- Extrusion
- Coextrusion
- Wire / Cable coating
A major feature of POLYFLOW is its ability to predict three-dimensional
free surfaces in the extrusion of generalized Newtonian and viscoelastic
fluids. This lets you predict the extrudate shape in the free flow out of the die.
Extrusion problems of industrial interest are often characterized by complex
geometries with many corners.
POLYFLOW's inverse extrusion capability enables you to calculate
the shape of the die lip section required to obtain a desired extrudate
shape.
The multidomain approach used in POLYFLOW for multifluid flow configuration
or fluid-solid heat transfer is applicable to coextrusion or more general
flows of different inmiscible fluids. Co-flow simulations may address
fluids which are either generalized Newtonian or viscoelastic in behavior.
The location of any fluid-fluid interface is a priori unknown. As in free
surface problems, the calculation starts with user selected interfaces
which deform together with the finite element mesh during the course of
the simulation.
Most problems of industrial relevance solved by POLYFLOW are highly non-linear,
be it because of the free surface deformations or because of the complex
behavior of the fluids. Because of this highly non-linear behavior, it
is usually impossible to reach the final value of the desired flow parameters
within a single iterative procedure. It is then necessary to obtain solutions
at a number of intermediate steps. The task of incrementing material parameters
or boundary conditions is handled automatically in POLYFLOW by a fully
automatic evolution procedure. The increment or decrement of parameters
is adapted on the basis of the convergence of the iterations.
Extrusion
- Process Description
- The Challenges: Velocity Redistribution
- Benefits Gained
- Advanced Numerical Aspects
Process Description
Extrusion is used to manufacture products in
continuous lengths with a uniform cross section. This section can be quite
simple, ie circular, annular, rectangular profiles, or very complex (window
profile, rubber car seal). Solid pellets are fed through the feed hopper.
The solid material is conveyed by a single, or several, rotating screws
inside a closed barrel. The friction from the interface between
the flowing resin and the wall increases the temperature through
a viscous heating process, locally melting the material.
After the resin has melted and has completed its flow around the screw(s),
the particles enter the die. It is the job of the die to convert the cylindrical
flow from the extruder into the required, sometimes quite complex, cross
section. The design of such dies is complicated and difficult. Traditionally,
dies have been designed using an expensive trial and error procedure,
with possibly ten or twenty trials and modifications. The main reason
for this lengthy design process is that the flow patterns inside the dies
are unknown.
Next, the material leaves the die across the die lip. Usually, significant
deformations of the extrudate are observed right after the die lip. The
material flows through the air or is dipped in a water or oil bath for
cooling purposes. Often external equipment such as conveying belts, calibrators
and curing ovens finalize the treatment of the extruded product.
The Challenges
A major challenge is faced by the die designer because of the deformation
undergone by the flowing material at the onset of the extrudate, i.e.
the free jet, right after the material has left the die. These deformations
are mainly due to the combined effect of the velocity redistribution and
the relaxation of the stress for viscoelastic materials as it leaves the
die.
The velocity profile across the die lip is far from being uniform. The
friction induced by the flowing particles rubbing along the die wall will
slow the speed of the plastic down to a very small, possibly vanishing
velocity. On the other hand, at the center of large flow sections where
the particles are barely decelerated by the friction with neighbouring
particles flowing at a low speed, the local velocity can be large. Throughout
the extrudate, where there are no walls and hence no friction along
the border of the flow domain, a flat velocity profile quickly appears.
The material flows at the same speed everywhere. So, the particles
that were flowing slowly in the vicinity of the wall will have to speed-up to uniform velocity of the free jet. Similarly, fast particles flowing
at the middle of large flow section will have to slow-down to the average
speed of the extrudate.
It is easy to understand how reducing the flow domain will accelerate
the velocity of the particles in this region. Considering a given flow
rate, reducing the flow section will automatically increase the velocity
in order to keep the same flow rate. Similarly, in order to slow down
particles, the extrudate has to swell. Even though this is easy to understand
for 2D or simple shape 3D flow, these phenomena become much more complex
for typical profile shape where narrow flow sections are close to large
flow parts. Complex 3D redistributions are observed across the flow domain
so that it becomes difficult to guess the final results.
In addition to velocity redistribution, other behavior can further complicate
the situation. Across narrow flow sections, the friction is significantly
higher leading to larger viscous heating. This higher temperature will
locally reduce the viscosity of the material improving its flowability.
Relaxation of the stress usually leads to larger deformation as explained
in more detail in the viscoelastic section. Foaming or chemical reaction
processes can also affect the material properties of the resin.
Benefits Gained with POLYFLOW
By solving the Navier-Stokes equations, possibly combined with the energy
equation, POLYFLOW is able to take into account tens-of-thousands and
sometimes hundreds-of-thousands of pieces of information simultaneously.
The flow pattern, the local pressure drop, the deformation of each section
of the profile, the temperature map all this information is taken into
consideration when predicting what the behavior of the particles throughout-the-die and after-the-die-lip will be.
Extrudate Shape Prediction
Considering a given material flowing through a given die under given
operating conditions, it is possible to predict the
shape of the final extrudate after the all the deformation due to the
velocity redistribution, as explained above. Furthermore, you may
modify some parameters such as operating conditions (flow rate, partial
slip along the wall, cable speed, global force, etc.) or thermal boundary
conditions (specified temperature, convective or radiative heat flux,
etc). It is also possible to analyze the behavior of another material
under the same conditions or understand the effect of a geometrical modification
on the final product shape.
Inverse Die Design
The critical question faced by the designer is to know what
die shape needs to be cut in order to compensate
for the deformation undergone by the fluid in the free jet.
Using POLYFLOW, you specify the shape of the
product you would like to obtain and POLYFLOW automatically adjusts
the shape of the die land.
Advanced Numerical Aspects
Because the border of the extrudate will change its shape during the
simulation, the position of the free surface becomes an unknown to solve.
Specific equations known as kinematic equations assure an accurate calculation
of the exact shape of the extrudate.
In addition to the position of the free surface, the internal nodes of
the extrudate need to be relocated. This stops the deformation of the
finite element mesh from being too large as that could lead to degenerated
elements. Also, POLYFLOW proposes different remeshing techniques such
as the Thompson technique, and the optimesh or streamwise method, which have
been specifically fit to take into account the very large deformations
sometimes encountered in the extrusion process.
Coextrusion
- Process Description
- The Challenges
- Benefits Gained
- Advanced Numerical Aspects
Process Description
The market demands cheaper, lighter,
more rigid and aesthetically appealing products. It is nearly impossible
to meet this goal with a single material. Coextrusion involves
combining several materials into a single product in order to benefit
from the different mechanical, chemical or material strengths of each
resin.
Solid pellets are fed through the different feed hoppers (one for each
material). The solid material is conveyed by a single, or several, rotating
screws inside a barrel. The friction induced by the flowing resins
along the wall increases the temperature through viscous heating,
locally melting the material. After the resins are completely melted and
the flow around the screw(s) is completed, the particles enter the die.
This is where the different material will flow together possibly after
complex feeding channels. It is the job of the die to convert the cylindrical
flows from the extruders into the required, sometimes quite complex, cross
section. The design of such dies is complicated and difficult. Traditionally,
dies have been designed by an expensive trial and error procedure, with
possibly ten or twenty stages of trial and modification. The main reason
for this lengthy design process is that the flow patterns inside the dies
are unknown.
The Challenges
A major challenge faced by the die designer is the deformation undergone
by the flowing material at the onset of the extrudate, i.e. the free jet,
right after the material has left the die. These deformations are mainly
due to the combined effect of the velocity redistribution and the relaxation
of the stress for viscoelastic materials as it leaves the die.
In addition to these typical challenges relating to the extrusion, other
difficulties more specifically relating to the coextrusion appear. The
materials come from different inlet sections or extruders with possibly
different relative flow rates which would lead to higher or lower velocity
profiles. In addition, the need to position several different feeding
equipments usually prevents the alignment of the whole extrusion line
with the flow direction. When the material is brought together in the
die it is quite common that they flow together along a complex path, not
mentioning some temperature gradients that could occur. Taking into account
the inertia term could lead to unexpected flow patterns that affect the
quality of the final product.
Furthermore, different materials will have different material properties,
including a different rheological behavior. As a consequence, the shape
of the interface between two or several fluids will change. The material
with the highest flow rate or viscosity will tend to push away the other
materials. The materials will also react differently to the thermal conditions
that can significantly influence the flow pattern as well.
Benefits Gained with POLYFLOW
By solving the Navier-Stokes equations, possibly combined with the energy
equation, POLYFLOW is able to take into account tens-of-thousands and
sometimes hundreds-of-thousands of pieces of information simultaneously.
The flow pattern, the local pressure drop, the deformation of each section
of the profile, the temperature map all this information is taken into
consideration when predicting what the behavior of the particle thoughout
the die and after the die lip will be.
Extrudate Shape Prediction
Considering a given material flowing through a given die under given
operating conditions, it is possible to predict, i.e. to calculate, the
shape of the final extrudate and the position of the interface(s) after
all the deformation due to the velocity redistribution, as explained above.
Furthermore, you may modify some parameters such as operating conditions
(flow rates, partial slip along the wall, cable speed, global force, etc.)
and thermal boundary conditions (specified temperature, convective or
radiative heat flux, etc). It is also possible to analyze the behavior
of another material under the same conditions or understand the effect
of a geometrical modification on the final product shape.
Inverse Die Design
The critical question faced by the designer to know what die shape needs to be
in order to compensate
for the deformations undergone by the fluid throughout the free jet.
Using POLYFLOW, you specify the shape of the
product you would like to obtain and POLYFLOW automatically adjusts
the shape of the die land. The die design capabilities of Polyflow can
be combined with the coextrusion feature. In this case POLYFLOW will not
only modify the die land in order to get the exact shape of the extrudate,
but it will also prescribe the position of the interface across the die
lip in order to have the different fluids at their exact location in the
final product. This is particularly important when a minimum thickness
for each layer is required.
Advanced Numerical Aspects
Because the border of the extrudate will change its shape during the
simulation, the position of the free surface becomes an unknown
to solve during the simulation. Specific equations known as kinematic
equations assure an accurate calculation of the exact shape of the extrudate.
In addition to the position of the free surface, the internal nodes of
the extrudate need to be relocated. This stops the deformation of the
finite element mesh from being too large as to degenerated elements. Also,
POLYFLOW proposes different remeshing techniques such as the Thompson technique,
the optimesh, or streamwise method, which have been specifically fit in
order to take into account the very large deformations sometimes encountered
in the extrusion process.
Wire / Cable Coating
- Process Description
- The Challenges
- Benefits Gained
- Advanced Numerical Aspects
Process Description
Pressure Coating
The wire coating process is very similar to the extrusion or coextrusion
process. Solid pellets are fed through the feed hopper. The solid material
is conveyed by a single, or several, rotating screws inside a closed barrel.
The friction induced at the interface between the flowing resin
and the wall increase the temperature through the viscous heating process,
locally melting the material. After flowing around a single screw or a
twin screw, the melted polymer enters the die that will bring the material
to its final shape. Both the velocity redistribution and the stress relaxation
will lead to significant deformation of the free surface, hence, to unexpected
or undesired product. The major difference is that the resin is in contact
with a moving border (the cable or the metal insert) inside the die itself.
After the die lip, the material deforms.
Tube Coating
For specific materials that can't undergo high shear rates (fluoropolymers
such as FEP), the pressure coating process, where the material is quickly
stretched as it touches the moving cable, can't be applied. In order to
avoid the polymer deterioration, a smoother contact between the FEP and
the wire is created after the polymer has left the die. The contact between
the moving cable and the flowing polymer occurs after the die lip. A vacuum is
created in order to push the resin toward the cable. The material enters
into contact with the cable at a position that can vary depending upon
the operating conditions.
The Challenges
In addition to the usual challenges faced by the extrusion or coextrusion
process (velocity redistribution, stress relaxation, internal position
of the free surface),
new difficulties arise. At the contact
between the polymer and the moving wire, the particles quickly change
from having a low velocity in the vicinity of the wall to having the possibly high cable
speed. This abrupt change of the flow boundary
conditions leads to a high shear rate that can significantly deteriorate
the grade of the material. In addition, at the first contact point between
the material and the cable, a large axial stress can occur leading to
further deterioration of the material.
Benefits Gained with POLYFLOW
By solving the Navier-Stokes equations, possibly combined with the energy
equation, POLYFLOW is able to take into account tens-of-thousands and
sometimes hundreds-of-thousands of pieces of information simultaneously. This information
can be related to both the flowing material and the cable itself. The
flow pattern, local pressure drop, deformation of each section
of the profile, temperature map - all this information is considered
in order to predict what the behavior of the particles throughout the
die and after the die lip will be. In this specific case, the wire is
usually modeled through a cartesian speed specified along a border of
the flow domain.
Extrudate Shape Prediction
Considering a given material flowing through a given die under given
operating conditions, it is possible to predict, the
shape of the final wire coat after the all the deformation due to the
velocity redistribution, as explained above. Furthermore, you may
modify some parameters such as operating conditions (flow rate, partial
slip along the wall, cable speed, global force, etc.) or thermal boundary
conditions (specified temperature, convective or radiative heat flux,
initial temperature of the cable, etc). It is also possible to analyze
the behavior of another material under the same conditions or understand
the effect of a geometrical modification on the final product shape. Local
shear rate and/or stress are also calculated. Comparing this data with
the maximum allowable limit for the considered material gives you
valuable information about whether the material might deteriorate or whether
the process could be pushed to higher production rates.
Inverse Die Design
The critical question the designer needs to answer is to know what shape
the die needs to be in order to compensate for fluid deformation in the free jet.
With POLYFLOW, you specify the shape of the product you would like to
obtain and POLYFLOW automatically adjusts the shape of the die land.
Advanced Numerical Aspects
Because the border of the extrudate will change its shape during the
simulation, the position of the free surface becomes an unknown
to solve. Specific equations known as kinematic equations assure an accurate
calculation of the exact shape of the extrudate.
In addition to the position of the free surface, the internal nodes of
the extrudate need to be relocated. This stops the deformation of the
finite element mesh from being to large as that could lead to degenerated
elements. Also, POLYFLOW proposes different remeshing techniques such
as the Thompson technique, the optimesh or streamwise method, which have
been specifically fit to take into account the very large deformations
sometimes encountered in the extrusion process simulation.
In the case of tube coating processes further numerical techniques allowing
for detection of the contact between the free surface and the moving cable
are used.
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