Multiscale Modeling of Expanding Polyurethane Foams via Computational Fluid Dynamics and Population Balance Equation

Summary This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics during mold filling. The model is formulated upon coupling of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) to...

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Published in:	Macromolecular symposia. Vol. 360; no. 1; pp. 108 - 122
Main Authors:	Karimi, Mohsen, Droghetti, Hermes, Marchisio, Daniele L.
Format:	Journal Article
Language:	English
Published:	Weinheim Blackwell Publishing Ltd 01.02.2016 Wiley Subscription Services, Inc
Subjects:	Bubbles Computational fluid dynamics computer modeling Computer simulation Fluid dynamics Mathematical analysis Mathematical models Modelling Plastic foam Polyurethane foam polyurethanes population balance equation quadrature method of moments Simulation
ISSN:	1022-1360, 1521-3900
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Abstract	Summary This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics during mold filling. The model is formulated upon coupling of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) to predict and simulate the evolution of foam features including apparent density and viscosity, bubble (or cell) size distribution (BSD) during the polymerization, as well as its kinetics. The solution of PBE inside the CFD code is performed with Quadrature Method of Moments (QMOM). The foam, constituted by a liquid polymer and gas bubbles, is simulated as a pseudo‐single‐phase system, while the interface between the foam and the surrounding air is tracked by a Volume‐of‐Fluid (VOF) solver within the open‐source CFD code OpenFOAM. The modeling is applied for a simple foaming experiment and attention is paid to the effect of the rheological model on the predictions.
AbstractList	Summary This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics during mold filling. The model is formulated upon coupling of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) to predict and simulate the evolution of foam features including apparent density and viscosity, bubble (or cell) size distribution (BSD) during the polymerization, as well as its kinetics. The solution of PBE inside the CFD code is performed with Quadrature Method of Moments (QMOM). The foam, constituted by a liquid polymer and gas bubbles, is simulated as a pseudo-single-phase system, while the interface between the foam and the surrounding air is tracked by a Volume-of-Fluid (VOF) solver within the open-source CFD code OpenFOAM. The modeling is applied for a simple foaming experiment and attention is paid to the effect of the rheological model on the predictions. Summary This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics during mold filling. The model is formulated upon coupling of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) to predict and simulate the evolution of foam features including apparent density and viscosity, bubble (or cell) size distribution (BSD) during the polymerization, as well as its kinetics. The solution of PBE inside the CFD code is performed with Quadrature Method of Moments (QMOM). The foam, constituted by a liquid polymer and gas bubbles, is simulated as a pseudo‐single‐phase system, while the interface between the foam and the surrounding air is tracked by a Volume‐of‐Fluid (VOF) solver within the open‐source CFD code OpenFOAM. The modeling is applied for a simple foaming experiment and attention is paid to the effect of the rheological model on the predictions. This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics during mold filling. The model is formulated upon coupling of Computational Fluid Dynamics (CFD) and Population Balance Equation (PBE) to predict and simulate the evolution of foam features including apparent density and viscosity, bubble (or cell) size distribution (BSD) during the polymerization, as well as its kinetics. The solution of PBE inside the CFD code is performed with Quadrature Method of Moments (QMOM). The foam, constituted by a liquid polymer and gas bubbles, is simulated as a pseudo-single-phase system, while the interface between the foam and the surrounding air is tracked by a Volume-of-Fluid (VOF) solver within the open-source CFD code OpenFOAM. The modeling is applied for a simple foaming experiment and attention is paid to the effect of the rheological model on the predictions.
Author	Droghetti, Hermes Marchisio, Daniele L. Karimi, Mohsen
Author_xml	– sequence: 1 givenname: Mohsen surname: Karimi fullname: Karimi, Mohsen email: mohsen.karimi@polito.it organization: Department of Applied Science and Technology, Institute of Chemical Engineering, Politecnico di Torino, C.so Duca degli Abrizzi 24, 10129, Torino, Italy – sequence: 2 givenname: Hermes surname: Droghetti fullname: Droghetti, Hermes email: hermes.droghetti@studenti.polito.it organization: Department of Applied Science and Technology, Institute of Chemical Engineering, Politecnico di Torino, C.so Duca degli Abrizzi 24, 10129, Torino, Italy – sequence: 3 givenname: Daniele L. surname: Marchisio fullname: Marchisio, Daniele L. email: daniele.marchisio@polito.it organization: Department of Applied Science and Technology, Institute of Chemical Engineering, Politecnico di Torino, C.so Duca degli Abrizzi 24, 10129, Torino, Italy
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Cites_doi	10.1002/ceat.200900202 10.1002/mats.201500014 10.1002/pen.760340804 10.1002/pen.760340805 10.1002/pen.11405 10.1002/fld.582 10.1016/S0009-2509(03)00211-2 10.1016/0009-2509(68)87018-6 10.1017/CBO9781139016599 10.1016/j.polymer.2005.03.126 10.1002/aic.690280213 10.1016/j.ces.2011.04.042 10.1063/1.1664624 10.1016/j.jaerosci.2004.07.009
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References_xml	– reference: G. Oretel, Polyurethane Handbook, Hanser, New York 1993. – reference: D. L. Marchisio, R. O. Fox, Computational Models for Polydisperse Particulate and Multiphase Systems, Cambridge University Press, Cambridge 2013. – reference: V. K. Gupta, D. V. Khakhar, Polym. Eng. Sci. 1999, 39, 164. – reference: S. A. Baser, D. V. Khakhar, Polym. Eng. Sci. 1994, 34, 632. – reference: D. L. Marchisio, R. D. Vigil, R. O. Fox, Chem. Eng. Sci. 2003, 58, 3337. – reference: M. Karimi, D. L. Marchisio, Macromol. Theory. Simul. 2015, 24, 291. – reference: R. B. Bird, P. J. Carreau, Chem. Eng. Sci. 1968, 23, 427. – reference: D. Klempner, K. C. Frisch, Handbook of Polymeric Foams and Foam Technology, Oxford University Press, New York 1991. – reference: S. Geier, C. A. Winkler, M. Piesche, Chem. Eng. Technol. 2009, 32, 1438. – reference: D. Seo, J. R. Youn, C. L. Tucker III, Int. J. Numer. Methods Fluids 2003, 42, 1105. – reference: G. Woods, The ICI Polyurethane Handbook, Wiley, New York 1990. – reference: S. A. Baser, D. V. Khakhar, Polym. Eng. Sci. 1994, 34, 642. – reference: D. Seo, J. R. Youn, Polymer 2005, 46, 6482. – reference: A. Buffo, M. Vanni, D. L. Marchisio, Chem. Eng. Sci. 2012, 70, 31. – reference: D. L. Marchisio, R. O. Fox, J. Aerosol Sci. 2005, 36, 43. – reference: R. G. Gordon, J. Math. Phys. 1968, 9, 655. – reference: J. M. Castro, C. W. Macosko, AIChE J. 1982, 28, 250. – volume: 39 start-page: 164 year: 1999 publication-title: Polym. Eng. Sci – year: 2009 – volume: 34 start-page: 642 year: 1994 publication-title: Polym. Eng. Sci – volume: 70 start-page: 31 year: 2012 publication-title: Chem. Eng. Sci – volume: 9 start-page: 655 year: 1968 publication-title: J. Math. Phys – volume: 46 start-page: 6482 year: 2005 publication-title: Polymer – year: 2002 – volume: 24 start-page: 291 year: 2015 publication-title: Macromol. Theory. Simul – volume: 34 start-page: 632 year: 1994 publication-title: Polym. Eng. Sci – volume: 58 start-page: 3337 year: 2003 publication-title: Chem. Eng. Sci – volume: 32 start-page: 1438 year: 2009 publication-title: Chem. Eng. Technol – volume: 42 start-page: 1105 year: 2003 publication-title: Int. J. Numer. Methods Fluids – volume: 23 start-page: 427 year: 1968 publication-title: Chem. Eng. Sci – year: 1991 – year: 1990 – year: 1993 – year: 2015 – volume: 36 start-page: 43 year: 2005 publication-title: J. Aerosol Sci – volume: 28 start-page: 250 year: 1982 publication-title: AIChE J – year: 2010 – year: 2013 – ident: e_1_2_7_10_1 – ident: e_1_2_7_20_1 – ident: e_1_2_7_11_1 doi: 10.1002/ceat.200900202 – ident: e_1_2_7_21_1 – ident: e_1_2_7_18_1 doi: 10.1002/mats.201500014 – volume-title: Handbook of Polymeric Foams and Foam Technology year: 1991 ident: e_1_2_7_3_1 – volume-title: Polyurethane Handbook year: 1993 ident: e_1_2_7_2_1 – ident: e_1_2_7_4_1 doi: 10.1002/pen.760340804 – ident: e_1_2_7_5_1 doi: 10.1002/pen.760340805 – ident: e_1_2_7_6_1 doi: 10.1002/pen.11405 – ident: e_1_2_7_7_1 doi: 10.1002/fld.582 – ident: e_1_2_7_13_1 doi: 10.1016/S0009-2509(03)00211-2 – ident: e_1_2_7_19_1 doi: 10.1016/0009-2509(68)87018-6 – ident: e_1_2_7_15_1 doi: 10.1017/CBO9781139016599 – volume-title: The ICI Polyurethane Handbook year: 1990 ident: e_1_2_7_1_1 – ident: e_1_2_7_8_1 doi: 10.1016/j.polymer.2005.03.126 – ident: e_1_2_7_9_1 doi: 10.1002/aic.690280213 – ident: e_1_2_7_12_1 – ident: e_1_2_7_14_1 doi: 10.1016/j.ces.2011.04.042 – ident: e_1_2_7_17_1 doi: 10.1063/1.1664624 – ident: e_1_2_7_16_1 doi: 10.1016/j.jaerosci.2004.07.009
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Snippet	Summary This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal... Summary This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal... This study is aimed to formulate a numerical modeling recipe for polyurethane foams. The model is capable of simulating the foam principal characteristics...
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SubjectTerms	Bubbles Computational fluid dynamics computer modeling Computer simulation Fluid dynamics Mathematical analysis Mathematical models Modelling Plastic foam Polyurethane foam polyurethanes population balance equation quadrature method of moments Simulation
Title	Multiscale Modeling of Expanding Polyurethane Foams via Computational Fluid Dynamics and Population Balance Equation
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