Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

Abstract : In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the traveling waves with a threefold rotational symmetry of Faisst & Eckhardt (2003); Wedin & Kerswell (2004) is analyzed. The rheological model is Carreau's law. Besides the shear-thinning index n_C , the dimensionless characteristic time λ of the fluid is considered as the main non-Newtonian control parameter. If λ = 0, the fluid is Newtonian. In the relevant limit λ → +∞, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov-Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number Re_w based on the mean velocity and wall viscosity are characterized. As λ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number Re_wc can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of 'drag reduction effect' is found.
Type de document :
Article dans une revue
Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 818, pp.595 - 622. 〈10.1017/jfm.2017.149〉
Liste complète des métadonnées

Littérature citée [35 références]  Voir  Masquer  Télécharger

https://hal.univ-lorraine.fr/hal-01517796
Contributeur : Emmanuel Plaut <>
Soumis le : mercredi 3 mai 2017 - 16:19:13
Dernière modification le : jeudi 11 janvier 2018 - 06:27:33
Document(s) archivé(s) le : vendredi 4 août 2017 - 13:34:14

Fichier

art.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Emmanuel Plaut, Nicolas Roland, Chérif Nouar. Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 818, pp.595 - 622. 〈10.1017/jfm.2017.149〉. 〈hal-01517796〉

Partager

Métriques

Consultations de la notice

99

Téléchargements de fichiers

70