sandra allart bruin modeling of glass press blow process (1)

8/13/2019 Sandra Allart Bruin Modeling of Glass Press Blow Process (1)

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Modelling of the glasspress-blow processECMI 2004

Sandra Allaart-Bruin, G.A.A.V. Haagh, D. Hegen,

B.J. van der Linden and R.M.M. Mattheij

[email protected]

ECMI 2004 – p.1




Overview

• Press-blow process

• Modelling approach

ECMI 2004 – p.2




Overview



• Level set method

ECMI 2004 – p.2




Overview




• Re-initialisation of thelevel set function

ECMI 2004 – p.2




Overview




• Re-initialisation of thelevel set function

• Results

ECMI 2004 – p.2




Press-blow process

ECMI 2004 – p.3




Press-blow process

Gob falls in blank mould

ECMI 2004 – p.3




Press-blow process

Plunger presses

ECMI 2004 – p.3




Press-blow process

Parison is finished

ECMI 2004 – p.3




Press-blow process

Parison transferred into the blow mould

ECMI 2004 – p.3




Press-blow process

Jar is finished

ECMI 2004 – p.3




Industrial Objectives

• Minimise unwanted variations in wallthickness distribution

ECMI 2004 – p.4






• Maintain strength (stress distribution)

ECMI 2004 – p.4







• Reduce weight

ECMI 2004 – p.4







• Reduce weight

• Optimise cooling conditions

ECMI 2004 – p.4







• Reduce weight

• Optimise cooling conditions

• Increase production speed

ECMI 2004 – p.4




Three dimensional model

Temperature

distributionof the gob

ECMI 2004 – p.5




Three dimensional model

Temperature distribution

of a bottle

ECMI 2004 – p.5




Modelling approach (1)

• Domain Ω is the wholeinterior of the mould. Ω

ECMI 2004 – p.6





• Domain Ω is the wholeinterior of the mould.

• Every point x ∈ Ω is eitherin glass or air.

Air

Glass

ECMI 2004 – p.6





Solve coupled set of equa-

tions with Finite ElementMethod

• Stokes equation

(flow)• Energy equation

(temperature)

ECMI 2004 – p.7





Solve coupled set of equa-

tions with Finite ElementMethod

• Stokes equation

(flow)• Energy equation

(temperature)

• Level set equation(interface)

Interface 1

Interface 2

ECMI 2004 – p.7





Initial conditions

ECMI 2004 – p.8





Initial conditions

• Parison shape

ECMI 2004 – p.8





Initial conditions

• Parison shape

• Parison temperature

ECMI 2004 – p.8





Initial conditions

• Parison shape


Boundary conditions

ECMI 2004 – p.8





Initial conditions

• Parison shape


Boundary conditions

• pressure

ECMI 2004 – p.8





Initial conditions

• Parison shape


Boundary conditions

• pressure

• Thermal boundary conditions

ECMI 2004 – p.8





Initial conditions

• Parison shape


Boundary conditions

• pressure

• Thermal boundary conditions

• No-slip/slip boundary conditions

ECMI 2004 – p.8




Level set method

Level set function:

φ(x(t), t)The interface is given by:

φ(x(t), t) = 0

ECMI 2004 – p.9




Level set method

Level set function:

φ(x

(t), t)The interface is given by:

φ(x(t), t) = 0

By the chain-rule:

φt + u · ∇φ = 0

ECMI 2004 – p.9




Level set method

Level set function:

φ(x

(t), t)The interface is given by:

φ(x(t), t) = 0

By the chain-rule:

φt + u · ∇φ = 0

velocity from Stokes problem

ECMI 2004 – p.9



R i iti li ti (1)




Re-initialisation (1)

Initially Level Set function is a “distance function”:

φ(x, 0) =

d(x), if x in air,−d(x), if x in glass,

where d(x) is the normal distance to the interface.

air glass

φ(tn)

ECMI 2004 – p.10

R i iti li ti (1)






φ(x, 0) =



air glass

φ(tn)

n+1~φ(t )

air glass

φ(tn)

ECMI 2004 – p.10

R i iti li ti (1)






φ(x, 0) =



air glass

φ(tn)

n+1~φ(t )

air glass

φ(tn)

n+1)(tφ

n+1~φ(t )

ECMI 2004 – p.10

R i iti li ti (2)





Boundary value problem

∇d(x

)2 = 1d(x) = 0 on Γ(0).

Fast Marching Method!

ECMI 2004 – p.11

Fast Marching Method (1)





Γ

Grid and interface Γ.

ECMI 2004 – p.12






Γ

Known

Initialise algorithm by computing d at gridpoints

close to Γ.ECMI 2004 – p.12






Γ

KnownTrial

Compute trial value of points with known

neighbours.ECMI 2004 – p.12






Γ

KnownTrial

D A

BC

All trial points have one or two known







Γ

KnownTrial

D A

BC

Freeze value at C .

ECMI 2004 – p.12






Γ

KnownTrial

D A

BC

Update Trial values of neighbouring points of C .

ECMI 2004 – p.12






One known neighbour:

(dD − dA)2

= h2

D A

BC

ECMI 2004 – p.13






One known neighbour:

(dD − dA)2

= h2

Two known neighbours:

(dC − dA)2 + (dC − dB)2 = h2

D A

BC

ECMI 2004 – p.13






How to do this on an unstructured triangular grid?

ECMI 2004 – p.14







• Consider Triangle ABC

C

B

A

ECMI 2004 – p.14







• Consider Triangle ABC • A and B are known points

C

B

A

ECMI 2004 – p.14







• Consider Triangle ABC • A and B are known points

• Compute a plane with

z = ux + vy + w,

such that u2 + v2 = 1.

(x ,y ,d )A A A

(x ,y ,d )B B B

(x ,y ,??)C C

C

B

A

ECMI 2004 – p.14






Γ

Grid and interface Γ.

ECMI 2004 – p.15






Γ

Initialise algorithm by computing d at gridpoints

close to Γ.ECMI 2004 – p.15




ast a c g et od ( )

Γ

Trial points can have more than two known






g ( )

Γ

Compute d considering this element ...

ECMI 2004 – p.15





g ( )

Γ

and take the minimum with the computed value

at this element.ECMI 2004 – p.15

Results: sagging




gg g

Before actual blowing, parisonhangs in the mould.

• Gravitational force• No energy equation

• Constant viscosity

ECMI 2004 – p.16

Results: sagging




gg g




ECMI 2004 – p.16



Results: sagging




gg g




ECMI 2004 – p.16

Results: sagging







ECMI 2004 – p.16

Results: sagging







ECMI 2004 – p.16

Results: temperature grad.




• Temperature gradient

·

20 degrees• VFT relation for viscosity

• Pressure prescribed scalex: 15.000

scaley: 15.000

time t: 0.000

LEVELS

0.000E+00

Contour levels of glass

ECMI 2004 – p.17

Future Work

http://quartergrad.avi/










• Thermal effects along interface

ECMI 2004 – p.18

Future Work





· realistic boundary condition

ECMI 2004 – p.18

Future Work






· not physically finding the interface

ECMI 2004 – p.18

Future Work






· not physically finding the interface· radiation

ECMI 2004 – p.18

Future Work







• 3D model

ECMI 2004 – p.18



Future Work







• 3D model· generalise to 3D

· FMM unstructured 3D

ECMI 2004 – p.18




Questions?

ECMI 2004 – p.19

sandra allart bruin modeling of glass press blow process (1)

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