cellules en aval de la conduite lorsque les forces centrifuges deviennent importantes. Les résultats montrent également que le passage du mode « deux cellules » au mode « quatre cellules » est anticipé pour le fluide viscoélastique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.11.001
Keywords: Fluid mechanics, Viscoelastic fluid, Dean vortices, Curved duct, Finite volume method
Mot clés : Mécanique des fluides, Fluide viscoélastique, Vortex de Dean, Conduite courbe, Méthode des volumes finis

Mohammed Boutabaa 1; Lionel Helin 2; Gilmar Mompean 2; Laurent Thais 2

1 Département de mécanique, faculté des sciences de l'ingénieur, Université de Chlef, Algérie
2 Laboratoire de mécanique de Lille, UMR-CNRS 8107, Polytech-Lille, cité scientifique, 59655 Villeneuve d'Ascq cedex, France
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Mohammed Boutabaa; Lionel Helin; Gilmar Mompean; Laurent Thais. Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section. Comptes Rendus. Mécanique, Volume 337 (2009) no. 1, pp. 40-47. doi : 10.1016/j.crme.2008.11.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.11.001/

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