MATHEMATICAL MODELING OF TUNGSTEN MELTING IN EXPOSURE TO PULSED ELECTRON BEAM

G. G. Lazareva; Лазарева Г. Г.; A. S. Arakcheev; Аракчеев А. С.; V.A. Popov; Попов В. А.

doi:10.31857/S2686954322600537

MATHEMATICAL MODELING OF TUNGSTEN MELTING IN EXPOSURE TO PULSED ELECTRON BEAM

Authors: Lazareva G.G.¹, Arakcheev A.S.², Popov V.²
Affiliations:
1. Рeoples Friendship University of Russia
2. Budker Institute of Nuclear Physics of Siberian Branch Russian Academy of Sciences
Issue: Vol 509 (2023)
Pages: 101-105
Section: COMPUTER SCIENCE
URL: https://ruspoj.com/2686-9543/article/view/647929
DOI: https://doi.org/10.31857/S2686954322600537
EDN: https://elibrary.ru/CQCAYT
ID: 647929

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription or Fee Access

Abstract
About the authors
References
Supplementary files
Statistics

Abstract

The paper is devoted to mathematical modeling of the melting process in a sample under the influence of a pulsed thermal load based on the solution of the two-phase Stefan problem. The free boundary is ignoring during the calculation, since the numerical model is based on the Samarsky approach. The calculation in axially symmetric geometry allowed us to show that about a quarter of the incident energy is consumed in the center of the melt region. This is five times more than estimates based on the solution of the one-dimensional heat equation give. Considering the evaporation of the substance a good correspondence between the calculated and experimental temperatures of the cooling surface and the rate of narrowing of the melt region is obtained. The results of mathematical modeling confirmed the existence of an evaporation cooling mode when tungsten is heated by an electron beam significantly above the melting threshold.

Keywords

mathematical modeling, tungsten evaporation, Stefan’s problem

References

Carpentier-Chouchana S., Hirai T., Escourbiac F., Durocher A., Fedosov A., Ferrand L., Firdaouss M., Kocan M., Kukushkin A.S., Jokinen T., Komarov V., Lehnen M., Merola M., Mitteau R., Pitts R.A., Stangeby P.C., Sugihara M., “Status of the ITER full-tungsten divertor shaping and heat load distribution analysis” Physica Scripta, T. 159, 014002, 2014.
Shi Y., Miloshevsky G., Hassanein A., “Boiling induced macroscopic erosion of plasma facing components in fusion” Fusion Engineering and Design, Т. 86(2–3), p. 155–162, 2011.
Huber A., Arakcheev A., Sergienko G., Steudel I., Wirtz M., Burdakov A.V., Coenen J.W., Kreter A., Linke J., Mertens Ph., Philipps V., Pintsuk G., Reinhart M., Samm U., Shoshin A., Schweer B., Unterberg B., Zlobinski M., “Investigation of the impact of transient heat loads applied by laser irradiation on ITER-grade tungsten” Physica Scripta, T. 159, 014005, 2014.
Safronov V.M., Arkhipov N.I., Klimov N.S., Landman I.S., Petrov D.S., Podkovyrov V.L., Poznyak I.M., Toporkov D.A., Zhitlukhin A.M. , “Investigation of erosion mechanisms and erosion products in tungsten targets exposed to plasma heat loads relevant to ELMS and mitigated disruptions in ITER” Problems of Atomic Science and Technology. Series: Plasma Physics (14), pp. 52–54, 2008.
Huber A., Burdakov A., Zlobinski M., Wirtz M., Coenen J. W., Linke J.,. Mertens Ph, Philipps V., Pintsuk G., Schweer B., Sergienko G., Shoshin A., Samm U., Unterberg B., “Investigation of the impact on tungsten of transient heat loads induced by laser irradiation, electron beams and plasma guns” Fusion Science and Technology, 63 (1T), pp. 197–200, 2013.
Vyacheslavov L., Arakcheev A., Burdakov A., Kandaurov I., Kasatov A., Kurkuchekov V., Mekler K., Popov V., Shoshin A., Skovorodin D., Trunev Y., Vasilyev A. Novel electron beam based test facility for observation of dynamics of tungsten erosion under intense ELM-like heat loads, AIP Conference Proceedings, 1771, 060004 (2016).
Apushkinskaya D. Free boundary problems: Regularity properties near the fixed boundary, Lecture Notes in Mathematics, 2218. Springer (2018).
Trunev Yu.A., Arakcheev A.S., Burdakov A.V., Kandaurov I.V., Kasatov A.A., Kurkuchekov V.V., Mekler K.I., Popov V.A., Shoshin A.A., Skovorodin D.I., Vasilyev A.A., Vyacheslavov L.N., Heating of tungsten target by intense pulse electron beam, AIP Conference Proceedings 1771, 060016 (2016).
Самарский А.А., Вабищевич П.Н. Вычислительная теплопередача // М.: Едиториал УРСС, 2003, 784 с.
Яненко Н.Н., Метод дробных шагов решения многомерных задач математической физики // Новосибирск, 1967. 196 с.
Davis J.W., Smith P.D., ITER material properties handbook, J. Nucl. Mater. 233 (1996) 1593–1596.
Ho C.Y., Powell R.W., Liley P.E. Thermal conductivity of elements, Journal of Physical and Chemical Reference Data, 1, p. 279 (1972).
Талуц С.Г. Экспериментальное исследование теплофизических свойств переходных металлов и сплавов на основе железа при высоких температурах: Автореф. дис. д-ра физ.-мат. наук: 01.04.14, Екатеринбург: 2001. 38 с.
Arakcheev A.S., Apushkinskaya D.E., Kandaurov I.V., Kasatov A.A., Kurkuchekov V.V., Lazareva G.G., Maksimova A.G., Popov V.A., Snytnikov A.V., Trunev Yu.A., Vasilyev A.A., Vyacheslavov L.N. Two-dimensional numerical simulation of tungsten melting under pulsed electron beam, Fusion Engineering and Design, vol. 132, p. 13–17 (2018).
Vasilyev A.A., Arakcheev A.S., Bataev I.A., Bataev V.A., Burdakov A.V., Kandaurov I.V., Kasatov A.A., Kurkuchekov V.V., Mekler K.I., Popov V.A., Shoshin A.A., Skovorodin D.I., Trunev Yu.A., Vyacheslavov L.N., In-situ imaging of tungsten surface modification under ITER-like transient heat loads, Nucl. Matter Energy 12 (2017) 553–558.