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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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 PRECEDED BY A GRADUAL CONTRACTION

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 PRECEDED BY A GRADUAL CONTRACTION

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 PRECEDED BY A GRADUAL CONTRACTION

0.1% PAA Re  120

Downstream


Objective
Objective PRECEDED BY A GRADUAL CONTRACTION

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 PRECEDED BY A GRADUAL CONTRACTION

1) Mass

2) Momentum

3) Constitutive equation

Newtonian solvent

Full PTT (linear stress coefficient)


Numerical method brief description
Numerical method: PRECEDED BY A GRADUAL CONTRACTIONbrief 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 PRECEDED BY A GRADUAL CONTRACTION and mesh

102 000 total cells

1 020 000 DF

5 m (62 DH)

120 h

20 cells

30 cells


Inlet flow
Inlet flow PRECEDED BY A GRADUAL CONTRACTION

x/h=-16


Non dimensional numbers
Non-dimensional numbers PRECEDED BY A GRADUAL CONTRACTION

Reynolds number

and

with

Bulk velocity at contraction exit

Deborah number

Extensional parameter

Slip parameter


Effect of 1
Effect of PRECEDED BY A GRADUAL CONTRACTION: 1

Several values of 

kitten’s ears

Absence of

kitten’s ears


Effect of 2
Effect of PRECEDED BY A GRADUAL CONTRACTION: 2

kitten’s ears:high De, high , low 


Effect of 3
Effect of PRECEDED BY A GRADUAL CONTRACTION: 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 PRECEDED BY A GRADUAL CONTRACTION

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 PRECEDED BY A GRADUAL CONTRACTIONDe

De

De


Effect of re 1
Effect of PRECEDED BY A GRADUAL CONTRACTIONRe’: 1

Re=0.6 Re’=0.43

Re=0.6 Re’=0.48


Effect of re 2
Effect of PRECEDED BY A GRADUAL CONTRACTIONRe’: 2

Re=1.7 Re’=1.3

Re=1.7 Re’=1.4


Effect of re 3
Effect of PRECEDED BY A GRADUAL CONTRACTIONRe’: 3

Re=3.4 Re’=2.6

Re=3.4 Re’=2.8


Effect of re 4
Effect of PRECEDED BY A GRADUAL CONTRACTIONRe’: 4

Re=6.3 Re’=4.7

Re=6.3 Re’=5.2


Conclusions
Conclusions PRECEDED BY A GRADUAL CONTRACTION

  • 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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