Extrusion Simulation and Optimization of Profile Die Design

1
Extrusion Simulation and Optimization of Profile
Die Design

• 03-25-2003

By Srinivasa Rao Vaddiraju
Advisor Prof. Milivoje Kostic
2
Introduction

• Extrusion describes the process by which a
  polymer melt is pushed across a metal die, which
  continuously shapes the melt into the desired
  form.

Gear pump
A Schematic of Profile Extrusion Line at FNAL
3
Quality factors
Extrudate swell
rearrangement of the velocity profile as the
polymer leaves the die
Draw down
Cooling Insufficient mixing in the extruder
Uneven die body temperatures and raw material
variations Non-uniform viscosity in the
die Non-uniform swelling Non-uniform draw down
4
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

5
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

6
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

7
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

8
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

9
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

10
Objectives

• An attempt to develop a possible strategy for
  effective die design in profile extrusion
• Investigate the die swell behavior of the polymer
  and to predict the optimum die profile-shape and
  dimensions, including the pin(s) profile, to
  obtain the required dimensions and quality of the
  extrudate.
• Investigate the swell phenomenon and mass flow
  balance affected by different parameters like die
  lengths, flow rates, exponent in viscosity
  function etc.
• Simulate the flow and heat transfer of molten
  polymer inside the die and in the free-flow
  region after the die exit, and compute pressure,
  temperature, velocity, stress and strain rate
  distributions over the entire simulation domain.
• Investigate and understand over-all polymer
  extrusion process, and integrate the simulation
  results with the experimental data, to optimize
  the die design and ultimately to achieve better
  quality and dimensions of the extrudate.
• Prepare the complete design of dies, including
  blue prints.

11
Design Methodology

• Using Finite Element based CFD code Polyflow?
• Using the method of Inverse Extrusion
• To fully understand the extrusion processes and
  the influence of various parameters on the
  quality of the final product.
• Integrate the simulation results and the
  experimental data to obtain more precise
  extrudate shape.

12
Literature Review

• The text book Dynamics of Polymeric Liquids by
  R.B.Bird gives a detailed overview of
  non-Newtonian fluid dynamics, which is important
  to understand the flow of polymers.
• The text book Extrusion Dies by Walter Michaeli
  gives an extensive representation of extrusion
  processes and guidelines for the design of dies.
• The text book Plastics Extrusion Technology
  Handbook by Levis gives a clear representation
  of the rheology of materials and the technology
  of extrusion processes.
• Woei-Shyong Lee and Sherry Hsueh-Yu Ho have
  investigated the die swell behavior of a polymer
  melt using finite element method and simulated
  flow of Newtonian fluid and designed a profile
  extrusion die with a geometry of a quarter ring
  profile
• Louis G. Reifschneider has designed a coat hanger
  extrusion die using a parametric based
  three-dimensional polymer flow simulation
  algorithm, where the shape of the manifold and
  land are modified to minimize the velocity
  variation across the die exit.
• W.A. Gifford has demonstrated through an actual
  example how the efficient use of 3-D CFD
  algorithms and automatic finite element mesh
  generators can be used to eliminate much of the
  cut and try from profile die design.

13
Governing Equations
Continuity Equation
Momentum Equation
Where, P is the pressure, t is the extra
stress tensor, v is the velocity.
14
Energy Equation
the accumulation term,
the convection term,
the conduction term,

the dissipation term,
Where, Cv is the specific heat capacity of the
material, T is the temperature, ? is the
density, k is the thermal conductivity.
15
Die Design

• The art of die design is to predict properly
  irregular die shape (with minimum number of
  trials) which will allow melt flow to reshape and
  solidify into desired (regular) extrudate
  profile.
• The correct geometry of the die cannot be
  completely determined from engineering
  calculations.
• Numerical methods

16
POLYFLOW?

• Finite-element CFD code
• Predict three-dimensional free surfaces
• Inverse extrusion capability
• Strong non-linearities
• Evolution procedure

17
Flowchart for numerical simulation using Polyflow?
1. Draw the geometry in Pro-E (or) other CAD
software and export to GAMBIT
2. Draw the geometry in GAMBIT (or) import from
other CAD software and mesh it.
Modify the mesh
3. Specify Polymer properties in Polydata
4. Specify boundary conditions in Polydata
Change the remeshing techniques and/or solver
methods
5. Specify remeshing technique and solver method
in Polydata
6. Specify the evolution parameters in Polydata
Modify the evolution parameters
7. Polyflow solves the conservation equations
using the specified data and boundary conditions
8.Is the solution converged?
No
Yes
Stop
18
General Assumptions
The flow is steady
and incompressible
Body forces and Inertia effects are negligible in
comparison with viscous and pressure forces.
Specific heat at constant pressure, Cp, and
thermal conductivity, k, are constant
19
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room- temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
20
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room- temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
21
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room- temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
22
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room- temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
23
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room-temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
24
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room- temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
25
Boundary Conditions
Inlet Fully developed inlet velocity
corresponding to actual mass flow rate of
50 kg/hr and uniform inlet temperature (473 K or
200 ?C).
Die, spider and pin walls No slip at the die
walls (Vn Vs 0 normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K.
Symmetry planes Shear stress Fs 0, normal
velocity Vn 0 and normal heat flux qn 0.
Free surface Zero pressure and traction/shear at
boundary (Fn 0, Fs 0, and Vn 0), and
convection heat transfer from the free surface to
surrounding room- temperature air.
Kinematic balance equation
on dOfree
Outlet Normal stress Fn 0, Tangential Velocity
Vs 0, Pressure 0.0 (reference pressure) and
normal heat flux qn 0.
All domains Viscous dissipation was neglected
for all flow conditions (after verification).
26
Material Data
Styron 663, mixed with Scintillator dopants
Measured by, Datapoint Labs
Carreau-Yasuda Law for viscosity data

• Zero shear rate viscosity, ?0 36,580 Pa-s
• Infinite shear rate viscosity, ?8 0 Pa-s
• Natural time, ? 0.902
• Transition Parameter, a 0.585
• Exponent, n 0.267
• Density, ? 1040 Kg/m3
• Specific Heat, cp 1200 J/Kg-K
• Thermal Conductivity, k 0.12307 W/m-K
• Coefficient of thermal expansion, ß 0.5e-5 m/m-K

27
Styron viscosity data, with and without
Scintillator dopants
28
Profiles

• Rectangular profile die with one hole
• Rectangular profile die with ten holes

29
Rectangular profile die with one hole
Required extrudate is a rectangular cross section
of 1 cm ? 2 cm with a circular hole of 1.1 mm
diameter at its center
ALL DIMENSIONS ARE IN CM
30
Sensitivity analysis of die swell and inverse
extrusion capabilities of Polyflow?
31
Full domain of the extrusion die
Melt flow direction
32
Half domain of the extrusion die
33
Simulation domain with boundary conditions

• . Inlet (Fully Developed Flow)
• 2. Wall (Vn 0, Vs 0)
• 3. Symmetry (Vn 0, Fs 0)
• . Free Surface (Fs 0, Fn 0, V.n 0)
• . Outlet (Fn 0, Vs 0)

34
Finite element 3-D domain and die-lip mesh
30,872 elements Skewness lt 0.33
35
19 hours and 36 minutes of CPU time

• Windows XP
• 2.52 GHz Processor
• 1 GB RAM

36
Contours of static pressure
37
Contours of velocity magnitude at different
iso-surfaces
38
Contours of temperature distribution
39
Contours of shear rate
40
Existing die, corresponding simulation and new
improved-die profiles
41
Exploded view of the extrusion die
42
2 D-View of the extrusion die
Melt flow direction
43
Blue prints
Preland
Dieland
Pin
44
Rectangular profile die with ten holes
Required extrudate is a rectangular cross section
of 0.5 cm ? 10 cm with ten equally spaced
centerline circular holes of 1.1 mm diameter.
ALL DIMENSIONS ARE IN CM
45
Full domain of the extrusion die
Melt flow direction
46
Half domain of the extrusion die
47
Simulation domain with boundary conditions
48
Finite element 3-D domain and half of extrudate
profile mesh
19,479 elements Skewness lt 0.5
49
Half domain of the extrusion die (without free
surface) and division of outlet into 10 areas
50
Percentage of Mass flow rate in different exit
segments
51
One hour of CPU time

• Windows XP
• 2.52 GHz Processor
• 1 GB RAM

52
Contours of Static pressure
53
Contours of Velocity magnitude at different
iso-surfaces and at centerline of exit
54
Contours of Temperature distribution
55
Contours of Shear rate and Viscosity
Shear rate
Viscosity
56
Simulated die and required extrudate profiles
57
Percentage of mass flow rate for designed and
balanced die
0
58
Exploded view of the extrusion die
59
Blue prints
Melt pump adapter
Whole die
Adapter 1
60
Adapter 2
Spider
Die land
61
Conclusions

• The optimum dimensions of the die to attain more
  balanced flow at the exit were obtained.
• The effect of inertia terms is found to be
  negligible for polymer flows at low Reynolds
  number.
• The exponent of the Carreau-Yasuda model, or the
  slope of the viscosity vs shear rate curve, has a
  significant effect on the die swell.
• The flow in the die appeared to be smooth with no
  re-circulation regions.

62
Recommendations for future improvements

• Polymer viscoelastic properties
• Include flow, cooling, solidification and
  vacuuming in and after the calibrator
• Radiation effects for free surface flow
• Pulling force at the end of the free surface
• Pressure of the compressed air
• Non-uniform mesh

63
ACKNOWLEDGEMENTS

• Prof. Milivoje Kostic
• Prof. Pradip Majumdar
• Prof. M.J. Kim
• Prof. Lou Reifschneider
• NICADD (Northern Illinois Centre for Accelerator
  and Detector Development), NIU
• Fermi National Accelerator Laboratory, Batavia, IL

64
QUESTIONS ?