Predicting large experimental excess pressure drops for Boger fluids in contraction–expansion flow

• Published in: Journal of non-Newtonian fluid mechanics 2016-04, Vol.230, p.43-67
• Main Authors: Tamaddon-Jahromi, H.R., Garduño, I.E., López-Aguilar, J.E., Webster, M.F.
• Format: Article
• Language: English
• Subjects: Axisymmetric contraction–expansion; Computational fluid dynamics; Constitutive relationships; Elasticity; Extensional White–Metzner_FENE-CR model; Fluid flow; Fluids; Mathematical models; Pressure drop; Pressure-drop prediction; Stresses; Viscoelastic fluid
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2016.01.019

•A swanINNFM model reflects epd in axisymmetric contraction–expansion flows.•No counterpart epd is observed in planar configurations.•Over 200% Boger fluid enhanced pressure drops captured above Newtonian.•Rothstein and McKinley experimental pressure-drop data is quantitatively captured.•Transition states detected between flow phases of steady, oscillatory and unstable. More recent finite element/volume studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional viscosity, normal stress and shear-thinning. In this study, the ability of an extensional White–Metzner construction with FENE-CR model is explored to reflect enhanced excess pressure drops (epd) in axisymmetric 4:1:4 contraction–expansion flows. Solvent-fraction is taken as β=0.9, to mimic viscoelastic constant shear-viscosity Boger fluids. The experimental pressure-drop data of Rothstein & McKinley [1] has been quantitatively captured (in the initial pronounced rise with elasticity, and limiting plateau-patterns), via two modes of numerical prediction: (i) flow-rate Q-increase, and (ii) relaxation-time λ1-increase. Here, the former Q-increase mode, in line with experimental procedures, has proved the more effective, generating significantly larger enhanced-epd. This is accompanied with dramatically enhanced trends with De-incrementation in vortex-activity, and significantly larger extrema in N1, shear-stress and related extensional and shear velocity-gradient components. In contrast, the λ1-increase counterpart trends remain somewhat invariant to elasticity rise. Moreover, under Q-increase and with elasticity rise, a pattern of flow transition has been identified through three flow-phases in epd-data; (i) steady solutions for low-to-moderate elasticity levels, (ii) oscillatory solutions in the moderate elasticity regime (coinciding with Rothstein and McKinley [1] data), and (iii) finally solution divergence. New to this hybrid algorithmic formulation are – techniques in time discretisation, discrete treatment of pressure terms, compatible stress/velocity-gradient representation; handling ABS-correction in the constitutive equation, which provides consistent material-property prediction; and introducing purely-extensional velocity-gradient component specification at the shear-free centre flow-line through the velocity gradient (VGR) correction.