Development of an integral viscoelastic flow solver in OpenFOAM®

The usual high cost of commercial codes, and some technical limitations, clearly limits the employment of numerical modelling tools in both industry and academia. Consequently, the number of companies that use numerical code is limited and there a lot of effort put on the development and maintenance of in-house academic based codes. Having in mind the potential of using numerical modelling tools as a design aid, of both products and processes, different research teams have been contributing to the development of open source codes/libraries. In this framework, any individual can take advantage of the available code capabilities and/or implement additional features based on his specific needs. These type of codes are usually developed by large communities, which provide improvements and new features in their specific fields of research, thus increasing significantly the code development process. Among others, OpenFOAM® multi-physics computational library, developed by a very large and dynamic community, nowadays comprises several features usually only available in their commercial counterparts; e.g. dynamic meshes, large diversity of complex physical models, parallelization, multiphase models, to name just a few. This computational library is developed in C++ and makes use of most of all language capabilities to facilitate the implementation of new functionalities. Concerning the field of computational rheology, OpenFOAM® solvers were recently developed to deal with the most relevant differential viscoelastic rheological models, and stabilization techniques are currently being verified. This work describes the implementation of a new solver in OpenFOAM® library, able to cope with integral viscoelastic models based on the deformation field method. The implemented solver is verified through the comparison of the predicted results with analytical solutions, results published in the literature and by using the Method of Manufactured Solutions.

A new integral viscoelastic flow solver in OpenFOAM®

The usual high cost of commercial codes, and some technical limitations, clearly limits the employment of numerical modelling tools in both industry and academia. Consequently, the number of companies that use numerical code is limited and there a lot of effort put on the development and maintenance of in-house academic based codes . Having in mind the potential of using numerical modelling tools as a design aid, of both products and processes, different research teams have been contributing to the development of open source codes/libraries. In this framework, any individual can take advantage of the available code capabilities and/or implement additional features based on his specific needs. These type of codes are usually developed by large communities, which provide improvements and new features in their specific fields of research, thus increasing significantly the code development process. Among others, OpenFOAM® multi-physics computational library, developed by a very large and dynamic community, nowadays comprises several features usually only available in their commercial counterparts; e.g. dynamic meshes, large diversity of complex physical models, parallelization, multiphase models, to name just a few. This computational library is developed in C++ and makes use of most of all language capabilities to facilitate the implementation of new functionalities. Concerning the field of computational rheology, OpenFOAM® solvers were recently developed to deal with the most relevant differential viscoelastic rheological models, and stabilization techniques are currently being verified. This work describes the implementation of a new solver in OpenFOAM® library, able to cope with integral viscoelastic models based on the deformation field method. The implemented solver is verified through the comparison of the predicted results with analytical solutions, results published in the literature and by using the Method of Manufactured Solutions

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

In this paper we present a finite difference MAC-type approach for solving three-dimensional viscoelastic incompressible free surface flows governed by the eXtended Pom-Pom (XPP) model, considering a wide range of parameters. The numerical formulation presented in this work is an extension to three-dimensions of our implicit technique [Journal of Non-Newtonian Fluid Mechanics 166 (2011) 165-179] for solving two-dimensional viscoelastic free surface flows. To enhance the stability of the numerical method, we employ a combination of the projection method with an implicit technique for treating the pressure on the free surfaces. The differential constitutive equation of the fluid is solved using a second-order Runge-Kutta scheme. The numerical technique is validated by performing a mesh refinement study on a pipe flow, and the numerical results presented include the simulation of two complex viscoelastic free surface flows: extrudate-swell problem and jet buckling phenomenon. © 2013 Elsevier B.V.

Técnica para dedução do modelo algébrico PTT, aplicações e análises numéricas em escoamentos bidimensionais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model

The Double Convected Pom-Pom model was recently introduced to circumvent some numerical and theological defects found in other formulations of the Pom-Pom concept. It is used here for the simulation of a benchmark problem: the flow in an abrupt planar contraction. The predictions are compared with birefringence measurements and show reasonable quantitative agreement with experimental data. A parametric study is also carried out with the aim of analysing the effect of the branching parameter on vortex dynamics and extrudate swell. The results show that the Double Convected Pom-Pom model (DCPP) model is able to discriminate between branched and linear macromolecular structures in accordance with experimental observations. In that respect, the role of the extensional properties in determining complex flow behaviour is stressed. Also, the ratio of the first normal stress difference to the shear stress appears to play a major role in die swell observation. For the time being, the role of the second normal stress difference appears to be less obvious to evaluate in this complex flow. (C) 2004 Elsevier B.V. All rights reserved.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Statistical analysis of a viscoelastic turbulent channel flow

Statiscal analysis related to a viscoelastic turbulent channel flow characterized as dilute polymer solution.

Protein-polysaccharide viscoelastic matrices: synergic effects of amylose on lysozyme physical gelation in aqueous dimethylsulfoxide

A synergic effect of amylose on rheological characteristics of lysozyme physical gels evolved out of dimethylsulfoxide-water was verified and analyzed. The dynamics of the gels were experimentally approached by oscillatory rheology. The synergic effect was characterized by a decrease in the threshold DMSO volume fraction required for lysozyme gelation, and by a significant strengthening of the gel structure at over-critical solvent and protein concentrations. Drastic changes in the relaxation and creep curve patterns for systems in the presence of amylose were verified. Complex viscosity dependence on temperature was found to conform to an Arrhenius-like equation, allowing the determination of an activation energy term (Ea, apparent) for discrimination of gel rigidity. A dilatant effect was found to be induced by temperature on the flow behavior of lysozyme dispersions in DMSO-H(2)O in sub-critical conditions for gelation, which was greatly intensified by the presence of amylose in the samples. That transition was interpreted as reflecting a change from a predominant colloidal flow regime, where globular components are the prevailing structural elements, to a mainly fibrillar, polymeric flow behavior.

Polyethylene flow prediction with a differential multi-mode Pom-Pom model

We report the first steps of a collaborative project between the University of Queensland, Polyflow, Michelin, SK Chemicals, and RMIT University; on simulation, validation and application of a recently introduced constitutive model designed to describe branched polymers. Whereas much progress has been made on predicting the complex flow behaviour of many - in particular linear - polymers, it sometimes appears difficult to predict simultaneously shear thinning and extensional strain hardening behaviour using traditional constitutive models. Recently a new viscoelastic model based on molecular topology, was proposed by McLeish and Larson (1998). We explore the predictive power of a differential multi-mode version of the pom-pom model for the flow behaviour of two commercial polymer melts: a (long-chain branched) low-density polyethylene (LDPE) and a (linear) high-density polyethylene (HDPE). The model responses are compared to elongational recovery experiments published by Langouche and Debbaut (1999), and start-up of simple shear flow, stress relaxation after simple and reverse step strain experiments carried out in our laboratory.

Slip flows of Newtonian and viscoelastic fluids in a 4:1 contraction

This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient.

Weld lines in extrusion: Understanding the role of the flow conditions

This work reports the implemen tation and verification of a new so lver in OpenFOAM® open source computational library, able to cope w ith integral viscoelastic models based on the integral upper-convected Maxwell model. The code is verified through the comparison of its predictions with anal ytical solutions and numerical results obtained with the differential upper-convected Maxwell model