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International Journal of Material Forming

, Volume 8, Issue 2, pp 197–210 | Cite as

Transient filling modelling at meso-level for RTM process using a single phase LSM

  • A. GiavarasEmail author
  • E. Boateng
Original Research
  • 219 Downloads

Abstract

A single phase level set method for capturing the propagating front within textile unit-cells is presented. The computational domain is embedded within an artificial Cartesian grid in order to avoid the difficulties associated with the meshing step. The flow is modelled by using the Stokes/Brinkman equations. Hence, the necessity of describing the yarn boundaries is avoided. The propagating front is represented by using a level set formulation where the extra step of reinitialization is avoided. The flow equations are solved only in the filled part of the domain. The velocity in the unfilled part is obtained through a harmonic continuation. Numerical tests on simple configurations in 2D and 3D space are presented in order to demonstrate the proposed method.

Keywords

Textiles Micro-voids Level set method Free surface modelling 

References

  1. 1.
    Wong CC (2006) Modelling the effects of textile preform architecture on permeability. PhD thesis, University of NottinghamGoogle Scholar
  2. 2.
    Schell JSU, Deleglise M, Binetruy C, Krawczak P, Ermani P (2007) Numerical prediction and experimental characterization of meso-scale-voids in liquid composite moulding. Compos Part A 38:2460–2470CrossRefGoogle Scholar
  3. 3.
    Tan H, Pillai MK (2010) Fast liquid composite molding simulation of unsaturated flow in dual-scale fiber mats using the imbibition characteristics of a fabric-based unit cell. Polym Compos 31:1790–1807CrossRefGoogle Scholar
  4. 4.
    Judd NCW, Wright WW (1978) Voids and their effects on the mechanical properties of composites-an appraisal. Sampe J 14:10–14Google Scholar
  5. 5.
    Lundstrom ST, Gebart RB (1994) Influence from process parameters on void formation in rtm. Polym Compos 15:25–33CrossRefGoogle Scholar
  6. 6.
    Rohtagi V, Patel N, Lee LJ (1996) Experimental investigation of flow-induced microvoids during impregnation of unidirectional stitched fiberglass mat. Polym Compos 17:161–170CrossRefGoogle Scholar
  7. 7.
    Patel N, Lee LJ (1995) Effects of fiber mat architecture on void formation and removal in liquid composite molding. Polym Compos 16:386–399CrossRefGoogle Scholar
  8. 8.
    Patel N, Rohtagi V, Lee LJ (1995) Micro scale flow behaviour and void formation mechanism during impregnation through a unidirectional stitched fiberglass mat. Polym Eng Sci 35(10):837–851CrossRefGoogle Scholar
  9. 9.
    Chen TY, Macosko CW, Davis TH (1995) Numerical simulation for the transverse impregnation in resin transfer molding. AIChE 41:2274–2281CrossRefGoogle Scholar
  10. 10.
    Chang YC, Hourng LW (1998) Wetting of fiber mats for composites manufacturing: Ii air entrapment model. J Reinf Plast Compos 17:165–182Google Scholar
  11. 11.
    Binetruy C, Hilaire B, Pabiot J (1997) The interactiobs between flows occuring inside and outside fabric tows during RTM. Compos Sci Technol 57:587–596CrossRefGoogle Scholar
  12. 12.
    Ruiz E, Achim V, Soukane S, Trochu F, Bréard J (2006) Optimization of injection flow rate to minimize micro/macro-voids formation in resin transfer molded composites. Compos Sci Technol 66:475–486CrossRefGoogle Scholar
  13. 13.
    Dimitrova Z, Advani SG (2004) Free boundary viscous flows at micro and mesolevel during liquid composites moulding process. Int J Numer Methods Fluids 46:435–455CrossRefGoogle Scholar
  14. 14.
    Junying Y, Yuxi A, Sheng S, Dongjun M, Tongfei S, Lijia A (2006) Mesoscopic simulation of the impregnating process of unidirectional fibrous preform in resin transfer molding. Mater Sci Eng A 435–436:515–520Google Scholar
  15. 15.
    Liu HL, Hwang WR (2009) Transient filling simulations in unidirectional fibrous porous media. Korea-Australia Rheol J 21:71–79Google Scholar
  16. 16.
    DeValve C, Pitchumani R (2011) A numerical simulation of air entrapment during resin transfer molding. In: Proceedings SAMPE, Long Beach CaliforniaGoogle Scholar
  17. 17.
    Brackbill JU, Kothe DB, Zemach C (1992) A continuum model for modeling surface tension. J Comput Phys 100:335–354CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Pacquaut G, Bruchon J, Moulin N, Drapier S (2012) Combining a level set method and a mixed stabilized P1/P1 formulation for coupling Stokes-Darcy. Int J Numer Methods Fluids 69:459–480CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Soukane S, Trochu F (2006) Application of the level set method to the simulation of resin transfer molding. Compos Sci Technol 66:1067–1080CrossRefGoogle Scholar
  20. 20.
    Gantois R, Cantarel A, Dusserre G, Félices J-N, Schmidt F (2010) Numerical simulation of resin transfer molding using bem and level set method. Int J Mater Form 3:635–638CrossRefGoogle Scholar
  21. 21.
    Smolianski A (2001) Numerical modeling of two-fluid interfacial flows. PhD thesis, University of JyvaskylaGoogle Scholar
  22. 22.
    Ngo ND, Tamma KK (2001) Microscale permeability predictions of porous fibrous media. Int J Heat Mass Transf 44:3135–3145CrossRefzbMATHGoogle Scholar
  23. 23.
    Phelan FR, Leung Y, Parnas SR (1994) Modelling of microscale flow in unidirectional fibrous porous media. J Thermoplast Compos Mater 7:208–218CrossRefGoogle Scholar
  24. 24.
    Ranganathan S, Phelan FR, Advani SG (1996) A generalized model for the transverse fluid permeability in unidirectional fibrous media. Polym Compos 17:222–230CrossRefGoogle Scholar
  25. 25.
    Saliger AG, Aris R, Derby JJ (1994) Finite element formulations for large-scale coupled flows in adjacent porous and open fluid domains. Int J Numer Methods Fluids 18:1185–1209CrossRefGoogle Scholar
  26. 26.
    Gartling KD, Hickox ED, Gilver CR (1996) Simulation of coupled viscous and porous flow problems. Comput Fluid Dyn 7:23–48CrossRefzbMATHGoogle Scholar
  27. 27.
    Martys N, Bentz PD, Garboczi J (1994) Computer simulation study of the effective viscosity in Brinkman’s equation. Phys Fluids 6:1434–1439CrossRefzbMATHGoogle Scholar
  28. 28.
    Verleye B (2008) Computation of the permeability of multi-scale porous media with application to technical textiles. PhD thesis, Katholique University of LeuvenGoogle Scholar
  29. 29.
    Sherburn M (2007) Geometrical and mechanical modelling of textiles. PhD thesis, University of NottinghamGoogle Scholar
  30. 30.
    Osher SJ, Fedkiw RP (2002) Level set methods and dynamic implicit surfaces. Springer-VerlagGoogle Scholar
  31. 31.
    Owen HC (2009) A finite element model for free surface and two fluid flows on fixed meshes. PhD thesis, Universitat Politecnica de CatalunyaGoogle Scholar
  32. 32.
    Ville L, Silva L, Coupez T (2011) Convected level set method for numerical simulation of fluid buckling. Int J Num Methods Fluids 66:324–344CrossRefzbMATHGoogle Scholar
  33. 33.
    Bui C, Frey P, Maury B (2011) A coupling strategy based on anisotropic mesh adaptation for solving two-fluid flows. Int J Numer Methods Fluids 66:1226–1247CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Adalsteinsson D, Sethian JA (1997) The fast construction of extension velocities in level set methods. J Comput Phys 148:2–22CrossRefMathSciNetGoogle Scholar
  35. 35.
    Dunne T (2007) Adaptive finite element approximation of fluid-structure interaction based on Eulerian and Arbitrary Lagrangian-Eulerian variational formulations. PhD thesis, Ruprecht Karls Universitat HeidelbergGoogle Scholar
  36. 36.
    Tiezheng Q, Xiap-Ping W, Ping S (2006) Molecular hydrodynamics of the moving contact line in two-phase immiscible flows. Comun Comput Phys 1:1–52zbMATHGoogle Scholar
  37. 37.
    Bangerth W, Hartmann R, Kanchat G (2007) deal.II – a general purpose object oriented finite element library. ACM Trans Math Softw 33:24/1–24/27CrossRefGoogle Scholar
  38. 38.
    Volker J (2002) Slip with friction penetration with resistance boundary conditions for the Navier-Stokes equations-numerical tests and aspects of the implementation. J Comput Appl Math 147:287–300CrossRefzbMATHMathSciNetGoogle Scholar
  39. 39.
    Elman H, Silvester DW, Wathen A (2005) Finite elements and fast iterative solvers with applications in incompressible fluid dynamics. Oxford PressGoogle Scholar
  40. 40.
    Giavaras A (2011) A finite element model for the permeability of textiles. PhD thesis, University of NottinghamGoogle Scholar

Copyright information

© Springer-Verlag France 2014

Authors and Affiliations

  1. 1.Division of Materials, Mechanics and Structures, Faculty of EngineeringUniversity of NottinghamNottinghamUK

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