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 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.

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

zyxx

P xzxyxx

zyxy

P yzyyyx

zyxz

P zzzyzx

disscondconvacc EEEE

t

TCE vacc

z

Tv

y

Tv

x

TvCE zyxvconv

z

Tk

zy

Tk

yx

Tk

xEcond

y

v

z

v

x

v

z

v

x

v

y

v

z

v

y

v

x

vE

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 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

POLYFLOW

Finite-element CFD code

Predict 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 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

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 = 0.902

Transition Parameter, a = 0.585

Exponent, n = 0.267

Density, ρ = 1040 Kg/m3

Specific Heat, cp = 1200 J/Kg-K

Thermal Conductivity, k = 0.12307 W/m-K

Coefficient of thermal expansion, β = 0.5e-5 m/m-K

a

na

1

0 1

Styron 663, mixed with Scintillator dopants

Carreau-Yasuda Law for viscosity data:Measured by, Datapoint Labs

Styron viscosity data, with and without Scintillator dopants

Shear Rate (1/s)

Vis

cosi

ty (

Pa-

s)

200 0C180 0C

220 0C

η – Styron 663

ηd– 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 flow

direction

Section 1

Section 2

Section 3

Die lip

Melt flow

direction

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 XP

2.52 GHz Processor

1 GB RAM

Die lip

Melt flow

direction

Contours of static pressure

Die lip

Melt flow

direction

Contours of velocity magnitude at different iso-surfaces

Melt flow

direction

Die lip

Contours of temperature distribution

Contours of shear rate

Melt flow

direction

Die lip

Existing die, corresponding simulation and new improved-die profiles

0

1

2

3

4

5

6

7

0 10X (mm)

Y (

mm

)

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 flow

direction

Half domain of the extrusion die

Melt Pump Adapter,

Adapter 1 and Adapter 2

Spider

Die land

Melt flow

direction

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 flow

direction

Simulation domain with boundary conditions

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

Melt flow

direction

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

Out10

Out

let

% of mass flow rate

Case 8

Case 7

Case 6

Case 5

Case 4

Case 3

Case 2

Case 1

One hour of CPU time

Windows XP

2.52 GHz Processor

1 GB RAM

Contours of Static pressure

Melt flow

direction

Die lip

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)

Contours of Temperature distribution

Melt flow

direction

Die lip

Contours of Shear rate and Viscosity

Melt flow

direction

Melt flow

direction

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 pump

adapterAdapter 1

Adapter 2

Preland

Melt flow

direction

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

ACKNOWLEDGEMENTS

Prof. 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 ?