The Paton Welding Journal, 2021, #8, 38-44 pages
Mathematical modeling of hydrodynamic and thermal processes at crystallization of titanium ingots produced by EBM
S.V. Akhonin1, V.O. Berezos1, O.I. Bondar2, O.I. Glukhenkyi2, Yu.M. Goryslavets2 and A.Yu. Severin1
E.O. Paton Electric Welding Institute of the NAS of Ukraine
11 Kazymyr Malevych Str., 03150, Kyiv, Ukraine. E-mail: email@example.com
Institute of Electrodynamics of the NAS of Ukraine
56 Peremohy Prosp., 03057, Kyiv, Ukraine. E-mail: firstname.lastname@example.org
It is shown that when specifying the efficiency of EBM process, the phenomenon of thermogravitational convection is
a weighty factor, which determines the thermal state of the ingot. A mathematical model of interrelated hydrodynamic
and thermal processes in the crystallizing metal, taking into account the phenomena of thermogravitational convection,
was formulated for a steady-state mode of the process of electron beam melting of titanium into a straight-through cylindrical
mould. The thermal state of the ingot as well as the position of the crystallization front at a continuous feeding
of liquid titanium from the cold hearth into the mould depending on metal temperature at the inlet and speed of ingot
drawing for a laminar mode of hydrodynamic flow in the liquid pool was determined. It is found that at increase of
metal temperature at the inlet into the mould in the studied range (2040‒2100 K) shifting of the point of maximum pool
depth from the ingot axis becomes smaller. Calculations within the constructed mathematical model were used to study
the impact of the rate of liquid metal feed from the cold hearth into the mould on the shape and depth of a liquid pool.
It is found that at increase of ingot drawing rate by 30 % the liquid pool depth increases by 1.5 times, and the point of
the maximum liquid pool depth becomes close to the ingot axis. 10 Ref., 1 Table, 9 Figures.
mathematical modeling; electron beam melting; hydrodynamic and thermal processes; ingot; titanium;
1. Bellot, J.-P., Flori, E., Ess, E., Ablizer, D. (1996) Mathematical
modeling of electron beam melting process with cold
hearth and its application for titanium manufacture. Problemy
Spets. Elektrometallurgii, 4, 27–37 [in Russian].
2. Paton, B.E., Trigub, N.P., Kozlitin, D.A. et al. (1997) Electron
beam melting. Kiev, Naukova Dumka [in Russian].
3. Paton, B.E., Trigub, N.P., Akhonin, S.V., Zhuk, G.V. (2006)
Electron beam melting of titanium. Kiev, Naukova Dumka [in
4. Lesnoj, A.B., Demchenko, V.F., Zhadkevich, M.L. (2001)
Modeling of hydrodynamics and heat exchange in crystallization
of ingots of electron beam remelting. Problemy Spets.
Elektrometallurgii, 2, 17–21 [in Russian].
5. Zhuk, G.V., Kalinyuk, A.N., Trigub, N.P. (2002) Modeling of
conditions of removal of shrinkage pipe from cylindrical ingots.
Advances in Electrometallurgy, 1, 19–21.
6. Zhuk, G.V., Akhonina, L.V., Trigub, N.P. (1998) Mathematical
modeling of crystallization processes of Ti–6Al–4V titanium
alloy in EBCH. Problemy Spets. Elektrometallurgii, 2,
21–25 [in Russian].
7. Akhonin, S.V., Gorislavets, Yu.M., Glukhenkiy, A.I. et al. (2019) Modeling hydrodynamic and thermal processes in the mould in cold-hearth electron beam melting. Suchasna Elektrometall., 4, 9-17 [in Russian]. https://doi.org/10.15407/sem2019.04.02
8. Mills, K. (2002) Recommended values of thermophysical properties for selected commercial alloys. Woodhead publishing limited. https://doi.org/10.1533/9781845690144
10. Zhuk, G.V. (2008) On influence of metal heating power distribution
in mould in EBCHM process on structure of titanium
ingots. Advances in Electrometallurgy, 2, 15–18.
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