Heat and Mass Transfer

, Volume 54, Issue 5, pp 1281–1288 | Cite as

3D simulation of polyurethane foam injection and reacting mold flow in a complex geometry

  • İ. Bedii Özdemir
  • Fırat Akar


The aim of the present work is to develop a flow model which can be used to determine the paths of the polyurethane foam in the mold filling process of a refrigerator cabinet so that improvements in the distribution and the size of the venting holes can be achieved without the expensive prototyping and experiments. For this purpose, the multi-component, two-phase chemically reacting flow is described by Navier Stokes and 12 scalar transport equations. The air and the multi-component foam zones are separated by an interface, which moves only with advection since the mass diffusion of species are set zero in the air zone. The inverse density, viscosity and other diffusion coefficients are calculated by a mass fraction weighted average of the corresponding temperature-dependent values of all species. Simulations are performed in a real refrigerator geometry, are able to reveal the problematical zones where air bubbles and voids trapped in the solidified foam are expected to occur. Furthermore, the approach proves itself as a reliable design tool to use in deciding the locations of air vents and sizing the channel dimensions.



This study has been funded by the Turkish Ministry of Industry (SANTEZ 01213.STZ-2012-1). The partial support by Arcelik Inc. is also acknowledged.


  1. 1.
    Klempner D, Sendijarevic V (2004) Handbook of polymeric foams and foam technology, 2nd edn. Hanser Publications, CincinnattiGoogle Scholar
  2. 2.
    Federation of European Rigid Polyurethane Foam Associations. Report No: 1, Thermal insulation materials made of rigid polyurethane foam (PUR/PIR): Properties – Manufacture, October 2006Google Scholar
  3. 3.
    Wu J-W, Sung W-F, Chu H-S (1999) Thermal conductivity of polyurethane foams. Int J Heat Mass Transf 42:2211–2217CrossRefGoogle Scholar
  4. 4.
    Morris DB, Fogg B (1979) Rigid polyurethane foam: refrigerator cabinet design and construction. Int J Refrig 2:105–112CrossRefGoogle Scholar
  5. 5.
    Hammond EC, Evans JA (2014) Application of vacuum insulation panels in the cold chain – analysis of viability. Int J Refrig 47:58–65CrossRefGoogle Scholar
  6. 6.
    Ozdemir IB, Akar F (2017) Effects of composition and temperature of initial mixture on the formation and properties of polyurethane foam. Adv Polym TechnolGoogle Scholar
  7. 7.
    Goods SH, Neuschwanger CL, Henderson C, Skala DM (1997) Mechanical properties and energy absorption characteristics of a polyurethane foam. Technical Paper SAND97–8490Google Scholar
  8. 8.
    Maier U, Wirtz H-G, Fietz J, Frahm A, Rüb T (2005) Polyurethane Processing Systems, Bayer Material Science, (24)19:1–12Google Scholar
  9. 9.
    Ashida K (2007) Polyurethane and related foams – chemistry and technology. Taylor and Francis, AbingdonGoogle Scholar
  10. 10.
    Everitt SL, Harlen OG, Wilson HJ, Read DJ (2003) Bubble dynamics in viscoelastic fluids with application to reacting and non-reacting polymer foams. J Non-Newton Fluid 114:83–107CrossRefzbMATHGoogle Scholar
  11. 11.
    Khazabi M (2015) Investigation of biopolyol spray foam insulation modified with natural fibers. PhD Thesis, Faculty of Forestry, University of TorontoGoogle Scholar
  12. 12.
    Hobbs ML, Erickson KL, Chu TY (2000) Modeling decomposition of unconfined rigid polyurethane foam. Polym Degrad Stab 69:47–66CrossRefGoogle Scholar
  13. 13.
    Schwartz LW, Roy RV (2003) A mathematical model for an expanding foam. J Colloid Interface Sci 264:237–249CrossRefGoogle Scholar
  14. 14.
    Geier S, Winkler C, Piesche M (2009) Numerical simulation of mold filling processes with polyurethane foams. Chem Eng Technol 32:1438–1447CrossRefGoogle Scholar
  15. 15.
    Xu W, Zhang H, Yang Z, Zhang J (2008) Numerical investigation on the flow characteristics and permeability of three-dimensional reticulated foam materials. Chem Eng J 140:562–569CrossRefGoogle Scholar
  16. 16.
    Kim YB, Kim KD, Hong SE, Kim JG, Park MH, Kim JH, Kweon JK (2005) Numerical simulation of PU foaming flow in a refrigerator cabinet. J Cell Plast 41:252–266CrossRefGoogle Scholar
  17. 17.
    Gopala VR, van Wachem BGM (2008) Volume of fluid methods for immiscible-fluid and free-surface flows. Chem Eng J 141:204–221CrossRefGoogle Scholar
  18. 18.
    Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114:146–159CrossRefzbMATHGoogle Scholar
  19. 19.
    Osher S, Fedkiw RP (2001) Level set methods: an overview and some recent results. J Comput Phys 169:463–502MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible multi-fluid flows. J Comput Phys 100:25–37CrossRefzbMATHGoogle Scholar
  21. 21.
    Prosperetti A, Tryggvason G (2007) Computational methods for multiphase flow. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  22. 22.
    Seo D, Youn JR, Tucker CL (2003) Numerical simulation of mold filling in foam reaction injection molding. Int J Numer Methods Fluids 42:1105–1134CrossRefzbMATHGoogle Scholar
  23. 23.
    Mitani T, Hamada H (2003) Prediction of flow patterns in the polyurethane foaming process by numerical simulation considering foam expansion. Polym Eng Sci 43:1603–1612CrossRefGoogle Scholar
  24. 24.
    Seo D, Youn JR (2005) Numerical analysis on reaction injection molding of polyurethane foam by using a finite volume method. Polymer 46:6482–6493CrossRefGoogle Scholar
  25. 25.
    Dodd AB, Lautenberger C, Fernandez-Pello AC (2009) Numerical examination of two-dimensional smolder structure in polyurethane foam. P Combust Inst 32:2497–2504CrossRefGoogle Scholar
  26. 26.
    Bikard J, Bruchon J, Coupez T, Silva L (2007) Numerical simulation of 3D polyurethane expansion during manufacturing process. Colloid Surface A 309:49–63CrossRefGoogle Scholar
  27. 27.
    Kee RJ, Coltrin ME, Glarborg P (2005) Chemically reacting flow: theory and practice. John Wiley and Sons, HobokenGoogle Scholar
  28. 28.
    Warnatz J (2002) HOMREA user guide, Steinbeis-Transferzentrum, Simulation Reaktiver Strömungen, HeidelbergGoogle Scholar
  29. 29.
    Maier RS, Petzold LR, Rath W (1995) Parallel solution of large differential-algebraic systems. Concurrency: Practice and Experience 7:795–822CrossRefGoogle Scholar
  30. 30.
    Ferziger JH, Peric M (2002) Computational methods for fluid dynamics. Springer, BerlinCrossRefzbMATHGoogle Scholar
  31. 31.
    ANSYS FLUENT, Release 6.3, Analysis guide, ANSYS, Inc.Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Professor and Head, Fluids Group, Faculty of Mechanical EngineeringIstanbul Technical UniversityIstanbulTurkey
  2. 2.PhD student, Fluids Group, Faculty of Mechanical EngineeringIstanbul Technical UniversityIstanbulTurkey

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