Plane contraction flows of upper convected Maxwell and Phan-Thien–Tanner fluids as predicted by a finite-volume method

Abstract

A finite-volume (FV) procedure is applied to the prediction of two-dimensional (2-D) laminar flow through a 4 : 1 planar contraction of upper convected Maxwell (UCM) and simplified Phan-Thien±Tanner (SPTT) fluids. The method incorporates general coordinates, indirect addressing for easy mapping of complex domains, and is based on the collocated mesh arrangement. Calculations with the UCM model at a Reynolds number of 0.01 were carried out with three consecutively refined meshes which enabled the estimation of the accuracy of the predictions of the main vortex characteristics through Richardson's extrapolation. Converged solutions with the first-order upwind differencing scheme for the convective terms were obtained up to at least De 8 in the finest mesh, but were limited to De 1, De 3 and De 5 for the fine, medium and coarse meshes, respectively, when using the second-order linear upwind scheme. The predicted flow patterns for increasing Deborah numbers with the UCM model resemble the well known lip vortex enhancement mechanism reported in the literature for constant-viscosity fluids in axisymmetric contractions and shear-thinning fluids in planar contraction, but very fine meshes were required in order to capture the described vortex activity. Predictions with the SPTT model also compared well with the behaviour reported in the literature. #

Investigating the stability of viscoelastic stagnation flows in T-shaped microchannels

“…The numerical code used here has been applied extensively in 2D calculations [53,54] and with axisymmetric geometries [55]. Additionally, it has also been used for full three-dimensional (3D) simulations including those of planar channels in which the depth of the channels is kept constant as is typical of microfluidic fabrication [50,56].…”

The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries

“…However for 2 < De < 8, mild vortex growth has been predicted in planar contractions for a UCM fluid [34].…”

The Finite Volume Method in Computational Rheology

“…For the pure FVM in computational rheology, there has been a significant effort at developing accurate and stable methods by the authors of this chapter: Oliveira and Pinho (1999b), Alves et al (2000Alves et al ( , 2001aAlves et al ( , 2003aAlves et al ( , 2003b and Afonso et al (2009Afonso et al ( , 2012. Oliveira and Pinho (1999b) used second-order interpolation schemes for the advective stress fluxes (either a linear upwind scheme or central differences), but difficulties associated with the intrinsic unboundedness of those schemes led them to the implementation of so-called high-resolution methods, often used in high-speed aerodynamics.…”

“…Oliveira and Pinho (1999b) used second-order interpolation schemes for the advective stress fluxes (either a linear upwind scheme or central differences), but difficulties associated with the intrinsic unboundedness of those schemes led them to the implementation of so-called high-resolution methods, often used in high-speed aerodynamics. These represent important landmark developments, where there was a remarkable improvement both in terms of stability and accuracy (Alves et al, 2000).…”