Linear stability of Taylor-Couette flow of shear-thinning fluids: modal and non-modal approaches

Y. Agbessi (1) , B. Alibenyahia (2) , Chérif Nouar (3) , C. Lemaitre (1) , L. Choplin (1)

1 LRGP - Laboratoire Réactions et Génie des Procédés
2 LApEH: Laboratoire des Applications énergétiques de l'hydrogène
3 LEMTA - Laboratoire d'Energétique et Mécanique Théorique et Appliquée

In this paper, the receptivity of circular Couette flow of shear-thinning fluids between two infinitely long coaxial cylinders to weak disturbances is addressed. It is highlighted by pseudospectra and transient growth analysis. Power-law model and Carreau model are used to describe the rheological behavior of the fluid. The first part of the paper deals with the asymptotic long-time behavior of three-dimensional infinitesimal perturbations. Using the normal-mode approach, an eigenvalue problem is derived and solved with spectral collocation method. Extensive description and classification of eigenspectra is presented. The influence of shear-thinning effects on the critical Reynolds numbers as well as on the critical azimuthal and axial wavenumbers is analyzed. The second part investigates the short-time behavior of the disturbance using the non-† Email address for correspondence: [e-mail] 2 Y. Agbessi, B. Alibenyahia, C. Nouar, C. Lemaitre and L. Choplin modal approach. For the same inner and outer Reynolds numbers, the amplification of the kinetic energy perturbation is much more important with increasing shear-thinning effects. Two different mechanisms are used to explain the transient growth depending on if there is or not a stratification of the angular momentum. The scaling laws for the optimal energy amplification proposed in the literature are extended to shear-thinning fluids.

Domaines: Sciences de l'ingénieur [physics]; Milieux fluides et réactifs; Mécanique [physics.med-ph]

Y. Agbessi, B. Alibenyahia, Chérif Nouar, C. Lemaitre, L. Choplin. Linear stability of Taylor-Couette flow of shear-thinning fluids: modal and non-modal approaches. Journal of Fluid Mechanics, 2015, ⟨10.1017/jfm.2015.326⟩. ⟨hal-02916859⟩