Turbulent flow of non-Newtonian liquids through an axisymmetric sudden expansion Rob Poole Department of Engineering, University of Liverpool Osborne Reynolds Seminar 30th April 2003

Introduction Osborne Reynolds Seminar 30th April 2003 Osborne Reynolds (1883,1895) Newtonian flows - large literature exists Non-Newtonian - Few previous studies [Pak et al (1990)] –Experimental: flow visualisation Aims of this study –Use of LDA to provide quantitative data –Investigate effect on reattachment length –Database for CFD validation

Osborne Reynolds Seminar 30th April 2003 Experimental rig Fully developed pipe flow d= 26 mmD=52 mm R = D 2 / d 2 = 4

Osborne Reynolds Seminar 30th April 2003 Working fluids Water Three concentrations of polyacrylamide (PAA) –0.02%, 0.05% and 0.1% –Shear thinning to various degrees –Increasing viscoelasticity with concentration –Large extensional viscosities –Highly drag reducing –Optically transparent

Osborne Reynolds Seminar 30th April 2003 Working fluids cont… Rheological data obtained –Shear viscosity vs shear rate –First normal stress difference vs shear stress N1N1

Osborne Reynolds Seminar 30th April 2003 Rheological data 0.02% PAA 0.05% PAA 0.1% PAA

Osborne Reynolds Seminar 30th April 2003 Rheological data cont … 0.1% PAA

Osborne Reynolds Seminar 30th April 2003 Estimation of Reynolds number Difficulty - no single value for the viscosity characterises the fluid. Method adopted - estimate the maximum shear rate at ‘inlet’ (x/h=1). Example 0.02% PAA

Osborne Reynolds Seminar 30th April 2003 Estimation of Reynolds number This shear rate is then used to obtain a viscosity from the Carreau-Yasuda model: μ C  2.82 x10 -3 Pa.s Hence a Reynolds number of

Mean axial velocity profiles Osborne Reynolds Seminar 30th April % PAA Water

Streamlines Water -0.08<  <0 [0.02 steps] 0<  <0.35 [0.05 steps] 0.02% PAA -0.09<  <-0.01 [0.02 steps] 0<  <0.3 [0.05 steps] Osborne Reynolds Seminar 30th April 2003

Axial Reynolds stresses (u) Osborne Reynolds Seminar 30th April % PAA Water

Radial Reynolds stresses (v) Osborne Reynolds Seminar 30th April % PAA Water

Osborne Reynolds Seminar 30th April % PAA Re  4000 X R  32 Mean axial velocity profiles No recirculation

Osborne Reynolds Seminar 30th April 2003 Concluding remarks Turbulent flow through an axisymmetric sudden expansion of area expansion ratio (i.e. D 2 /d 2 ) 4. Water and two lowest conc. of PAA - axisymmetric. Reattachment lengths were Water X R  10 step heights 0.02% and 0.05% PAA X R  20 step heights

Osborne Reynolds Seminar 30th April 2003 Concluding remarks cont… Increase in X R caused by modifications to turbulence structure with large reductions in v and w resulting in reduced transverse transfer of axial momentum. At highest conc. of PAA axisymmetric flow could not be achieved. This could be due to an elastic instability or a slight geometric imperfection that is accentuated by viscoelasticity.