Effect of Typical Melt Temperature Non-Uniformity on Flow Distribution in Flat Dies
Olivier Catherine, Cloeren Incorporated, Orange, TX Abstract
In this study, the influence of non-uniform incoming
melt temperature profiles on the flow in a flat die is
evaluated. Flat film die flow channels are typically
designed to provide uniform flow distribution at the die
exit assuming uniform incoming melt temperature
profiles. However, in real extrusion conditions, it can be
challenging to obtain an ideally uniform melt temperature
delivery to the die. There are many reasons why the melt
temperature non-uniformity is obtained. Two typical
scenarios are evaluated; (i) the temperature profiles
generated by an incorrect melt pipe design will be
calculated and input in a die flow model as inlet boundary
condition and (ii) the influence of a polymer subject to
excessive viscous dissipation in the extruder. This work
uses 3D computational fluid dynamics (CFD) models.
Introduction
When troubleshooting a film extrusion process, it is
sometimes challenging to determine the origin of the
problem. Die maker experience suggests that thermal
effects and particularly temperature non-uniformity in the
melt does have a large impact on the film quality and its
mass distribution. In a coextrusion process, such melt
temperature gradients can indiscriminately affect
individual layer uniformities. Because experiments and
measurements to evaluate the effect of melt temperature
profiles on the flow behavior in a flat die can be tedious
and subject to many influences, flow simulations using a
commercial 3D CFD program can be a beneficial tool.
In the first part of the study, the thermal regime of the
flow in a melt pipe will be studied. The resulting
temperature profile at the exit of the pipe is then used as
the inlet temperature profile for the flow through a flat
die.
A second study will evaluate the effects of a
temperature profile resulting from excessive viscous
dissipation in the extruder.
Extrusion layout and die geometry¶
This work deals with a monolayer polypropylene cast
film extrusion scenario as illustrated by Figure 1. A
typical extrusion tooling for this application is made of a
melt pipe, which feeds the melt from the extruder to the die and a flat die equipped with a vacuum box that
improves the contact between the web and the chill roll. In
this study, we consider a monolayer die with a two-stage
preland[1] designed by Cloeren Incorporated for the
process parameters presented in Table 1 and for the
material specifications detailed in the following section.
The die is 2032 mm wide and a view of the flow channel
is shown in Figure 2.
Table 1: Process parameters
Polymer and rheology¶
The polymer used for this study is a cast film grade
isotactic homopolymer polypropylene (Ho-PP)
manufactured by Borealis, with a Melt Flow Rate (MFR)
of 8.0 g/10 min (230°C, 2.16 kg) and density of 0.905
g/cm3. No data was available for thermal properties of the
melt and the following generic properties were used: melt
density U = 0.74 g.cm
-3; thermal conductivity k=0.20
W.m
-1.K
-1 and specific heat C
p= 1.50 J.g
-1.K
-1.
The shear viscosity behavior was determined by
measurements tested by capillary rheometry at
temperatures of 210°C, 230°C and 250°C. The data was
corrected according to Bagley[2] and Rabinowitsch[3]
methods. The shear viscosity data is summarized by the
viscosity master curve at a reference temperature (T
ref) of
230°C, resulting from the Time Temperature
Superposition (TTS) principle[4] and shown in Figure 3.
Acceptable superposition was achieved with the shift
factor values shown in Table 2.
Table 2: TTS shift factors
The shear rate and temperature dependency of
viscosity was modeled according to the well accepted
combination of the Cross model[5] and the Williams
Landel Ferry (WLF) model[6] respectively, given by the
two following equations:
WhereK is the shear viscosity (Pa.s), J is the shear rate
(1/s), T is the temperature (K), ή
0 is the zero shear
viscosity (Pa.s), τ
* is the characteristic shear stress (Pa)
and m is the pseudo-plastic index. ή
0, τ
* and m are the
Cross model parameters and are determined by curve
fitting. The TTS is included in the Cross model through
the shift factor a
T, which follows a WLF model. The
model parameters C
1 and C
2 (K) are also determined by
curve fitting (Table 3). Both curve fittings were done
using the KaleidaGraph 4.1.0 software[7] and the resulting
parameters are summarized in Figure 3.
Table 3. WLF parameters from curve fitting
Flow simulations
Literature dealing with elastic effects on the flow
distribution in mono-layer cast film dies is sparse. A flow
simulation study however showed that the effects of
elongational viscosity may slightly affect the velocity
distribution at die exit for highly branched polymers like
low density polyethylene (LDPE)[8]. In the case of linear
polymers such as a homopolymer polypropylene, it is
reasonable to neglect the elastic or elongational behaviors
for purposes of mass flow distribution. Finally, an a priori
dimensional analysis shows that the consideration of
viscous dissipation and coupled thermal and flow
solutions are necessary, especially when strong
temperature gradients are involved. For these reasons, a
generalized Newtonian non-isothermal approach was
taken.
For a steady state problem, the continuity (3) and
momentum balance (4) equations for an incompressible
flow with negligible inertia and gravity effects write:
For a generalized Newtonian fluid, we have:
The fluid viscosity depends on temperature and shear rate
as described by the Cross and WLF models detailed
earlier. The energy balance for a steady state problem
writes:
A commercial CFD software, SolidWorks Flow
Simulation 2011 SP1.0[9] was used to solve the coupled
thermal-flow problem and a mesh with brick elements
was built. The boundary conditions for this model are: (i)
a symmetry condition at the centerline for flow and
temperature; (ii) a fully developed flow at the entrance ;
(iii) a tabulated fluid radial temperature profile and a flow
rate (453.6 kg/h for the total geometry) are imposed at the
entrance; (iv) at the outlet surface, the pressure is set to 1
atm and; (v) finally, on the flow channel walls, we assume
a non-slip condition (v=0) and a uniform temperature
(260°C) is applied.
1 - Uniform melt temperature at inlet
First, a reference flow simulation of the die with
uniform incoming melt temperature was carried out. The
main results are shown as follows:
- Velocity contour plot on the parting plane of the
die (Figure 4) - Temperature contour plot on the parting plane of
the die (Figure 5) - Velocity and melt temperature profiles at the die
exit on the parting line (Figure 6).
As expected, the die flow is well balanced as the total
amplitude of flow variation of 1.60 % is predicted for exit
velocity. Shear heating is also well controlled as the
average melt temperature at the exit on the parting line of
the flow is 261.46°C for an initial entrance temperature of
260°C.
2 - Non-uniform melt temperature resulting from poor melt pipe design
An initial study was carried out to determine the type
of temperature profile that could result from a poor melt
pipe flow channel design. It is not uncommon to see
poorly designed melt pipe adaptors in the field due to lack
of attention to design details. A typical design mistake is
the combination of a small flow channel diameter with a
long flow length. This situation was simulated with a melt
pipe length of 4m and channel diameter of 19.05 mm. A 3D flow simulation was run for the material specified
earlier and the process parameters detailed in Table 1. The
resulting melt temperature profiles at 0.5m length
increments are shown in Figure 7. This simulation
predicts substantial viscous dissipation with a maximum
temperature of 292.5°C at the exit of the 4m-long pipe, for
an initial melt temperature of 260°C. The result of the
pipe flow simulation agrees with literature for thermal
regimes that are not fully developed [10,11] as the maximum
of temperature develops initially very close to the wall,
which corresponds to the high shear stress region.
Downstream, as the thermal regime develops, the
temperature maximum moves gradually away from the
wall toward the center. This is explained by the increasing
importance of radial conduction as the temperature
gradient from wall to center becomes large.
The radial temperature profile resulting from the pipe
flow simulation at a flow length of 4.0 m (Figure 8) was
used as a new boundary condition at the entrance of the
film die. The achieved velocity and temperature contour
plots on the parting plane at the exit of the flat die are
shown in Figure 9 and Figure 10 respectively. Excessively
non-uniform temperature and velocity profiles are found
in the preland section as well as in the land region. A
comparison of the velocity and temperature profiles at die
exit for all three studies is summarized in Figure 14 and
Figure 15.
3 - Non-uniform melt temperature resulting from poorly performing extruder screw
Poorly performing extruder screw is another well known
cause of melt temperature non-uniformity and,
generally, melt quality issues. Typically, thermocouples
that are used to measure melt temperature are mounted in
the wall of the extruder barrel. Consequently, the resulting
measurements are predominantly influenced by the barrel
temperature and give only a rough idea of the actual melt
temperature[11]. Recent experimental work using a
thermocouple mesh technique has been done to map the
temperature profile of a melt coming from an extruder at
various operating conditions[12]. Inspired by these results,
a temperature profile representative of a poorly
performing extruder screw was created. For sake of
comparison with the previous study, a similar temperature
deviation of +32.5°C was included, as shown in Figure 11.
The 3D flow simulation of the die with this incoming
temperature profile was completed and the resulting
velocity and temperature contour plot are shown in Figure
12 and Figure 13 respectively.
Discussion
While the die provides relatively uniform
temperature and velocity profiles when the incoming melt
temperature is uniform, the situation changes when the
melt temperature is not uniform.
When excessive viscous dissipation occurs in a melt
pipe, the resulting melt temperature profile exhibits a
strong radial temperature gradient with a maximum
temperature near the wall. This ultimately affects the flow
in the flat die characterized by a flow increase near the die
ends. This is explained by the reduced polymer viscosity
(by temperature) flowing along the path of higher flow
resistance, i.e. toward the end regions of the die flow
channel. The magnitude of the flow imbalance at the exit
of the die is found to be about 10%. This number can
seem small in contrast to the initial melt temperature
gradient at the entrance. This can be explained by the
thermal boundary condition at the wall of the die, which is
very strong with an imposed uniform wall temperature of
260°C. While an imposed temperature at the wall is a
typical boundary condition applied by most 3D die flow
simulation work found in literature [13 - 16], it may not be
perfectly reflect real conditions. In practice, the excessive
heat from the melt is dissipated to the wall of the die, and
may show a thermal over-ride by the die thermocouples.
When excessive viscous dissipation occurs in the
extruder, the incoming melt temperature profile also
shows a radial gradient. It is however characterized by a
maximum temperature at the center with a temperature
plateau from the center to about half of the radial profile,
followed by a sharp decrease near the wall. The 3D die
flow simulation taking this incoming melt temperature
profile into account shows less flow variation compared to
the previous case. Figure 13 shows that the melt stream
distributes somewhat uniformly in the flow channel.
Consequently, the amplitude in flow variation at the exit
is only 5.4%.
Conclusion
3D coupled thermal-flow simulations were built and
computed using a commercial CFD program to investigate
the response of non-uniform melt temperature profiles fed
into a polypropylene cast film die. The two cases of nonuniform
temperature investigated are somewhat
representative of two common extrusion issues: excessive
shear heating in melt pipe or by an extruder screw. In both
cases, the flow is found to be affected as both temperature
and velocity exhibit non-uniform profiles at the exit.
Ultimately, this could explain some of film quality issues
observed in a process, such as gauge non-uniformity.
Acknowledgement
The author would like to thank Mr. Peter Cloeren for
his most kind support and for allowing this work to be
presented.
References
[1] P. F. Cloeren, United States Patent 5,256,052 (1993)
[2] E.B. Bagley, J. Appl. Phys., 28, 264 (1957)
[3] B. Rabinowitsch, Z. Physik. Chem., A145, 1 (1929)
[4] J.D. Ferry, Viscoelastic properties of polymers. 3rd edit. (1980)
[5] M.M. Cross, Polymer Systems: Deformation and Flow
(1968)
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Figure 1. Typical monolayer cast film layout (Note: extruder is not shown)
Figure 2. Die flow channel featuring a two-stage preland used for the study
Figure 3. Master curve of viscosity and Cross fit for 8.0 MFR Ho-PP
Figure 4. Velocity contour on parting plane for uniform entrance melt temperature
Figure 5. Melt temperature contour on parting plane for uniform entrance melt temperature
Figure 6. Velocity and temperature profile at die exit for uniform entrance temperature conditions
Figure 7. Melt temperature profiles as a result of the melt pipe flow simulation
Figure 8: Entrance temperature profile input as a boundary condition (pipe shear)
Figure 9. Velocity contour on the parting plane with non-uniform entrance melt temperature resulting from excessive shear in the melt pipe
Figure 10. Temperature contour on the parting plane with non-uniform entrance melt temperature resulting from excessive shear in the melt pipe
Figure 11. Entrance temperature profile representative of poorly operating extruder input as a boundary condition
Figure 12. Velocity contour on the parting plane with non-uniform entrance melt temperature resulting from excessive shear in the melt pipe
Figure 13. Velocity contour on the parting plane with non-uniform entrance melt temperature resulting from excessive shear in the melt pipe
Figure 14. Normalized exit velocity profiles on parting plane with different incoming melt temperature conditions
Figure 15. Resulting exit melt temperature profiles with different incoming temperature conditions
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