[Étude numérique des vortex de Dean de fluides Newtonien et viscoélastique en écoulement non établi dans une conduite courbe à section carrée]
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.
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.
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Mot clés : Mécanique des fluides, Fluide viscoélastique, Vortex de Dean, Conduite courbe, Méthode des volumes finis
@article{CRMECA_2009__337_1_40_0,
author = {Mohammed Boutabaa and Lionel Helin and Gilmar Mompean and Laurent Thais},
title = {Numerical study of {Dean} vortices in developing {Newtonian} and viscoelastic flows through a curved duct of square cross-section},
journal = {Comptes Rendus. M\'ecanique},
pages = {40--47},
publisher = {Elsevier},
volume = {337},
number = {1},
year = {2009},
doi = {10.1016/j.crme.2008.11.001},
language = {en},
}
TY - JOUR AU - Mohammed Boutabaa AU - Lionel Helin AU - Gilmar Mompean AU - Laurent Thais TI - Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section JO - Comptes Rendus. Mécanique PY - 2009 SP - 40 EP - 47 VL - 337 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2008.11.001 LA - en ID - CRMECA_2009__337_1_40_0 ER -
%0 Journal Article %A Mohammed Boutabaa %A Lionel Helin %A Gilmar Mompean %A Laurent Thais %T Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section %J Comptes Rendus. Mécanique %D 2009 %P 40-47 %V 337 %N 1 %I Elsevier %R 10.1016/j.crme.2008.11.001 %G en %F CRMECA_2009__337_1_40_0
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/
[1] Fluid motion in a curved channel, Proc. R. Soc. London, Ser. A, Volume 121 (1928), pp. 402-420
[2] Flow in curved pipes, Annu. Rev. Fluid Mech., Volume 15 (1983), pp. 461-512
[3] H. Ito, Theory on laminar flow through curved pipes of elliptic and rectangular cross sections, in: Rep. Inst. High Speed Mech., Tohoku Univ., Sendai, Japan, vol. 1, 1951, pp. 1–16
[4] Flow through curved rectangular channels of large aspect ratio, AIChE J., Volume 41 (1995), pp. 1061-1070
[5] Laminar forced convection heat transfer in curved rectangular channels, Int. J. Heat Mass Transfer, Volume 13 (1970), pp. 471-490
[6] Fully developed laminar flow in curved rectangular channels, Trans. ASME C: J. Fluids Engrg., Volume 98 (1976), pp. 41-48
[7] Numerical treatment of laminar flow in helically coiled tubes of square cross section. Part 1. Stationary helically coiled tubes, AIChE J., Volume 21 (1975), pp. 965-974
[8] Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions, J. Fluid Mech., Volume 188 (1988), pp. 337-361
[9] An experimental and numerical study of the Dean problem: flow development towards two-dimensional multiple solutions, J. Fluid Mech., Volume 244 (1992), pp. 339-376
[10] Flow of second order fluids in curved pipes, J. Non-Newtonian Fluid Mech., Volume 90 (2000), pp. 91-116
[11] Viscoelastic flow in rotating curved pipes, Phys. Fluids, Volume 18 (2006), p. 083103
[12] Viscoelastic flow in a curved channel: A similarity solution for the Oldroyd-B fluid, J. Appl. Math. Phys., Volume 41 (1990), pp. 766-781
[13] Viscoelastic Poiseuille flow through a curved channel: A new elastic instability, Phys. Fluids A, Volume 3 (1991) no. 9, pp. 2043-2046
[14] Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method, J. Non-Newtonian Fluid Mech., Volume 59 (1995), pp. 191-213
[15] A nonlinear network viscoelastic model, J. Rheol., Volume 22 (1978), pp. 259-283
[16] The calculation of turbulent recirculating flows in general orthogonal coordinates, J. Comp. Phys., Volume 26 (1978), pp. 197-217
[17] Numerical simulation of viscoelastic flows with Oldroyd-B constitutive equation and novel algebraic stress models, J. Non-Newtonian Fluid Mech., Volume 140 (2006), pp. 145-158
[18] Vectors, Tensors and the Basic Equations of Fluid Mechanics, Dover Publications Inc., New York, 1962
[19] Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, 1980
[20] Finite element methods for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity, J. Non-Newtonian Fluid Mech., Volume 36 (1990), pp. 159-192
[21] Numerical calculation of time-dependent viscous incompressible fluid with free surface, Phys. Fluids, Volume 8 (1965), pp. 2182-2189
[22] Unsteady finite volume simulation of Oldroyd-B through a three-dimensional planar contraction, J. Non-Newtonian Fluid Mech., Volume 72 (1997), pp. 847-859
[23] Flow of Oldroyd-B fluids in curved pipes of circular and annular cross-section, Int. J. Non-Linear Mech., Volume 31 (1996), pp. 1-20
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