The Contraction Point for Phan-Thien/Tanner Model of Tube-Tooling Wire-Coating Flow

Authors: V. Ngamaramvaranggul, S. Thenissara

Abstract:

The simulation of extrusion process is studied widely in order to both increase products and improve quality, with broad application in wire coating. The annular tube-tooling extrusion was set up by a model that is termed as Navier-Stokes equation in addition to a rheological model of differential form based on singlemode exponential Phan-Thien/Tanner constitutive equation in a twodimensional cylindrical coordinate system for predicting the contraction point of the polymer melt beyond the die. Numerical solutions are sought through semi-implicit Taylor-Galerkin pressurecorrection finite element scheme. The investigation was focused on incompressible creeping flow with long relaxation time in terms of Weissenberg numbers up to 200. The isothermal case was considered with surface tension effect on free surface in extrudate flow and no slip at die wall. The Stream Line Upwind Petrov-Galerkin has been proposed to stabilize solution. The structure of mesh after die exit was adjusted following prediction of both top and bottom free surfaces so as to keep the location of contraction point around one unit length which is close to experimental results. The simulation of extrusion process is studied widely in order to both increase products and improve quality, with broad application in wire coating. The annular tube-tooling extrusion was set up by a model that is termed as Navier-Stokes equation in addition to a rheological model of differential form based on single-mode exponential Phan- Thien/Tanner constitutive equation in a two-dimensional cylindrical coordinate system for predicting the contraction point of the polymer melt beyond the die. Numerical solutions are sought through semiimplicit Taylor-Galerkin pressure-correction finite element scheme. The investigation was focused on incompressible creeping flow with long relaxation time in terms of Weissenberg numbers up to 200. The isothermal case was considered with surface tension effect on free surface in extrudate flow and no slip at die wall. The Stream Line Upwind Petrov-Galerkin has been proposed to stabilize solution. The structure of mesh after die exit was adjusted following prediction of both top and bottom free surfaces so as to keep the location of contraction point around one unit length which is close to experimental results.

Keywords: wire coating, free surface, tube-tooling, extrudate swell, surface tension, finite element method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082229

References:

[1] B. Caswell and R. I. Tanner, "Wirecoating Die Design Using Finite Element Methods", Polym. Eng. Sci., vol 18, no. 5, pp 416-421, 1978.
[2] C.D. Han and D. Rao, "Studies on Wire Coating Extrusion. I. The Rheology of Wire Coating Extrusion", Polym. Eng. Sci., vol 18, no. 13, pp 1019-1029, 1978.
[3] E. Mitsoulis, "Finite Element Analysis of Wire Coating", Polym. Eng. Sci., vol 26, no. 2, pp 171-186, 1986.
[4] D.M. Binding, A.R. Blythe, S. Gunter, A.A. Mosquera, P. Townsend and M.F. Webster, "Modelling Polymer Melt Flows in Wirecoating Processes", J. Non-Newtonian Fluid Mech., vol 64, pp 191-206, 1996 D.M. Binding, A.R. Blythe, S. Gunter, A.A. Mosquera, P. Townsend and M.F. Webster, "Modelling Polymer Melt Flows in Wirecoating Processes", J. Non-Newtonian Fluid Mech., vol 64, pp 191-206, 1996.
[5] I. Mutlu, P. Townsend and M.F. Webster, "Simulation of Cable-coating Viscoelastic Flows with Coupled and Decoupled Schemes", J. Non- Newtonian Fluid Mech., vol 74, pp 1-23, 1998.
[6] V. Ngamaramvaranggul and M.F. Webster, "Simulation of Viscoelastic Flows", Int. J. Num. Meth. Fluids, vol 36, pp 539-595, 2001.
[7] V. Ngamaramvaranggul and M.F. Webster, "Simulation of Pressuretooling Wire- coating Flow with Phan-Thien/Tanner Models", Int. J. Num. Meth. Fluids, vol 38, pp 677-710, 2002.
[8] R. I. Tanner, ÔÇÿEngineering Rheology-, Oxford University Press, London, 1985.
[9] H. Matallah, P. Townsend and M.F. Webster, "Viscoelastic Multi-mode Simulations of Wire-Coating", J. Non-Newtonian Fluid Mech., vol 90, pp 217-241, 2000.
[10] S. H. Anastasiadis, "The work of adhesion of polymer/wall interfaces and its association with the onset of wall slip", J. Rheol., vol 42, no. 4 pp 795-84-12, 1998.
[11] A.W. Neumann and J.K. Spelt, "Applied Surface Thermodynamics", Surfacetant Science Series, vol 63Marcel Dekker, Inc., New York, 1996 A.W. Neumann and J.K. Spelt, "Applied Surface Thermodynamics", Surfacetant Science Series, vol 63Marcel Dekker, Inc., New York, 1996.
[12] A.N. BROOKS AND T.J.R. HUGHES, "Streamline upwind/Petrov- Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations", Comp. Meth. Appl. Mech. Engng., vol 32, pp. 199-259, 1982.
[13] S. Bashforth and J. C. Adams, "An Attempt to Test the Theory of Capillary Action", Cambridge University Press and Deighton, Bell & Co., London, 1882.
[14] V. Ngamaramvaranggul and M. F. Webster, "Computation of Free Surface Flows with a Taylor-Galerkin/Pressure-Correction Algorithm", Int. J. Num. Meth. Fluids, vol 33, pp 993-1026, 2000.
[15] V. Ngamaramvaranggul and M. F. Webster, "Simulation of Coating Flows with Slip Effects", Int. J. Num. Meth. Fluids, vol 33, pp 961-992, 2000.
[16] G.J. Borse, "Fortran 77 and Numerical methods for Engineers", PWSKENT Publishing Company, Boston, 1991.