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Extrusion Simulation and Optimization of Profile Die Design
03-25-2003
Advisor
Prof. Milivoje Kostic
By
Srinivasa Rao Vaddiraju
Extrusion describes the process by which a polymer melt is pushed across a metal die, which continuously shapes the melt into the desired form.
Gear pump
A Schematic of Profile Extrusion Line at FNAL
IntroductionD
ryer
Cutter
Feeding
Hopper
Extruder
Die
Calibrator
Cooling
Measurement
Haul-off
Polymer pellets Dopants
Breaker plate
Quality factorsExtrudate swell
Draw down CoolingInsufficient mixing in the extruder Uneven die body temperatures and raw material variations Non-uniform viscosity in the die
Non-uniform swellingNon-uniform draw down
rearrangement of the velocity profile as the polymer leaves the die
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.
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.
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.
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.
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.
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.
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.
Objectives
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.
Literature ReviewThe 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.
Governing Equations
Where, P is the pressure,τ is the extra stress tensor, v is the velocity.
Continuity Equation
Momentum Equation
0
zyx vz
vy
vx
zyxxP xzxyxx
zyxyP yzyyyx
zyxzP zzzyzx
disscondconvacc EEEE
tTCE vacc
zTv
yTv
xTvCE zyxvconv
zTk
zyTk
yxTk
xEcond
yv
zv
xv
zv
xv
yv
zv
yv
xvE
zyyz
zxxz
yxxy
zzz
yyy
xxxdiss
Energy Equation
Where, Cv is the specific heat capacity of the material,
T is the temperature, ρ is the density,k is the thermal conductivity.
the accumulation term,
the convection term,
the conduction term,
the dissipation term,
Die DesignThe ‘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
POLYFLOW
Finite-element CFD codePredict three-dimensional free surfaces Inverse extrusion capability Strong non-linearities Evolution procedure
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.
3. Specify Polymer properties in Polydata
4. Specify boundary conditions in Polydata
8.Is the solution converged?
Stop
5. Specify remeshing technique and solver method in Polydata
Yes
No
6. Specify the evolution parameters in Polydata
7. Polyflow solves the conservation equations using the specified data and boundary conditions
Modify the evolution
parameters
Change the remeshing techniques and/or
solver methods
Modify the mesh
General Assumptions
0t
and incompressible 0 v
Body forces and Inertia effects are negligible in comparison with viscous and pressure forces.
The flow is steady
Specific heat at constant pressure, Cp, and thermal conductivity, k, are constant
Boundary Conditions
0. nv
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).
Boundary Conditions
0. nv
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).
Boundary Conditions
0. nv
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).
Inlet: Fully developed inlet velocity corresponding to actual mass flow rate of 50 kg/hr and uniform inlet temperature (473 K or 200 C).
Boundary Conditions
0. nv
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).
Boundary Conditions
0. nv
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 δΩfreeOutlet: 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).
Boundary Conditions
0. nv
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).
Boundary Conditions
0. nv
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).
Material Data
Zero shear rate viscosity, η0 = 36,580 Pa-s
Infinite shear rate viscosity, η∞ = 0 Pa-s
Natural time, λ = 0.902Transition Parameter, a = 0.585Exponent, n = 0.267Density, ρ = 1040 Kg/m3
Specific Heat, cp = 1200 J/Kg-K
Thermal Conductivity, k = 0.12307 W/m-KCoefficient of thermal expansion, β = 0.5e-5 m/m-K
an
a1
0 1
Styron 663, mixed with Scintillator dopantsCarreau-Yasuda Law for viscosity data:
Measured by, Datapoint Labs
Styron viscosity data, with and without Scintillator dopants
Shear Rate (1/s)
Visc
osity
(Pa-
s)
200 0C180 0C
220 0C
η – Styron 663ηd– Doped Styron 663
106
105
104
103
102
10-210-1 100 101 102 103
Profiles
•Rectangular profile die with one hole•Rectangular profile die with ten holes
Rectangular profile die with one hole
2.0
1.00.11
ALL DIMENSIONS ARE IN CM
Required extrudate is a rectangular cross section of 1 cm 2 cm with a circular hole of 1.1 mm diameter at its center
Percentage Differences P1(0,y) P5(x,0) P2(0,y) P4(x,0) P3(x) P3(y) Reference 0 0 0 0 0 0 Inertia terms not included -0.007% -0.001% -0.002% -0.001% -0.001% 0.002% Exponent in Carreau - 0.252 0.003% 0.001% 0.000% 0.000% 0.000% 0.000% Yasuda model, n 0.28271 1.495% -1.765% 0.646% 0.380% 0.465% 0.358% 0.3522 3.692% -4.583% 1.619% 0.979% 1.138% 0.864% 0.453 8.439% -11.776% 3.935% 2.521% 2.686% 1.995% 0.5286 11.354% -17.410% 5.718% 3.806% 3.876% 2.843% Zero shear 1.20E+05 0.007% 0.002% 0.000% 0.000% 0.000% -0.001% rate viscosity, 0 (Pa-s) 1.34E+05 0.006% 0.002% 0.000% 0.000% 0.000% -0.001% 2.00E+05 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 2.40E+05 0.001% 0.002% -0.001% -0.001% 0.000% 0.001% 2.80E+05 0.000% 0.002% -0.001% -0.001% -0.001% 0.001% Flow rate (m3/s) 1.54E-05 0.640% 0.017% 0.232% 0.190% 0.245% 0.095% 2.15E-05 0.207% 0.014% 0.073% 0.060% 0.079% 0.030% 2.58E-05 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 3.04E-05 -0.189% -0.010% -0.069% -0.058% -0.074% -0.029% 3.61E-05 -0.352% -0.016% -0.128% -0.105% -0.136% -0.054% Transition 2 -2.757% 0.104% -1.025% -0.701% -0.932% -0.406% Parameter, a 0.5 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% Time constant, 2.31685 0.914% 0.020% 0.329% 0.269% 0.346% 0.133% 4.6337 0.000% 0.000% 0.000% 0.000% 0.000% 0.000% 7.53 -0.507% -0.030% -0.182% -0.148% -0.193% -0.075% 9.2674 -0.693% -0.042% -0.249% -0.203% -0.262% -0.102% Inverse Extrusion -0.18% 1.82% 0.17% 0.04% 0.3% 0.61%
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)
Full domain of the extrusion die
Melt flowdirection
Section 1
Section 2
Section 3
Die lip
Melt flowdirection
Half domain of the extrusion die
Simulation domain with boundary conditions
1. 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)
Finite element 3-D domain and die-lip mesh
Melt flow direction
Die Lip
30,872 elements
Skewness < 0.33
19 hours and 36 minutes of CPU time
Windows XP2.52 GHz Processor1 GB RAM
Die lip
Melt flowdirection
Contours of static pressure
Die lip
Melt flowdirection
Contours of velocity magnitude at different iso-surfaces
Melt flowdirection
Die lip
Contours of temperature distribution
Contours of shear rate
Melt flowdirection
Die lip
Existing die, corresponding simulation and new improved-die profiles
0
1
2
3
4
5
6
7
0 10X (mm)
Y (m
m)
New Die (Simulated)Existing Die
Desired ExtrudateExisting-Die Extrudate
(Simulated)
Exploded view of the extrusion die
2 D-View of the extrusion die
Melt flow direction
Blue prints
Preland Dieland
Pin
Rectangular profile die with ten holes
10.00.5
0.11
ALL DIMENSIONS ARE IN CM
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.
Full domain of the extrusion die
Melt flowdirection
Half domain of the extrusion die
Melt Pump Adapter,Adapter 1 and Adapter 2
Spider
Die land
Melt flowdirection
Die lip
Free Surface
1
2
3
4
5
1. 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 flowdirection
Simulation domain with boundary conditions
Finite element 3-D domain and half of extrudate profile mesh
Melt flowdirection
19,479 elements
Skewness < 0.5
Half domain of the extrusion die (without free surface) and division
of outlet into 10 areas
d0
d1
d2
Melt flow direction
out1out2out3out4out5out6out7out8out9out10
Percentage of Mass flow rate in different exit segments
0.00% 5.00% 10.00%
Out1
Out2
Out3
Out4
Out5
Out6
Out7
Out8
Out9
Out10O
utle
t
% of mass flow rate
Case 8Case 7Case 6Case 5Case 4Case 3Case 2Case 1
One hour of CPU time
Windows XP2.52 GHz Processor1 GB RAM
Contours of Static pressure
Melt flowdirection
Die lip
Contours of Velocity magnitude at different iso-surfaces and at centerline of exit
Melt flowdirection
Die lip
Velocity Magnitude (m/s)
X-Coordinate (m)
Contours of Temperature distribution
Melt flowdirection
Die lip
Contours of Shear rate and Viscosity
Melt flowdirection
Melt flowdirection
Die lipShear rate
Viscosity
-3
0
3
0 10 20 30 40 50
-1
0
1
4 5 6 7
-1
0
1
24 25 26 27
-1
0
1
14 15 16 17
-1
0
1
44 45 46 47
-1
0
1
34 35 36 37
Simulated DieRequired Extrudate
Simulated die and required extrudate profiles
0.00% 5.00% 10.00%
Out1Out2Out3Out4Out5Out6Out7Out8Out9Out1
Out
let
% of Mass Flow Rate
Designed Die Balanced Die
Percentage of mass flow rate for designed and balanced die
0
Exploded view of the extrusion dieMelt pumpadapter
Adapter 1
Adapter 2
Preland
Melt flowdirection
Dieland
Blue prints
Whole die Melt pump adapter
Adapter 1
Adapter 2 Spider
Die land
ConclusionsThe 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.
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
ACKNOWLEDGEMENTSProf. Milivoje KosticProf. 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
QUESTIONS ?