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Journal of Non-Newtonian Fluid Mechanics, 7 February 2015.
Pérez-Camacho1, J.E. López-Aguilar1,2, F. Calderas1, O. Manero1, M.F. Webster2
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, A.P. 70-360, México, D.F. 04510, Mexico
- Institute of Non-Newtonian Fluid Mechanics, College of Engineering, Swansea University, SA2 8PP, United Kingdom.
Abstract
One of the relevant benchmark problems in pressure-driven flows, that of flow through an axisymmetric expansion–contraction geometry, is addressed in this study. Three fluids have been considered: a Newtonian (theoretically simulated based on the Poiseuille and Samson solutions), Boger and a shear-thinning polymer solution. Particular attention is given to the pressure-drop and kinematics obtained in a flow apparatus specifically designed for various contraction-ratios (2:1:2, 4:1:4, 6:1:6, 8:1:8, 10:1:10). Both viscoelastic fluids present large magnitudes of normal stress under simple shear flow. The three fluids have the same viscosity at low shear-rates. The Boger fluid (polyacrylamide in a syrup-water solution) possesses a constant viscosity over a wide range of shear-rates. The shear-thinning fluid also has a wide range of first Newtonian plateau before the onset of shear-thinning. Findings for the Boger fluid reflect, initially, a decreasing pressure-drop below the Newtonian reference line (excess pressure-drop “epd” lower than unity), followed by values larger than one as the contraction-ratio increases. This can be explained on the basis of the extensional viscosity behaviour in the contraction section of the geometry. The shear-thinning polymer solution (HASE-type associative polymer) shows a reduction in epd below the Newtonian curve for small contraction-ratios (due to shear-thinning). However, in more abrupt contractions, the extensional flow behaviour dominates the shear-thinning effects: first attaining a Newtonian equivalent value (producing an epd of one), and then, showing values larger than unity as the contraction-ratio becomes more severe.
Kinematic fields illustrated by flow visualization reveal several different sizes of the corner-vortex, which are related to the relative contributions from the first normal stress difference (N1) and extensional stress throughout the geometry. Transitions from lip-to-corner vortex are related to the transition from shear-dominated to extension-dominated flows. Experimental data, for the Boger fluid on 4:1:4 contraction-ratio, are contrasted against numerical simulation results for a constant-shear-viscosity/extension-hardening FENE-CR model. Trends demonstrate qualitative agreement on epd and vortex activity, which also reveal an interesting interplay between N1 and extensional viscosity.
