3D FLOW OF VISCOELASTIC FLUIDS OVER A BACKWARD-FACING STEP PRECEDED BY A GRADUAL CONTRACTION
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3D FLOW OF VISCOELASTIC FLUIDS OVER A BACKWARD-FACING STEP PRECEDED BY A GRADUAL CONTRACTION. A. Afonso Centro de Estudos de Fenómenos de Transporte, DEMEGI Faculdade de Engenharia, Universidade do Porto, Portugal, [email protected] F. T. Pinho

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R. J. Poole and M. P. Escudier Dept. Engineering, Mechanical Engineering, University of Liverpool

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R j poole and m p escudier dept engineering mechanical engineering university of liverpool

3D FLOW OF VISCOELASTIC FLUIDS OVER A BACKWARD-FACING STEP PRECEDED BY A GRADUAL CONTRACTION

A. Afonso

Centro de Estudos de Fenómenos de Transporte, DEMEGI

Faculdade de Engenharia, Universidade do Porto, Portugal, [email protected]

F. T. Pinho

Centro de Estudos de Fenómenos de Transporte, Dep. Eng. Mecânica

Escola de Engenharia, Universidade do Minho, Portugal, [email protected]

R. J. Poole and M. P. Escudier

Dept. Engineering, Mechanical Engineering, University of Liverpool

Liverpool L69 3GH, UK, [email protected],[email protected]

AERC 2005

22nd to 24th April 2005 Grenoble, France


Flow geometry

Flow geometry

Experiments of Poole et al (2004) with solutions of PAA

Upstream spanwise velocity profiles (x-z plane) at x/h=-8.33 and 0

Aspect ratios A1 = w/h = 13.3

A2 = w/d= 2.86

d = 28mm, h = 6mm,

D = 40mm, w = 80mm

Inlet duct: 120 DH long

Area ratio R = d/D = 0.7

(area ratio > 2/3  double backward-facing step )


Experimental and numerical findings

Experimental and numerical findings

Spanwise variation at y/D=0.5

GNF

0.1% PAA Re  120

PTT

(N2=0)

Cat’s ears


Experimental and numerical findings 3

Experimental and numerical findings 3

0.1% PAA Re  120

Downstream


Objective

Objective

Cat’s ears: Why?

Shear-thinning:No

Elasticity - : No

Qualitative calculation with PTT: parametric investigation

Effect of

Effect of De

Effect of

Effect of Re

Individual and combined effects


Governing equations

Governing equations

1) Mass

2) Momentum

3) Constitutive equation

Newtonian solvent

Full PTT (linear stress coefficient)


Numerical method brief description

Numerical method: brief description

1) Finite volume method (Oliveira et al,1998; Oliveira & Pinho, 1999)

2) Structured, colocated and non-orthogonal meshes

3) Momentum (ui)

polymer

solvent

4) Discretization (formally 2nd order)

Diffusive terms: central differences (CDS)

Advective terms: CUBISTA (deferred correction)

(Alves et al, 2000, 2003)

5) Special formulations for cell-face velocities and stresses


Computational domain and mesh

Computational domain and mesh

102 000 total cells

1 020 000 DF

5 m (62 DH)

120 h

20 cells

30 cells


Inlet flow

Inlet flow

x/h=-16


Non dimensional numbers

Non-dimensional numbers

Reynolds number

and

with

Bulk velocity at contraction exit

Deborah number

Extensional parameter

Slip parameter


Effect of 1

Effect of : 1

Several values of 

kitten’s ears

Absence of

kitten’s ears


Effect of 2

Effect of : 2

kitten’s ears:high De, high , low 


Effect of 3

Effect of : 3

Effect of

inertia

kitten’s ears

x/h=-0.1

x/h=-2.06

x/h=-4

x/h=-8


Effect of

Effect of 

x/h=-0.1

Closed symbols: kitten’s ears

(b)

(a)

x/h=-2.06

x/h=-4

x/h=-8

Effect of De (next slide)


Effect of de

Effect of De

De

De


Effect of re 1

Effect of Re’: 1

Re=0.6 Re’=0.43

Re=0.6 Re’=0.48


Effect of re 2

Effect of Re’: 2

Re=1.7 Re’=1.3

Re=1.7 Re’=1.4


Effect of re 3

Effect of Re’: 3

Re=3.4 Re’=2.6

Re=3.4 Re’=2.8


Effect of re 4

Effect of Re’: 4

Re=6.3 Re’=4.7

Re=6.3 Re’=5.2


Conclusions

Conclusions

  • Cat’s ears are qualitatively predicted by PTT (kitten’s ears)

    • N2≠ 0 (essential)— high 

    • Low 

    • High De

    • Intermediate Re

  • Sometimes enhanced peaks observed at corners

  • Low Re: very slim profiles at contraction exit, no peaks

  • High Re: flat profiles at contracton exit, no peaks

  • Accurate predictions: different transient properties ???


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