Pipe flow of purely viscous shear-thinning fluids is studied using numerical simulations. The rheological behavior is described by the Carreau model. The flow field is decomposed as a base flow and a disturbance. The perturbation equations are then solved using a pseudo-spectral Petrov–Galerkin method. The time marching uses a fourth-order Adams–Bashforth scheme. In the case of an infinitesimal perturbation, a three-dimensional linear stability analysis is performed based on modal and non-modal approaches. It is shown that pipe flow of shear-thinning fluids is linearly stable and that for the range of rheological parameters considered, streamwise-independent vortices are optimally amplified. Nonlinear computations are done for finite amplitude two-dimensional disturbances, which consist of one pair of longitudinal rolls. The numerical results highlight a strong modification of the viscosity profile associated with the flow reorganization. For a given wall Reynolds number, shear-thinning reduces the energy gain of the perturbation. This is due to a reduction of the exchange energy between the base flow and the perturbation. Besides this, viscous dissipation decreases with increasing shear-thinning effects.
Lʼécoulement de fluides rhéofluidifiants en conduite cylindrique est étudié à lʼaide de simulations numériques. Le comportement rhéofluidifiant est modélisé par la loi de Carreau. Lʼécoulement est décomposé en un écoulement de base et une perturbation. Les équations aux perturbations sont résolues en utilisant une méthode pseudo-spectrale de Petrov–Galerkin. La discrétisation temporelle utilise un schéma dʼAdams–Bashforth dʼordre quatre. Dans le cas dʼune perturbation infinitésimale, une analyse linéaire tridimensionnelle est effectuée suivant une approche modale puis non-modale. Les résultats obtenus montrent que dans la gamme des paramètres rhéologiques considérés, lʼécoulement dʼun fluide rhéofluidifiant est linéairement stable. La perturbation optimale est constituée dʼune paire de rouleaux longitudinaux contra-rotatifs. Des simulations numériques non linéaires sont ensuite effectuées pour une perturbation bidimensionnelle dʼamplitude finie constituée dʼune paire de rouleaux longitudinaux. Les résultats numériques montrent que la réorganisation de lʼécoulement sʼaccompagne dʼune forte modification du profil de viscosité. En outre, pour une valeur donnée du nombre de Reynolds basé sur la viscosité pariétale, la rhéofluidification réduit lʼamplification de lʼénergie de la perturbation. On montre que cela est dû à la réduction des échanges dʼénergie entre lʼécoulement de base et la perturbation. Parallèlement à cela, la dissipation visqueuse décroit avec lʼaugmentation des effets rhéofluidifiants.
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Mots-clés : Instabilité, Écoulement en conduite cylindrique, Fluides non-Newtoniens, Méthodes spectrales
Santiago Nicolas López-Carranza 1; Mathieu Jenny 1; Chérif Nouar 1
@article{CRMECA_2012__340_8_602_0,
author = {Santiago Nicolas L\'opez-Carranza and Mathieu Jenny and Ch\'erif Nouar},
title = {Pipe flow of shear-thinning fluids},
journal = {Comptes Rendus. M\'ecanique},
pages = {602--618},
publisher = {Elsevier},
volume = {340},
number = {8},
year = {2012},
doi = {10.1016/j.crme.2012.05.002},
language = {en},
}
Santiago Nicolas López-Carranza; Mathieu Jenny; Chérif Nouar. Pipe flow of shear-thinning fluids. Comptes Rendus. Mécanique, Volume 340 (2012) no. 8, pp. 602-618. doi : 10.1016/j.crme.2012.05.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.05.002/
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