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Delaying transition to turbulence in channel flow: revisiting the stability of shear-thinning fluids

Published online by Cambridge University Press:  14 November 2007

C. NOUAR ,
A. BOTTARO  and
J. P. BRANCHER
C. NOUAR
Affiliation:
LEMTA, UMR 7563 (CNRS-INPL-UHP), 2 Avenue de la Fort de Haye, BP 160 54504 Vandoeuvre Lès Nancy, France
A. BOTTARO
Affiliation:
Università di Genova, Dipartimento di Ingegneria, delle Costruzioni, Ambiente e Territorio, Via Montallegro 1, 16145 Genova, Italy
J. P. BRANCHER
Affiliation:
LEMTA, UMR 7563 (CNRS-INPL-UHP), 2 Avenue de la Fort de Haye, BP 160 54504 Vandoeuvre Lès Nancy, France
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Abstract

A viscosity stratification is considered as a possible mean to postpone the onset of transition to turbulence in channel flow. As a prototype problem, we focus on the linear stability of shear-thinning fluids modelled by the Carreau rheological law. To assess whether there is stabilization and by how much, it is important both to account for a viscosity disturbance in the perturbation equations, and to employ an appropriate viscosity scale in the definition of the Reynolds number. Failure to do so can yield qualitatively and quantitatively incorrect conclusions. Results are obtained for both exponentially and algebraically growing disturbances, demonstrating that a viscous stratification is a viable approach to maintain laminarity.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 177 - 194
Copyright
Copyright © Cambridge University Press 2007

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