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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 DescriptionExtrusion 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 ChallengesA 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 POLYFLOWBy 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 AspectsBecause 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. CoextrusionProcess DescriptionThe 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 ChallengesA 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 POLYFLOWBy 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 AspectsBecause 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 CoatingProcess DescriptionPressure 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 ChallengesIn 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 POLYFLOWBy 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 AspectsBecause 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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