polymer processing laboratory university of maryland transient behavior of extruders by rajath...
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POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Transient Behavior of Extruders
by
Rajath Mudalamane, Dr. David I. Bigio
University of Maryland at College Park
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION: Research goals
• STAGE-I: Robust screw design- ‘Minimize variations/fluctuations in the process by using the inherent damping nature of transient behavior of extruders’
• STAGE-II: Unsteady state extrusion process ‘Design for the manufacture of materials with engineered variations in quality (based on performance requirements of the material)’
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Research goals contd
Knowledge of transient behavior of extruders
Experimental observations [1,2,3,4,5,6,7]
Extrusion Extrusion ProcessProcess
QN
Temperatures
d1 d2
d3
d4
?
Theoretical modeling
[8,9,10]
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION: Schematic of an Extruder
FEEDER
MELTING
PARTIALLY FILLED, MELT CONVEYING
MIXINGDIE PRESSURE GENERATION
Downstream Processing
•Feeder Dynamics
•Feed stock variations
•Bed instability
•Die flow instability: Spurt flow, shark skin surface roughness
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION: Disturbance rejecting characterisics of partly filled extruders
0
50
100
150
200
250
0 20 40 60 80 100 120Time (s)
Pre
ssur
e (p
si)
2 lb/hr7 lb/hr9 lb/hr11 lb/hr
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Introduction contd.
Qin
Qout
Qin
Qout
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Transient model: Extruder Geometry
Kneading block / restrictive element
Starved region Fill length (Lf)
Filled region
Conveying section
FLOW DIRECTION
Control Volume (dotted lines)
H
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Flow into Control Volume, supplied by starved regions
outin QQ
(1)
Apply law of conservation of mass to control volume:
Rate of change of accumulation of material in Control Volume
= -
Flow out of Control Volume driven by pressurization in filled region
=
Macroscopic material balance
Modified White et al approach
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
flstf QQ
dt
dV
• Vf - volume in the filled region
• Qst - flow in the starved regions
• Qfl - flow in the filled region
• Lf - length of the filled region
• – Fill fraction in starved region
flstf QQ
dt
dLWH )1(
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
drag
fst
fflfstf
Q
tLQWH
geometrytLQtLQ
dt
tdL
),(1
rheology,,,rheology,,
L is the total length of the extruder section and L= Lst+Lf
tLfdt
tdLf
f ,)(
For a given geometry and fluid:
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Simulation results: Step response
0.0
0.2
0.4
0.6
0.8
1.0
1.2
8 8.5 9 9.5 10Time (s)
Feed
Output
Pressure
Fill length
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Frequency response
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Sinusoidal disturbance in feedrate
T=0.01s
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.70 8.75 8.80 8.85Time (s)
Flo
wra
te (
cc/s
)
Feed
Output
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Sinusoidal disturbance in feedrate
T=1s
6.06.26.46.66.87.07.27.47.67.88.0
6 8 10 12 14 16Time (s)
Flo
wra
te (
cc/s
)
Feed
Output
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Effect of fill level in extruder
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5
time (s)
Flo
wra
tes
(cc/
s)
Feed10%30%50%80%
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Effect of Depth
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
0 5 10 15 20 25 30 35 40 45
Time (s)
Flo
w r
ate
(cc/
s)
FeedRoot diameter =0.9"0.8"0.7"0.7",80%df
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Step change in screw speed
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
0 0.5 1 1.5 2Time (s)
Fill
leng
th (
cm)
5
5.5
6
6.5
7
7.5
8
8.5
9
Flow
rate
(cc
/s)
Fill length
OutputFlowrate
Screw Speed changed from 300 to 250 rpm at t=0sInput Flowrate constant
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Sinusoidal disturbance in N
6.94E-06
6.96E-06
6.98E-06
7.00E-06
7.02E-06
7.04E-06
7.06E-06
7.08E-06
0 2 4 6 8 10 12Time
Out
put
flow
rate
(cu
bic
met
ers/
s)
T=1s
T=2s
T=4s
T=10s
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Conclusions
• Critical Frequency:– All higher frequencies are damped out and lower
frequencies experience little damping– Function of Screw geometry and operating conditions
• Critical frequency decreases with increasing fill level and vice versa
• Self-leveling response by output rate to changes in screw speed
• Screw speed CAN be used to control output rate with limitations on frequency
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
Bibliography1. Tadmor, Z., Klein, I., Van
Nostrand Reinhold Co., N.Y., 1976.
2. White, F.M.,’Viscous Flow’, McGraw-Hill, 1997.
3. Bird, B.S., Stewart, Lightfoot, ‘Transport Phenomena’, McGraw-Hill, 1986
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
8. White, J.L. and Kim, E.K., SPE ANTEC, 2000.
9. White, J.L. and Kim, E.K., Poly. Eng. & Sci., Vol. 41, n 2, 2001.
10. Rauwendaal, C., ‘Polymer Extrusion’, Hanser, 1994.
11. Booy, M.L., Poly. Eng. & Sci., Vol. 20, 1980.
Bibliography (contd.)
POLYMER PROCESSING
LABORATORY UNIVERSITY OF MARYLAND
INTRODUCTION contd.
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200Time (s)
Pre
ssur
e (p
si)
2-5lb/hr2-7lb/hr2-9lb/hr