Numerical Simulation of Viscoelastic & Thixo-Viscoelastoplastic Complex Flows at Highly Non-Linear Regimes

J. Esteban López-Aguilar

Universidad Nacional Autónoma de México, Mexico

Abstract

The High Weissenberg Number Problem (HWNP), which is the ceiling posed by the degree of non-linearity a numerical scheme can resolve in the approximation of the solution to a complex flow, is one of the main challenges to the Computational Rheology community [1]. Research on this facet of non-Newtonian Fluids Mechanics has been traditionally focused on increasing resolution and capability to computationally capture non-linear phenomena in complex flow [1]. In this talk, a proposal will be presented to increase the critical Weissenberg number Wi_crit a numerical scheme can attain, via the generally-applicable ABS-f and the VGR corrections reported previously [2], and their use to predict some experimental and numerical signatures in complex flow will be reviewed. The ABS-f correction acts upon stress-invariants used to promote non-linear features in conventional differential-type constitutive equations for viscoelastic fluids, helping in problem-regularisation and physically-consistent material-property calculation in complex deformations [2]. The VGR correction deals with proper velocity-gradient estimation, used to impose conservation-of-mass discretely over the flow-domain and to consistently specify velocity-gradient components at boundary symmetry lines [2]. Here, predictions with an advanced hybrid finite-element/volume sub-cell algorithm on the benchmark circular 4:1:4 contraction-expansion flow of concentrated wormlike micellar solutions prove notably extended in their Wi-span, where Wi_crit -adjustment is reported over three orders-of-magnitude from uncorrected variants, and with some cases presenting no limitation [2-3]. Finally, use of these computational tools is exemplified in various contraction-expansion flow settings through the prediction of key experimental features for Boger fluids [4-5], thixo-viscoelastoplasticity in sharp-cornered geometries [6] and shear-banding in contraction-expansion flow of highly concentrated worm-like micellar solutions [7].

[1] K. Walters, M.F. Webster, The distinctive CFD challenges of computational rheology, Int. J. Numer. Meth. Fluids 43 (2003) 577–596. https://doi.org/10.1002/fld.5222

[2] J.E. López-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero, High-Weissenberg predictions for micellar fluids in contraction–expansion flows, J. Non-Newton. Fluid Mech. 222 (2015) 190–208. https://doi.org/10.1016/j.jnnfm.2014.11.008

[3] J.E. López-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero, Convoluted models and high-Weissenberg predictions for micellar thixotropic fluids in contraction–expansion flows, J. Non-Newton. Fluid Mech. 232 (2016) 55–66. https://doi.org/10.1016/j.jnnfm.2016.03.004

[4] J.E. López-Aguilar, H.R. Tamaddon-Jahromi, Computational Predictions for Boger Fluids and Circular Contraction Flow under Various Aspect Ratios, Fluids 5 (2020) 85; https://doi.org/10.3390/fluids5020085

[5] M.F. Webster, H.R. Tamaddon-Jahromi, J.E. López-Aguilar, D.M. Binding. Enhanced pressure drop, planar contraction flows and continuous spectrum models. J. Non-Newton. Fluid Mech. 273 (2019) 104184. http://doi.org/10.1016/j.jnnfm.2019.104184

[6] J.E. López-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero. Predictions for circular contraction-expansion flows with viscoelastoplastic & thixotropic fluids. J. Non-Newton. Fluid Mech. 261 (2018) 188–210. http://doi.org/10.1016/j.jnnfm.2018.09.001

[7] J.E. López-Aguilar, M.F. Webster, H.R. Tamaddon-Jahromi, O. Manero. On shear-banding and wormlike micellar system response under complex flow. Annual Transactions of the Nordic Rheology Society, 25 (2017) 197–203.

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