1. Extrusion Simulation and Optimization of Profile Die Design By
Srinivasa Rao Vaddiraju
Advisor
Prof. Milivoje Kostic

2. A Schematic of Profile Extrusion Line at FNAL
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.
Dryer
Cutter
Feeding
Hopper
Extruder
Die
Calibrator
Cooling
Measurement
Haul-off
Polymer pellets
Dopants
Breaker plate
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. Prepare the complete design of dies, including blue prints.
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,
τ 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,
ρ 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. Kinematic balance equation
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 δΩfree
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. Kinematic balance equation
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 δΩfree
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. Kinematic balance equation
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 δΩfree
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. Kinematic balance equation
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 δΩfree
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. Kinematic balance equation
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 δΩfree
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. Kinematic balance equation
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 δΩfree
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. Kinematic balance equation
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 δΩfree
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. Carreau-Yasuda Law for viscosity data:
Material Data
Styron 663, mixed with Scintillator dopants
Measured by, Datapoint Labs
Carreau-Yasuda Law for viscosity data:
Zero shear rate viscosity, η0 = 36,580 Pa-s
Infinite shear rate viscosity, η∞ = 0 Pa-s
Natural time, λ = 0.902
Transition Parameter, a = 0.585
Exponent, n = 0.267
Density, ρ = 1040 Kg/m3
Specific Heat, cp = 1200 J/Kg-K
Thermal Conductivity, k = W/m-K
Coefficient of thermal expansion, β = 0.5e-5 m/m-K

27. Styron viscosity data, with and without Scintillator dopants
ηd– Doped Styron 663
106
105
104
103
102
10-2
10-1
100
101

28. Profiles Rectangular profile die with one hole
Rectangular profile die with ten holes

29. Rectangular profile die with one hole
2.0
1.0
0.11
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
P1 (0,y)
P2 (0,y)
P3 (x,y)
P4 (x,0)
P5 (x,0)

31. Full domain of the extrusion die
Melt flow
direction

32. Half domain of the extrusion die
Section 1
Section 2
Section 3
Die lip
Melt flow
direction

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
Melt flow direction
Die Lip
30,872 elements
Skewness < 0.33

35. 19 hours and 36 minutes of CPU time
Windows XP
2.52 GHz Processor
1 GB RAM
19 hours and 36 minutes of CPU time

36. Contours of static pressure
Die lip
Melt flow
direction

37. Contours of velocity magnitude at different iso-surfaces
Die lip
Melt flow
direction

38. Contours of temperature distribution
Melt flow
direction
Die lip

39. Contours of shear rate
Melt flow
direction
Die lip

40. Existing die, corresponding simulation and new improved-die profiles
X (mm)
Y (mm)
New Die (Simulated)
Existing Die
Desired Extrudate
Existing-Die Extrudate (Simulated)

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
10.0
0.5
0.11
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
Melt Pump Adapter,
Adapter 1 and Adapter 2
Spider
Die land
Melt flow
direction
Die lip
Free Surface

47. Simulation domain with boundary conditions1 2 3 4 5
. Inlet (Fully Developed Flow)
2. Wall (Vn = 0, Vs = 0)
3. Symmetry (Vn = 0, Fs = 0)
4. Free Surface (Fs = 0, Fn = 0, V.n = 0)
5. Outlet (Fn = 0, Vs = 0)
Melt flow
direction

48. Finite element 3-D domain and half of extrudate profile mesh
Melt flow
direction
19,479 elements
Skewness < 0.5

49. Half domain of the extrusion die (without free surface) and division of outlet into 10 areas
Melt flow
direction
out1
out2
out3
out4
out5
out6
out7
out8
out9
out10

50. Percentage of Mass flow rate in different exit segments

51. Windows XP
2.52 GHz Processor
1 GB RAM
One hour of CPU time

52. Contours of Static pressure
Melt flow
direction
Die lip

53. Contours of Velocity magnitude at different iso-surfaces and at centerline of exit
Melt flow
direction
Die lip
Velocity Magnitude (m/s)
X-Coordinate (m)

54. Contours of Temperature distribution
Melt flow
direction
Die lip

55. Contours of Shear rate and Viscosity
Melt flow
direction
Die lip
Shear rate
Viscosity

56. Simulated die and required extrudate profiles

57. Percentage of mass flow rate for designed and balanced die

58. Exploded view of the extrusion die
Melt pump
adapter
Adapter 1
Adapter 2
Preland
Melt flow
direction
Dieland

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 ?