The Paton Welding Journal, 2025, №08

2025 №08 (04)

DOI of Article 10.37434/tpwj2025.08.05

2025 №08 (06)

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The Paton Welding Journal, 2025, #8, 44-54 pages

Model of the anode boundary layer in welding arcs

I.V. Krivtsun¹, A.I. Momot^1,2, I.B. Denysenko^1,3, U. Reisgen⁴, O. Mokrov⁴, R. Sharma⁴

¹E.O. Paton Electric Welding Institute of the NASU. 11 Kazymyr Malevych Str., 03150, Kyiv, Ukraine. E-mail: momot.andriy@gmail.com
²Taras Shevchenko National University of Kyiv 64/13 Volodymyrs’ka Str., 01601, Kyiv, Ukraine,
³V.N. Karazin Kharkiv National University 4 Svobody Sq., 61022, Kharkiv, Ukraine
⁴Welding and Joining Institute, RWTH Aachen University 49 Pontstrasse, 52062, Germany

Abstract
A one-dimensional model of the anode boundary layer in atmospheric pressure electric arcs with refractory cathode and evaporating anode is proposed for two modes of the anode metal evaporation: diffusive and convective. The corresponding systems of differential and algebraic equations are formulated to compute the spatial distributions of the number densities and diffusive flux densities of electrons, ions, and atoms; the electron temperature and the heavy particle (atoms and ions) temperature; and the electric potential in the plasma of the anode layer. Additionally, the model allows to calculate the heat flux introduced by the arc into the anode. The boundary conditions for the differential equations of this model at the boundaries of the anode layer with the arc column plasma and the space-charge sheath are formulated. An approach for determining the plasma parameters at these boundaries is also proposed for each evaporation mode.
Keywords: anode boundary layer, welding arc, modelling, evaporating anode, metal vapor, diffusive evaporation, convective evaporation

Received: 12.05.2025
Received in revised form: 17.06.2025
Accepted: 24.07.2025

References

1. Murphy, A.B. (2010) The effects of metal vapour in arc welding. J. of Physics D: Applied Physics, 43, 434001, 91-104. https://doi.org/10.1088/0022-3727/43/43/434001
2. Schnick, M., Fuessel, U., Hertel, M. et al. (2010) Modelling of gas-metal arc welding taking into account metal vapour. J. of Physics D: Applied Physics, 43, 434008. https://doi.org/10.1088/0022-3727/43/43/434008
3. Hertel, M., Trautmann, M., Jäckel, S., Füssel, U. (2017) The role of metal vapour in gas metal arc welding and methods of combined experimental and numerical process analysis. Plasma Chemistry and Plasma Processing, 37, 531-547. https://doi.org/10.1007/s11090-017-9790-1
4. Cho, Y.T., Cho, W.I., Na, S.J. (2011) Numerical analysis of hybrid plasma generated by Nd:YAG laser and gas tungsten arc. Optics & Laser Technology, 43, 711-720. https://doi.org/10.1016/j.optlastec.2010.09.013
5. Tanaka, M., Tsujimura, Y., Yamazaki, K. (2012) Dynamic behaviour of metal vapour in arc plasma during TIG welding. Welding in the World, 56, 30-36. https://doi.org/10.1007/BF03321142
6. Mougenot, J., Gonzalez, J.J., Freton, P., Masquère, M. (2013) Plasma-weld pool interaction in tungsten inert-gas configuration. J. of Physics D: Applied Physics, 46, 135206. https://doi.org/10.1088/0022-3727/46/13/135206
7. Krivtsun, I., Demchenko, V., Krikent, I. et al. (2015) Distributed and integrated characteristics of the near-anode plasma of the welding arc in TIG and hybrid (TIG+CO2-laser) welding. Mathematical Modelling of Weld Phenomena, 11, 837-874. https://doi.org/10.15407/tpwj2015.04.01
8. Krivtsun, I.V. (2018) Anode processes in welding arcs. The Paton Welding J, 11-12, 91-104. https://doi.org/10.15407/tpwj2018.12.10
9. Knight, C.J. (1979) Theoretical modeling of rapid surface vaporization with back pressure. AIAA J., 17, 519-523. https://doi.org/10.2514/3.61164
10. Krivtsun, I.V., Momot, A.I., Denysenko, I.B. et al. (2024) Transport properties and kinetic coefficients of copper thermal plasmas. Physics of Plasmas, 31, 083505. https://doi.org/10.1063/5.0216753
11. Krivtsun, I.V., Momot, A.I., Antoniv, D.V., Qin, B. (2023) Characteristics of atmospheric pressure Ar-plasma around a spherical particle: Numerical study. Physics of Plasmas, 30, 043513. https://doi.org/10.1063/5.0141015
12. Heberlein, J., Mentel, J., Pfender, E. (2009) The anode region of electric arcs: a survey. J. of Physics D: Applied Physics, 43, 023001. https://doi.org/10.1088/0022-3727/43/2/023001
13. Zhdanov, V.M. (2002) Transport processes in multicomponent plasma. CRC Press. https://doi.org/10.1201/9781482265101
14. Almeida, N.A., Benilov, M.S., Naidis, G.V. (2008) Unified modelling of near-cathode plasma layers in high-pressure arc discharges. J. of Physics D: Applied Physics 41, 245201. https://doi.org/10.1088/0022-3727/41/24/245201
15. Semenov, I.L., Krivtsun, I.V., Reisgen, U. (2016) Numerical study of the anode boundary layer in atmospheric pressure arc discharges. J. of Physics D: Applied Physics, 49, 105204. https://doi.org/10.1088/0022-3727/49/10/105204
16. Krikent, I.V., Krivtsun, I.V., Demchenko, V.F. (2014) Simulation of electric arc with refractory cathode and evaporating anode, The Paton Welding J., 9, 17-24. https://doi.org/10.15407/tpwj2014.09.02
17. Benilov, M.S., Marotta, A. (1995) A model of the cathode region of atmospheric pressure arcs. J. of Physics D: Applied Physics, 28, 1869. https://doi.org/10.1088/0022-3727/28/9/015
18. Gao, S., Momot, A., Krivtsun, I. et al. (2025) Interaction between a spherical particle and atmospheric pressure currentless argon plasma. East European J. of Physics, 388-395. https://doi.org/10.26565/2312-4334-2025-1-48
19. Lieberman, M.A., Lichtenberg, A.J. (1994) Principles of plasma discharges and materials processing. Wiley.
20. Krivtsun, I.V., Momot, A.I., Denysenko, I.B. (2025) Model of the anode layer of an electric arc with an evaporating anode, Avtomatyche Zvaryuvannya, 3, 3-9. https://doi.org/10.37434/as2025.03.01
21. Frezzotti, A. (2007) A numerical investigation of the steady evaporation of a polyatomic gas. European J. of Mechanics-B/Fluids, 26, 93-104. https://doi.org/10.1016/j.euromechflu.2006.03.007
22. Bird, E., Liang, Z. (2019) Transport phenomena in the Knudsen layer near an evaporating surface. Physical Review E, 100, 043108. https://doi.org/10.1103/PhysRevE.100.043108
23. Godyak, V.A., Sternberg, N. (2002) Smooth plasma-sheath transition in a hydrodynamic model. IEEE Transact. on Plasma Sci., 18, 159-168. https://doi.org/10.1109/27.45519
24. Zhang, Y., Evans, J.R., Yang, S. (2011) Corrected values for boiling points and enthalpies of vaporization of elements in handbooks. J. of Chemical & Engineering Data, 56, 328-337. https://doi.org/10.1021/je1011086
25. Kramida, A., Ralchenko, Yu., Reader, J., NIST ASD Team (2024) NIST Atomic Spectra Database (ver. 5.12), Online. https://physics.nist.gov/asd National Institute of Standards and Technology, Gaithersburg, MD. DOI: https://doi.org/10.18434/T4W30F
26. Loock, H.P., Beaty, L.M., Simard, B. (1999) Reassessment of the first ionization potentials of copper, silver, and gold. Physical Review A, 59, 873. https://doi.org/10.1103/PhysRevA.59.873

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Suggested Citation

I.V. Krivtsun, A.I. Momot, I.B. Denysenko, U. Reisgen, O. Mokrov, R. Sharma (2025) Model of the anode boundary layer in welding arcs. The Paton Welding J., 08, 44-54.

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