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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
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
Department of Polymer Engineering
University of Minho
• Plasticating phenomena
• Mathematical models
- conventional screws
- morphology development
- barrier screws
• Results
• Summary of mathematical models
• New developments
contents
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Department of Polymer Engineering
University of Minho
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.
Department of Polymer Engineering
University of Minho
mathematical models: simplifications
Two important simplifications
� Considering the barrel rotating
� Unrolled screw channel
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Department of Polymer Engineering
University of Minho
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
Department of Polymer Engineering
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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Department of Polymer Engineering
University of Minho9
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
Department of Polymer Engineering
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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Department of Polymer Engineering
University of Minho11
• 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
Department of Polymer Engineering
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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Department of Polymer Engineering
University of Minho
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
Department of Polymer Engineering
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
mathematical models: conventional screw
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Department of Polymer Engineering
University of Minho
Rupture
Erosion
mathematical models: morphology development
Liquid-Liquid System Solid-Liquid System
Department of Polymer Engineering
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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Department of Polymer Engineering
University of Minho
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
mathematical models: conventional screw
Modelling conventional screws
Department of Polymer Engineering
University of Minho
Type of barrier screws modelled
Dray and Lawrence
mathematical models: barrier screws
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Department of Polymer Engineering
University of Minho
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
Department of Polymer Engineering
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
11
Department of Polymer Engineering
University of Minho
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)
Department of Polymer Engineering
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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Department of Polymer Engineering
University of Minho
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
Department of Polymer Engineering
University of Minho
Grooves geometry
new developments: grooves in the barrel
26-07-2017
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Department of Polymer Engineering
University of Minho
new developments: grooves in the barrel
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 =
Department of Polymer Engineering
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
new developments: grooves in the barrel
Some results
26-07-2017
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Department of Polymer Engineering
University of Minho
new developments: grooves in the barrel
Potential problems
1.Difficulty in measuring the “real” friction
coefficients;
2.Modelling the real behavior of the pellets flow
in the grooves.
Department of Polymer Engineering
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.
26-07-2017
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Department of Polymer Engineering
University of Minho
Thanks!
Debate