final stcephaniegeierslidesofw7

Stephanie Geier and Manfred Piesche

Institute of Mechanical Process Engineering

University of Stuttgart

Numerical simulation of polyurethane

foaming processes on bubble scale

7th OpenFOAM Workshop

Darmstadt, 25-28 June 2012

7th OpenFOAM Workshop, Darmstadt

26.06.2012 Stephanie Geier

2

Outline

Motivation

Foaming process

Modeling approach

Phase change modeling

Bubble-bubble interaction

Examples

Conclusion and outlook



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Motivation

Polyurethane foaming process

Mixing of polyol and isocyanate

Foaming and mold filling due to reaction progress

Local foam structure?

Foam properties, e.g. thermal conductivity and impact strength

depend on local foam structure



Foaming process

Gelling reaction

Increasing viscosity (urethane links)

Blowing reaction

Increasing viscosity (urea links)

Density reduction - chemical blowing of the foam (CO2)

Evaporation of physical blowing agent

Density reduction physical blowing of the foam (e.g. pentanes)

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5

Modeling approach

Assumptions and simplifications

Foam is a two-phase system

Gas bubbles

Liquid reacting polymer phase

Isothermal

Gas and liquid phase are incompressible

Constant viscosities

Numerical approach

Volume-of-fluid (VOF)

based on solver interPhaseChangeFoam



Modeling approach-

Governing equations

Continuity equation

= 1

1

(1)

Momentum balance

+ = + + + + (2)

Volume fraction balance

+ + 1 =

(3)

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source terms describing phase change

additional body forces



Modeling approach Phase change

Phenomenological approach

Density evolution known from mold filling simulations or

experiments

Volumetric gas creation rate accounting for phase change

=

(4)

7

t

foam

t1 t1+t

- total volume of liquid in phase interface cells



Modeling approach Bubble-bubble interaction

Repulsive forces between neighboring bubbles expressed through

disjoining pressure [1]

= < 0

(5)

Conversion to body force

= (6)

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[1] C. Krner et al.: Lattice Boltzmann Model for Free Surface Flow for Modeling Foaming. J. Stat. Phys., 121 (2005), 179196.



Modeling approach Determination of disjoining pressure

Volume fraction field

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[1] marker [1]

Bubble marker field [N/m]

Phase interface region (blue) and

region of disjoining pressure (red)

Disjoining pressure field in phase

interface region



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Examples Rising bubble

t = 0 s t = 2,5 s t = 5 s t = 6,25 s

t = 6,75 s t = 7 s t = 7,25 s t = 10 s

Effect of disjoining pressure implementation

No disjoining pressure



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Examples Rising bubble

t = 6,75 s t = 7 s t = 7,25 s

Effect of disjoining pressure implementation

Disjoining pressure included

t = 10 s

t = 0 s t = 2,5 s t = 5 s t = 6,25 s



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Examples Bubbles in confined geometry

Boundary and initial conditions:

Solid walls: base and sides

repulsive forces

53 bubbles randomly distributed

Initial bubble diameter: 16 m

fo

am

[kg/m

]

t [s]

Foam density (from experiments)

200

400

600

800

1000

1200

0 2,5 5 7,5 1012,51517,5

= 2 /

= 1100 /

, = 1095 /




Bubbles growing in a confined geometry

t = 0 s t = 2 s t = 4 s t = 6 s t = 8 s

t = 10 s t = 12 s t = 14,25 s

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200

400

600

800

1000

1200

0 2,5 5 7,5 10 12,5 15 17,5

fo

am

[kg/m

]

t [s]

experiment

simulation



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Deforming and rearranging bubbles

t = 9 s t = 9,5 s t = 10 s

t = 12 s t = 12,75 s t = 13,5 s t = 14,25 s



Conclusion and outlook

Model for polyurethane foaming processes on bubble scale

Phenomenological phase change model

Bubble-bubble interaction

Work in progress:

Foams with lower density

Extension to

time-varying polymer viscosity

appropriate boundary conditions accounting for varying flow conditions during foaming process

15

u

u

Stephanie Geier and Manfred Piesche

Institute of Mechanical Process Engineering

University of Stuttgart

Numerical simulation of polyurethane

foaming processes on bubble scale

7th OpenFOAM Workshop

Darmstadt, 25-28 June 2012

Thank you very much for your attention.

final stcephaniegeierslidesofw7

Documents

bubble t

openfoam workshop darmstadt

th openfoam workshop

modeling foaming

liquid phase

modeling approach assumptions

bubble scale

phase interface cells