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In this paper we propose a novel approach to solve the inverse problem of three-dimensional die design for extrudate swell, using a real-time active control scheme. To this end, we envisioned a feedback connection between the corner-line finite element method, used to predict the positions of the free surfaces of the extrudate, and the controller. The corner-line method allows for local mesh refinement and transient flow to be taken into account (Spanjaards et al., 2019). We show the validity of this method by showing optimization results for 2D axisymmetric extrusion flows of a viscoelastic fluid for different Weissenberg numbers. In 3D we first give a proof of concept by showing the results of a Newtonian fluid exiting dies with increasing complexity in shape. Finally, we show that this method is able to obtain the desired extrudate shape of extrudates of a viscoelastic fluid for different Weissenberg numbers and different amounts of shear-thinning.

A new transient 3D finite element method for predicting extrudate swell of domains containing sharp edges is proposed. Here, the sharp edge is maintained over a large distance in the extrudate by describing the corner lines as material lines. The positions of these lines can be used to describe the transverse swelling of the 2D free surfaces and expand the domain over which a 2D height function on the free surfaces is applied. Solving the 2D height functions gives the positions of the free surfaces. First a 2D axisymmetric case was tested for comparison, using three different constitutive models. The Giesekus, linear Phan-Thien Tanner (PTT) and exponential PTT constitutive models all showed convergence upon mesh- and time-step refinement. It was found that convergence remains challenging due to the singularity at the die exit. The new method is validated by comparing the final volume change of the extrudate of a 3D cylinder to the final volume change of a reference mesh of the 2D axisymmetric case. Finally, simulations were performed for different, complex, die shapes for a viscous fluid and for viscoelastic fluids. The results compared favorably with literature. Viscoelastic results, using the Giesekus model and the exponential PTT model, were compared for different Weissenberg numbers and different values for the non-linear parameters of the constitutive models. It was found that the swell is highly dependent on the rheological parameters and the constitutive model used.

Understanding how the deformation history affects the retraction dynamics of viscoelastic liquid films can provide a tool to design materials. In this paper, we investigate the stretching and retraction of circular viscoelastic liquid films through finite element numerical simulations. We consider a discoid domain made of a viscoelastic liquid. Its central hole is first ‘closed’ and then released, being left free to open under the effect of inertial, surface, viscous, and elastic forces. We perform a parametric study of film retraction, aiming at understanding the effects of the physical and operating parameters on it. In particular, we consider different viscoelastic constitutive equations, namely, Oldroyd-B, Giesekus (Gsk), and Phan Thien-Tanner (PTT) models, and different values of the film initial thickness. For each liquid and geometry, we investigate the effects of the film stretching rate and of liquid inertia, elasticity, and flow-dependent viscosity on the dynamics of the hole opening.

Complex fluid–fluid interfaces determine for a large part the macroscopic material properties of foams and emulsions that appear in applications such as food, materials processing and consumer care products. As a step towards predicting these properties, a 2D axisymmetric and a 3D finite element model have been developed for simulating the dynamics of a single Newtonian drop in a Newtonian matrix fluid with a rheologically complex sharp interface in between. Interfaces with constant interfacial tension and with viscous, elastic and viscoelastic extra interfacial stresses are considered. The model has been validated by means of the method of manufactured solutions and by comparison with results from other studies using different discretisation methods. Higher-order convergence in space and time is obtained, demonstrating correct implementation of our numerical methods. Benchmark solutions for a drop with a Kelvin–Voigt interface under simple shear flow have been provided. Compared to a viscous interface, the drop deformation becomes smaller and the drop becomes less oriented in the direction of flow if interfacial elasticity is added.

This study is concerned with finite element/volume modelling of contraction–expansion axisymmetric pipe flows for thixotropic and non-thixotropic viscoelastic models. To obtain solutions at high Weissenberg numbers (Wi) under a general differential form W i τ p ∇ = 2 ( 1 − β ) D − f τ p , both thixotropic Bautista–Manero micellar and non-thixotropic EPTT f-functionals have been investigated. Here, three key modifications have been implemented: first, that of convoluting EPTT and micellar Bautista–Manero f-functionals, either in a multiplicative (Conv*) or additive (Conv+) form; second, by adopting f-functionals in absolute form (ABS-f-correction); and third, by imposing pure uniaxial-extension velocity-gradient components at the pure-stretch flow-centreline (VGR-correction). With this combination of strategies, highly non-linear solutions have been obtained to impressively high Wi [=O(5000+)]. This capability permits analysis of industrial applications, typically displaying non-linear features such as thixotropy, yield stress and shear banding. The scope of applications covers enhanced oil-recovery, industrial processing of plastics and foods, as well as in biological and microfluidic flows. The impact of rheological properties across convoluted models (moderate-hardening, shear-thinning) has been observed through steady-state solutions and their excess pressure-drop (epd) production, stress, f-functional field structure, and vortex dynamics. Three phases of vortex-behaviour have been observed with rise in elasticity, along with upstream–downstream Moffatt vortices and plateauing epd-behaviour at high-Wi levels. Moreover, enhancement of positive-definiteness in stress has improved high-Wi solution attenuation.

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.

Made available in DSpace on 2020-12-12T01:48:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-12-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Ministério da Educação Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) In this paper, we investigate the influence of non-Newtonian blood flow models on drug diffusion from a coronary drug-eluting-stent (DES). We consider the Oldroyd-B, Phan-Thien-Tanner (PTT) and Giesekus viscoelastic models for the description of fluid dynamics of blood. The model for blood flow is coupled with plasma filtration and mass transport from a DES. The model for the transport problem takes into consideration non-Fickian diffusion, drug dissolution, polymer degradation and binding. We propose an Implicit-Explicit (IMEX) finite element method and show numerical experiments that confirm the effectiveness and order of convergence of the employed methodology. The numerical results indicate that an increase in the elastic properties of the blood leads to an increase of the concentration of free drug in the arterial wall. Finally, we present unsteady simulations comparing the Newtonian and non-Newtonian blood flow models. Department of Mathematics Universidade Federal do Paraná Department of Mathematics and Computer Science Universidade Estadual Paulista (Unesp), Faculdade de ciências e tecnologia, Pres. Department of Mathematics and CEMAT-IST Instituto Superior Técnico Universidade de Lisboa Department of Mathematics and Computer Science Universidade Estadual Paulista (Unesp), Faculdade de ciências e tecnologia, Pres. FAPESP: 2013/07375-0 Ministério da Educação: 304256/2017-0 CNPq: 307459/2016-0 Ministério da Educação: 408215/2018-6

In the last few years, we have developed a fairly general adaptive finite element solution procedure which can be applied to a large variety of problems. In this paper, this strategy is briefly recalled and applied to the solution of two-dimensional viscoelastic fluid flow problems. A log-conformation formulation recently introduced by Fattal and Kupferman [R. Fattal, R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, J. Non-Newtonian Fluid Mech. 126 (2005) 23-37] was implemented in order to improve the convergence properties of the numerical scheme. We confirm some results obtained in Hulsen, Fattal and Kupferman [M. Hulsen, R. Fattal, R. Kupferman, Flow of viscoelastic fluids past a cylinder at high Weissenberg number: stabilized simulations using matrix logarithm, J. Non-Newtonian Fluid Mech. 127 (2005) 27-39] and in some instances, we show that mesh adaptation allows to almost automatically reproduce accurate results obtained on very fine structured meshes.

We analyse and contrast different stabilisation methodologies embedded within a time-marching incremental pressure-correction formulation. Numerical solutions are presented for an Oldroyd-B model under compressible implementations, considering flow through a planar four-to-one abrupt contraction. Various alternative stabilisation strategies and their combinations are analysed to hone the response of the base hybrid finite element/volume implementation. To reflect the stabilised properties of each scheme, the study interrogates levels of stable Weissenberg number ( We ) solution. Results indicate that most improvement has been encountered with a Strain-Rate Stabilisation scheme, where critical We -levels have more than doubled above neutral variants, while stress peaks levels have been constrained. Here, differed-correction characterises temporal error norm stress behaviour and the nature of the re-entrant corner stress singularity. At a selected We -level and under a specific flow setting, all scheme variants have produced similar salient-corner vortex behaviour, predicting vortex reduction under increasing We . In contrast, lip-vortex features are found to be significantly affected by the particular re-entrant corner treatment applied. When present, lip vortices grow with increasing We . Relaxation of the incompressible constraint points to important numerical anomalies, present under certain discretisations.

In this article we study the numerical approximation of an Oseen type model for viscoelastic fluid flow. Existence and uniqueness of the continuous and approximate solutions, under a small data assumption, are proved. Error estimates for the numerical approximations are also derived. Numerical experiments are presented which support the error estimates, and which demonstrate the relevance of the small data assumption for the solvability of the continuous and discrete systems.

The accuracy, stability and consistency of new stress interpolation schemes are investigated, based upon sub-cell approximations. This includes the contrast of two alternative hybrid spatial discretisations: a cell-vertex finite element/volume (fe/fv) scheme and a finite element equivalent (fe). Here, the interest is to explore the consequences of utilizing conventional methodology and to demonstrate resulting drawbacks in the presence of complex stress equation source terms. Alternative strategies worthy of consideration are presented for a constant shear viscosity model, that of Oldroyd-B, with strain-hardening and unbounded extensional properties. We demonstrate how high-order accuracy may be achieved by respecting consistency in our algorithmic constructions. Both fe- and fv-spatial discretisations are embedded within this methodology. Linear interpolation for stress, of either fe- or fv-form on triangular sub-cells, is referenced within parent triangular finite elements in two dimensions. Finite element discretisation is employed for the momentum and continuity system, via a second-order pressure-correction scheme. In this regard, a complex filament-stretching flow with a free-surface is selected to compute the transient evolution of kinematic and stress fields. Shortcomings of various upwinding schemes are discussed, whilst dealing with such free-surface type problems and appropriate strategies for dealing with these types of problems are outlined.

A time-stepping finite element method is used to predict the viscoelastic stresses that arise in a tube-tooling wire-coating problem. The polymer melt HDPE is modelled by a multi-mode Phan-Thien/Tanner constitutive equation. Different flow geometries are considered to address optimisation of the process with respect to minimising the stress induced within the coating produced. The influence of the die itself and the various modes are considered. Relaxation times range for a three-mode model from 10 −2 to 10 2 s and for a seven-mode model from 10 −3 to 10 3 s. Typical Weissenberg numbers may range up to 10 4 . Three modes are sufficient to adequately describe the flow, and shorter/narrower draw-down regions are identified as being preferable. Once an adequate land length has been gathered, that has relaxed the flow stresses prior to draw-down, the actual details of die design are found to be inconsequential to the induced stresses in the delivered coatings.