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

Outline Introduction Expansion geometry Fluid Rheology (Shear rheology, N 1, extensional viscosity) Approach flow (smooth contraction) Downstream flow (sudden expansion) Conclusions

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) Why? Investigate viscoelastic fluid flow in a basic geometry which exhibits interesting fluid-dynamic behaviour. Extend previous studies (Re < 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.

Experimental arrangement Area ratio R = d/D = 0.7 Upstream spanwise profiles (x-z plane) at x/h=-8.33 and 0 d = 28mm, h = 6mm, D = 40mm, w = 80mm Fully-developed inlet flow through a square duct 80mm x 80 mm (120 D H development length) (area ratio > 2/3  double backward-facing step ) Downstream profiles at 0<x/h<10 in x-y plane Aspect ratios A 1 = w/h = 13.3 A 2 = w/d= 2.86

Rheology Fluid: Polyacrylamide (PAA) Seperan AP 273 E 0.05%, 0.1% 0.4% w/w including Carreau-Yasuda (5-parameter) model fits

Rheology Fluid: Polyacrylamide (PAA) Seperan AP 273 E 0.1%, 0.4% w/w

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

Extensional rheology c (%) (Pa.s)(mPa.s)(Pa.s)

Results: Flow through smooth contraction Spanwise variation of streamwise velocity (U/U B ) profiles within smooth contraction 0.05% PAA and 0.1% PAA Re  120

Results: Flow through smooth contraction Spanwise variation of streamwise velocity (U/U B ) profiles within smooth contraction 0.4% PAA Re  5

Results: Flow downstream of expansion Streamwise velocity (U/U B ) profiles downstream of expansion for 0.05% PAA Re=120

Results: Flow downstream of expansion Streamwise velocity (U/U B ) profiles downstream of expansion for 0.05% PAA Re=120

Results: Flow downstream of expansion Streamwise velocity (U/U B ) profiles downstream of expansion for 0.1% PAA Re=120

Results: Flow downstream of expansion Streamwise velocity (U/U B ) profiles downstream of expansion for 0.1% PAA Re=120

Results: Flow downstream of expansion Streamwise velocity (U/U B ) profiles downstream of expansion for 0.4% PAA Re=5

Results: Flow downstream of expansion Streamwise velocity (U/U B ) profiles downstream of expansion for 0.4% PAA Re=5

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”

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