Experiments and numerical simulations of laminar viscoelastic flow through sudden expansions

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Experiments and numerical simulations of laminar
viscoelastic flow through sudden expansions M P
Escudier1, P J Oliveira2, F T Pinho3, A Afonso3
and R J Poole1 1Department of Engineering,
University of Liverpool, UK 2Departmento de
Engenharia Electromecanica, Universidade da Beira
Interior, Portugal 3Departamento de Engenharia
Mecanica, Universidade do Minho, Portugal
Industrial Rheology Conference, Hoole Hall,
Chester, UK. April 5th 7th 2004
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Outline

• Introduction
• Expansion geometry
• Fluid Rheology
• (Shear rheology, N1, extensional viscosity)
• Approach flow (smooth contraction)
• Downstream flow (sudden expansion)
• Conclusions

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Introduction

• Experimental and numerical investigation of
  laminar viscoelastic fluid flow
• through a plane sudden expansion of expansion
  ratio (D/d) 1.43 and aspect ratio (w/h) 13.3.

• Why?
• Investigate viscoelastic fluid flow in a basic
  geometry which exhibits interesting fluid-dynamic
  behaviour.

• Extend previous studies (Re lt 1) to higher
  Reynolds numbers where inertia starts to play an
  important role.

• Are there qualitative changes compared to
  Newtonian fluid flow? Is the flow 2D?

• Extend previous studies by providing L.D.A
  velocity data for quantitative comparisons with
  numerical simulations.

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Experimental arrangement
Fully-developed inlet flow through a square duct
80mm x 80 mm (120 DH development length)
Downstream profiles at 0ltx/hlt10 in x-y plane
Upstream spanwise 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
Area ratio R d/D 0.7
(area ratio gt 2/3 ? double backward-facing step )
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Rheology
Fluid Polyacrylamide (PAA) Seperan AP 273 E
0.05, 0.1 0.4 w/w including Carreau-Yasuda
(5-parameter) model fits
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Rheology
Fluid Polyacrylamide (PAA) Seperan AP 273 E
0.1, 0.4 w/w
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Extensional rheology
Fluid Polyacrylamide (PAA) Seperan AP 273 E
0.05, 0.1, 0.2 and 0.4 w/w Thermo Haake CaBER
Extensional rheometer
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Extensional rheology
c () (Pa.s) (mPa.s) (Pa.s)
0.05 0.614 2.82 466 760 165 000
0.1 8.83 4.37 548 63 125 000
0.2 26.6 9.44 1087 41 115 000
0.4 162 9.37 1506 9 160 000
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Results Flow through smooth contraction
Spanwise variation of streamwise velocity (U/UB)
profiles within smooth contraction 0.05 PAA and
0.1 PAA Re ? 120
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Results Flow through smooth contraction
Spanwise variation of streamwise velocity (U/UB)
profiles within smooth contraction 0.4 PAA Re ? 5
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Results Flow downstream of expansion
Streamwise velocity (U/UB) profiles downstream of
expansion for 0.05 PAA Re120
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Results Flow downstream of expansion
Streamwise velocity (U/UB) profiles downstream of
expansion for 0.05 PAA Re120
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Results Flow downstream of expansion
Streamwise velocity (U/UB) profiles downstream of
expansion for 0.1 PAA Re120
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Results Flow downstream of expansion
Streamwise velocity (U/UB) profiles downstream of
expansion for 0.1 PAA Re120
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Results Flow downstream of expansion
Streamwise velocity (U/UB) profiles downstream of
expansion for 0.4 PAA Re5
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Results Flow downstream of expansion
Streamwise velocity (U/UB) profiles downstream of
expansion for 0.4 PAA Re5
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Conclusions

• Flow through smooth contraction
• Flow becomes increasingly three-dimensional (but
  symmetrical about x-y centreplane) and complex
  with increasing concentration.
• Simulations fail to predict velocity overshoot
  near side-walls.

• Flow over double backward-facing step
• Flow symmetrical about x-z centreplane.
• 0.05 PAA flow predicted reasonably well by PTT
  model (consequence of flow being more
  two-dimensional?)
• 0.1 and 0.4 PAA profiles not predicted well by
  any model (consequence of poor agreement through
  contraction and hence inlet velocity profiles?)
• PTT model corrects shear-thinning
  over-prediction

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Latest experimental study
Spanwise variation of streamwise velocity (U/UB)
profiles within smooth contraction 0.05 PAA
(x-z centreplane)
Plane sudden expansion d 10 mm D 40 mm h
15 mm R d/D 0.25 (lt 2/3) A w/h 5.33
(lt10) 0.05 PAA Re ? 200