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Research Papers: Fundamental Issues and Canonical Flows

Suction-Injection Control of Shear Banding in Non-Isothermal and Exothermic Channel Flow of Johnson-Segalman Liquids

[+] Author and Article Information
T. Chinyoka

Center for Research in Computational and Applied Mechanics,  University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa e-mail: tchinyok@vt.edu

J. Fluids Eng 133(7), 071205 (Jul 22, 2011) (12 pages) doi:10.1115/1.4004363 History: Received January 25, 2011; Revised June 01, 2011; Published July 22, 2011; Online July 22, 2011

For certain values of the material parameters, certain viscoelastic fluid models allow for a nonmonotonic relationship between the shear stress and shear rate in simple flows. We consider channel flow of such a fluid, the Johnson-Segalman liquid, subjected to exothermic reactions. A numerical algorithm based on the finite difference method is implemented in time and space for the solution process of the highly nonlinear governing equations. The phenomenon of shear banding is observed and explained in terms of the jump discontinuities in shear rates. We demonstrate that for a reacting Johnson-Segalman fluid, the shear banding can be catastrophic as it leads to large temperature buildup within the fluid and hence makes it easily susceptible, say, to thermal runaway. We also demonstrate that the shear banding can be eliminated by making the walls porous and hence allowing for suction and injection. The suction/injection flow is shown to significantly decrease fluid temperatures for the nonmonotonic viscoelastic Johnson-Segalman model but leads to significant temperature increases for the monotonic viscoelastic Oldroyd-B model.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 10

Thermal runaway and the effects of polymer viscosity, γ = ξ = 0, We = 0.01

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Figure 11

Profiles of flow quantities, Johnson-Segalman liquid

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Figure 12

Effects of suction/injection, Johnson-Segalman liquid, V0  = 1

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Figure 13

Development of steady solutions with suction/injection, Johnson-Segalman liquid, V0  = 1

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Figure 14

Plot of γ versus γ·; We = 2

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Figure 15

Weak solutions, Johnson-Segalman liquid, We = 2

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Figure 16

Weak solutions, Johnson-Segalman liquid, We = 2 and t = 50

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Figure 17

Development of steady temperature and velocity profiles, We = 2

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Figure 18

Development of steady diagonal stress profiles, We = 2

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Figure 19

Development of steady τ12 and N1 profiles, We = 2

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Figure 20

Smooth solutions, Johnson-Segalman liquid, V0  = 1, We = 2, t = 50

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Figure 21

Time evolution of solutions, Johnson-Segalman liquid, V0  = 1

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Figure 22

Evolution of N1 at the wall with V0 , Johnson-Segalman liquid, t = 10

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Figure 23

Persistent weak solutions, Johnson-Segalman liquid, V0  = 0.008

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Figure 24

Evolution of N1 at the wall with V0 , Johnson-Segalman liquid, t = 1.5

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Figure 25

Weak solutions in isothermal flow, We = 2, α = δ1  = Br = 0

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Figure 26

Smooth solutions, Johnson-Segalman liquid, isothermal flow, V0  = 1, We = 2, α = δ1  = Br = 0, t = 50

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Figure 27

Variation of maximum temperature and velocity with Reynolds number

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Figure 28

Variation of maximum temperature and velocity with suction velocity

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Figure 29

Variation of maximum temperature and velocity with polymer viscosity

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Figure 30

Variation of maximum temperature and velocity with ξ

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Figure 1

Schematics of the model problem

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Figure 2

Shear stress versus velocity gradient; We = 1, ξ = 0.5

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Figure 3

Plot of γ versus γ·; We = 0.47, β = 0.95, ξ = 0.8, Re = 1, G = 1

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Figure 4

Plot of ymin and ymax versus ξ; β = 0.95, Re = 1, G = 1

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Figure 5

Development of steady temperature and velocity profiles

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Figure 6

Development of steady diagonal stress profiles

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Figure 7

Development of steady τ12 and N1 profiles

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Figure 8

Dependence of solutions on time step size

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Figure 9

Dependence of solutions on mesh size

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