Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study

Laminar flow in three-dimensional square-square expansions

In this work we investigate the three-dimensional laminar flow of Newtonian and viscoelastic fluids through square–square expansions. The experimental results obtained in this simple geometry provide useful data for benchmarking purposes in complex three-dimensional flows. Visualizations of the flow patterns were performed using streak photography, the velocity field of the flow was measured in detail using particle image velocimetry and additionally, pressure drop measurements were carried out. The Newtonian fluid flow was investigated for the expansion ratios of 1:2.4, 1:4 and 1:8 and the experimental results were compared with numerical predictions. For all expansion ratios studied, a corner vortex is observed downstream of the expansion and an increase of the flow inertia leads to an enhancement of the vortex size. Good agreement is found between experimental and numerical results. The flow of the two non-Newtonian fluids was investigated experimentally for expansion ratios of 1:2.4, 1:4, 1:8 and 1:12, and compared with numerical simulations using the Oldroyd-B, FENE-MCR and sPTT constitutive equations. For both the Boger and shear-thinning viscoelastic fluids, a corner vortex appears downstream of the expansion, which decreases in size and strength when the elasticity of the flow is increased. For all fluids and expansion ratios studied, the recirculations that are formed downstream of the square–square expansion exhibit a three-dimensional structure evidenced by a helical flow, which is also predicted in the numerical simulations

A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

The dilation-free semi-staggered finite volume method presented in Sabin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown Copyright (C) 2007 Published by Elsevier B.V. All rights reserved

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square-square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR¼2.4, 4,8and12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streakline photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at DeE200, 300, 70 and 450 for CR¼2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments

Simulation of neutrophil motion and deformation: influence of rheology and flow configuration

non

Simulation of blood flows in a stenosed and bifurcating artery using finite volume methods and OpenFOAM

Numerical simulations of the complex flows of complex (viscoelastic) fluids are investigated. The primary fluid investigated in this thesis is human blood, a complex fluid which can be modelled via viscoelastic constitutive models. The most commonly used constitutive models for viscoelastic fluids include the OldroydB, Giesekus, Johnson-Segalman, Finitely Extensible Non-Linear Elastic (FENE), Phan-Thein-Tanner (PTT) models etc. Our Numerical approach is based on the finite volume methods implemented on the OpenFOAM platform. We employ the Giesekus, Oldroyd-B, and Generalized Oldroyd-B viscoelastic constitutive models in this thesis, depending on the underlying context. Numerical validation of our results is conducted via the most used benchmark flow problems for viscoelastic fluid flow. The robust and efficient numerical methodologies are then deployed to investigate the flow characteristics, and hence illustrate various novel behavior, for blood flow in stenosed and bifurcated arteries. The present work took advantage of the availability of a reasonable set of viscoelastic constitutive model solvers within OpenFOAM, specifically the viscoelasticFluidFoam solver which we modified and developed to suit our focused needs for blood flow computations. The modified computational algorithms were successfully validated against well-known benchmark flow problems in the literature. Noting that the Giesekus viscoelastic constitutive model is a generalization of both the Oldroyd-B and Generalized Oldroyd-B models, the validation of results is carried out via the Giesekus model enabling us to develop a general-purpose code capable of simulating several viscoelastic constitutive models. The main results were otherwise presented for the Oldroyd-B and Generalized Oldroyd-B models as these are the most applicable to blood flow modelling. The results demonstrate that the velocity spurt through the stenosis is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher the corresponding velocity spurt through the constriction. This velocity behavior, as the constriction blockage increases, correspondingly increase the wall shear stresses. High wall shear stresses significantly increase the possibility of rupture of the stenosis/blockage. This can lead to catastrophic consequences in the usual case where the stenosis is caused by tumor growth

Numerical Simulation for Polymer Blend using OpenFOAM

This thesis models the flow behaviour of polymer blends using a new constitutive model derived from tube theory and double reptation called the bidisperse Rolie-Double-Poly equation (Boudara et al., Journal of Rheology, 63, 71 (2019)) in two different geometrical flows using finite-volume based OpenFOAM software. This model incorporates the molecular mechanisms of reptation motion, thermal and convective constraint release, chain stretch and accounts for the interactions between polymer chain of different lengths in a polydisperse melt. In this thesis, the model was implemented within OpenFOAM using the RheoTool library. This implementation was validated against published results for the transient extensional viscosity. Numerical simulations for the bidisperse Rolie-Double-Poly were performed for two different flow geometries used to characterise extension flow properties, the hyperbolic contraction and a cross-slot with both sharp and hyperbolic corners. For each flow the effects of varying the geometric details, the flow-rate and composition of the blend are examined. In addition, we compare the results to those obtained from the equivalent multimode Rolie-Poly model that is based on linear superposition to distinguish the coupling effect predicts by the Rolie-Double-Poly model. The study of the cross-slot flow is extended to investigate the symmetry-breaking bifurcation for a single mode Rolie-Poly and bidisperse Rolie-Double-Poly model. We find that the bifurcation to a steady asymmetric flow depends on the ratio of the stretch to orientation relaxation times and is not observed when this ratio is small even for high Deborah numbers in the Rolie-Poly model, but is observed in blends described by the Rolie-Double-Poly model