By
Prof. M. Kostic, Ph.D, P.E.
Dan Wu, M.S.
Mechanical Engineering Department
Northern Illinois University

Simulation Improvement-Refined non-uniform mesh

Fine non-uniform mesh in the corner area and in the axial flow-direction after the die exit

Convective and Radiation heat transfer in the free surface
Parametric Study


Effect of hole non-zero nitrogen pressure
Effect of non-zero normal force in the outlet of the free surface

Effect of the length of the free surface flow domain
Extrusion Simulation Including Viscoelastic Properties


Choose non-linear differential viscoelastic model
(Giesekus Model)
Comparison of results with and without viscoelastic properties using PolyFLOW 2-D and 3-D inverse extrusion www.kostic.niu.edu/extrusion

Geometry of the quarter computational domain
Z
Y
X
1.1mm
L
FS
– Length of the free surface flow domain
L
DL
– Length of the die land flow domain www.kostic.niu.edu/extrusion

Boundary conditions in a quarter of computational flow domain
Flow Inlet
Symmetric Plane
Free Surfaces
Die Walls
Flow Outlet
In our current simulation, we consider nonzero nitrogen pressure ( P n
) in this free surface
In our current simulation, we consider radiation heat transfer in these two free surface www.kostic.niu.edu/extrusion

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. v n
= v s
= 0
A symmetry plane with zero tangential forces and zero normal velocity, f s
= v n
=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 (N
2 gage pressure) in insidesurface of the hole will be applied in our new simulation
Exit for the flow is specified as, f s
= f n
= 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.
www.kostic.niu.edu/extrusion

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)
Free surface flow domain
Die exit
Die land flow domain
Melt Polymer Flow Direction www.kostic.niu.edu/extrusion

Non-isothermal generalized Newtonian flow setting up In PolyFLOW inverse simulation
MATERIAL DATA





Density (ρ) 1040 kg/m 3
Specific Heat (H) 1200 J/Kgo K
Thermal Conductivity (k) 0.1231 W/mo K
Coefficient of Thermal Expansion (

) 6.6 x 10 -5 m/mo K
Reference Temperature (theta or T

) 300K www.kostic.niu.edu/extrusion


( T ,

)
 h ( T ) *

0
 h ( T ) *
  www.kostic.niu.edu/extrusion

Current simulation results analysis
(Carreau-Yasuda model)
According to the velocity profile in the computational domain, it changes only in the partial free surface flow domain (z =2.54-3.8cm). 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).
www.kostic.niu.edu/extrusion

Die lip profile comparison by using our current and previous mesh
 x%,

Y%
0.006
0.005
0.004
0.003
0.002
0.001
0
0 non-uniform mesh (current; % change) uniform mesh (previous; reference 100% )
0%, 2.8%
0.002
0.004
0.006
X (m)
3.9%, 4.6%
Much more element is applied in these areas in our current nonuniform mesh to capture the big gradient of the velocity and temperature in the flow domain
0.85%, 0%
0.008
0.01
www.kostic.niu.edu/extrusion

Parametric Study of Die Lip Profile
(1) free surface length
0.007
0.006
0.005
0.004
Y (m)
0.003
L
FS
:L
DL
0.002
0.001
0
0 0.002
0.004
0.006
X (m)
0.008
0.01
0.012



The free surface length range: 0.5-2 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 www.kostic.niu.edu/extrusion

Parametric Study of Die Lip Profile
(2) nitrogen pressure in inside-surface hole
0.006
0.005
0.004
0.003
0.002
0.001
0
0
6.3%-15.0%
5.6%-11.3%
0.002
0.004
0.006
X (m)
0.008
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.
www.kostic.niu.edu/extrusion
0.01

Parametric Study of Die Lip Profile
(3) normal force at the outlet of the free surface flow domain
0.007
0.006
0.005
0.004
0.003
0.002
0.001
Fn = 0.01 N
0.1 N
0.15 N
0 N
0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011
X (m)
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.
www.kostic.niu.edu/extrusion

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.
www.kostic.niu.edu/extrusion

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 T
1 and a purely-viscous component T
2
:
T = T
1
+ T
2
(
Ι 


1
T
1
)

T
1
  
T
1

2

1
D T
2

2

2
D
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

2
: the viscoelastic part of the zero shear-rate viscosity
: the purely-viscous part of the zero shear-rate viscosity
I : the unit tensor
D : the rate-of –deformation tensor www.kostic.niu.edu/extrusion

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)
0.18
0.32
0.56
1
2
3
6
10
18
32
56
100
178
316
11804.60
11681.30
10794.60
9264.48
7887.63
6414.58
5109.40
3858.33
2823.44
2009.96
1393.89
940.27
622.95
404.88
319
828
1870
3640
6900
11600
18100
27100
38200
51600
66500
82500
99700
117000
G” (Pa)
2070
3600
5780
8520
12200
16700
22300
27400
32600
37100
41600
45000
48300
Styron663 with additives
η
G’
G”
Cal.
Exp.
Cal.
Exp.
Cal.
Exp.
γ (s -1 )

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.
3
4
5
Table 2: Parameters for the fit of the experimental
Data with a 5-mode Giesekus model i
1
λ i
(s)
0.01
α
(-) i
0.316
η i
(Pa.s)
890 s i
(-)
0.18e-5
2 0.1
0.691
3698 0
1
10
100
0.513
0.206
0.206
8855
3
32
0
0
0 www.kostic.niu.edu/extrusion

Geometry, mesh and Boundary Conditions of the computational flow domain
Inlet
(Q=3.005e-6 m 2 /s)
Fully developed velocity
Die land
Wall (v s
=0)
Free surface flow domain
Free surface Outlet
(f n
= 0)
Symmetric plane
(f s
=0) Flow Direction www.kostic.niu.edu/extrusion

Comparison of the 2-D inverse extrusion results
Die land Free surface flow domain
0.005
0.004
0.003
5 % difference
Larger extrudate swelling
Occurs by using Giesekus model
0.001
Carreau-Yasuda Model; reference 100%
5-mode Giesekus Model; % difference
0
-1.00E-02 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02
X (m) www.kostic.niu.edu/extrusion

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.
(
Ι 


1
T
1
)

T
1
  
T
1

2

1
D
Table 2: Model parameters used in the calculation of the die lip profile applying PolyFLOW 3-D inverse extrusion
λ
(s)
0.01
α
(-)
0.316
η
(Pa.s)
890 www.kostic.niu.edu/extrusion s
(-)
0.18e-5

The comparison of the simulation results
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0
0%, 9.2%
11.2%, 10.6%
 x%,

Y%
Viscoelastic Model (Giesekes)
Purely viscous model (Carreau-Yasuda)
0.002
8.9%, 0%
0.004
0.006
x (m)
0.008
0.01
www.kostic.niu.edu/extrusion

Improve the curve fitted parameters with 1-mode
Giesekus model
Most viscoelastic fluid researchers 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
PS663

V
(Pa.S)
8000

G
(s)
0.1

G
(-)
0.5

Giesekus model
Experimental data

(s -1 )
The experimental shear rate steady-state viscosity and

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.
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0
0%, 26%
Giesekus-Model; % difference
Carreau-Model; reference 100%
Product profile
0.002
0.004
0.006
26%, 13%
0.008
X www.kostic.niu.edu/extrusion
0.01
23%, 0%
0.012

Die exit Die exit
The similar big extrudate swelling occurs at the die exit in the real extrusion experiment and in 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 ) www.kostic.niu.edu/extrusion
3. the Simulation of the extrudate
Swelling ( Carreau-Yasuda model )




www.kostic.niu.edu/extrusion



Apply other viscoelastic models and compare the die lip profiles between different models
Optimize a viscoelastic model for Styron663 with
Sintillator dopants www.kostic.niu.edu/extrusion




www.kostic.niu.edu/extrusion

www.kostic.niu.edu/extrusion

Department of Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
Mail to: kostic@niu.edu
Mail to: danwu2004@yahoo.com
www.kostic.niu.edu/extrusion