Skip to main content
SpringerLink
Log in

Numerical Simulation of the Plasma Arc Melting Cold Hearth Refining Process (PAMCHR)

  • Topical Collection: Liquid Metal Processing & Casting Conference 2019
  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

In order to improve our understanding of the PAMCHR process applied to the processing of Ti alloys, a 3D numerical simulation of the thermal and hydrodynamic behavior of the metal flowing in the refining hearth has been set up, based on Ansys-Fluent CFD software. The solid and liquid phases are governed by a set of transport equations expressing the conservation of mass, momentum, heat, and solutes. The turbulence of the liquid flow is modeled through the standard k–ε model. Heat input and tangential shear stress caused by the plasma jet originating from the torches, as well as the themocapillary effect, are accounted for as boundary conditions. Their effects on the turbulent liquid metal flow have been modeled together with the displacement of the torches. Simulation results are presented for a pilot furnace and representative operating conditions. Turbulent fluid flow in the Ti64 molten pool is analyzed in detail and the role of each momentum source is examined. Comparison between the measured and calculated pool profiles is also reported and reveals a satisfactory agreement.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Abbreviations

C p :

Specific heat (J/kg/K)

D :

Diffusion coefficient (m2/s)

D t :

Turbulent diffusion coefficient (m2/s)

g :

Gravitational acceleration (m2/s)

g l :

Liquid fraction

h wall :

Heat-transfer coefficient at the crucible walls (W/m2)

k :

Coefficient of mass transfer (m/s)

K :

Permeability of the mushy zone (m2)

K 0 :

Permeability constant of the Kozeny-Carman law (m2)

P :

Pressure (Pa)

P i :

Saturating vapor pressure of the element i

r :

Distance from the plasma torch center (m)

R :

Ideal gas constant (J/mol/K)

T :

Temperature (K)

v :

Velocity of the fluid (m/s)

x i :

Mole fraction of the element i

x, y, z :

Cartesian coordinates (m)

β T :

Thermal expansion coefficient (K−1)

γ i :

activity coefficient of the element i

∆Hf :

Latent heat of melting (J/kg)

ε :

Thermal emissivity

φ torch :

Heat flux density of the plasma jet (W/m2)

φ wall :

Heat flux density on the walls (W/m2)

\( \varphi_{\text{i}}^{\text{eq}} \) :

Flux density of heat volatilization of the element i (kg/m2/s)

λ :

Thermal conductivity (W/m/K)

λ t :

Turbulent thermal conductivity (W/m/K)

σ s :

Stefan constant (W/m2/K4)

τ m :

Marangoni shear stress (Pa)

τ max :

Maximum value of shear stress due to the plasma impact (Pa)

τ s :

Shear stress due to the plasma impact (Pa)

µ :

Dynamic viscosity (kg/m/s)

µ t :

Turbulent viscosity (kg/m/s)

ρ :

Density (kg/m3)

ρ 0 :

Density value at a temperature T0 (kg/m3)

ω i :

Weight fraction of the element i

References

  1. C.E. Schamblen: Technical Information Series Report No. R89AERB141, GEAE, OH, 1989.

  2. Y. Honnorat: La Revue de Métallurgie-CIT, 1996, pp. 1029–41.

  3. J.P. Bellot, B. Foster, S. Hans, E. Hess, D. Ablitzer and A. Mitchell: Metall. Trans. B, 1997, vol. 28B, pp. 1001-1010

    Article  CAS  Google Scholar 

  4. J.P. Bellot, E. Hess and D. Ablitzer: Metall. Mater. Trans. B, 2000, vol. 31B, pp. 845-854

    Article  CAS  Google Scholar 

  5. [5] M.J. Blackburn and D.R. Malley: Materials & Design, 1993, vol.14 pp. 19-27

    Article  CAS  Google Scholar 

  6. C. Reimer, J. Jourdan and J.P. Bellot: Calphad, vol. 58, 2017, pp. 122-127.

    Article  CAS  Google Scholar 

  7. X. Huang, J.S. Chou, D. Tilly, K.O. Yu: In Proceeding of the Int Conf. on Liquid Metal Processing and Casting, Santa Fe (NM, USA), 1997, pp. 179–203.

  8. R.M. Lothian and M. Mclean: In Proceedings of the International Symposium on Liquid Metal Processing and Casting, Santa Fe (NM, USA), 1997, pp. 133–44.

  9. X. Huang, J.S. Chou, and Y. Pang: 1999. In Proceeding of the Int Conf. on Liquid Metal Processing and Casting, Santa Fe (NM, USA), 1999, pp. 224–43.

  10. S.C. Chu and S.S. Lian: Computational Materials Science, 2004, vol. 30, pp. 441–447

    Article  Google Scholar 

  11. X. Xu, H. Chang, H. Kou, Z.Yang, and J. Li: Int. J. Innovative Technol. Explor. Eng.(IJITEE), 2013, vol. 2, pp. 1123-1133

    Google Scholar 

  12. S. Ji, J. Duan, L. Yao, D.M. Maijer, S.L. Cockcroft, D. Fiore and D. W. Tripp: Int. J. Heat Mass Transf. 2018, vol.119, pp. 271–281

    Article  CAS  Google Scholar 

  13. L. Yao, D.M. Maijer, S. L. Cockcroft, D. Fiore and D.W. Tripp: Int J. Heat Mass Transfer, 2018, vol.126, pp. 1123-1133

    Article  CAS  Google Scholar 

  14. L. Décultot, A. Jardy, S.Hans, E. Doridot, J. Delfosse, F. Ruby-Meyer and J.P. Bellot: In Proceeding of the Int Conf. on Titanium, Nantes, (France), 2019, USB key.

  15. [15] B.E. Launder and D.B. Spalding: Computer Methods in Applied Mechanics and Eng., 1974, vol.3, pp. 269-289

    Article  Google Scholar 

  16. R.Rai, P.Burgardt, J.O. Milewski, T.J. Lienert and T.DebRoy: J. Phys. D.: Appl. Phys., 2009, vol.42, pp. 1-12

    Article  Google Scholar 

  17. W. Choi, J.Jourdan, A.Matveichev, A.Jardy and J.P.Bellot: High Temperature Materials and Processes, 2017, vol. 36, pp. 815-823

    Article  CAS  Google Scholar 

  18. F. Qian, B. Farouk and R. Mutharasan: Metall. Mater. Trans. B, 1995, vol. 26B, pp. 1057–67.

  19. E. Hess: Ph.D. Thesis, 1997, Institut National Polytechnique de Lorraine.

  20. Y. Pang, S. Srivatsa, and K.-O. Yu: Modeling for Casting and Solidification Processing, Marcel Dekker, New York, 2002, Ch. 8, pp. 621–26.

  21. P.A. Kobryn and S.L. Semiatin: Metall. Mater. Trans. B, 2001, vol. 32B, pp. 685–95.

  22. Zhao X., Reilly C., Yao L., Maijer D.M., Cockcroft S.L., Zhu J.: Applied Mathematical Modelling,2014, vol.38, pp. 3607-3623

    Article  Google Scholar 

  23. P.G. Clites and R.A. Beall: Report No. 7035, United States Bureau of Mines, Albany, OR, 1967.

  24. G.A. Khasin, V.Z. Bigashev, and N.A. Ermanovich: Steel USSR, 1973, vol. 3, pp. 383–85.

  25. M. Boivineau, C. Cagran, D. Doytier, V. Eyraud, M. Nadal, B. Wilthan, B. and G. Pottlacher: In Proceedings of the International Journal of Thermophysics, 2006, vol. 27, pp. 507–29.

  26. ANSYS Fluent-Solver Theory Guide, Released 17.1, ANSYS INC PA, 2017.

Download references

Author information

Authors and Affiliations

  1. Institut Jean Lamour - UMR CNRS 7198, LabEx DAMAS, Université de Lorraine, 2 allée André Guinier, Campus Artem, 54000, Nancy, France

    Jean-Pierre Bellot, Léa Décultot & Alain Jardy

  2. Aubert & Duval Les Ancizes, BP1, 63770, Les Ancizes Cedex, France

    Léa Décultot, Stéphane Hans & Emiliane Doridot

  3. Safran Tech - Rue des Jeunes Bois, Châteaufort, 78772, Magny-les-Hameaux, France

    Jérôme Delfosse

  4. MetaFensch, 109 rue de Thionville, 57270, Uckange, France

    Neill McDonald

Authors
  1. Jean-Pierre Bellot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Léa Décultot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alain Jardy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stéphane Hans
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Emiliane Doridot
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jérôme Delfosse
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Neill McDonald
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean-Pierre Bellot.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Manuscript submitted January 16, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bellot, JP., Décultot, L., Jardy, A. et al. Numerical Simulation of the Plasma Arc Melting Cold Hearth Refining Process (PAMCHR). Metall Mater Trans B 51, 1329–1338 (2020). https://doi.org/10.1007/s11663-020-01866-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11663-020-01866-0

Search

Navigation