Eng
Ukr
Rus
Print

2019 №04 (01) DOI of Article
10.15407/sem2019.04.02
2019 №04 (03)

Electrometallurgy Today 2019 #04
Electrometallurgy Today (Sovremennaya Elektrometallurgiya), 2019, #4, 9-17 pages

Journal                    SEM
Publisher                International Association «Welding»
ISSN                      2415-8445 (print)
Issue                       № 4, 2019 (November)
Pages                      9-17
 

Modeling hydrodynamic and thermal processes in the mould in cold-hearth electron beam melting

S.V. Akhonin1, Yu.M. Gorislavets2, A.I. Glukhenkiy2, V.A. Berezos1, A.I. Bondar2, A.N. Pikulin1


1E.O. Paton Electric Welding Institute of the NAS of Ukraine. 11 Kazymyr Malevych Str., 03150, Kyiv, Ukraine. E-mail: office@paton.kiev.ua
2Institute of Electrodynamics of the NAS of Ukraine. 56 Pobedy Prosp., 03507, Kyiv, Ukraine. E -mail: gai56@ied.org.ua

A 3D mathematical model was formulated for conjugated hydrodynamic and thermal processes in the solidifying metal for the steady-state mode of the process of electron beam melting of titanium alloy in the continuous-operation cylindrical mould. A hydrodynamic problem for viscous turbulent flow was computed, using k-ε model of turbulence. At consideration of thermal processes the method of total heat capacity was used to allow for the heat of phase transition, heat and mass transfer and turbulent heat conductivity of the melt were taken into account. The 3d fields of metal movement velocity and its temperature were obtained, position of a two-phase zone in the ingot was determined. Ref. 16, Tabl. 2, Fig. 7.
Key words: electron beam melting; mould; intermediate crucible; mathematical modeling; hydrodynamic and thermal processes
 
Received:                24.05.19
Published:               23.09.19
 

References

1. Samojlovich, Yu.A., Krulevetsky, S.L., Goryainov, V.A., Kabakov, Z.K. (1982) Thermal processes in continuous casting of steel. Ed. by Yu.A. Samojlovich. Moscow, Metallurgiya [in Russian].
2. Volokhonsky, L.A. (1985) Vacuum arc furnaces. Moscow, Energoatomizdat [in Russian].
3. Bellot, J.-P., Jardy, A., Ablitzer, D. (1992) Thermal modelling of solidification and cooling of an electron beam melted titanium ingot. In: Proc. of the 7th Intern. Conf. on Titanium. Titanium'92. Science and Technology (San Diego, California, June 29-July 2, 3, 2347-2354.
4. Paton, B.E., Trigub, N.P., Akhonin, S.V., Zhuk, G.V. (2006) Electron beam melting of titanium. Kiev, Naukova Dumka [in Russian].
5. Bellot, J.P., Jardy, A., Ablitzer, D. (1995) Simulation numérique des transports couplés au sein du puits liquide d'un lingot de titane refondu par bombardement électronique. Revue de Métallurgie. C.I.T. Science et Génie des Matériaux, 92(12), 1399-1410. https://doi.org/10.1051/metal/199592121399
6. Lesnoj, A.B., Demchenko, V.F. (2003) Modelling of hydrodynamics and mass exchange in electron beam remelting of titanium alloys. Advances in Electrometallurgy, 3, 17-21.
7. Bellot, J.P., Defay, B., Jourdan, J. et al. (2012) Inclusion behavior during the electron beam button melting test. J. Mater. Eng. Perform., 21, 2140-2146. https://doi.org/10.1007/s11665-012-0153-z
8. Boettinger, W.J., Warren, J.A., Beckermann, C., Karma, A. (2002) Phase-field simulation of solidification. Annual Review of Materials Research, 32, 163-194. https://doi.org/10.1146/annurev.matsci.32.101901.155803
9. Wilcox, D.C. (2006) Turbulence modeling for CFD. DCW Industries, 3rd edition.
10. Avnaim, M.H., Levy, A., Mikhailovich, B. et al. (2016) Comparison of three-dimensional multidomain and single-domain models for the horizontal solidification problem. J. of Heat Transfer, 138(11). https://doi.org/10.1115/1.4033700
11. Civan, F., Sliepcevich, C.M. (1987) Limitation in the apparent heat capacity formulation for heat transfer with phase change. Proc. Okla. Acad. Sci., 67, 83-88.
12. Rogozhkin, S.A., Aksenov, A.A., Zhluktov, S.V. et al. (2014) Development of model of turbulent heat transfer for liquid metal sodium heat-transfer agent and its verification. Vychisl. Mekh. Splosh. Sred, 7(3), 300-316 [in Russian].
13. Weigand, B., Ferguson, J.R., Crawford, M.E. (1997) An extended Kays and Crawford Turbulent Prandtl number model. J. Heat and Mass Transfer, 40(17), 4191-4196. https://doi.org/10.1016/S0017-9310(97)00084-7
14. Reference book on nonferrous metals. https://libmetal.ru/titan/phisproptitan.htm
15. Westerberg, K.W., Meier, T.C., McClelland, M.A. et al. (1997) Analysis of the E-Beam evaporation of titanium and Ti-6Al-4V. In: Proc. of Conf. on Electron Beam Melting and Refining - State of the Art 1997. Ed. by R. Bakish. Bakish Materials Corp., Englewood, NJ, 208-221.
16. Bojarevics, V., Harding, R.A., Pericleous, K., Wickins, M. (2004) The development and experimental validation of a numerical model of an induction skull melting furnace. Metallurg. and Mater. Transact., 35 B, 785-803. https://doi.org/10.1007/s11663-004-0019-3