The Contraction Point for Phan-Thien/Tanner Model of Tube-Tooling Wire-Coating Flow
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63039", author = "V. Ngamaramvaranggul and S. Thenissara", title = "The Contraction Point for Phan-Thien/Tanner Model of Tube-Tooling Wire-Coating Flow", 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.", volume = "4", number = "4", pages = "480-7", }