1. Prepared by Dan Wu with the supervision under Prof. M. Kostic
Extrusion Die Design Optimization Including Viscoelastic Polymer Simulation
Prepared by Dan Wu
with the supervision under Prof. M. Kostic
Mechanical Engineering Department
Northern Illinois University
April 14th, 2004

2. Parametric Study of Die Lip Profile
Improvement of Extrusion Simulation
Apply fine enough non-uniform mesh in the corner area and in the axial flow-direction after the die exit
Consider the radiation heat transfer in the free surface
Apply more realistic Arrhenius Shear Stress Temperature Dependent Viscosity Law in non-Isothermal Inverse Extrusion Simulation
Parametric Study of Die Lip Profile
The effect of non-zero nitrogen pressure in inside-surface hole
The effect of non-zero normal force in the outlet of the free surface flow domain
The effect of the length of the free surface flow domain
Extrusion Simulation Including Viscoelastic Properties
Choose one of the most realistic non-linear differential viscoelastic model (Giesekus Model)
Comparison of the results between including viscoelastic properties and not including them applying PolyFLOW 2-D and 3-D inverse extrusion

3. Geometry of the quarter computational domain
LFS– Length of the free surface flow domain
LDL– Length of the die land flow domain

4. Boundary conditions in a quarter of computational flow domain
Die Walls
Flow Inlet
Free Surfaces
Symmetric Plane
Die land
Flow Direction
Free surface
Flow Outlet
In our current simulation, we consider non-zero nitrogen pressure in this free surface
In our current simulation, we consider radiation
heat transfer in these two free surface

5. Description of Boundary Conditions
Flow Boundary Conditions
The flow inlet is given by fully developed volumetric flow rate
At the walls the flow is given as zero velocity, i.e. vn = vs = 0
A symmetry plane with zero tangential forces and zero normal velocity, fs = vn =0 are applied at half plane of the geometry.
Free surface is specified for the moving boundary conditions of the die with atmospheric pressure, p = p.The different pressure (N2 gage pressure) in inside-surface of the hole will be applied in our new simulation
Exit for the flow is specified as, fs = fn = 0. The different normal force (pulling force) will be applied in our new simulation.
Thermal Boundary Conditions
Temperature imposed along the inlet and the walls of the die = 483K
Along the symmetry planes, the condition imposed is Insulated/Symmetry along the boundaries.
Heat flux is imposed on the free surfaces covering radiation heat transfer, which can not be negligible. The vale of radiation heat flux is close to that of convection heat flux. This will be applied in our new simulation.
Outflow condition is selected at the outlet for a vanishing conductive heat flux.

6. Mesh Refinement in the computational domain
Current non-uniform mesh
Previous uniform mesh
Fine enough non-uniform around corner and close to the wall and in the axial flow direction after die exit (our current simulation)
Die exit
Free surface flow domain
Die land flow domain
Melt Polymer Flow Direction

7. Curve-fitting viscosity function
"shear stress'' version of the temperature-dependence
laws (our new viscosity function)
"shear rate'' version of the temperature-dependence
laws (our previous viscosity function) [ ] h ( T , g ) = h ( T ) * h g h ( T ) .

8. We are currently using Styron663 with additives
We are currently using Styron663 with additives. From this chart the viscosity-shear rate curve is not translating at a different temperature. This means we can not choose our previous form but our new form.

9. Non-isothermal generalized Newtonian flow setting up In PolyFLOW inverse simulation
MATERIAL DATA
Density (ρ) kg/m3
Specific Heat (H) J/Kg-oK
Thermal Conductivity (k) W/m-oK
Coefficient of Thermal Expansion () 6.6 x 10-5 m/m-oK
Reference Temperature (theta or T) 300K

10. Parameters in the new general form

11. Current simulation results analysis (Carreau-Yasuda model)
Fully developed velocity
profile (die land)
developing velocity
Profile (free surface)
Uniform velocity
Profile (free surface)
Flow direction
Z=2.54cm
Z=3.5cm
Z=3.8cm
According to the velocity profile in the computational domain, it changes only in the partial free surface flow domain (z = cm). It is necessary to apply enough fine non-uniform mesh in this partial domain than others to capture the bigger change of velocity Profile. Vice versa from the computational cost point of view, we do not have to use fine mesh in fully developed velocity profile zone and uniform velocity profile zone and select free surface length longer than 3.8cm (1.5inches).

12. Die lip profile comparison by using our current and previous mesh
x%, Y%
3.9%, 4.6%
Much more element is applied
in these areas in our current non-uniform mesh to capture the big gradient of the velocity and temperature in the flow domain
0%, 2.8%
0.85%, 0%

13. Parametric Study of Die Lip Profile (1) free surface length
LFS:LDL
The free surface length range: inches
Influence of the free surface length is minimal in the simulation results
The free surface length 1 inches is selected to pursue the following parametric study

14. Parametric Study of Die Lip Profile (2) nitrogen pressure in inside-surface hole
6.3%-15.0%
5.6%-11.3%
In our real extrusion experiment we select nitrogen pressure range 3-8 inches of water. We
have applied the boundary condition (non-zero nitrogen pressure) in our current simulation
instead of zero nitrogen pressure boundary condition. Our simulation results means the
Nitrogen pressure only influence the shape of the central pin and we must include this
boundary condition in our simulation.

15. Parametric Study of Die Lip Profile (3) normal force at the outlet of the free surface flow domain
According to the simulation results, the pressure in the outlet of the free surface flow domain does not influence the shape of the pin, but the shape of die lip profile. Bigger pressure causes bigger shape of the die lip.

16. Parametric Study of Die Lip Profile (3) pressure in the outlet of the free surface flow domain (Cont’d)
Close-up of the die lip profile around the corner
The pressure in the outlet of the free surface flow domain makes bigger effect of
die lip width than die lip height.

17. Extrusion simulation including viscoelastic properties
Introduction of one of the most realistic differential viscoelastic models : Giesekus model
The total extra-stress tensor is decomposed into a viscoelastic component T1 and a purely-viscous component T2:
T = T1 + T2
α: the material constant (a non-zero value leads to a bounded steady extensional viscosity and a shear-rate dependence of the shear viscosity)
λ: the relaxation time (A high relaxation time indicates that the memory retention of the flow is high. A low relaxation time indicates significant memory loss, gradually approaching Newtonian flow)
1: the viscoelastic part of the zero shear-rate viscosity
2: the purely-viscous part of the zero shear-rate viscosity
I: the unit tensor
D: the rate-of –deformation tensor

18. Curve fitting to the parameters with Giesekus model
To quickly and accurately investigate the effect of the viscoelastic properties of Styron663 with additives
we apply a 2-D inverse extrusion simulation first. 5-mode Giesekus model is used in this simulation.
γ: shear rate η: viscosity G’: storage moduli G: loss moduli
Table 1: the experimental data from Datapoint report
Giesekus Model
Carreau-Yasuda Model
γ (s-1)
η (Pa·s)
G’ (Pa)
G” (Pa)
0.18
319
2070
0.32
828
3600
0.56
1870
5780 1
3640
8520 2
6900
12200 3
11600
16700 6
18100
22300 10
27100
27400 18
38200
32600 32
51600
37100 56
66500
41600
100
940.27
82500
45000
178
622.95
99700
48300
316
404.88
117000
Styron663 with additives
η (Pa·s), G’ (Pa), G” (Pa)
Cal. η
Exp.
Cal. G’
Exp.
Cal. G”
Exp.
γ (s-1)

19. Curve fitted parameters with Giesekus model
5-mode Giesekus model is used in a 2-D inverse extrusion simulation. All the fitted
curves agree with their corresponding experimental data. Multi-mode Giesekus
model are only for 2-D case since the computational cost associated with such a choice would be prohibitive.
Table 2: Parameters for the fit of the experimental
Data with a 5-mode Giesekus model i λi
(s) αi
(-) ηi
(Pa.s) si 1
0.01
0.316
890
0.18e-5 2
0.1
0.691
3698 3
0.513
8855 4 10
0.206 5
100 32

20. Geometry, mesh and Boundary Conditions of the computational flow domain
Die land
Free surface flow domain
Inlet (Q=3.005e-6 m2/s)
Fully developed velocity
Wall (vs=0)
Free surface
Outlet (fn = 0)
Symmetric plane
(fs=0)
Flow Direction

21. Comparison of the 2-D inverse extrusion results
Purely Viscous
Die land
Free surface flow domain
Larger extrudate swelling
Occurs by using Giesekus model
5 % difference
Viscoelastic

22. First try for 3-D inverse extrusion applying Giesekus model
Since most research about the flow simulation using viscoelastic models (highly nonlinear), which have been done, is for 2-D problems. Although some research is for 3-D problems, the cross section of its computational flow domains (rectangle and circle) are regular. We just try to run 3-D inverse extrusion using PolyFLOW to make sure if the PolyFLOW inverse extrusion program is effective for our 3-D problem.
Because multi-mode Giesekus model is only suggested for 2-D problems, we try to use 1-mode
Giesekus model to run 3-D PolyFLOW inverse extrusion. From our curve fitting, we select the parameter of the first mode to run our 3-D isothermal problem. The same flow boundary conditions are applied with Carreau-Yasuda model.
Table 2: Model parameters used in the calculation of the
die lip profile applying PolyFLOW 3-D inverse extrusion λ
(s) α
(-) η
(Pa.s) s
0.01
0.316
890
0.18e-5

23. The comparison of the simulation results
x%, Y%
11.2%, 10.6%
0%, 9.2%
8.9%, 0%

24. Improve the curve fitted parameters with 1-mode Giesekus model
Most viscoelastic fluid researcher use the experimental first normal stress difference and the steady-state shear viscosity to curve fit the parameters with 1-mode Giesekus model. By using our experimental data in table 2, we can fit the parameters with 1-mode Giesekus model.
Styron663 with additives
at 473K
Table 3.4: The fitted parameters used in our PolyFLOW®3-D inverse extrusion V
(Pa.S) G
(s) G
(-)
PS663
8000
0.1
0.5
()[Pa.S], N1[Pa]
Giesekus model
 Experimental data
 (s-1)
The experimental shear rate steady-state viscosity and
the experimental first normal stress difference with Giesekus model

25. The simulation of the die land and free surface flow domain without the central hole
We apply the same boundary conditions in this simulation with the first try3-D inverse extrusion.
The simulation using Carreau-Yasuda model is also done in this computational domain. The comparison
results is shown in the following.
26%, 13%
0%, 26%
23%, 0%

26. The extrudate swelling in the real extrusion experiment
Big extrudate swelling
at the die exit

27. Comparison of the bottom views of the extrudate swelling
Die exit
Die exit
Flow direction
The similar big extrudate swelling occurs at the die exit
in the real extrusion experiment and in the simulation using viscoelastic nonlinear differential model. In our 3-D problem, using viscoelastic model can predict better the extrudate swelling at the die exit.
1. The Simulation of the extrudate
Swelling (viscoelastic Giesekus model)
2. Experimental extrudate Swelling
(photo taken in Fermi Lab)
3. the Simulation of the extrudate
Swelling (Carreau-Yasuda model)