influence of thermal material properties on the heating...

Upper Austria University of Applied Sciences Research and Development Ltd.

Influence of Thermal Material Properties on the

Heating Step of Pipe Belling

Simulation of the heating phase in the manufacturing of belled pipe ends of thermoplastic sewer pipes

J. F. Pühringer, G. Zitzenbacher

Upper Austria University of Applied Sciences Research and Development Ltd. page 2

Content

Introduction

Physical and Mathematical Model

Parameter Study-Motivation-Procedure-Variation of material-Variation of material parameters

Summary


Introduction: What is Pipe Belling?

sewer pipes

corrugated pipes

Pipe Belling is the formation of bells or sockets at sewer pipes or corrugated pipes for drainage or pipe fittings.


Introduction:Process steps of Pipe Belling

Heating of the pipe end to processing temperature

Rubber elastic state of material

Formation of the pipe bell or socket

Cooling

Demoulding


Introduction:Heating Process

relevant wavelength interval: 1 to 8 µm

radiation heating

The heating of the pipe end to forming temperature is done by:

of the pipe belling and the socket formation

radiator

HT

convection cooling

contact heating


Introduction: The Equipment

mandrel

source: homepage HMS Schnallinger, Austriahttp://www.hms-schnallinger.com/

source: SICA S.p.A, Italyhttp://www.sica-italy.com/

Vihan Eng. Pvt. Ltd., Indiahttp://www.vihanindia.com/


Physical & mathematical Model:coordinate system

radiator

contact heating

HT

( ) ( )[ ]Errrr

TtrTr

trTi

i

−⋅=∂

∂−

==

,, ακ

convectionfor cooling

radius r

outer radius ro

inner radius ri

radiator radius rrad.

.radT

pipe end


Physical & mathematical model:transient heat transfer equation

( ) ( ) ( ) ( ) ( ) ( )trQr

trTrTrrt

trTTcT p ,,1,+⎟

⎠⎞

⎜⎝⎛

∂∂⋅⋅

∂∂

⋅=∂

∂⋅⋅ κρ

( ) ( ) ( )[ ] ( ) ( ) ⎟⎟⎠⎞

⎜⎜⎝

⎛ −⋅⋅−⋅⋅⋅= ∫

∞

λλλλλ

prr

pR

rrqdtrQ irad exp11,

0

.0

material properties:reflection

penetration depth ( )λp( )λR


Physical & mathematical model:absorption of radiation

-3

-2

-1

0

0 0,5 1relative intensity

1

2

3

p

1/e = 36.79 %

x

( )λ0q( ) Rq ⋅λ0

( ) ( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅−⋅=

pxRqxq exp1, 0 λλ

Bouguer Beer Lambert‘s law

( ) ( ) ( )( ) ( ) ⎟⎟⎠⎞

⎜⎜⎝

⎛ −−⋅−⋅⋅=

λλλλ

prrR

rrqrq irad exp1, .

0 0.5


Physical & mathematical model:Boundary conditions

( ) ( )rTtrT 00, ==

( ) ( ) ( ) ( ) ( )[ ]tTtrTr

trTTtrq Errrri ii−⋅=

∂∂⋅−= == |,|,, ακ

Initial conditions

( ) ( )tTtrT surfaceo =,

Contact heating or given surface temperature

Convective heat transfer


.radT = 300, 400, 500, 600, 800, 1000, 1200, 1400°C

= 5 and 30 KmW²

( )λR( )λp

α

transient heat transfer equation including the heat source term + boundary conditions

partial differential equation

set of algebraic equations

discretization temperature distribution

( )trT ,

solution

material parameters

radiator temperature

heat transfer coefficient

Physical & mathematical model:Implementation

( )Tρ ( )Tκ( )Tcp


Parameter StudyMotivation

Reasons for accomplishing a parameter study

the material parameters

the variations of the material properties

on the process

the measurement errors of the material properties

Study the influence of …


Parameter StudyProcedure - Reflection

0

2

4

6

8

1 2 3 4 5 6 7 8wavelength in µm

refle

ctio

n in

% 0

2

4

6

8

0 5 10 15

materials:PP homopolymerPP extrusion grade


0,01

0,1

1

1 3 5 7 9 11 13wavelength in µm

pene

trat

ion

dept

h in

mm

polypropylene homopolymer polypropylene (extrusion type)

Parameter StudyProcedure - Penetration Depth

0.01

0.1


0

20

40

60

80

100

120

140

160

180

200

73 74 75 76 77 78 79 80radius in mm

tem

pera

ture

in °C

T(radiator) = 400°C, ε(radiator) = 0.95, r(radiator) = 50 mm, α = 5 W/(m²K)

0 s5 s

20 s

50 s

100 s

250 s steady state solution

0 s5 s

Parameter Study:Procedure – Temperature Curves

outer surface

inner surface


Parameter Study:Procedure - Evaluation

James L. Throne: Technology of THERMOFORMING, Hanser / Gardner Publ., 1997, p. 69


Parameter Study:Procedure - Results


Parameter Study:Procedure - Results

680°C

580°C


0,01

0,1

1

1 3 5 7 9 11 13wavelength in µm

pene

trat

ion

dept

h in

mm

polypropylene homopolymer polypropylene (extrusion type)

670°C550°CPP extrusion grade

680°C580°CPP homopolymer

α = 30 W/(m²K)α = 5 W/(m²K)material

nearly pure homopolymer(no filler)

polymer with high filler content (44 wt %)

Parameter Study:Variation of Material

0.1

0.01


75

100

125

150

175

200

225

250

0 0,05 0,1 0,15 0,2 0,25 0,3heat conduction in W/(m K)

time

in s

95

100

105

110

115

120

125

130

delta

T(m

in) i

n °C

3

2

1

4

Parameter Study:Variation of Material Properties



0

10

20

30

40

0 0,05 0,1 0,15 0,2 0,25 0,3heat conduction in W/(m K)

time

in s

0

2

4

6

8

10

12

14

16

18

delta

T(m

in) i

n °C

1

2

3

4

3

4



0

50

100

150

200

250

0,1 1 10multiplicator of the determined penetration depth

t(min

) or

t(max

) in

s

T(Str.) / alphat(min)400°C / 5 W/(m²K)400°C / 30 W/(m²K)1000°C / 5 W/(m²K)1000°C / 30 W/(m²K)t(max)400°C / 5 W/(m²K)1000°C / 5 W/(m²K)1000°C / 30 W/(m²K)

1

1

2

4

34

3



0

25

50

75

100

125

0,1 1 10

ΔT(

min

) in

K

-50

0

50

100

150

200

t[ ΔT(

min

)] in

s

T(Str.) / alphadelta T(min)400°C / 5 W/(m²K)400°C / 30 W/(m²K)1000°C / 5 W/(m²K)1000°C / 30 W/(m²K)t[delta T(min)]

400°C / 5 W/(m²K)1000°C / 5 W/(m²K)1000°C / 30 W/(m²K)

1

1

2

4

3

4

3

multiplicator of the determined penetration depth


( ) ( ) ( ) ( ) ( ) ( )trQr

trTrTrrt

trTTcT p ,,1,+⎟

⎠⎞

⎜⎝⎛

∂∂⋅⋅

∂∂

⋅=∂

∂⋅⋅ κρ

Summary Parameter Study with the SIMULATION TOOL

• Material

-10 K-30 KPP extrusion grade

680°C580°CPP homopolymer

α = 30 W/(m²K)α = 5 W/(m²K)material

• optical penetration depth p(λ): minimum for times / maximum for temperature

pcC ⋅= ρ

nearly linear dependence on time quantities and temperature difference with different slopes

• density ρ

• specific heat capacity cp

• heat conductivity κ

variation by +/- 20%

• reflection R(λ): slight positive slope for times / slight negative slope for temperature

}


Acknowledgements

Financial support for this work was provided by the Local Govern-ment of Upper Austria with the frame-work of the funding program “Kunststoffstandort Oberösterreich”.

We also thank and acknowledge the contribution of our colleagues and of the Austrian Solar Innovation Centre in Wels for providing equipment and assistance for the measurements.


Thank you for your attention!

influence of thermal material properties on the heating...

Documents