Research Papers: Fundamental Issues and Canonical Flows

Slipping of a Viscoplastic Fluid Flowing on a Circular Cylinder

[+] Author and Article Information
Hamdullah Ozogul

Laboratoire Rhéologie et Procédés,
UMR 5520,
Université Grenoble Alpes;
LRP, Grenoble F-38000, France

Pascal Jay

Laboratoire Rhéologie et Procédés,
UMR 5520,
Université Grenoble Alpes;
LRP, Grenoble F-38000, France
e-mail: pascal.jay@ujf-grenoble.fr

Albert Magnin

Laboratoire Rhéologie et Procédés,
UMR 5520,
Université Grenoble Alpes;
LRP, Grenoble F-38000, France

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 6, 2014; final manuscript received January 28, 2015; published online March 19, 2015. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 137(7), 071201 (Jul 01, 2015) (9 pages) Paper No: FE-14-1293; doi: 10.1115/1.4029760 History: Received June 06, 2014; Revised January 28, 2015; Online March 19, 2015

The slipping effect during creeping flow of viscoplastic fluids around a circular cylinder has been investigated via numerical simulations. For the bulk behavior of the fluid, a Herschel–Bulkley law is considered. For the parietal behavior, an original and recent slip law based on an elastohydrodynamic lubrication model defined with a physical approach has been implemented. In particular, this law represents the behavior of Carbopol gels, which are commonly used during experimental studies on yield stress fluid mechanics and in industry. This law has two parameters that control the kinematic conditions at the fluid–structure interface. Variations in the plastic drag coefficient are given as a function of these parameters. It has been shown in particular the decreasing of the drag coefficient when there is slipping at the fluid–structure interface. The kinematic field has been analyzed and the evolution of rigid zones is illustrated. Results are provided for different slipping conditions ranging from the no-slip to the perfect-slip (PS) case. The sheared zone becomes smaller so the flow is more and more confined due to the slip, which induces modifications on the rigid zones. Some of the results are compared with existing asymptotic plastic drag coefficients and experimental data.

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Fig. 1

Flow chart of a yield stress fluid (Carbopol gel) under different surface conditions [16]

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Fig. 2

Variation of the slip law for α = 0.5

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Fig. 3

Overview of the problem

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Fig. 4

Different rigid zones around a cylinder for steady creeping flow

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Fig. 5

Change in Cd* relative to V* for different S' values, for Od = 0.01; 1; 100

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Fig. 6

Change in Cd* as a function of Od for limiting cases

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Fig. 7

Velocity on the cylinder as a function of θ when varying S' for Od = 100: S′ = 0(—), S′ = 0.3 (– -), S′ = 0.7 (- -), S′ = 1 (······), PS (), and ADH ()

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Fig. 8

Velocity from the equator when varying V* for Od = 100: ADH (), V* = 0.1 (– ·), V* = 0.5 (- -), V* = 1 (—), V* = 10 (– -), V* = 103 (- · -), V = 105 (·······), and PS ()

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Fig. 9

Velocity from the pole when varying S′ for Od = 100: S' = 0 (—), S′ = 0.3 (– -), S' = 0.7 (- -), S' = 1 (······), PS (), and ADH ()

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Fig. 10

Changes of rigid zones according to the slip parameters for Od = 100. The flow direction occurs from the left to the right.




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