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Turbulent flow of non-Newtonian liquids through an axisymmetric sudden expansion

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 (1883,1895) Newtonian flows - large literature exists

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Turbulent flow of non-Newtonian liquids through an axisymmetric sudden expansion

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  1. 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

  2. Introduction • 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

  3. Experimental rig Fully developed pipe flow d= 26 mm D=52 mm R = D2 / d2 = 4 Osborne Reynolds Seminar 30th April 2003

  4. 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

  5. Working fluids cont… N1 • Rheological data obtained • Shear viscosity vs shear rate • First normal stress difference vs shear stress Osborne Reynolds Seminar 30th April 2003

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

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

  8. 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

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

  10. Mean axial velocity profiles 0.02% PAA Water Osborne Reynolds Seminar 30th April 2003

  11. 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

  12. Axial Reynolds stresses (u) 0.02% PAA Water Osborne Reynolds Seminar 30th April 2003

  13. Radial Reynolds stresses (v) 0.02% PAA Water Osborne Reynolds Seminar 30th April 2003

  14. Mean axial velocity profiles 0.1% PAA Re  4000 XR32 No recirculation Osborne Reynolds Seminar 30th April 2003

  15. Concluding remarks • Turbulent flow through an axisymmetric sudden expansion of area expansion ratio (i.e. D2/d2) 4. • Water and two lowest conc. of PAA - axisymmetric. • Reattachment lengths were • Water XR 10 step heights 0.02% and 0.05% PAA XR 20 step heights Osborne Reynolds Seminar 30th April 2003

  16. Concluding remarks cont… • Increase in XR 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. Osborne Reynolds Seminar 30th April 2003

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