Viscoelastic fluid analysis in internal and in free surface flows using the software OpenFOAM

Synthetic polymer products are of great importance in several industrial sectors, such as for production of packaging, parts of appliances, electronics, cars and food processing industries. Due to the increasing demand for this kind of material, reduction of waste and increase of quality has become a key issue in polymer industry. In this sense modeling and simulation of processing operations appears as a fundamental tool, leading to better understanding of how the rheological properties of polymers affect their processability and final product quality, and reducing time and costs related to the development of processes and products. This work presents some basic results that aims to validate a developed methodology for internal viscoelastic fluid flows, which was developed in a previous work in the OpenFOAM computational fluid dynamics package and also will be showed a extension of this methodology for analysis of free surface viscoelastic fluid flows, using the VOF methodology. A classical flow phenomena used in the rheology literature to present the concept of viscoelastic effects was simulated, i.e., the die swell experiment. The results obtained using Giesekus model showed the great potential of the developed formulation, once phenomena observed experimentally were reproduced in the simulations.

[1]  P. J. Dotson,et al.  Polymer solution rheology based on a finitely extensible bead—spring chain model , 1980 .

[2]  R. Larson Constitutive equations for polymer melts and solutions , 1988 .

[3]  R. Rutgers,et al.  On the evaluation of some differential formulations for the pom-pom constitutive model , 2003 .

[4]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[5]  Hrvoje Jasak,et al.  Error analysis and estimation for the finite volume method with applications to fluid flows , 1996 .

[6]  J. Azaiez,et al.  Numerical simulation of viscoelastic flows through a planar contraction , 1996 .

[7]  R. I. Issa,et al.  A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes , 1999 .

[8]  H. Giesekus A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility , 1982 .

[9]  Cláudio Augusto Oller do Nascimento,et al.  10th international symposium on process systems engineering , 2009 .

[10]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[11]  M. A. Ajiz,et al.  A robust incomplete Choleski‐conjugate gradient algorithm , 1984 .

[12]  Andrew Pollard,et al.  COMPARISON OF PRESSURE-VELOCITY COUPLING SOLUTION ALGORITHMS , 1985 .

[13]  O. Basaran,et al.  Dynamics of formation and dripping of drops of deformation-rate-thinning and -thickening liquids from capillary tubes , 2006 .

[14]  A. I. Leonov Nonequilibrium thermodynamics and rheology of viscoelastic polymer media , 1976 .

[15]  James J. Feng,et al.  Viscoelastic effects on drop deformation in a converging pipe flow , 2008 .

[16]  Christopher W. Macosko,et al.  Rheology: Principles, Measurements, and Applications , 1994 .

[17]  S. Acharya,et al.  Comparison of the Piso, Simpler, and Simplec Algorithms for the Treatment of the Pressure-Velocity Coupling in Steady Flow Problems , 1986 .

[18]  R. Bird Dynamics of Polymeric Liquids , 1977 .

[19]  F. Baaijens,et al.  Differential constitutive equations for polymer melts: The extended Pom–Pom model , 2001 .

[20]  R. Larson,et al.  Molecular constitutive equations for a class of branched polymers: The pom-pom polymer , 1998 .

[21]  R. Tanner,et al.  A new constitutive equation derived from network theory , 1977 .

[22]  D. V. Boger Viscoelastic Flows Through Contractions , 1987 .

[23]  R. P. G. Rutgers,et al.  Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model , 2004 .

[24]  N. Phan-Thien,et al.  Three dimensional numerical simulations of viscoelastic flows through planar contractions , 1998 .

[25]  James Clerk Maxwell,et al.  IV. On the dynamical theory of gases , 1868, Philosophical Transactions of the Royal Society of London.

[26]  A. B. Metzner,et al.  Development of constitutive equations for polymeric melts and solutions , 1963 .

[27]  Sang-Wook Kim,et al.  Comparison of the SMAC, PISO and iterative time-advancing schemes for unsteady flows , 1992 .

[28]  H. Rusche Computational fluid dynamics of dispersed two-phase flows at high phase fractions , 2003 .

[29]  Dalton J. E. Harvie,et al.  Deformation of a viscoelastic droplet passing through a microfluidic contraction , 2008 .

[30]  J. Oldroyd On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[31]  Yuriko Renardy,et al.  Development and implementation of VOF-PROST for 3D viscoelastic liquid–liquid simulations , 2006 .

[32]  V. G. Ferreira,et al.  A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows , 2008 .

[33]  X. Luo Numerical simulation of Weissenberg phenomena – the rod-climbing of viscoelastic fluids , 1999 .

[34]  Hrvoje Jasak,et al.  Viscoelastic Flow Simulation: Development of a Methodology of Analysis Using the Software OpenFOAM and Differential Constitutive Equations , 2009 .

[35]  V. G. Ferreira,et al.  The MAC method , 2008 .

[36]  F. Pinho,et al.  Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions , 2003 .

[37]  F. Pinho,et al.  On the effect of contraction ratio in viscoelastic flow through abrupt contractions , 2004 .

[38]  R. Armstrong,et al.  Birefringence and laser-Doppler velocimetry (LDV) studies of viscoelastic flow through a planar contraction , 1994 .

[39]  Gerrit W. M. Peters,et al.  Viscoelastic flow past a confined cylinder of a low-density polyethylene melt , 1997 .

[40]  Caicheng Lu,et al.  Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems , 2003 .

[41]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[42]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[43]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[44]  A. D. Gosman,et al.  The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme , 1986 .

[45]  J. M. Rallison,et al.  Creeping flow of dilute polymer solutions past cylinders and spheres , 1988 .

[46]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[47]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .