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Developing A CFD Solver for Simulation ofPolyurethane Foams
Mohsen Karimi,Daniele Marchisio
November 21, 2018
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 1 / 20
Outline
● Challenges:
◇ Simulate polyurethane foam expansion,◇ Link it to lower-scale modeling tools.
● Solutions & Implementations:
◇ Computational Fluid Dynamics (CFD) enhanced by Population BalanceEquation (PBE),
◇ Link lower scale models to the CFD code (apply MoDeNa).
● Results:
◇ Validations using literature data,◇ Mixing cup experiment.
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 2 / 20
Challenges
What do we simulate?
● Foaming/expansion: Mixing of polyols and isocyanates with water andadditives a onsets a number of chemical reactions and physical phenomenaleading to polymerization, gas formation and eventually foam expansion.
● Solver should communicate with other modeling tools to send/receive data.
awater, physical blowing agents, catalysts and surfactants
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 3 / 20
Challenges
What are the industrial concerns?
● Bubble size distribution (BSD),
● Polymerization progress,
● Foam expansion (mobile interface),
● Evolution of material properties.
What are the academic concerns?
● The foam is a multiphase system constituted by a continuous liquid phase(undergoing polymerization) and a disperse gas phase (gas bubbles or cells).
● The bubbles can growth and coalesce during the expansion.
● The foam rheology is very complex.
● The kinetics of chemical reactions is very complex.
● Connecting nano-, meso-, and macro scale tools is very complex.
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 4 / 20
Challenges
Previous Models
Kinetics-based
● Polymerization progress Ð→ conversion of hydroxyl group and water,
● Temperature rise Ð→ energy equation,
● Foam density Ð→ based on kinetics,
● Expansion due to blowing agents Ð→ empirical expressions for maximumsolubility,
● Foam interface and BSD Ð→ not included!
CFD-based
● Kinetics based models Ð→ additional partial differential equations,
● Interface capturing Ð→ volume of fluid (VOF),
● Foam rheology Ð→ Newtonian or non-Newtonian,
● Evolution of BSD Ð→ not included!
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 5 / 20
Challenges
How to tackle the problem?Polyurethane foam → pseudo-fluid
● Bubble/cell sizedistribution (BSD):
◇ Population BalanceEquation (PBE)
● Interface tracking:
◇ Volume-of-Fluid(VOF)
● Material properties:
◇ density of reactingmixture,
◇ foam rheology,◇ foam conductivity.
● Polymerization kinetics:
◇ Kinetic model◇ MoDeNa framework
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 6 / 20
Solution Methods & Implementations
Solution Methods & Implementations
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 7 / 20
Solution Methods & Implementations
MoDeNa-independent (Standalone or PUFoam )
● Macro-scale model: CFD coupled with PBE (VOF & QMOM),
● Apply simple models:◇ bubble growth rate → diffusion controlled model,◇ polymerization kinetics → activation energy, pre-exponential factor,◇ density of reacting mixture → constant,◇ foam rheology → constant, Newtonian, and non-Newtonian,◇ foam conductivity → empirical equation.
MoDeNa Solver (MODENAFoam)
● Macro-scale model: CFD coupled with PBE (VOF & QMOM),
● Apply MoDeNa to connect to different models for:◇ bubble growth rate → University of Chemistry and Technology Prague◇ polymerization kinetics → BASF◇ density of reacting mixture → University of Trieste◇ foam rheology → Eindhoven University of Technology◇ foam conductivity → University of Chemistry and Technology Prague
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 8 / 20
Solution Methods & Implementations
MoDeNa solver (MODENAFoam)
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 9 / 20
Solution Methods & Implementations
Implementation
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 10 / 20
Results
Results
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 11 / 20
Results
Validation
● Mixing cup experiments
● 12 different experiments with changing recipe:
◇ Initial concentrations of isocyanate and polyol◇ Initial concentration of water◇ Initial concentration of blowing agent◇ Kinetics details
● Measurements:
◇ Rising height of the foam◇ Temperature
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 12 / 20
Results
Foam expansion: (A) physically-blown & (B) chemically-blown
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 13 / 20
Results
Macro-scale: stand-alone (PUFoam)
Model predictions (line) against experimental data (symbols)
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 14 / 20
Results
Macro-scale: stand-alone (PUFoam)
Model predictions (line) against experimental data (symbols)
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 15 / 20
Results
MoDeNa-Independent (PUFoam) vs. MoDeNa solver (MODENAFoam)
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 16 / 20
Results
MoDeNa-Independent (PUFoam) vs. MoDeNa solver (MODENAFoam)
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 17 / 20
Concluding Remarks
Conclusions
● PUFoam and MODENAFoam solvers for simulation of PU foams,
● Coupling CFD with PBE,
● The following features of PU foams have been included:
◇ Evolution of bubble size distribution,◇ Kinetics of reactions,◇ Fate of different blowing agents,◇ Material properties such as thermal conductivity.
● Using MoDeNa framework, the macro-scale code is coupled with lowerscale modeling tools,
● Validations for different PU recipes.
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 18 / 20
Thank You!
Acknowledgements
MOdelling of morphology DEvelopment of micro- and NAnostructures(MoDeNa)
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 19 / 20
Thank you
M. Karimi, D. Marchisio OFGBG 18 November 21, 2018 20 / 20
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