polymer processing laboratory university of maryland transient behavior of extruders by rajath...

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

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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

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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

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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(

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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

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LABORATORY UNIVERSITY OF MARYLAND

Frequency response

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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%

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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

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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.)

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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