Skip to main content
Log in

Implementation of surface tension force in fluid flow during reactive rotational molding

  • Original Research
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

During Reactive Rotational Molding (RRM), it is very important to predict the fluid flow in order to obtain the piece with homogeneous shape and high quality. This prediction may be possible by simulation the fluid flow during rotational molding. In this study we have used a mixture of isocyanate and polyol as reactive system. The kinetic rheological behaviors of thermoset polyurethane are investigated in anisothermal conditions. Thanks to these, rheokinetik model of polyurethane was identified. Then, to simulate the RRM, we have applied Smoothed Particles Hydrodynamics (SPH) method which is suited method to simulate the fluid flow with free surface such as occurs at RRM. Modelling and simulating reactive system flow depend on different parameters; one of them is the surface tension of reactive fluid. To implement force tension surface, the interface between polymer and air is dynamically tracked by finding the particles on this border. First, the boundary particles are detected by free-surface detection algorithm developed by Barecasco, Terissa and NAA [1, 2] in two and three dimension. Then, analytical and geometrical algorithms have been used for interface reconstructions. The aim of this work is the implementation of surface tension force in the SPH solver applied to RRM. To illustrate that, we used novel and simple geometric algorithm fitting circle and fitting sphere, in two and three dimensional configurations, respectively. The model has been validated using a well-known dam break test case which covered the experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Barecasco A, Terissa H, Naa CF (2013) Simple free-surface detection in two and three-dimensional SPH solver

  2. Terissa H, Barecasco A, Naa CF (2013) Three-dimensional smoothed particle hydrodynamics simulation for liquid droplet with surface tension

  3. Tcharkhtchi A (2004) Rotomoulage de pièces en matière thermoplastique. Techniques de l’ingénieur Plastiques et composites (AM3706):AM3706. 3701-AM3715

  4. Ortega Z, Monzon MD, Benitez AN, Kearns M, McCourt M, Hornsby PR (2013) Banana and abaca fiber-reinforced plastic composites obtained by rotational molding process. Math Manuf Proc 28(8):879–883

    Google Scholar 

  5. Rashmi BJ, Rusu D, Prashantha K, Lacrampe MF, Krawczak P (2013) Development of bio-based thermoplastic polyurethanes formulations using corn-derived chain extender for reactive rotational molding. Expr Polym Lett 7(10):852–862

    Article  Google Scholar 

  6. Mounif E, Bellenger V, Ammar A, Ata R, Mazabraud P, Tcharkhtchi A (2008) Simulation de l’écoulement au cours du procédé de rotomoulage par la méthode Smoothed Particle Hydrodynamics (SPH). Mat Technol 96(6):263–268

    Article  Google Scholar 

  7. Mounif E (2008) Résines époxy/amine pour le rotomoulage réactif: étude de la rhéocinétique et simulation numérique de l’écoulement. Thèse de doctorat, Arts et Métiers ParisTech

  8. Riviere S, Khelladi S, Farzaneh S, Bakir F, Tcharkhtchi A (2013) Simulation of polymer flow using smoothed particle hydrodynamics method. Polym Eng Sci 53(12):2509–2518

    Article  Google Scholar 

  9. Nugent S, Posch HA (2000) Liquid drops and surface tension with smoothed particle applied mechanics. Phys Rev E 62(4):4968–4975

    Article  Google Scholar 

  10. Meleàn Y, Sigalotti LDG, Hasmy A (2004) On the SPH tensile instability in forming viscous liquid drops. Comp Phys Commun 157(3):191–200

    Article  Google Scholar 

  11. Meleàn Y, Sigalotti LDG (2005) Coalescence of colliding van der Waals liquid drops. Int J Heat Mass Transf 48(19–20):4041–4061

    Article  MATH  Google Scholar 

  12. Tartakovsky A, Meakin P (2005) Modeling of surface tension and contact angles with smoothed particle hydrodynamics. Phys Rev E 72(2):026301

    Article  Google Scholar 

  13. Tartakovsky AM, Meakin P (2005) A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh-Taylor instability. J Comp Physiol 207(2):610–624

    Article  MathSciNet  MATH  Google Scholar 

  14. Brackbill JU (1992) A continuum method for modeling surface tension. J Comp Physiol 100(2):335–354

    Article  MathSciNet  MATH  Google Scholar 

  15. Morris JP (2000) Simulating surface tension with smoothed particle hydrodynamics. Int J Numer Meth Fluids 33(3):333–353

    Article  MATH  Google Scholar 

  16. Zhang M (2010) Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method. J Comp Physiol 229(19):7238–7259

    Article  MathSciNet  MATH  Google Scholar 

  17. Dilts GA (2000) Moving least-squares particle hydrodynamics II: conservation and boundaries. Int J Numer Methods Eng 48(10):1503–1524

    Article  MathSciNet  MATH  Google Scholar 

  18. Haque A, Dilts GA (2007) Three-dimensional boundary detection for particle methods. J Comp Physiol 226(2):1710–1730

    Article  MathSciNet  MATH  Google Scholar 

  19. Marrone S, Colagrossi A, Le Touzé D, Graziani G (2010) Fast free-surface detection and level-set function definition in SPH solvers. J Comp Physiol 229(10):3652–3663

    Article  MATH  Google Scholar 

  20. Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comp Meth Appl Mech Eng 139(1–4):375–408

    Article  MathSciNet  MATH  Google Scholar 

  21. Król P (1995) Generalization of kinetics in the reaction of isocyanates and polyols for modeling a process-yielding linear polyurethane, 1. J Appl Polym Sci 57(6):739–749

    Article  Google Scholar 

  22. Farzaneh S, Riviere S, Tcharkhtchi A (2012) Rheokinetic of polyurethane crosslinking time‐temperature‐transformation diagram for rotational molding. J Appl Polym Sci 125(2):1559–1566

    Article  Google Scholar 

  23. Kamal M, Sourour S (1973) Kinetics and thermal characterization of thermoset cure. Pol Eng Sci 13(1):59–64

    Article  Google Scholar 

  24. Castro J, Macosko C (1982) Studies of mold filling and curing in the reaction injection molding process. AIChE J 28(2):250–260

    Article  Google Scholar 

  25. Pavier C, Gandini A (2000) Urethanes and polyurethanes from oxypropylated sugar beet pulp: I. Kinetic study in solution. Eur Pol J 36(8):1653–1658

    Article  Google Scholar 

  26. Dong TW, Jiang SL, Huang XY, Liu HS, Huang QQ (2012) Investigation on the Non-Newtonian fluid flow in a single screw extruder using incompressible SPH (ISPH). Adv Mater Res 482:745–748

    Article  Google Scholar 

  27. Violeau D (2012) Fluid mechanics and the SPH method theory and applications. Oxford University express, Oxford

    Book  MATH  Google Scholar 

  28. Xu X, Ouyang J, Yang B, Liu Z (2013) SPH simulations of three-dimensional non-Newtonian free surface flows. Comput Methods Appl Mech Eng 256:101–116

    Article  MathSciNet  Google Scholar 

  29. Takeda H, Miyama SM, Sekiya M (1994) Numerical simulation of viscous flow by smoothed particle hydrodynamics. Prog Theor Phys 92(5):939–960

    Article  Google Scholar 

  30. Ata R, Soulaïmani A (2005) A stabilized SPH method for inviscid shallow water flows. Int J Numer Methods Eng 47(2):139–159

    Article  MathSciNet  MATH  Google Scholar 

  31. Roa MA, Argus MJ, Leidner D, Borst C, Hirzinger G (2012) Power grasp planning for anthropomorphic robot hands. In: Robotics and Automation (ICRA), 2012 I.E. Int Conf 14–18: 63–569

  32. Pueschel P, Newnham G, Rock G, Udelhoven T, Werner W, Hill J (2013) The influence of scan mode and circle fitting on tree stem detection, stem diameter and volume extraction from terrestrial laser scans. ISPRS J Photogramm Remote Sens 77(5):44–56

    Article  Google Scholar 

  33. Kasa I (1976) A circle fitting procedure and its error analysis. IEEE Trans Instrum Meas IM-25(1):8–14

    Article  Google Scholar 

  34. Umbach D, Jones KN (2003) A few methods for fitting circles to data. IEEE Trans Instrum Meas 52(6):1881–1885

    Article  Google Scholar 

  35. Ahn SJ, Rauh W, Warnecke H-J (2001) Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recogn 34(12):2283–2303

    Article  MATH  Google Scholar 

  36. Violeau D, Issa R (2007) Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview. Int J Numer Methods Eng 53(2):277–304

    Article  MathSciNet  MATH  Google Scholar 

  37. Martin JC, Moyce WJ (1952) Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos Trans R Soc Lond A Math Phys Sci 244(882):312–324

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Hamidi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hamidi, A., Khelladi, S., illoul, A. et al. Implementation of surface tension force in fluid flow during reactive rotational molding. Int J Mater Form 9, 131–148 (2016). https://doi.org/10.1007/s12289-015-1217-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-015-1217-z

Keywords

Navigation