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**Extrusion Simulation and Optimization of Profile Die Design**

By Srinivasa Rao Vaddiraju Advisor Prof. Milivoje Kostic

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**A Schematic of Profile Extrusion Line at FNAL**

Introduction Extrusion describes the process by which a polymer melt is pushed across a metal die, which continuously shapes the melt into the desired form. Dryer Cutter Feeding Hopper Extruder Die Calibrator Cooling Measurement Haul-off Polymer pellets Dopants Breaker plate Gear pump A Schematic of Profile Extrusion Line at FNAL

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**Quality factors Extrudate swell**

rearrangement of the velocity profile as the polymer leaves the die Draw down Cooling Insufficient mixing in the extruder Uneven die body temperatures and raw material variations Non-uniform viscosity in the die Non-uniform swelling Non-uniform draw down

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Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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**Prepare the complete design of dies, including blue prints.**

Objectives An attempt to develop a possible strategy for effective die design in profile extrusion Investigate the die swell behavior of the polymer and to predict the optimum die profile-shape and dimensions, including the pin(s) profile, to obtain the required dimensions and quality of the extrudate. Investigate the swell phenomenon and mass flow balance affected by different parameters like die lengths, flow rates, exponent in viscosity function etc. Simulate the flow and heat transfer of molten polymer inside the die and in the free-flow region after the die exit, and compute pressure, temperature, velocity, stress and strain rate distributions over the entire simulation domain. Investigate and understand over-all polymer extrusion process, and integrate the simulation results with the experimental data, to optimize the die design and ultimately to achieve better quality and dimensions of the extrudate. Prepare the complete design of dies, including blue prints.

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**Design Methodology Using Finite Element based CFD code Polyflow**

Using the method of Inverse Extrusion To fully understand the extrusion processes and the influence of various parameters on the quality of the final product. Integrate the simulation results and the experimental data to obtain more precise extrudate shape.

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Literature Review The text book “Dynamics of Polymeric Liquids” by R.B.Bird gives a detailed overview of non-Newtonian fluid dynamics, which is important to understand the flow of polymers. The text book “Extrusion Dies” by Walter Michaeli gives an extensive representation of extrusion processes and guidelines for the design of dies. The text book “Plastics Extrusion Technology Handbook” by Levis gives a clear representation of the rheology of materials and the technology of extrusion processes. Woei-Shyong Lee and Sherry Hsueh-Yu Ho have investigated the die swell behavior of a polymer melt using finite element method and simulated flow of Newtonian fluid and designed a profile extrusion die with a geometry of a quarter ring profile Louis G. Reifschneider has designed a coat hanger extrusion die using a parametric based three-dimensional polymer flow simulation algorithm, where the shape of the manifold and land are modified to minimize the velocity variation across the die exit. W.A. Gifford has demonstrated through an actual example how the efficient use of 3-D CFD algorithms and automatic finite element mesh generators can be used to eliminate much of the “cut and try” from profile die design.

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**Governing Equations Continuity Equation Momentum Equation**

Where, P is the pressure, τ is the extra stress tensor, v is the velocity.

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**Energy Equation the accumulation term, the convection term,**

the conduction term, the dissipation term, Where, Cv is the specific heat capacity of the material, T is the temperature, ρ is the density, k is the thermal conductivity.

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Die Design 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. The correct geometry of the die cannot be completely determined from engineering calculations. Numerical methods

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**POLYFLOW Finite-element CFD code**

Predict three-dimensional free surfaces Inverse extrusion capability Strong non-linearities Evolution procedure

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**Flowchart for numerical simulation using Polyflow**

1. Draw the geometry in Pro-E (or) other CAD software and export to GAMBIT 2. Draw the geometry in GAMBIT (or) import from other CAD software and mesh it. Modify the mesh 3. Specify Polymer properties in Polydata 4. Specify boundary conditions in Polydata Change the remeshing techniques and/or solver methods 5. Specify remeshing technique and solver method in Polydata 6. Specify the evolution parameters in Polydata Modify the evolution parameters 7. Polyflow solves the conservation equations using the specified data and boundary conditions 8.Is the solution converged? No Yes Stop

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**General Assumptions The flow is steady and incompressible**

Body forces and Inertia effects are negligible in comparison with viscous and pressure forces. Specific heat at constant pressure, Cp, and thermal conductivity, k, are constant

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room- temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room- temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room- temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room- temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room-temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room- temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Kinematic balance equation**

Boundary Conditions Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C). Die, spider and pin walls: No slip at the die walls (Vn =Vs = 0; normal and streamline velocities, respectively), and uniform die wall temperature 473 K. Symmetry planes: Shear stress Fs = 0, normal velocity Vn = 0 and normal heat flux qn =0. Free surface: Zero pressure and traction/shear at boundary (Fn = 0, Fs = 0, and Vn =0), and convection heat transfer from the free surface to surrounding room- temperature air. Kinematic balance equation on δΩfree Outlet: Normal stress Fn =0, Tangential Velocity Vs = 0, Pressure = 0.0 (reference pressure) and normal heat flux qn =0. All domains: Viscous dissipation was neglected for all flow conditions (after verification).

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**Carreau-Yasuda Law for viscosity data:**

Material Data Styron 663, mixed with Scintillator dopants Measured by, Datapoint Labs Carreau-Yasuda Law for viscosity data: Zero shear rate viscosity, η0 = 36,580 Pa-s Infinite shear rate viscosity, η∞ = 0 Pa-s Natural time, λ = 0.902 Transition Parameter, a = 0.585 Exponent, n = 0.267 Density, ρ = 1040 Kg/m3 Specific Heat, cp = 1200 J/Kg-K Thermal Conductivity, k = W/m-K Coefficient of thermal expansion, β = 0.5e-5 m/m-K

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**Styron viscosity data, with and without Scintillator dopants**

ηd– Doped Styron 663 106 105 104 103 102 10-2 10-1 100 101

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**Profiles Rectangular profile die with one hole**

Rectangular profile die with ten holes

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**Rectangular profile die with one hole**

2.0 1.0 0.11 Required extrudate is a rectangular cross section of 1 cm 2 cm with a circular hole of 1.1 mm diameter at its center ALL DIMENSIONS ARE IN CM

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**Sensitivity analysis of die swell and inverse extrusion capabilities of Polyflow**

P1 (0,y) P2 (0,y) P3 (x,y) P4 (x,0) P5 (x,0)

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**Full domain of the extrusion die**

Melt flow direction

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**Half domain of the extrusion die**

Section 1 Section 2 Section 3 Die lip Melt flow direction

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**Simulation domain with boundary conditions**

. Inlet (Fully Developed Flow) 2. Wall (Vn = 0, Vs = 0) 3. Symmetry (Vn = 0, Fs = 0) . Free Surface (Fs = 0, Fn = 0, V.n = 0) . Outlet (Fn = 0, Vs = 0)

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**Finite element 3-D domain and die-lip mesh**

Melt flow direction Die Lip 30,872 elements Skewness < 0.33

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**19 hours and 36 minutes of CPU time**

Windows XP 2.52 GHz Processor 1 GB RAM 19 hours and 36 minutes of CPU time

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**Contours of static pressure**

Die lip Melt flow direction

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**Contours of velocity magnitude at different iso-surfaces**

Die lip Melt flow direction

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**Contours of temperature distribution**

Melt flow direction Die lip

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Contours of shear rate Melt flow direction Die lip

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**Existing die, corresponding simulation and new improved-die profiles**

X (mm) Y (mm) New Die (Simulated) Existing Die Desired Extrudate Existing-Die Extrudate (Simulated)

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**Exploded view of the extrusion die**

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**2 D-View of the extrusion die**

Melt flow direction

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Blue prints Preland Dieland Pin

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**Rectangular profile die with ten holes**

10.0 0.5 0.11 Required extrudate is a rectangular cross section of 0.5 cm 10 cm with ten equally spaced centerline circular holes of 1.1 mm diameter. ALL DIMENSIONS ARE IN CM

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**Full domain of the extrusion die**

Melt flow direction

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**Half domain of the extrusion die**

Melt Pump Adapter, Adapter 1 and Adapter 2 Spider Die land Melt flow direction Die lip Free Surface

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**Simulation domain with boundary conditions**

1 2 3 4 5 . Inlet (Fully Developed Flow) 2. Wall (Vn = 0, Vs = 0) 3. Symmetry (Vn = 0, Fs = 0) 4. Free Surface (Fs = 0, Fn = 0, V.n = 0) 5. Outlet (Fn = 0, Vs = 0) Melt flow direction

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**Finite element 3-D domain and half of extrudate profile mesh**

Melt flow direction 19,479 elements Skewness < 0.5

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**Half domain of the extrusion die (without free surface) and division of outlet into 10 areas**

Melt flow direction out1 out2 out3 out4 out5 out6 out7 out8 out9 out10

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**Percentage of Mass flow rate in different exit segments**

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Windows XP 2.52 GHz Processor 1 GB RAM One hour of CPU time

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**Contours of Static pressure**

Melt flow direction Die lip

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**Contours of Velocity magnitude at different iso-surfaces and at centerline of exit**

Melt flow direction Die lip Velocity Magnitude (m/s) X-Coordinate (m)

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**Contours of Temperature distribution**

Melt flow direction Die lip

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**Contours of Shear rate and Viscosity**

Melt flow direction Die lip Shear rate Viscosity

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**Simulated die and required extrudate profiles**

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**Percentage of mass flow rate for designed and balanced die**

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**Exploded view of the extrusion die**

Melt pump adapter Adapter 1 Adapter 2 Preland Melt flow direction Dieland

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Blue prints Melt pump adapter Whole die Adapter 1

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Adapter 2 Spider Die land

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Conclusions The optimum dimensions of the die to attain more balanced flow at the exit were obtained. The effect of inertia terms is found to be negligible for polymer flows at low Reynolds number. The exponent of the Carreau-Yasuda model, or the slope of the viscosity vs shear rate curve, has a significant effect on the die swell. The flow in the die appeared to be smooth with no re-circulation regions.

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**Recommendations for future improvements**

Polymer viscoelastic properties Include flow, cooling, solidification and vacuuming in and after the calibrator Radiation effects for free surface flow Pulling force at the end of the free surface Pressure of the compressed air Non-uniform mesh

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**ACKNOWLEDGEMENTS Prof. Milivoje Kostic Prof. Pradip Majumdar**

Prof. M.J. Kim Prof. Lou Reifschneider NICADD (Northern Illinois Centre for Accelerator and Detector Development), NIU Fermi National Accelerator Laboratory, Batavia, IL

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