modelling of single screw extrusion - zamakmercator.com€¦ · modelling of single screw extrusion...

26-07-2017

1

António Gaspar-Cunha

Institute of Polymers and Composites,

Department of Polymer Engineering, University of Minho,

Guimarães, Portugal

Modelling of Single Screw Extrusion

11th July, 2017

Zamak Mercator

Prostokąt

26-07-2017

2

Department of Polymer Engineering

University of Minho

people

Name Type

1 António Gaspar-Cunha ER

2 José Covas ER

3 Roman Denysiuk ER

4 Lino Costa ER

5 M. Fernanda Costa ER

6 Ana Rocha ER

7 Carla Martins ER

University of Minho


University of Minho

• Plasticating phenomena

• Mathematical models

- conventional screws

- morphology development

- barrier screws

• Results

• Summary of mathematical models

• New developments

contents

26-07-2017

3


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plasticating phenomena

i)

iv) v)iii)ii) vi)

Transversal

cuts

Hopper

Solids

conveying

Delay Melting Pumping

Die

Heating bands

Physical phenomena inside the extruder

i) Solids conveying in the hopper– conveying due to gravity;

ii) Solids conveying in the screw – conveying due to friction;

iii) Delay –conveying of solids (partially) surrounded by a melt film;

iv) Melting – accordingly with a specific melting mechanism;

v) Pumping;

vi) Melt flow trough the die.


University of Minho

mathematical models: simplifications

Two important simplifications

� Considering the barrel rotating

� Unrolled screw channel

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Barrel

Screw

FlightFlight

qb

qs

qf qf

y

x

∆z

H

W

Vb V

bz

Vbx V

sz

H

T(y)

Tb

Tm

Tso

Ts

A

CδC

z

y

xT(y)

B

Vbz

VbxVsz

H

Tb

Tm

Tso

Ts

A

Tm

C

Vb

δDE

WB

δC

D

E

Vbz

VbxVsz

H

T(y)

Tb

Tm

Tso

Ts

B

E

DA

Tm

D

C

Vb

δDE

WB

δC

Vbz

Vbx

H

T(y)

Tb

Tb

Vb

II- Solids conveying

III- Delay (1)

IV- Delay (2)

IV- Melting

V- Melt conveying

mathematical models: conventional screw

Global modelling


University of Minho

s

Barrel

Screw

FlightFlight

b

q

qf

y

x

qf

q

• Elastic solid plug moving in the down-channel direction at constant velocity, with

heat dissipation at all contact surfaces

• This stage develops until temperature near to the barrel surface reaches

polymer melting temperature

Z. Tadmor and E. Broyer, Polym. Eng. Sci., 378, 12 (1972)

Model

mathematical models: solids conveying

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Heat fluxes in transversal direction of the channel Heat fluxes in transversal direction of the channel Heat fluxes in transversal direction of the channel Heat fluxes in transversal direction of the channel

( )φθθ

π+

=b

bmbbb PfDNqsin

sin ( ) 1sin

sin

sin

sinr

tg

tgPfDNq

s

b

s

b

b

bmsss θ

θθθ

φθθ

π+

=

qb, qs and qf – heat rates generated by friction

at the surfaces of barrel, screw root and screw

flanks, respectively;

qb,cond, qs,cond heat conducted from the barrel

and from screw root, respectively.

Hy

scondby

yTkq

=∂

∂−=

)(,

0

,

)(

=∂

∂=

y

pcondsy

yTkq

Energy balance

Barrel

Screw root

qb

qs

qf qf

y

x

qb,cond

Screw

flank

qs,cond

Screw

flank

mathematical models: solids conveying


University of Minho

Vbz

Vbx V sz

H

T(y)

Tb

TmTso

Ts

A

Vb

C

• Melt film of growing thickness develops near to the barrel surface;

• Co-existence of this melt film (C) with the solid plug (A)

L. Kacir and Z. Tadmor, Polym. Eng. Sci., 387, 12 (1972)

Model

mathematical models: delay zone 1

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• Identical to the melting zone (section B corresponds to the melt pool).

• Develops until the width of section B be greater than the channel height.

H

xz

y

T(y)

Tb

Tm

Tso

Ts

A

Tm

Vbz

Vb

Vbx Vsz

Cδ

DB

EδDE

WB

Model

mathematical models: delay zone 2


University of Minho

HδDE

Vbz

Vbx VszTb

Tm

Tso

Ts

B ATm

WB

C

T(y)

D

E

5-zone model developed for melting in single-screw extruders

(solid plug surrounded by melt films near to the barrel and screw

surfaces and by a melt pool near to the active flank).

J.T. Lindt and B. Elbirli, Polym. Eng. Sci., 412, 25 (1985)

.

Model

mathematical models: melting

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VbzVbx

H

T(y)

Tb

Tb

Vb

2D non-isothermal flow of a Non-Newtonian fluid.

R.T. Fenner, Principles of Polymer Processing, McMillan, London (1979).

Model

mathematical models: melt conveying


University of Minho

I- Solids conveying in the hopper (1D )Gravity conveying of granular materials

II- Solids conveying (1D+ )Non-isothermal Flow of a solid plug with heat friction at all surfaces

III- Delay I (1D+)Solid plug with a melt film near the inner barrel surface

IV- Delay II and Melting (1D and 2D+)5-Zone Lindt model (the delay zone II ends when the width of the meltpool equals its height)

V- Melt conveying (2D+)2D non-isothermal flow of a Non-Newtonian fluid

VI- Melt flow trough the die (2D+)2D non-isothermal flow of a Non-Newtonian fluid

General characteristics


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Rupture

Erosion

mathematical models: morphology development

Liquid-Liquid System Solid-Liquid System


University of Minho

initial agglomerates

aggregates

particles

Morphology evolution along the extruder

Liquid-Liquid System Solid-Liquid System

mathematical models: morphology development

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conventional scre

w Barrel

Screw

FlightFlight

qb

qs

q f qf

y

x

∆z

H

W

Solids conveying

H

T(y)

Tb

Ts

A

Vb

C

Delay (1)

T(y)

B

Vsz

Tb

Ts

A

Vb

WB

D

E

Delay (2)x

T(y)

Tb

Ts

A

D

Vb

WB

Melting

H

T(y)

Tb

Ts

Vb

Melt conveying

C

B

E

D

WB

H

H

C

B


Modelling conventional screws


University of Minho

Type of barrier screws modelled

Dray and Lawrence

mathematical models: barrier screws

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barr

ier

scre

w

Barrel

Screw

FlightFlight

qb

qs

qf q

f

y

xW

Solids conveying

H

T(y)

Tb

Ts

A

Vb

C

Delay (1)

T(y)B

Vbx

Tb

Ts

A

Vb

D

E

Delay (2)

H

bVSolids conveying (Barrier)

H

x T(y)

Tb

Ts

A

GH

T(y)

Tb

Ts

A

b

BWB

F

VDelay (2) (Barrier)

H

T(y)

Tb

Tb

Vb

B

Melt conveying (Barrier)

H

T(y)

Tb

Tb

Vb

Melt conveying

H

T(y)

Tb

Ts

DA

Vb

Melting (Barrier)

GH

T(y)

Tb

Ts

A

bVDelay (1) (Barrier)

HC

B

H D

C

B

E

E

DB G B

E

F CC

G

F C

D

VbMelting

mathematical models: barrier screws

Modelling barrier screws


University of Minho

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

L (m)

X/W

0

10

20

30

40

0.0 0.2 0.4 0.6 0.8 1.0

L (m)

P (

MP

a)

Tb = 150 - 170 - 190 ºC

N (rpm) Output (Kg/hr) WATS Power (W)

20 3.15 271.6 942

40 6.36 215.1 2043

60 9.43 164.6 3289

0

40

80

120

160

200

0.0 0.2 0.4 0.6 0.8 1.0

L (m)

T (

ºC)

Tb

Effect of screw speed

results: barrier screws

26-07-2017

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MAILLEFERScrew 1: L1 = 10.4D

L2 = 7.0D

L3 = 8.6D

Screw 2: L1 = 3.6DL2 = 7.0D

L3 = 15.4D

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0L(m)

X/W

0

20

40

60

80 WATS x 10

Q x 0.2 (kg/h)

Zt x 0.02 (m)

Tmelt x 10 (ºC)

Power x 100 (W)

Pmax (MPa)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0L(m)

X/W

0

20

40

60

80 WATS x 10

Q x 0.2 (kg/h)

Zt x 0.02 (m)

Tmelt x 10 (ºC)

Power x 100 (W)

Pmax (MPa)

20rpm 40rpm 60rpm 80rpm 100rpm Ws Wm

results: barrier screws (effect of location of the barrier)


University of Minho

summary of mathematical models

• Conventional screws

• Barrier screws

• Mixing sections

• Grooves

• Morphology development: specific systems

• Discrete Element Method (DEM): solid particles

Modelling capabilities for single screw extrusion

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INPUT DATA:

• Geometry

• Polymer Properties

• Operating Conditions

RESULTS:

• Output

• Power consumption

• Melt temperature

• Temperature homogeneity

• Degree of Mixing

• Length required for melting

• Pressure generation

• ...MODELLING SOFTWARE

Extrusion modelling

mathematical models: global software


University of Minho

Grooves geometry

new developments: grooves in the barrel

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fp-p

fb

fs

1485

6 7 3 2

bN

hN

H

h* γ2

γ1

Effective mean coefficient of friction: 2 type of models

( )

−−−+= −

β

απ N

N

b

bppbef NB

h

D

Bffff exp1 NNbNB =


University of Minho

0.4

0.425

0.45

0.475

0.5

0.525

0.55

0.575

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

h/b

Mean friction coef.

B = 48 mm

B = 60 mm

B = 72 mm


Some results

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Potential problems

1.Difficulty in measuring the “real” friction

coefficients;

2.Modelling the real behavior of the pellets flow

in the grooves.


University of Minho

VbzVbx

H

T(y)

Tb

Tb

Vb

new developments: barrel rotating

HδDE

Vbz

Vbx VszTb

Tm

Tso

Ts

B ATm

WB

C

T(y)

D

E

Introducing the barrel velocity

To consider a velocity

difference between the

screw and barrel velocities?

SIMPLIFICATION:

The barrel rotates.

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Thanks!

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