Skip to main content
SpringerLink
Log in

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

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  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):121–133

    Article  Google Scholar 

  2. Bašić H, Demirdžić I, Muzaferija S (2005) Finite volume method for simulation of extrusion processes. Int J Numer Methods Eng 62(4):475–494

    Article  MATH  Google Scholar 

  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):3–47

    Article  MATH  Google Scholar 

  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):333–338

    Google Scholar 

  5. Campbell J (2003) Castings, 2nd edn. Elsevier, Amsterdam

    Google Scholar 

  6. Cleary PW, Ha J (2000) Three dimensional modelling of high pressure die casting. Int J Cast Metal Res 12(6):357–365

    Article  Google Scholar 

  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):169–183

    Article  Google Scholar 

  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):1406–1427

    Article  Google Scholar 

  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):2018–2033

    Article  Google Scholar 

  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):229–243

    Article  Google Scholar 

  11. Fang J, Parriaux A (2008) A regularized Lagrangian finite point method for the simulation of incompressible viscous flows. J Comput Phys 227(20):8894–8908

    Article  MathSciNet  MATH  Google Scholar 

  12. Gavete L, Benito JJ, Ureña F (2016) Generalized finite differences for solving 3d elliptic and parabolic equations. Appl Math Model 40(2):955–965

    Article  MathSciNet  Google Scholar 

  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):251–267

    Article  Google Scholar 

  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 205–221

    Chapter  Google Scholar 

  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):62–68

    Article  Google Scholar 

  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):149–152

    Article  Google Scholar 

  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):1582–1604

    Article  MathSciNet  MATH  Google Scholar 

  18. Kuhnert J (1999) General smoothed particle hydrodynamics. Ph.D. thesis, Technische Universität Kaiserslautern

  19. Lewis RW, Ravindran K (2000) Finite element simulation of metal casting. Int J Numer Methods Eng 47(1–3):29–59

    Article  MATH  Google Scholar 

  20. Liu GR (2009) Mesh free methods: moving beyond the finite element method, 2nd edn. CRC Press, Boca Raton

    Book  Google Scholar 

  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):731–741

    Article  MathSciNet  MATH  Google Scholar 

  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):493–507

    Article  Google Scholar 

  23. Narowski P, Wilczynski K (2016) Simulation of polymer injection molding: a new practical approach to improve computation accuracy. Chall Mod Technol 7(3):25–28

    Article  Google Scholar 

  24. Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3):763–813

    Article  MathSciNet  MATH  Google Scholar 

  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):263–276

    Article  MATH  Google Scholar 

  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. 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 341–354

    Chapter  Google Scholar 

  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):1554–1563

    Article  MathSciNet  MATH  Google Scholar 

  29. Rao TVR (2007) Metal casting: principles and practice, 1st edn. New Age International, New Delhi

    Google Scholar 

  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 49:643–665

    Article  MATH  Google Scholar 

  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 127:29–40

    Article  Google Scholar 

  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):450–469

    Article  MathSciNet  MATH  Google Scholar 

  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):1509–1523

    Article  MathSciNet  Google Scholar 

  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 324:619–639

    Article  MathSciNet  Google Scholar 

  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 93–99

  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 136:11–34

    Article  MathSciNet  MATH  Google Scholar 

  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 108:242–255

    Article  MathSciNet  MATH  Google Scholar 

  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):3421–3431

    Article  Google Scholar 

  39. Tiwari S, Kuhnert J (2001) Grid free method for solving the Poisson equation. Berichte des Fraunhofer ITWM 25

  40. Tiwari S, Kuhnert J (2002) A meshfree method for incompressible fluid flows with incorporated surface tension. Revue Europeenne des Elements 11(7–8):965–987

    MATH  Google Scholar 

  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 889–898

    Chapter  Google Scholar 

  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):376–386

    Article  MathSciNet  MATH  Google Scholar 

  43. Xu X, Yu P (2017) Modeling and simulation of injection molding process of polymer melt by a robust SPH method. Appl Math Model 48:384–409

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Postgraduate Studies and Research, The Technological Institute of Saltillo, National Institute of Technology of Mexico, Blvd. V. Carranza 2400, Col. Tecnológico, C.P. 25280, Saltillo, Coahuila, Mexico

    Felix R. Saucedo-Zendejo & Edgar O. Reséndiz-Flores

  2. Fraunhofer-Institut für Techno-und Wirtschaftsmathematik, Fraunhofer-Platz-1, 67663, Kaiserslautern, Germany

    Jörg Kuhnert

Authors
  1. Felix R. Saucedo-Zendejo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edgar O. Reséndiz-Flores
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jörg Kuhnert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Felix R. Saucedo-Zendejo.

Ethics declarations

Conflict of interest

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saucedo-Zendejo, F.R., Reséndiz-Flores, E.O. & Kuhnert, J. Three-dimensional flow prediction in mould filling processes using a GFDM. Comp. Part. Mech. 6, 411–425 (2019). https://doi.org/10.1007/s40571-019-00222-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-019-00222-7

Keywords

Search

Navigation