Paulo Jorge Oliveira

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• Professor
• Professor (Full) at University of Beira Interior

We propose a novel approach for non-Newtonian viscoelastic steady flows based on a decomposition of the rate-of-deformation tensor which here, in a simplified version, leads to an anisotropic generalised Newtonian fluid-like model with separated treatment of kinematics pertaining to shear and extensional flows. Care is taken to assure that the appr...

This study numerically investigates the characteristics of a non‐Newtonian magnetohydrodynamic flow in a cross‐slot. Numerical simulations are performed using power law, Bird–Carreau and Casson non‐Newtonian fluid models. The flow characteristics and shear viscosity behavior in the flow region are analyzed for different values of magnetic field. Ad...

The main purpose of this paper is to study fuel cell performance using an interdigitated flow field with intermediate channel blocks on the cathode side. Application of an intermediate block in the middle of the interdigitated flow channel is a very new idea aimed at increasing the performance of polymer membrane fuel cells, which in practice resul...

For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior is that of the Oldroyd-B model. Here, we compare the response of the simplified linear form of the Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new constitutive equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2,...

Fundamentals of applied thermodynamics, encompassing both energy and exergy analysis of thermodynamical systems. Includes a large number of solved problems. Contents: - Essential concepts of thermodynamics · First Law for closed systems · Second Law - Entropy · Thermodynamical relations. Ideal gases and incompressible fluids · First Law for open sy...

A novel design of the DBD actuator/sensor is proposed for mapping the location of the icing on a surface. The new design uses segmentation of the embedded electrode of the DBD actuator. Segmented DBD actuator/sensor devices were fabricated and experimentally tested in terms of mechanical, thermal and sensing abilities. The sensing capability of the...

Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow instabilities and major modifications to the fluid dynamics. Recent developments in the numerical methods...

The principal mechanisms by which DBD plasma actuators influence flow characteristics, and are thus able to control that flow, depend strongly on their modes of actuation. Here two different modes based on steady and unsteady actuation are compared and investigated. A simple sinusoidal voltage distribution and a duty cycled sinusoidal voltage were...

Most calculation procedures for time-dependent viscoelastic flows require iteration within the time step used to advance the solution, in order to satisfy simultaneously the momentum and the constitutive equations for each stress component. We have devised a way of reformulating the constitutive equation for the FENE-P model, or models described by...

We examine fluid flow through cross-slot devices with various depth to width ratios α. At low Reynolds number, Re, flow is symmetric and a sharp boundary exists between the two incoming fluid streams. Above an α-dependent critical value, Rec(α), a steady symmetry-breaking bifurcation occurs and a spiral vortex structure develops. Order parameters c...

The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical methods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-c...

The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical methods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-c...

To simulate the coupled plasma and fluid flow physics of dielectric-barrier discharge, a plasma-fluid model is utilized in conjunction with a compressible flow solver. The flow solver is responsible for determining the bulk flow kinetics of dominant neutral background species including mole fractions, gas temperature, pressure and velocity. The pla...

In this work, we perform creeping-flow simulations of upper-convected Maxwell and simplified Phan-Thien–Tanner fluids to study the purely-elastic steady bifurcation and transition to time-dependent flow in three-dimensional planar cross-slots. By analysing the flow in geometries with aspect ratios ranging from the near Hele-Shaw flow like limit, up...

Experimental measurements and numerical simulations are made on fluid flow through cross-slot devices with a range of aspect (depth:width) ratios, 0.4 < alpha < 3.87. For low Reynolds numbers Re, the flow is symmetric and a sharp boundary exists between fluid streams entering the cross-slot from opposite directions. Above an alpha-dependent critica...

A self-field magnetoplasmadynamic (MPD) thruster is a low-thrust electric propulsion space-system that enables the usage of magnetohydrodynamic (MHD) principles for accelerating a plasma flow towards high speed exhaust velocities. It can produce an high specific impulse, making it suitable for long duration interplanetary space missions. In this pa...

Two dimensional numerical simulations of plasma actuator flow control of the ACHEON nozzle are conducted to give insight on the design of an experimental setup. Three configurations of the plasma actuators with single and multi AC-DBD actuators are used in steady mode of operation. AC-DBD actuators in standard mode (forward forcing mode), reverse m...

To achieve the specified geometry for an extruded profile together with a minimal degree of internal stresses, flow balancing of the die is required. To fulfil this requisite, a set of operating conditions/polymer rheological properties are assumed during the design step, which are particularly relevant in the definition of the extrusion die flow c...

The development of the thermal boundary layer in a pipe for a FENE-P fluid is investigated using the method of separation of variables. The ensuing Sturm-Liouville problem is then solved for the eignevalues by means of an adequate solver, while the ordinary differential equations for the eigenfunctions and their derivatives are calculated with a fo...

A numerical investigation was carried out to quantify the local loss coefficient in the laminar flow of shear-thinning inelastic fluids through an axisymmetric sudden expansion having a diameter ratio of 1 to 2.6. The finite-volume code used collocated meshes and second order interpolation schemes to discretize the diffusion and convective terms of...

Polymer melts are very viscous fluids that can often be accurately described in shear flow by a single mode simplified linearised Phan-Thien— Tanner (SPTT) constitutive equation [1,2]. Of practical relevance, as in mold filling, is the thermal development of this fluid in a channel which takes place for a condition of fully developed hydrodynamic i...

Resumo — Este artigo trata do estudo numérico de um fenómeno de bifurcação matemática que ocorre para escoamento de um fluido viscoelástico numa geometria que consiste na ju nção de 2 canais planos. O interesse será analisar o comportamento do escoamento na zona do cruzamento dos canais e verificar se a simetria da geometria conduz, como seria intu...

This paper reports the development and application of a finite-volume based methodology which has been extended to cater for material non-linearities in the governing equations of solid stress analysis. The finite volume computational methodology uses indirect addressing to map multi-block geometries with complex shape, the governing equations are...

Resumo — Neste estudo p rocedeu-se à simulação do escoamento de fluidos viscoelásticos, como é o caso do sangue, numa bifurcação de 90º, com o objectivo de estudar o seu comportamento com a variação da elasticidade do fluido , para diferentes razões entre a viscosidade do solvente e a viscosidade total. Pretendeu-se observar a variação do tamanho e...

Resumo — O escoamento não-estacionário de fluidos viscoelásticos assume um papel relevante em diversos processos industriais. Neste trabalho, pretende-se testar um programa de simulação numérica, baseado no método dos volumes finitos e adaptado de forma a permitir o cálculo eficiente de problemas unidimensionais não-estacionários. O problema de ref...

A computational fluid dynamics simulation study has been carried out for unsteady laminar flow in a planar 2D T-junction, using non-Newtonian viscoelastic fluids with characteristics similar to those of blood. In the large blood vessels, blood can be modelled as a Newtonian fluid, however in smaller vessels it exhibits non-Newtonian behaviour, show...

In this work we propose the cross-slot geometry as a candidate for a numerical benchmark flow problem for viscoelastic fluids. Extensive data of quantified accuracy is provided, obtained via Richardson extrapolation to the limit of infinite refinement using results for three different mesh resolutions, for the upperconvected Maxwell, Oldroyd-B and...

a b s t r a c t The influence of nanosecond pulse-driven, surface-mounted dielectric barrier discharge (DBD) actuators on a transonic flow is studied numerically. An airfoil representing turbo-machinery blades in transonic flow is considered as a test case. A two-dimensional fluid model of DBD is used to describe the plasma dynamics. The model coup...

Surface DBD plasma actuators are novel means of actively controlling flow. They have shown promising ability in reducing drag, postponing transition from laminar to turbulent flow, suppression of separation, noise reduction and enhancement of mixing in differ ent applications. The CFD simulation of the effect of plasma actuator in such kind of appl...

Nowadays numerical codes are indispensable tools for the research and project phase of electric propulsion systems. The application of such codes for the analyses of magnetoplasmadynamic (MPD) thrusters is very important since it allows us to understand relevant flow-field parameters that are quite difficult to visualize and analyse in experiments....

A self-field MPD thruster in its most basic form consists in a central cathode surrounded by a concentric anode. With this coaxial geometric shape is very difficult to use experimental techniques to visualize the plasma flow parameters. In the following paper a previously proposed numerical method for the ideal magnetohydrodynamics (MHD) equations...

In order to better understand the three-dimensional non-Newtonian flow in an 180° curved duct of square cross-section, simulations were carried out considering an incompressible viscoelastic fluid, which follows the non-linear FENE-CR model, having constant shear viscosity. A fully implicit finite-volume method was used for the solution of the gove...

SUMMARY In this paper, we propose an extension of a PISO method, previously developed to solve the Euler equations, and which is here extended to the ideal magnetohydrodynamic (MHD) equations. By following a pressure-based approach, we make use of the flexibility given by pressure equation for calculating flows at arbitrary Mach numbers. To handle...

A self-field MPD thruster, in its most basic form, comprises a central cathode sur-rounded by a concentric anode. With this coaxial geometric shape it is very difficult to use experimental techniques to analyse the plasma flow parameters. In the following paper we present some preliminary results for a 2D self-field MPD thruster. These were obtaine...

In the present work, we propose a reformulation of the fluxes and interpolation calculations in the PISO method, a well-known pressure-correction solver. This new reformulation introduces the AUSM+ − up flux definition as a replacement for the standard Rhie and Chow method of obtaining fluxes and central interpolation of pressure at the control vol...

In this paper we present a method for solving the ideal compressible MHD equations at arbitrary Mach number flows. Our method is based on the well-known PISO algorithm, which is a pressure based solver. In order to handle all the possible discontinuities that can be generated by the hyperbolic system of MHD equations the AUSM-MHD technique is appli...

The flow of Newtonian and viscoelastic fluids in a mixing-separating geometry that consists of two opposed channel flows interacting through a gap in the common separating wall is investigated. The flow in this type of geometry was studied experimentally by Cochrane etal. (Philos Trans R Soc Lond A301:163–181, 1981) using Newtonian and viscoelastic...

The finite volume method (FVM) is widely used in traditional computational fluid dynamics (CFD), and many commercial CFD codes are based on this technique which is typically less demanding in computational resources than finite element methods (FEM). However, for historical reasons, a large number of Computational Rheology codes are based on FEM. T...

This paper describes the effects of Plasma actuators for the purpose of efficiency increase of propulsion systems. For solving the 3D steady/unsteady turbulent flows a numerical method based on the finite volume scheme by adopting the two-equation κ - ω turbulence model is used. Moreover, a body force treatment is devised to model the effect of pla...

The present study is aimed to the implementation and validation of the compressibility effects in a existing finite volume method procedure, prepared to simulate isothermal incompressible non-Newtonian viscoelastic flows. The applications of this numeric algorithm are centred in flows at low Mach numbers, generated by high pressure differences and...

In the field of aeronautical and aerospace engineering there is often the need of solving complex flow problems that involve a wide range of Mach numbers. In these problems a near incompressible regime may co-exist within a larger supersonic flow domain. Thus, it is important that the algorithms developed are able of solving flow problems encompass...

High-elasticity simulations of flows through a two-dimensional (2D) 4 : 1 abrupt contraction and a 4 : 1 three-dimensional square–square abrupt contraction were performed with a finite-volume method implementing the log-conformation formulation, proposed by Fattal & Kupferman (J. Non-Newtonian Fluid Mech., vol. 123, 2004, p. 281) to alleviate the h...

In the numerical simulation of classic gas dynamics problems the use of density based solvers has been the most common practice. However, realistic Magneto-Plasma Dynamics (MPD) thruster geometries, which are the motivation for the current investigation, develop flows that range from the nearly incompressible to the hypersonic limit. In the nearly...

The present numerical study is an introductory computer simulation work on the characteristics of incompressible fluid flow in curved ducts of square cross section. Here, the fluid is assumed Newtonian and the conditions of Bara et al [3], Mees et al [4] and Helin et al [7] were considered, in order to make comparison of results. Good agreement bet...

A cross-slot geometry is formed by an " horizontal " planar channel along which two incoming fluid streams are made to impinge on each other, and an intersecting " vertical " channel which carries the outlet flow, with other two streams now moving away from the central section and leaving through the vertical channel ends. A stagnation point is for...

The modeling of transonic flow using a pressure based solver is here tackled with the PISO method, in particular with the rhoPISOFoam code. This code has been applied for a wide range of Mach numbers in order to evaluate its limits under high speed flow conditions. Computations are obtained for canonical geometries and the results are compared with...

In this paper we compare different methods currently used in the stabilization of numerical simulations of time-dependent viscoelastic fluid flows described with the Oldroyd-B and related models. The methods under consideration, based on the separation of newtonian-like components from the stress tensor, are applied to a finite volume analysis of t...

Start-up times in viscoelastic channel and pipe flows generated by the sudden imposition of a pressure gradient are here determined by a mixed analytical/numerical procedure. The rheological models considered are the upper convected Maxwell and the Oldroyd-B equations. With these models the flow evolves asymptotically to the steady state solution a...

a b s t r a c t A systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelas-ticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (...

In this study, a new formulation is proposed for the calculation of stress components at control-volume faces, within the context of cell-centered finite-volume methods which have the stress tensor as one of the main dependent variables. Test case results from calculations with viscoelastic fluids flowing through a T-junction demonstrate the merits...

In this investigation the evaluation of a viscoelastic flow code under unsteady pulsating flow conditions is under taken. The time-dependent problem considered is simple and its analytical solutions is known; The flow generated by a periodic pressure gradient superimposed on a constant Poiseuille flow between two parallel plates. Results were obtai...

A correcta implementação de condições fronteira é crucial na resolução numérica de problemas envolvendo o escoamento de fluidos, especialmente quando estes se comportam de forma não newtoniano e ocorrem em regime variável. É mostrado que a aproximação habitualmente empregue para calcular a tensão de corte na parede, em que esta é igual ao produto d...

The flow of a viscoelastic fluid through a microfluidic flow-focusing device is investigated numerically with a finite-volume code using the upper-convected Maxwell (UCM) and Phan-Thien–Tanner (PTT) models. The conceived device is shaped much like a conventional planar “cross-slot” except for comprising three inlets and one exit arm. Strong viscoel...

Now that almost 60 years have passed since the pioneering works of J.G. Oldroyd it seems appropriate as an homage to consider here constitutive equations that can be viewed as generalisations of the by now classical Oldroyd-B model. In this short communication we shall address heuristically the theme of differential constitutive models and will pro...

Resumo. O tempo de arranque de escoamento viscoelástico num canal plano, após imposição súbita de um gradiente de pressões, foi calculado por um método analítico/ numérico. Os modelos reológicos utilizados foram o convectivo-superior de Maxwell (UCM) e o Oldroyd-B. Com estes modelos, o escoamento tende assimptóticamente para a solução de estado est...

The present study aims to explore the advantages of Computational Fluid Dynamics (CFD) in improving the evaluation of Indoor Air Quality in ventilated rooms through calculation of contaminant concentration fields. The results in pollutant concentration may vary along breathing zones, so it is very useful to establish the best place to install any p...

The log-conformation formulation, proposed by Fattal and Kupferman [J. Non-Newt. Fluid Mech. 123 (2004) 281], has helped to provide further insights into the High-Weissenberg Number Problem. In this work, we investigate the performance of the log-conformation formulation in the Finite Volume Method (FVM) framework for creeping flows of viscoelastic...

The flow of finite-extensibility models in a two-dimensional planar cross-slot geometry is studied numerically, using a finite-volume method, with a view to quantifying the influences of the level of extensibility, concentration parameter, and sharpness of corners, on the occurrence of the bifurcated flow pattern that is known to exist above a crit...

valores de Re elevados (Re > 1500) o escoamento bifurca para uma solução assimétrica, com o comprimento da recirculação a tornar-se maior num dos lados da parede do canal de saída comparativamente à parede oposta. Esta instabilidade mostra semelhanças com a que ocorre numa expansão plana. Palavras-chave: Fluido newtoniano; Escoamento assimétrico; S...

The flow of viscoelastic liquids through a cross-slot geometry is studied by means of numerical simulations. The geometry is planar and the constitutive model follows the FENE-CR (constant shear viscosity) equation, valid for relative dilute solutions of polymeric fluids, under fully developed flow conditions. A fully implicit finite-volume numeric...

The inertialess three-dimensional (3D) flow of viscoelastic shear-thinning fluids in a 4:1 sudden square-square contraction was investigated experimentally and numerically and compared with the flow of inelastic fluids. Whereas for a Newtonian fluid the vortex length remains unchanged at low Reynolds numbers, with the non-Newtonian fluid there is a...

In this paper two test cases adequate for the assessment of viscoelastic flow codes under unsteady flow conditions are investigated. For one of them an analytical solution is also derived. First, the start-up of planar Poiseuille flowbetween two parallel plateswas tackled. For upper-convected Maxwell and Oldroyd-B models there exist analytical solu...

In this work we investigate the flow of Newtonian and viscoelastic fluids in a mixing-separating geometry consisting of two opposed channel flows interacting through a gap in the common separating wall. This type of flow was experimentally investigated by Cochrane et al. [1] using Newtonian and viscoelastic fluids at low Reynolds number flows (Re <...

The flow visualizations of viscoelastic flows in the mixing-separating geometry of Cochrane et al. [1] showed provocative flow features that inspired the current numerical research using the upper-convected Maxwell (UCM) model. The effects of Deborah (De) and Reynolds (Re) numbers and gap size were analyzed in depth in this two-dimensional flow inv...

Viscoelastic flow in a cross‐slot geometry are known to give rise to purely‐elastic flow instabilities even under inertia‐less flow conditions. Here, the flow of the finite extensibility FENE‐CR model in a two‐dimensional planar cross‐slot configuration is studied numerically, using a finite‐volume method, with a view to quantifying the influences...

In order to understand the conditions for the onset of purely-elastic instabilities occurring in creeping flows (Re ≈ 0) of viscoelastic fluids we have carried out a systematic set of simulations in a planar cross-slot geometry governed by the non-linear constitutive equation FENE-CR. A finite-volume method is used for the calculation of the govern...

An investigation of laminar steady and unsteady flows in a two-dimensional T-junction was carried out for Newtonian and a non-Newtonian fluid analogue to blood. The flow conditions considered are of relevance to hemodynamical applications and the localization of coronary diseases, and the main objective was to quantify the accuracy of the predictio...

A finite-volume method is applied to the numerical simulation of flows of viscoelastic fluids in the benchmark confined-cylinder problem under creeping flow conditions. The fluids are modeled using the Oldroyd-B constitutive equation, the calculation of the polymer stress contribution is carried out using the log-conformation methodology [1] and th...

Uniform steady flow of viscoelastic fluids past a cylinder placed between two moving parallel plates is investigated numerically with a finite-volume method. This configuration is equivalent to the steady settling of a cylinder in a viscoelastic fluid, and here, a 50% blockage ratio is considered. Five constitutive models are employed (UCM, Oldroyd...

Many flows of practical relevance tend to develop elastic instabilities that are often a limitation in processing operations. Nowadays, considerable effort is expended in developing microfluidic devices which involve the flow of non-Newtonian fluids, and geometries with intersection of ducts are common (i.e. “cross-slot” flows). A numerical investi...

The inertialess three-dimensional (3D) flow of viscoelastic shear-thinning fluids in a 4:1 sudden square-square contraction was investigated experimentally and numerically and compared with the flow of inelastic fluids. Whereas for a Newtonian fluid the vortex length remains unchanged at low Reynolds numbers, with the non-Newtonian fluid there is a...

A comprehensive numerical study of the effects of the contraction ratio upon viscoelastic flow through axisymmetric contractions was carried out. Six contraction ratios were examined (CR = 2, 4, 10, 20, 40 and 100) using the Oldroyd-B and Phan–Thien–Tanner (PTT) constitutive equations, under creeping-flow conditions and for a wide range of Deborah...

Using a numerical technique we demonstrate that the flow of the simplest differential viscoelastic fluid model (i.e., the upper-convected Maxwell model) goes through a bifurcation to a steady asymmetric state when flowing in a perfectly symmetric "cross-slot" geometry. We show that this asymmetry is purely elastic in nature and that the effect of i...

In this work we demonstrate numerically, using a 3D finite-volume method, that viscoelastic flow in a microfluidic cross-slot geometry can lead to flow asymmetries under perfectly symmetric flow conditions. This supercritical instability is predicted using the upper-convected Maxwell model under creeping flow conditions, thus demonstrating that it...

We report a systematic numerical investigation of the creeping flow of three different viscoelastic models, the UCM, Oldroyd-B and the linear form of the PTT model, through a 1:3 planar sudden expansion. Although the effect of elasticity is to reduce both the length and intensity of the recirculation region downstream of the expansion, we show that...

In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilis...

Resumo. O objectivo principal deste trabalho numérico é analisar efeitos de viscoelasticidade na transição de um escoamento simétrico para outro assimétrico num canal plano com razão de expansão 1:4. O fluido viscoelástico segue o modelo FENE-CR e o estudo foi efectuado recorrendo ao método dos volumes finitos para resolver as equações que regem o...

We present analytical solutions for fully developed pipe and channel flows of two viscoelastic fluids possessing a Newtonian solvent, where the polymer contribution is either described by the Phan-Thien–Tanner (PTT) or FENE-P models. We derive in detail the pipe flow solution for the PTT fluid, and present the final solutions for the remaining thre...

Visualizations of the 3-D flow in a 4:1 square–square sudden contraction for two viscoelastic Boger fluids and two Newtonian fluids were carried out at low Reynolds numbers. In these creeping flow conditions, the vortex length remained unchanged for Newtonian fluids, whereas a nonmonotonic variation with flow rate was observed for the Boger fluids....

Experimental observations are reported for the laminar flow of a viscoelastic liquid through a symmetrical plane sudden expansion preceded by a gradual contraction from a square duct. As is well known, for Newtonian fluid flow above a critical Reynolds number the flowfield downstream of an expansion becomes asymmetric. For the viscoelastic liquid i...

We consider two-dimensional, inertia-free, flow of a constant-viscosity viscoelastic fluid obeying the FENE-CR equation past a cylinder placed symmetrically in a channel, with a blockage ratio of 0.5. Through numerical simulations we show that the flow becomes unsteady when the Deborah number (using the usual definition) is greater than De ≈ 1.3, f...

Resumo — A reologia computacional é uma área científica relativamente recente na qual se procura resolver, através de métodos numéricos, as equações de conservação e reológicas que regem o movimento de fluidos não newtonianos. Um aspecto novo relativamente à mais tradicional dinâmica dos fluidos computacional (CFD) é que, para os fluidos não newton...

Resumo — O escoamento de fluidos viscoelásticos através de expansões planas assume, actualmente, um papel de relevo em diversas aplicações industriais. O objectivo deste trabalho prende-se com a análise numérica do comportamento do fluido viscoelástico numa expansão plana com razão 1:4. Os resultados apresentados são relativos à estrutura do escoam...

The parameters influencing the calibration/cooling stage of profile extrusion are discussed, and a numerical finite-volume method code to model the heat transfer is described and validated. For this purpose, the numerical predictions are compared with the analytical solution of a simple problem, with results available in the literature and with tho...

A numerical study of the creeping flow of a PTT fluid through planar sudden contractions was carried out to quantify the effect of contraction ratio upon the flow characteristics (streamlines and size and intensity of recirculation vortices). The relevant governing equations were solved with a finite volume method embodying a new high-resolution sc...

A computer code, previously developed by the authors for the automatic die design, is used to optimise the flow distribution in a profile extrusion die using two alternative strategies: one based on length optimisation and the other on thickness optimisation. The numerical predictions are then compared with experimental data gathered during extrusi...

Numerical simulations of the 3D steady flow in a 4:1 square/square sudden contraction were carried out for a Newtonian and a 4 mode PTT model representing a viscoelastic fluid. The simulations, all for conditions of negligible inertia, compared well with the experimental visualizations for both fluids. For the viscoelastic fluid an intense vortex e...