Numerical simulation of casting processes: coupled mould filling and solidification using VOF and enthalpy-porosity method

Abstract

Within the scope of industrial casting applications a numerical model for the simultaneous mould filling and solidification process has been formulated, implemented in a finite volume code and successfully validated using analytical and experimental data. In order to account for the developing of free surface flow and the liquid/solid phase change, respectively, the volume-of-fluid and enthalpy-porosity method have been coupled under a volume averaging framework on a fixed Eulerian grid. The coupled method captures the basic physical effects of a combined mould filling and solidification process and provides a trustful method for comprehensive casting simulations.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Abbreviations

A :

Surface area (\(\hbox {m}^2\))

B :

Edge length of cube (\(\hbox {m}\))

C :

Large constant in Dracy-type source term (\(\hbox {kg/m}^3 \hbox {s}\))

\(c_p\) :

Specific heat capacity (\(\hbox {J/kg K}\))

E :

Width of rectangular prism (\(\hbox {m}\))

\(F_D\) :

Darcy-type source term (\(\hbox {N/m}^3\))

\(F_{\sigma }\) :

Surface tension force (\(\hbox {N/m}^3\))

g :

Gravitational acceleration (\(\hbox {m/s}^2\))

\(\varDelta H\) :

Latent heat (\(\hbox {J}\))

h :

Specific enthalpy (\(\hbox {J/kg}\))

\(h_t\) :

Heat transfer coefficient (\(\hbox {W/m}^2 \hbox {K}\))

L :

Specific latent heat (\(\hbox {J/kg}\))

P :

Porosity function (\(\hbox {kg/m}^3 \hbox {s}\))

Pr :

Prandtl number

p :

Pressure (\(\hbox {Pa}\))

p :

Dynamic pressure (\(\hbox {Pa}\))

\({\dot{Q}}\) :

Heat flux (\(\hbox {W}\))

R :

Heat resistance (\(\hbox {K/W}\))

Re :

Reynolds number

T :

Temperature (\(\hbox {K}\))

t :

Time (\(\hbox {s}\))

U :

Velocity magnitude (\(\hbox {m/s}\))

u :

Velocity (\(\hbox {m/s}\))

\(u_r\) :

Relative velocity (\(\hbox {m/s}\))

V :

Volume (\(\hbox {m}^3\))

x :

Spatial coordinate (\(\hbox {m}\))

\(\alpha\) :

Volume fraction

\(\beta\) :

Volume expansion coefficient (\(\hbox {1/K}\))

\(\gamma\) :

Liquid fraction

\(\epsilon\) :

Small numerical constant in Darcy-type source term

\(\delta\) :

Wall thickness (\(\hbox {m}\))

\(\kappa\) :

Curvature (\(\hbox {1/m}\))

\(\lambda\) :

Heat conductivity (\(\hbox {W/m K}\))

\(\mu\) :

Dynamic viscosity (\(\hbox {kg/m s}\))

\(\nu\) :

Kinematic viscosity (\(\hbox {m}^2/\hbox {s}\))

\(\rho\) :

Density (\(\hbox {kg/m}^3\))

\(\sigma\) :

Surface tension coefficient (\(\hbox {N/m}\))

1:

Phase change material, first phase

2:

Air, second phase

A :

Ambient

b :

Buoyancy

c :

Pure cooling

calc :

Analytical calculation

cut :

Threshold value

D :

Darcy-type

exp :

Experiment

F :

Final

I :

Initial

ij :

Spatial component

L :

Liquidus

l :

Liquid

m :

Melting

S :

Solidus

s :

Solid

sim :

Simulation

sign :

Sign function

Al:

Aluminium

CFD:

Computational fluid dynamics

RHS:

Right-hand side

P:

Profile

PCM:

Phase change material

PEG:

Polyethylene glycol

PIT:

Particle image thermometry

PIV:

Particle image velocimetry

References

  1. 1.

    Barkhudarov MR, Hirt CW (1995) Casting simulation: mold filling and solidification—benchmark calculations using flow-3d\(\textregistered\). In: Cross M, Campbell J (eds) Modeling of casting, welding, and advanced solidification processes VII. Minerals, Metals & Materials Society, London, pp 935–946 E.F. (U.S.)

    Google Scholar 

  2. 2.

    Berberović E, van Hinsberg NP, Jakirlić S, Roisman IV, Tropea C (2009) Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys Rev E 79:036–306

    MathSciNet  Google Scholar 

  3. 3.

    Campbell J (2003) Castings, 2nd edn. Butterworth Heinemann, Oxford

    Google Scholar 

  4. 4.

    Ferziger J, Perić M (2002) Computational methods for fluid dynamics, 3rd edn. Springer, Berlin

    Google Scholar 

  5. 5.

    Galusinski C, Vigneaux P (2008) On stability condition for bifluid flows with surface tension: application to microfluidics. J Comput Phys 227(12):6140–6164

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Hirt CW, Nichols BD (1981) Volume of fluid (vof) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225

    Article  MATH  Google Scholar 

  7. 7.

    Im IT, Kim WS, Lee KS (2001) A unified analysis of filling and solidification in casting with natural convection. Int J Heat Mass Transf 44(8):1507–1515

    Article  MATH  Google Scholar 

  8. 8.

    Kim Y, Hossain A, Nakamura Y (2013) Numerical study of melting of a phase change material (pcm) enhanced by deformation of a liquid-gas interface. Int J Heat Mass Transf 63:101–112

    Article  Google Scholar 

  9. 9.

    Kowalczyk M, Kowalewski TA, Cybulski A, Michałek T (2005) Selected laboratory benchmarks for validating numerical simulation of casting problems. In: Nowak A, Białecki R (eds) EUROTHERM 82, numerical heat transfer. Gliwice-Cracow

  10. 10.

    Kowalewski TA, Cybulski A, Michałek T, Kowalczyk M (2005) Laboratoryjne wzorce do walidacji programÓw odlewniczych. Ph.D. thesis, Institute of Fundamental Technological Research, Polish Academy of Sciences

  11. 11.

    Rusche H (2002) Computational fluid dynamics of dispersed two-phase flows at high phase fractions. Ph.D. thesis, Imperial College of Science, Technology and Medicine, London

  12. 12.

    Rösler F(2014) Modellierung und simulation der phasenwechselvorgänge in makroverkapselten latenten thermischen speichern. Ph.D. thesis, University of Bayreuth, Berlin

  13. 13.

    Rösler F, Brüggemann D (2011) Shell-and-tube type latent heat thermal energy storage: numerical analysis and comparison with experiments. Heat Mass Transf 47(8):1027–1033

    Article  Google Scholar 

  14. 14.

    Saldi ZS (2012) Marangoni driven free surface flows in liquid weld pools. Ph.D. thesis, TU Delft, Delft

  15. 15.

    Sirrell B, Holliday M, Campbell J (1996) Benchmark testing the flow and solidification modeling of Al castings. JOM 48(3):20–23

    Article  Google Scholar 

  16. 16.

    Stefanescu DM (2010) Science and engineering of casting solidification, 2nd edn. Springer, New York

    Google Scholar 

  17. 17.

    Stephan P (2015) VDI-Wärmeatlas, 11th edn. Springer, Berlin

    Google Scholar 

  18. 18.

    van Tol R, van den Akker H, Katgerman L (1994) Cfd study of the mould filling of a horizontal thin wall aluminium casting. In: Transport Phenomena in Solidification, vol. HTD 284/AMD 182, pp 203–213. ASME Heat Transfer Division

  19. 19.

    Vakhrushev A, Ludwig A, Wu M, Tang Y, Hackl G, Nitzl G (2012) Advanced multiphase modelling of solidification with openfoam®. In: 7th OpenFOAM® Workshop, June 2012, Frankfurt, Germany, pp 29–30

  20. 20.

    Voller V, Brent A, Prakash C (1990) Modelling the mushy region in a binary alloy. Appl Math Model 14(6):320–326

    Article  Google Scholar 

  21. 21.

    Voller VR, Prakash C (1987) A fixed grid numerical modelling methodology for convection–diffusion mushy region phasechange problems. Int J Heat Mass Transf 30(8):1709–1719

    Article  Google Scholar 

  22. 22.

    Voller VR, Swaminathan CR (1991) General source-based method for solidification phase change. J Heat Mass Transf Part B Fundam 19(2):175–189

    Article  Google Scholar 

Download references

Acknowledgements

The support of the authors by the Deutsche Forschungsgemeinschaft (DFG, Grant INST 264/113-1 FUGG) is gratefully acknowledged.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Johann Turnow.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Richter, O., Turnow, J., Kornev, N. et al. Numerical simulation of casting processes: coupled mould filling and solidification using VOF and enthalpy-porosity method. Heat Mass Transfer 53, 1957–1969 (2017). https://doi.org/10.1007/s00231-016-1954-7

Download citation

Keywords

  • Particle Image Velocimetry
  • Mushy Zone
  • Phase Change Material
  • Rectangular Prism
  • Mould Filling