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Three-dimensional flow prediction in mould filling processes using a GFDM

  • Felix R. Saucedo-ZendejoEmail author
  • Edgar O. Reséndiz-Flores
  • Jörg Kuhnert
Article

Abstract

The aim of this work is to achieve a meshfree implementation for the numerical prediction of 3D flows during mould filling processes in metal casting using a generalized finite difference method. The free surface incompressible flow problem is numerically solved using a semi-implicit Chorin–Uzawa’s projection scheme where the normal vectors needed for the free surface computations are computed with a simple and efficient idea. Further, the boundary conditions incorporation involved in this industrial problem is done in a simple and direct manner. The main characteristics in this meshfree formulation together with details of its computational implementation are given. The numerical results of a benchmark example using this formulation are reported and compared with published numerical and experimental results, and finally, the numerical solution of some three-dimensional test problems is reported which show that this formulation is promising for predicting three-dimensional complex free surface flows in mould filling processes in casting.

Keywords

Casting Generalized finite difference method FPM Free surface flow Meshless method Finite pointset method 

Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

  1. 1.
    Acevedo-Malavé A, García-Sucre M (2012) Many drops interactions I: simulation of coalescence, flocculation and fragmentation of multiple colliding drops with smoothed particle hydrodynamics. J Comput Multiph Flows 4(2):121–133CrossRefGoogle Scholar
  2. 2.
    Bašić H, Demirdžić I, Muzaferija S (2005) Finite volume method for simulation of extrusion processes. Int J Numer Methods Eng 62(4):475–494CrossRefzbMATHGoogle Scholar
  3. 3.
    Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139(1–4):3–47CrossRefzbMATHGoogle Scholar
  4. 4.
    Bohdal Ł, Tandecka K, Kałduński P (2017) Numerical simulation of shear slitting process of grain oriented silicon steel using SPH method. Acta Mech Autom 11(4):333–338Google Scholar
  5. 5.
    Campbell J (2003) Castings, 2nd edn. Elsevier, AmsterdamGoogle Scholar
  6. 6.
    Cleary PW, Ha J (2000) Three dimensional modelling of high pressure die casting. Int J Cast Metal Res 12(6):357–365CrossRefGoogle Scholar
  7. 7.
    Cleary PW, Ha J (2002) Three-dimensional smoothed particle hydrodynamics simulation of high pressure die casting of light metal components. J Light Met 2(3):169–183CrossRefGoogle Scholar
  8. 8.
    Cleary PW, Ha J, Nguyen T (2006) 3D SPH flow predictions and validation for high pressure die casting of automotive components. Appl Math Model 30(11):1406–1427CrossRefGoogle Scholar
  9. 9.
    Cleary PW, Ha J, Prakash M, Nguyen T (2010) Short shots and industrial case studies: understanding fluid flow and solidification in high pressure die casting. Appl Math Model 34(8):2018–2033CrossRefGoogle Scholar
  10. 10.
    Cleary PW, Savage G, Ha J, Prakash M (2014) Flow analysis and validation of numerical modelling for a thin walled high pressure die casting using SPH. Comput Part Mech 1(3):229–243CrossRefGoogle Scholar
  11. 11.
    Fang J, Parriaux A (2008) A regularized Lagrangian finite point method for the simulation of incompressible viscous flows. J Comput Phys 227(20):8894–8908MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Gavete L, Benito JJ, Ureña F (2016) Generalized finite differences for solving 3d elliptic and parabolic equations. Appl Math Model 40(2):955–965MathSciNetCrossRefGoogle Scholar
  13. 13.
    Gimenez JM, Ramajo DE, Damián SM, Nigro NM, Idelsohn SR (2017) An assessment of the potential of PFEM-2 for solving long real-time industrial applications. Comput Part Mech 4(3):251–267CrossRefGoogle Scholar
  14. 14.
    Jefferies A, Kuhnert J, Aschenbrenner L, Giffhorn U (2015) Finite pointset method for the simulation of a vehicle travelling through a body of water. In: Griebel M, Schweitzer MA (eds) Meshfree methods for partial differential equations VII, vol 100. Lecture notes in computational science and engineering. Springer, Berlin, pp 205–221Google Scholar
  15. 15.
    Kermanpur A, Mahmoudi S, Hajipour A (2008) Numerical simulation of metal flow and solidification in the multi-cavity casting moulds of automotive components. J Mater Process Technol 206(1–3):62–68CrossRefGoogle Scholar
  16. 16.
    Kimatsuka A, Ohnaka I, Zhu JD, Ohmichi T (2003) Mold filling simulation with consideration of gas escape through sand mold. Int J Cast Metal Res 15(3):149–152CrossRefGoogle Scholar
  17. 17.
    Koh CG, Gao M, Luo C (2012) A new particle method for simulation of incompressible free surface flow problems. Int J Numer Methods Eng 89(12):1582–1604MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kuhnert J (1999) General smoothed particle hydrodynamics. Ph.D. thesis, Technische Universität KaiserslauternGoogle Scholar
  19. 19.
    Lewis RW, Ravindran K (2000) Finite element simulation of metal casting. Int J Numer Methods Eng 47(1–3):29–59CrossRefzbMATHGoogle Scholar
  20. 20.
    Liu GR (2009) Mesh free methods: moving beyond the finite element method, 2nd edn. CRC Press, Boca RatonCrossRefGoogle Scholar
  21. 21.
    López YR, Roose D, Morfa CR (2013) Dynamic particle refinement in sPH: application to free surface flow and non-cohesive soil simulations. Comput Mech 51(5):731–741MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Mirbagheri SMH, Esmaeileian H, Serajzadeh S, Varahram N, Davami P (2003) Simulation of melt flow in coated mould cavity in the casting process. J Mater Process Technol 142(2):493–507CrossRefGoogle Scholar
  23. 23.
    Narowski P, Wilczynski K (2016) Simulation of polymer injection molding: a new practical approach to improve computation accuracy. Chall Mod Technol 7(3):25–28CrossRefGoogle Scholar
  24. 24.
    Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3):763–813MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Park JS, Kim SM, Kim MS, Lee WI (2005) Finite element analysis of flow and heat transfer with moving free surface using fixed grid system. Int J Comput Fluid Dyn 19(3):263–276CrossRefzbMATHGoogle Scholar
  26. 26.
    Prohl A (1997) Projection and quasi-compressibility methods for solving the incompressible Navier–Stokes equations. Advances in numerical mathematics, 1st Edn. Vieweg + Teubner Verlag.  https://doi.org/10.1007/978-3-663-11171-9
  27. 27.
    Quinlan NJ, Lobovskỳ L (2018) The finite volume particle method: toward a meshless technique for biomedical fluid dynamics. In: Cerrolaza M, Shefelbine S, Garzón-Alvarado D (eds) Numerical methods and advanced simulation in biomechanics and biological processes. Academic Press, London, pp 341–354CrossRefGoogle Scholar
  28. 28.
    Quinlan NJ, Lobovskỳ l, Nestor RM (2014) Development of the meshless finite volume particle method with exact and efficient calculation of interparticle area. Comput Phys Commun 185(6):1554–1563MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Rao TVR (2007) Metal casting: principles and practice, 1st edn. New Age International, New DelhiGoogle Scholar
  30. 30.
    Ren J, Ouyang J, Jiang T, Li Q (2011) Simulation of complex filling process based on the generalized Newtonian fuid model using a corrected SPH scheme. Comput Mech 49:643–665CrossRefzbMATHGoogle Scholar
  31. 31.
    Reséndiz-Flores EO, Saucedo-Zendejo FR (2018) Meshfree numerical simulation of free surface thermal flows in mould filling processes using the finite pointset method. Int J Therm Sci 127:29–40CrossRefGoogle Scholar
  32. 32.
    Reséndiz-Flores EO, Kuhnert J, Saucedo-Zendejo FR (2018) Application of a generalized finite difference method to mould filling process. Eur J Appl Math 29(3):450–469MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Salinas C, Vasco DA, Moraga NO (2013) Two-dimensional non-Newtonian injection molding with a new control volume FEM/volume of fluid method. Int J Numer Methods Fluids 71(12):1509–1523MathSciNetCrossRefGoogle Scholar
  34. 34.
    Saucedo-Zendejo FR, Reséndiz-Flores EO (2017) A new approach for the numerical simulation of free surface incompressible flows using a meshfree method. Comput Method Appl Mech Eng 324:619–639MathSciNetCrossRefGoogle Scholar
  35. 35.
    Schmid M, Klein F (1995) Fluid flow in die cavities-experimental and numerical simulation, NADCA 18. In: International die casting congress and exposition, pp 93–99Google Scholar
  36. 36.
    Shadloo MS, Oger G, Touzé DL (2016) Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: motivations, current state, and challenges. Comput Fluids 136:11–34MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Sigalotti LDG, Klapp J, Rendón O, Vargas CA, Peña-Polo F (2016) On the kernel and particle consistency in smoothed particle hydrodynamics. Appl Numer Math 108:242–255MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Szucki M, Suchy JS, Lelito J, Malinowski P, Sobczyk J (2017) Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry. Heat Mass Transf 53(12):3421–3431CrossRefGoogle Scholar
  39. 39.
    Tiwari S, Kuhnert J (2001) Grid free method for solving the Poisson equation. Berichte des Fraunhofer ITWM 25Google Scholar
  40. 40.
    Tiwari S, Kuhnert J (2002) A meshfree method for incompressible fluid flows with incorporated surface tension. Revue Europeenne des Elements 11(7–8):965–987zbMATHGoogle Scholar
  41. 41.
    Tiwari S, Kuhnert J (2003) Particle method for simulation of free surface flows. In: Hou Y, Tadmor E (eds) Hyperbolic problems: theory, numerics, applications. Springer, Berlin, pp 889–898CrossRefGoogle Scholar
  42. 42.
    Tiwari S, Kuhnert J (2007) Modeling of two-phase flows with surface tension by finite pointset method (FPM). J Comput Appl Math 203(2):376–386MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Xu X, Yu P (2017) Modeling and simulation of injection molding process of polymer melt by a robust SPH method. Appl Math Model 48:384–409MathSciNetCrossRefGoogle Scholar

Copyright information

© OWZ 2019

Authors and Affiliations

  1. 1.Division of Postgraduate Studies and Research, The Technological Institute of SaltilloNational Institute of Technology of MexicoSaltilloMexico
  2. 2.Fraunhofer-Institut für Techno-und WirtschaftsmathematikKaiserslauternGermany

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