COMPUTATIONAL ANALYSIS AND COMPUTATIONAL ANALYSIS AND DESIGN OF SINGLE SCREW DESIGN OF SINGLE SCREW

EXTRUDERS HAVING SCREWS OF EXTRUDERS HAVING SCREWS OF COMPLEX GEOMETRY WITH MIXING COMPLEX GEOMETRY WITH MIXING

ELEMENTSELEMENTS

SPE EUROTEC 2011SPE EUROTEC 2011

BARCELONA, SPAINBARCELONA, SPAIN

John VlachopoulosJohn VlachopoulosMcMaster University McMaster University

Nick PolychronopoulosNick Polychronopoulos **Polydynamics, Inc.Polydynamics, Inc.

Shinichiro TanifujiShinichiro TanifujiHyper Advanced Simulation Laboratory (H.A.S.L.) Hyper Advanced Simulation Laboratory (H.A.S.L.)

The The ““heartheart”” of every extruder is an of every extruder is an

ARCHIMEDEAN SCREW attributed to ARCHIMEDEAN SCREW attributed to

Archimedes 287Archimedes 287--212 BC but, actually 212 BC but, actually

known to Egyptians for irrigation in the Nile known to Egyptians for irrigation in the Nile

Delta and the auger (screw drill) for Delta and the auger (screw drill) for

carpentry was known to the Greeks beforecarpentry was known to the Greeks before

the 3rd Century BC.the 3rd Century BC.

See:See:

Chris Rorres, J.Hydraul.Eng., Vol.126, 71Chris Rorres, J.Hydraul.Eng., Vol.126, 71--80, 80,

(January 2000)(January 2000)

SINGLE SCREW EXTRUDER:SINGLE SCREW EXTRUDER:

Rotating screw in a heated barrel.Rotating screw in a heated barrel.

Early developments for rubber Early developments for rubber

due to Thomas Hancock in 1820 indue to Thomas Hancock in 1820 in

England.England.

Modern developments started in Modern developments started in

the 1950the 1950’’s.s.

MODELING of EXTRUSION MODELING of EXTRUSION started in the started in the

19501950’’ss

Prominent names Prominent names

at DUPONT (USA)at DUPONT (USA)

oo McKelveyMcKelvey

oo GoreGore

oo SquiresSquires

19501950’’ss

oo Maillefer (parallel Maillefer (parallel

developments in developments in

Switzerland, 1950Switzerland, 1950’’s)s)

-- Maddock (Union Carbide) 1950Maddock (Union Carbide) 1950’’ss-- McKelveyMcKelvey’’s book on P.P. appeared in 1962s book on P.P. appeared in 1962

-- The book by Z. Tadmor and I. Klein appeared in The book by Z. Tadmor and I. Klein appeared in

19701970

MODELING OF EXTRUSION IS 60 YEARS MODELING OF EXTRUSION IS 60 YEARS

OLD, BUT MANY CHALLENGES REMAINOLD, BUT MANY CHALLENGES REMAIN

SINGLE SCREW EXTRUSION IS THE MOST SINGLE SCREW EXTRUSION IS THE MOST

COSTCOST--EFFECTIVE WAY TO MELT AND PUMP A EFFECTIVE WAY TO MELT AND PUMP A

POLYMER POLYMER

SCREW DESIGN calls forSCREW DESIGN calls for

-- OUTPUT MAXIMIZATIONOUTPUT MAXIMIZATION

-- MELT TEMPERATURE MINIMIZATIONMELT TEMPERATURE MINIMIZATION

-- EXTRUSION STABILITYEXTRUSION STABILITY

-- MELT QUALITYMELT QUALITY

OPTIONS:OPTIONS:

-- CONVENTIONAL single flighted screwsCONVENTIONAL single flighted screws

-- BARRIER screwsBARRIER screws

-- Screws with MIXING SECTIONSScrews with MIXING SECTIONS

Conventional single screw (also Conventional single screw (also

called: plasticating) extruders arecalled: plasticating) extruders are

composed of three sections:composed of three sections:

In all screws at In all screws at leastleast the first 70% or so of the first 70% or so of

melting is due to the shear stress in the melting is due to the shear stress in the

melt film between the barrel and the solid melt film between the barrel and the solid

bed surface. bed surface.

BARRIER SCREW PRINCIPLEBARRIER SCREW PRINCIPLE

-- Increased melting.Increased melting.

-- At least 80% is melted by At least 80% is melted by shearshear over over

the solid bed (i.e. very little conductive the solid bed (i.e. very little conductive

melting).melting).

MADDOCK (Union Carbide) MADDOCK (Union Carbide)

MIXING SECTIONMIXING SECTION

�� SOLID PARTICLES TRANSPORTSOLID PARTICLES TRANSPORT

(pellets, size, properties, powders, (pellets, size, properties, powders,

difficult to describe mathematically difficult to describe mathematically

particle flow)particle flow)

�� MELTING OF THE PACKED BED OF SOLID MELTING OF THE PACKED BED OF SOLID

PARTICLESPARTICLES

(how do solid particle properties affect (how do solid particle properties affect

the melting rate?)the melting rate?)

�� COMPLEX SCREW GEOMETRYCOMPLEX SCREW GEOMETRY

(barrier screws, screws with various (barrier screws, screws with various

types of mixing elements)types of mixing elements)

CHALLENGES:CHALLENGES:

Our present modeling approachOur present modeling approach

MODULAR, EASY TO UPGRADE MODELS FOR EACH SECTION

Current focus

DARNELL AND MOL (1956) MODELDARNELL AND MOL (1956) MODEL

BALANCE OF BALANCE OF FORCESFORCES AND AND TORQUESTORQUES

MELTING (TadmorMELTING (Tadmor’’s Model)s Model)In the late 50In the late 50’’s, Bruce Maddock did experiments, s, Bruce Maddock did experiments,

pulling the screw and examining what happened. pulling the screw and examining what happened.

The conclusion was that MELTING REALLY OCCURS The conclusion was that MELTING REALLY OCCURS

IN A FILM BETWEEN BARREL AND SOLID BED. A IN A FILM BETWEEN BARREL AND SOLID BED. A

MELT POOL FORMS IN FRONT OF THE REAR MELT POOL FORMS IN FRONT OF THE REAR

FLIGHT, as shown: FLIGHT, as shown:

Metering section:Metering section:

We decided to use the We decided to use the Hele Hele –– Shaw Shaw

flow approximation layer flow approximation layer –– by by –– layerlayer

2.5D analysis with 3D geometry2.5D analysis with 3D geometry

Because our objective is screw design Because our objective is screw design

which means, simulation for a starting which means, simulation for a starting

geometry, geometry upgradegeometry, geometry upgrade……..till ..till

satisfactory results obtained. satisfactory results obtained.

50 or more runs maybe need.50 or more runs maybe need.

““trial trial –– and and –– error on the computer error on the computer

screenscreen””..

�� HELE HELE –– SHAW FLOW APPROXIMATIONSHAW FLOW APPROXIMATION

�� 33--D NAVIER D NAVIER –– STOKES for creepingSTOKES for creeping

non non –– Newtonian flowNewtonian flow=

⋅∇+−∇= τP0

∂∂

+∂∂=

i

j

j

iij x

V

x

Ve

2

1 )( ijij ef=τ 3,2,1, =ji

VTkTVC P ∇+∇=∇⋅=

:2 τρENERGY:ENERGY:

0=

∂∂

∂∂+

∂∂

∂∂

y

PS

yx

PS

x( ) ( )∫=

h

o zyx

duzyxS

,,,

2

η

x

P

h

SVx ∂

∂−=y

P

h

SVy ∂

∂−= ( ) ( )∫ ′′′

∂∂−=

h

x z

zdz

x

PzV

0 η( ) ( )∫ ′′′

∂∂−=

h

y z

zdz

y

PzV

0 η

0=⋅∇ V

VTkTVC P ∇+∇=∇⋅=

:2 τρENERGY:ENERGY: 3D3D

COMPRESSIONCOMPRESSION METERINGMETERINGFEEDFEED

BarrelBarrel Diameter = 40 mmDiameter = 40 mm

5D5D 10D10D

PLABOR JAPAN EXPERIMENTSPLABOR JAPAN EXPERIMENTS

�� give measured value of pressure at give measured value of pressure at both ends as boundary condition.both ends as boundary condition.

�� predict pressure distribution / predict pressure distribution / temperature distribution / extruder temperature distribution / extruder outputoutput

MaterialMaterial：：：：：：：：LDPE, PowerLDPE, Power--law approximationlaw approximation

12D12D

McMaster University ExperimentsMcMaster University Experiments-- Single flighted screw, no mixing element Single flighted screw, no mixing element

-- D=38 mm, L/D=24D=38 mm, L/D=24

Material: HDPE (80 RPM)Material: HDPE (80 RPM)

•• FLOW RATEFLOW RATE

-- Measured: 13.34 kg/hrMeasured: 13.34 kg/hr

-- Predicted: 13.67 kg/hrPredicted: 13.67 kg/hr

•• PEAK PRESSUREPEAK PRESSURE

-- Measured: 29.75 MPaMeasured: 29.75 MPa

-- Predicted: 27.21 MPaPredicted: 27.21 MPa

Somewhat better results for LDPESomewhat better results for LDPE----------------------------

-- L/D=30, Diameter (D)= 88.9mmL/D=30, Diameter (D)= 88.9mm

-- 4 different screw designs4 different screw designs

-- LDPE MI 0.3LDPE MI 0.3

-- LLDPE MI 1 LLDPE MI 1

BRAMPTON ENGINEERING/McMASTERBRAMPTON ENGINEERING/McMASTER

UNIVERSITY EXPERIMENTS CANADAUNIVERSITY EXPERIMENTS CANADA

Experimental conditionsExperimental conditions

•• 16 runs performed: 4 screws 16 runs performed: 4 screws x x 22

polymers polymers x x 2 output rates2 output rates

•• Pressures measured at 8 locationsPressures measured at 8 locations

along screw, plus at end of screwalong screw, plus at end of screw

-- values recorded once per secondvalues recorded once per second

•• Melt temperature measured atMelt temperature measured at

end of screw end of screw

L/D=30, Diameter (D)= 88.9mmL/D=30, Diameter (D)= 88.9mm

Barrier screw with MaddockBarrier screw with Maddock

Measurement

Simulation

Lagrangian melting particle simulationLagrangian melting particle simulation

(Diameter of the initial solid particles: 5 mm)(Diameter of the initial solid particles: 5 mm)

HDPEHDPE

Lagrangian melting particle simulationLagrangian melting particle simulation

(Diameter of the initial solid particles: 5 mm)(Diameter of the initial solid particles: 5 mm)

HDPEHDPE

Lagrangian melting particle simulationLagrangian melting particle simulation

(Diameter of the initial solid particles: 2.5 mm)(Diameter of the initial solid particles: 2.5 mm)

HDPEHDPE

Lagrangian melting particle simulationLagrangian melting particle simulation

(Diameter of the initial solid particles: 2.5 mm)(Diameter of the initial solid particles: 2.5 mm)

HDPEHDPE

THANKSTHANKS

Q & AQ & A