Home >> Resources/Information >> EXTRUSION, SIMULATION
EXTRUSION SIMULATION AND EXPERIMENTAL VALIDATION TO OPTIMIZE PRECISION DIE DESIGN
EXTRUSION SIMULATION AND EXPERIMENTAL VALIDATION TO OPTIMIZE
PRECISION DIE DESIGN
Srinivasa R. Vaddiraju
*)
, M. Kostic
*)1)
, L. Reifschneider
&)
, A. Pla-Dalmau
$)
, V. Rykalin
%)
, A. Bross
$)
*)
Northern Illinois University (NIU);
&)
Illinois State University,
$)
Fermi National Accelerator Laboratory,
%)
NICADD-
Northern Illinois Center for Accelerator and Detector Development, NIU.
Abstract
A CFD-simulation is performed for an existing die and
compared with the actual polymer flow and dimensions of
the extrudate. Experimental validation of the simulation is
used to improve new die design by integrating flow
simulation through the 3-D die geometry and the free-
surface flow with swelling after the die. Modified die-land-
and-lip profile is optimized using the so-called “inverse
extrusion” simulation with an objective to improve
accuracy of extrudate dimensions.
Introduction
A twin-screw extrusion line has been commissioned
recently at Fermi National Accelerator Laboratory (FNAL)
in collaboration with Northern Illinois Center for
Accelerator and Detector Development (NICADD), to
perform R&D, prototyping, and economical production of
extruded plastic scintillators for large-scale accelerator
detectors. For example, MINOS (Main Injector Neutrino
Oscillation Search), a long-baseline neutrino-oscillation
experiment, requires several hundred tons of finished
plastic scintillators [1]. At about $40 per kilogram cost of
cast plastic scintillator, a large-scale detector will not be
affordable. However, using extruded plastic scintillators
the cost is estimated at about $10/kg, and with further
developments, it is expected to go down to $5/kg. The
extrusion line consists of a Berstorff 40-mm diameter, 1.36
m long, twin-screw extruder (ZE 40A UTS; 200 HP), two
K-Tron automated feeders (for polymer pellets and
fluorescent dopants) and Conair downstream equipment
(40 cm square, 5.2 m long vacuum and 6.4 m long spray
cooling-tanks, belt-puller and saw). A Novatec
compressed-nitrogen drier is utilized to purge and dry the
polymer pellets before extrusion, in order to improve
optical properties of the extrudate.
In a collaborative project with NICADD/FNAL the
Department of Mechanical Engineering at Northern Illinois
University is developing more effective die design utilizing
CFD simulation of extrusion flow and heat transfer
processes. The objective is to achieve ultimate precision
and quality of different, hollow-extrudate final profiles.
Due to inherited sensitivity of final-product quality and
precision on multiple controlling parameters of rather
_______________________________________________
1)
Corresponding author
complex extrusion processes, the optimal extrusion die
design is the first step, to be complemented by an optimal
design of vacuum-calibrator sizing-and-cooling tools, as
well as investigation and optimization of the extrusion
process control for an ultimate quality and precision of the
final product. Initial experiments at FNAL with two
existing dies are used to validate CFD simulations and to
provide critical data, not accounted for by the simulation,
for more accurate die design. It has been realized that
limitations and benefits of simulation and experimentation
cannot replace each-other, but they may complement each-
other synergistically. Furthermore, it has been realized that
full comprehension of all extrusion processes and polymer
melt properties is very important for effective die and
calibrator design, and critical for extrusion process set-up
and control, to achieve ultimate goal, high quality and
precision of final extrudate profiles for plastic scintillators.
Plastic Scintillator Properties
A commercial grade, general-purpose polystyrene,
Styron 663, made by Dow Chemical Co, was used as the
base material. Its price range is about $1.50 per kg of
pellets. The plastic scintillator is made by adding pre-
mixed dopants, 1% PPO and 0.03% POPOP, available
from Curtiss laboratories (Bensalem, PA, at about
$200/kg), into Styron 663 pellets. The measured melt
viscosity of Styron 663 with and without dopants, as
function of shear rate and temperature are presented on
Fig. 1. The viscosity data are curve fitted using the least-
square method with the Carreau-Yasuda model, see Eq.
(1), and the corresponding coefficients with other relevant
thermo-mechanical properties are given in Table 1.
(
) ( )
[
]
a
n
a
1
0
1
-
µ
µ
+
-
+
=
gl
h
h
h
h
&
(1)
The polystyrene melt is known as moderately
viscoelastic material, however its viscoelastic properties
were not available and neglected in our simulation at this
time. In addition, viscosity is not only function of
temperature and shear rate as measured under isometric
flow conditions in a laboratory [2], but also depends on
previous shearing and thermo-mechanical degradation in
general, which in turn depends on velocity gradients,
pressure, and temperature in extrusion barrel and other
components, including die. Also, scintillator optical
properties are influenced by thermo-mechanical polymer
degradation, as well as residual stresses due to finite
76 / ANTEC 2004
------------------------------------------------------------------------
Page 2
cooling and solidification rates including pulling
drawdown during extrusion. These drawbacks could be
minimized by better design and control of extrusion
components and processes.
Extrusion Die Design and CFD Simulation
According to polymer extrusion experts [3], the
complete simulation of the twin-screw extrusion processes
should be regarded as one of the ‘grand challenge’
problems in polymer processing. However, the continuous
and fast development of powerful computing hardware and
proficient numerical techniques are now making it possible
to simulate, analyze and optimize three-dimensional
extrusion processes with complex geometries, as well as
non-linear and viscoelastic polymer behavior. However,
this is a grand challenge and is not going to be an easy
task, but newly developing computing tools have a
tremendous potential to uncover important inside details of
the extrusion processes, like velocity, pressure and
temperature fields in the region of interest, which is not
possible to be done experimentally. The main challenge is
and will be to completely and accurately represent the
polymer material behavior, a very complex viscoelastic
melt, which properties are changing from batch-to-batch
and are dependent and changing with process parameters,
like shearing flow rate and temperature. Another challenge
is to properly represent the complex geometry of extrusion
devices and accurate boundary conditions which inherently
change along the boundaries and in time.
The desired extrudate final-profile is 10 mm ¥ 20 mm
rectangular cross section with 1.1 mm diameter circular
hole at its center, to accommodate wavelength-shifting
optical fiber, which has much higher light attenuation
length than the Scintillator bulk. A suitable die is designed
and fabricated to provide a streamlined flow and desired
extrudate profile, see Fig. 2. In order to simplify
fabrication and handling, the die consists of 5 plates, each
having its own specific function. After polymer melt exits
the extruder barrel and flows through screened breaker
plate, it is metered by a melt gear-pump before entering the
die. The first die plate, Melt-Pump Adapter, connects the
55 mm diameter output of melt gear-pump to the Spider
Adapter plate which in turn connects to the Spider plate
with three spiders. The spiders are used to hold a hollow
pin to shape the extrudate center hole. A connected hole is
made in one of the spiders, from pressurized Nitrogen line
to the hollow pin, to maintain gas pressure and thus shape
of the hole in the extrudate. Then, the polymer flows
through Pre-Land plate (with a centering Bushing),
changing its shape from circular to a curved, rectangular-
like cross-section of the last, Die Land plate with the
uniform cross section, allowing the polymer melt to ‘relax’
before exiting the die. The center pin is fixed to the spider
structure and its exit cross section is an elliptical-like so as
to obtain a circular hole in the final extrudate after free
flow swelling and relaxation. At the same time the polymer
melt exiting the curved, rectangular-like die land cross-
section is expected to reshape into desired rectangular
profile downstream. 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.
Powerful
computational simulations, when properly utilized, will
improve and speedup die design, resulting in over-all cost
reduction.
The objective of this CFD simulation is to determine
the optimum die shape including the die land and pin
profiles to obtain the desired dimensions of the extrudate
profile. A commercial, CFD finite-element code
Polyflow® [4] is used to simulate the three-dimensional
(3-D) die flow and heat transfer as well as the free surface
flow 25 mm downstream from the die exit, see the
corresponding computational simulation domain in Fig. 2.
The computational domain resembles the real 3-D die
geometry and a free surface flow after the die, where
velocity redistribution (equalization) and stress relaxation
take place in a short distance downstream from the die exit.
Even though the extrudate profile and the die-lip are
quadri-symmetrical, due to complex spider-and-transition
die structure, it was necessary to simulate half of the real
flow domain. The domain is further divided into several
sub-domains to facilitate application of related boundary
conditions, see Fig. 2, i.e.:
Inlet (1): fully developed inlet velocity corresponding
to actual mass flow rate of 50 kg/hr and uniform inlet
temperature (473 K or 200 °C); walls (2): no slip at
the die walls (V
n
=V
s
= 0; normal and streamline
velocities, respectively), and uniform die wall
temperature 473 K; symmetry planes (3): shear stress
F
s
= 0, V
n
= 0, normal heat flux q
n
=0; free surface (4):
zero pressure and traction/shear at boundary (F
n
= 0, F
s
= 0, and V
n
=0), and convection heat transfer from the
free surface to surrounding room-temperature air;
outlet (5): normal stress
F
n
=0 or specified;
all domains: viscous dissipation was neglected for our
flow conditions (after verification)
Due to the complex 3-D geometry of the die and the
nonlinear relationship between polymer viscosity and shear
rate, an elaborate finite element mesh was developed to
facilitate numerical stability of the solution, see Fig. 3. It
consists of 30,872 elements with structured hexahedral
mesh in the die land and free surface, and unstructured
tetrahedral mesh in the remaining portion. Simulations are
run on a Windows 2.52-GHz-processor PC with 1-GB
RAM. On this platform, 19 hours and 36 minutes of CPU
time was required to obtain full, non-isothermal inverse
simulation results (new die-land profile). However
parametric analysis may be and was performed much more
efficiently by simulating flow in the die-land and/or pre-
land regions only, neglecting inertia term, and with a
ANTEC 2004 / 77
------------------------------------------------------------------------
Page 3
quarter of the real flow domain due to quadri-symmetry in
that region.
Simulation and Actual Test Results
Extrusion simulations were run for the existing die
geometry and actual extrusion process parameters. The
extrudate profile obtained with simulation is similar to the
shape obtained during actual extrusion, compare Fig. 4
(existing-die extrudate simulation profile) with Fig. 5.
Midsection sample sagging is due to non-uniform cooling
in the calibrator and drawdown downstream which was
outside simulation domain. About 5% deviations in width
and height may be justified with simulation limitations as
well as with effects of cooling and drawdown pulling
during actual extrusion. It is also known that die swell ratio
becomes smaller as the melting temperature and melting
residence time are increased [5]. The powerful ‘inverse
extrusion’ feature of the CFD application software [4] was
used to obtain a modified die-land and center-pin profiles
to produce a rectangular extrudate with a circular hole at its
centre, see Fig. 4. The target product dimensions were
given 5% larger (2.1 cm ¥ 1.05 cm) to compensate for the
drawdown and cooling effects in the calibrator and further
downstream. The program takes into effect the die swell
due to velocity relaxation of the melt in the free-surface
region as it exits the die, and computes the required die-
land and center-pin profiles to obtain the desired extrudate
dimensions after the melt exits the free surface region.
Typical results of velocity and pressure distributions
are given in Fig. 6. From careful inspection of velocity
distribution and the fact that pressure decreases steadily
downstream, it is evident that there are no re-circulating
regions within the die and that the die is well streamlined.
The maximum velocity of the polymer is approximately
14.1 cm/s and the average velocity at the outlet is 6.1 cm/s.
The shear rate ranges from zero to 300 sec
-1
, being the
highest at the center-pin wall. Around the die-land walls
the shear rate varies in the range from 70 to 150 sec
-1
. The
outer surface of the polymer is cooled from 473 K to 465 K
when it comes out of the free surface flow region, 2.54 cm
from the die exit.
Conclusion
Simulation results, including 3-D existing die
geometry, measured polymer melt viscosity and actual
extrusion boundary conditions, were calculated and
compared with extrudate profile obtained during actual
extrusion.
Discrepancies
between
computational
simulation and extrudate dimensions under the well-
controlled extrusion process were within 5% and on
occasion 10%. It was hard to maintain consistency of final
extrudate product, due to some issues in achieving
consistent stock feeding and optimum vacuum-calibrator
sizing and cooling. However, the existing die simulation
profile-form-shape was in qualitative agreement with
actual extrusion sample profile.
New, improved die-land profile was designed using
so-called inverse extrusion simulation. It is evident that
further improvements are possible by including polymer
melt viscoelastic properties when available, and
improvement of vacuum-calibrator design is critical, since
precise hollow-profile dimensions are finalized during
cooling and solidification in the vacuum-calibrator and
further cooling downstream. Observed inconsistencies in
the final extrudate profile indicate the importance of better
process optimization and control.
Considering the experience and initial progress in
using powerful simulation software and well-equipped and
instrumented extrusion line in FNAL, as well as specific
issues identified
for further investigation
and
improvements, it is expected to achieve consistent quality
and dimensions of the extrudate profile within 1% in the
future. Regardless of rather simple final profile, this is still
going to be a challenge, due to inherited difficulties in
balancing localized cooling of rather thick extrudate profile
with internal hole and corners related asymmetry.
References
[1] Pla-Dalmau, A, A.D. Bross, and V. Rykalin,
“Extruding Plastic Scintillator at Fermilab,” IEEE
Nuclear Science Symposium, Portland, OR, 2003.
[2] Styron viscosity data, Test Report # 7903 and 7914,
DatapointLabs, Ithaca, NY, 2003.
[3] Osswald, T.A. and P.J. Gramann, “Polymer Processing
Simulation Trends”, Society for the Advancement of
Material and Process Engineers, Erlangen, Germany,
2001.
[4] Polyflow application software, Fluent Inc., Lebanon,
NH.
[5] Lee, W.S. and S.H.Y. Ho, Extrudate prediction and die
design of profile extrusion, ANTEC 1999.
Acknowledgements
We would like to acknowledge financial support by
NIU’s Northern Illinois Center for Accelerator and
Detector Development (NICADD) and Fermi National
Accelerator Laboratory (Fermilab) for the Scintillator
Extrusion Project and research partially described in this
paper, and in particular to Dr. Gerald Blazey of NICADD
and Dr. John Cooper of Fermilab.
Key Words
CFD simulation, inverse extrusion, hollow-profile
extrusion, die design
78 / ANTEC 2004
------------------------------------------------------------------------
Page 4
TABLE 1: Doped Styron 663 thermo-
mechanical and viscosity properties
Property
Value
Carreau-Yasuda
coefficients,
Eq.(1), at 473K
Density
r
[Kg/m
3
]
1040
0
h
[Pa-s]
13,400
Specific heat
C
p
[J/Kg-K]
1200
?
h
[Pa-s]
0
Thermal
conductivity
K [W/m-K]
0.1231
n
0.351
l
0.527
Thermal
volumetric
coefficient
b
[m/m-K]
6.60e-5
a
0.845
Melt-Pump Adapter
Spider Adapter
Spider
Pin
Bushing
P
r
e-l
and
D
i
e
l
and
1
2
3
4
5
2
1. Inlet
2. Die Walls
3. Symmetry
4. Free Surface
5. Outlet
Fig. 2: Exploded view of extrusion die and
computational and boundary
domains
Melt flow
direction
Sh e a r R a t e (1 /s )
V
i
sco
si
ty (P
a-s)
200
0
C
180
0
C
220
0
C
Fig. 1: Styron viscosity data, with and without
Scintillator dopants
h – Styron 663
h
d
– Doped Styron 663
10
6
10
5
10
4
10
3
10
2
10
-2
10
-1
10
0
10
1
10
2
10
3
Fig. 3: Finite element 3-D domain and
half of extrudate profile mesh
Melt
flow
Die lip
ANTEC 2004 / 79
------------------------------------------------------------------------
Page 5
Melt flow
direction
Velocity magnitude
[m/s]
Pressure [Pa]
Fig. 6: Contours of velocity field at different cross-sections and
pressure distribution simulation results
Free-surface
flow
Die lip
0
1
2
3
4
5
6
7
0
10
X (mm)
Y (
mm)
Fig 4: Existing die, corresponding simulation
and new improved-die profiles
New Die (Simulated)
Existing Die
Desired Extrudate
Existing-Die Extrudate
(Simulated)
V
take-up
= 6.02 cm/s, P
Vacuum
= 2.5 H
2
O,
and P
N2
= 7.9 H
2
O
Fig. 5: Typical extrudate sample profile
80 / ANTEC 2004
