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Fundamental Issues and Canonical Flows

Numerical Analysis of Viscoelastic Fluids in Steady Pressure-Driven Channel Flow

[+] Author and Article Information
Kerim Yapici1

Department of Chemical Engineering,  Cumhuriyet University, 58140 Sivas, Turkeykyapici@cumhuriyet.edu.tr

Bulent Karasozen

Department of Mathematics and Institute of Applied Mathematics,  Middle East Technical University, 06531 Ankara, Turkey

Yusuf Uludag

Department of Chemical Engineering,  Middle East Technical University, 06531 Ankara, Turkey

1

Corresponding author.

J. Fluids Eng 134(5), 051206 (May 22, 2012) (9 pages) doi:10.1115/1.4006696 History: Received June 22, 2011; Revised March 22, 2012; Published May 18, 2012; Online May 22, 2012

The developing steady flow of Oldroyd-B and Phan-Thien-Tanner (PTT) fluids through a two-dimensional rectangular channel is investigated computationally by means of a finite volume technique incorporating uniform collocated grids. A second-order central difference scheme is employed to handle convective terms in the momentum equation, while viscoelastic stresses are approximated by a third-order accurate quadratic upstream interpolation for convective kinematics (QUICK) scheme. Momentum interpolation method (MIM) is used to evaluate both cell face velocities and coefficients appearing in the stress equations. Coupled mass and momentum conservation equations are then solved through an iterative semi-implicit method for pressure-linked equation (SIMPLE) algorithm. The entry length over which flow becomes fully developed is determined by considering gradients of velocity, normal and shear stress components, and pressure in the axial direction. The effects of the mesh refinement, inlet boundary conditions, constitutive equation parameters, and Reynolds number on the entry length are presented.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of planar channel flow geometry

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Figure 2

Comparison of the predicted dimensionless entry length with the nonlinear correlation proposed by Durst [8]

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Figure 3

Average error versus mesh size for Oldroyd-B fluid at We = 0.6, Re = 0.001 and β=0.1, L:H = 16. Results presented are calculated in fully developed flow region.

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Figure 4

Effect of We on stream-wise profile of the centerline velocity along the channel length at Re = 0.001. (a) Oldroyd-B fluid with β = 0.1. (b) PTT-linear fluid with β = 0.1 and ɛ = 0.25.

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Figure 5

Axial stress distribution along the centerline with respect to We at Re = 0.001. (a) Oldroyd-B fluid with β = 0.1. (b) PTT-linear fluid with β = 0.1 and ɛ = 0.25.

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Figure 6

Entry length Lfd versus We at Re = 0.001. (a) Oldroyd-B fluid with β = 0.1. (b) PTT-linear fluid with β = 0.1 and ɛ = 0.25. Symbols □ and ○ represent Lfd ’s based on axial normal stress and stream-wise velocity, respectively.

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Figure 7

Entry length Lfd versus mesh size for Oldroyd-B fluid at We = 0.6, Re = 0.001, and β = 0.1

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Figure 8

Influence of the inlet boundary conditions on predicted Lfd based on axial normal stress for Oldroyd-B fluid at We = 0.6, Re = 0.001, and β = 0.1

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Figure 9

Entry length Lfd versus β at Re = 0.001. (a) Oldroyd-B fluid for We = 0.6 and (b) PTT-linear fluid for We = 1 and ɛ = 0.25.

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Figure 10

Entry length Lfd versus ɛ for PTT-linear fluid at We = 0.6, Re = 0.001, and β = 0.1

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Figure 11

Entry length Lfd versus Re. (a) Oldroyd-B fluid at We = 0.5 and β = 0.1 and (b) PTT-linear fluid at We = 0.8, β = 0.1, and ɛ = 0.25.

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