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TECHNICAL PAPERS

Temporal Stability of Carreau Fluid Flow Down an Incline

[+] Author and Article Information
F. Rousset1

 Université de Lyon, Université Lyon 1, INSA de Lyon, Ecole Centrale de Lyon, Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, Villeurbanne, 69622, Francefrancois.rousset@univ-lyon1.fr

S. Millet, V. Botton, H. Ben Hadid

 Université de Lyon, Université Lyon 1, INSA de Lyon, Ecole Centrale de Lyon, Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, Villeurbanne, 69622, France

1

Corresponding author.

J. Fluids Eng 129(7), 913-920 (Jan 16, 2007) (8 pages) doi:10.1115/1.2742737 History: Received September 07, 2006; Revised January 16, 2007

This paper deals with the temporal stability of a Carreau fluid flow down an inclined plane. As a first step, a weakly non-Newtonian behavior is considered in the limit of very long waves. It is found that the critical Reynolds number is lower for shear-thinning fluids than for Newtonian fluids, while the celerity is larger. In a second step, the general case is studied numerically. Particular attention is paid to small angles of inclination for which either surface or shear modes can arise. It is shown that shear dependency can change the nature of instability.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Definition sketch

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Figure 3

Critical Reynolds number Rc versus β with I=5×10−5 and n=0.5. Parameter δ is set to 0 in the Newtonian case and to 0.1 in the shear-thinning case.

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Figure 5

Normalized critical Reynolds number versus L for different angles of inclination with I=5×10−5 and n=0.5

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Figure 6

Critical Reynolds number versus L for different values of n with I=5×10−5 and β=1°

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Figure 7

Neutral curves for β=0.3′, I=0.1, and n=0.5

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Figure 2

Effect of shear-thinning behavior. Solid lines stand for the shear-thinning fluid (I=0, L=5, and n=0.8) and dotted lines for the Newtonian fluid. Comparison is made at equal angle β and at equal Reynolds number: (a) Velocity profiles, (b) rates of strain profiles, and (c) viscosity profiles.

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Figure 4

Critical Reynolds number versus L for different angles of inclination with I=5.10−5 and n=0.5

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Figure 8

Growth rate ωI versus wave number α for β=0.3′, I=0.1, and n=0.5: (a)δ=0 and Re=9500, (b)δ=0.1 and Re=6000

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Figure 9

Neutral curves for β=1′, I=0.1, and n=0.5

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