Calculation of thermal currents in a tungsten plate and in a thin layer of tungsten vapor during pulse heating with allowance for temperature- and phase-dependent electrical resistance and thermo emf
Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 3, pp. 95-110 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we consider a model of current distribution in a tungsten specimen and the evaporated substance when the surface is heated by an electron beam. The model is based on solving the equations of electrodynamics and the two-phase Stefan problem for calculating the specimen area temperature in a cylindrical coordinate system. We use a model temperature distribution in a thin layer of evaporated tungsten that replicates the surface temperature. Thermal currents are obtained using approximate temperature dependences of the electrical resistance and thermo emf of tungsten and its vapor. The model parameters are taken from experiments at the Beam of Electrons for materials Test Applications (BETA) stand, created at the Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy of Sciences.
Keywords: mathematical modelling, thermal current, tungsten, pulsed heating, successive overrelaxation method, BETA stand, divertor.
@article{SJIM_2024_27_3_a6,
     author = {G. G. Lazareva and V. A. Popov},
     title = {Calculation of thermal currents in a tungsten plate and in a thin layer of tungsten vapor during pulse heating with allowance for temperature- and phase-dependent electrical resistance and thermo emf},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {95--110},
     year = {2024},
     volume = {27},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a6/}
}
TY  - JOUR
AU  - G. G. Lazareva
AU  - V. A. Popov
TI  - Calculation of thermal currents in a tungsten plate and in a thin layer of tungsten vapor during pulse heating with allowance for temperature- and phase-dependent electrical resistance and thermo emf
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2024
SP  - 95
EP  - 110
VL  - 27
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a6/
LA  - ru
ID  - SJIM_2024_27_3_a6
ER  - 
%0 Journal Article
%A G. G. Lazareva
%A V. A. Popov
%T Calculation of thermal currents in a tungsten plate and in a thin layer of tungsten vapor during pulse heating with allowance for temperature- and phase-dependent electrical resistance and thermo emf
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2024
%P 95-110
%V 27
%N 3
%U http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a6/
%G ru
%F SJIM_2024_27_3_a6
G. G. Lazareva; V. A. Popov. Calculation of thermal currents in a tungsten plate and in a thin layer of tungsten vapor during pulse heating with allowance for temperature- and phase-dependent electrical resistance and thermo emf. Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 3, pp. 95-110. http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a6/

[1] 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 Conf. Proc., 1771 (2016), 060004 | DOI

[2] 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 Eng. Des., 132 (2018), 13–17 | DOI

[3] Lazareva G. G., Popov V. A., Arakcheev A. S., Burdakov A. V., Shwab I. V., Vaskevich V. L., Maksimova A. G., Ivashin N. E., Oksogoeva I. P., “Mathematical simulation of the distribution of the electron beam current during pulsed heating of a metal target”, J. Appl. Ind. Math., 24:2 (2021), 97–108 | MR | Zbl

[4] G. G. Lazareva, V. A. Popov, and V. A. Okishev, “Mathematical model of current distribution in a tungsten plate during pulsed heating”, J. Appl. Ind. Math., 18:1 (2024), 93–102 | DOI | MR | Zbl

[5] G. G. Lazareva, A. S. Arakcheev, and V. A. Popov, “Mathematical modeling of melting tungsten exposed to pulsed laser beam”, Dokl. Math., 107:1 (2023), 83–87 | DOI | DOI | Zbl

[6] Lazareva G. G., Popov V. A., “Effect of Temperature Distribution on the Calculation of the thermal current in the Mathematical Model of Pulsed Heating of a Tungsten”, Lobachevskii J. Math., 44 (2023), 4457–4468 | DOI | MR | Zbl

[7] Lazareva G. G., Maksimova A. G., “Numerical Simulation of the Propagation of Tungsten Vapor above a Heated Surface”, J. Appl. Ind. Math., 16:3 (2022), 472–480 | DOI

[8] Lazareva G. G., Arakcheev A. S., Maksimova A. G., Popov V. A., “Numerical model of evaporation of tungsten in vacuum under high-power transient heating”, J. Phys. Conf. Ser., 1391:8 (2019), 012074 | DOI

[9] Lazareva G., Korneev V., Maksimova A., Arakcheev A., “Parallel algorithm for calculating the dynamics of tungsten vapor distribution”, J. Phys. Conf. Ser., 2028:1 (2021), 012010 | DOI

[10] Chen X., Pang Sh., Shao X., Wang Ch., Xiao J., Jiang P., “Three-dimensional transient thermoelectric currents in deep penetration laser welding of austenite stainless steel”, Opt. Lasers Eng., 91 (2017), 196–205 | DOI

[11] Lange A., Cramer A., Beyer E., “Thermoelectric currents in laser induced melts pools”, J. Laser Appl., 21:2 (2009), 82–87 | DOI

[12] Thoren E., Tolias P., Ratynskaia S., Pitts R. A., Krieger K., “Self-consistent description of the replacement current driving melt layer motion in fusion devices”, Nucl. Fusion, 58:10 (2018), 106003 | DOI

[13] Takamura S., Ohno N., Ye M. Y., Kuwabara T., “Space-Charge Limited Current from Plasma-Facing Material”, Contrib. Plasma Phys., 44:1–3 (2004), 126–137 | DOI

[14] Popov V. A., Arakcheev A. S., Kandaurov I. V., Kasatov A. A., Kurkuchekov V. V., Trunev Yu. A., Vasilyev A. A., Vyacheslavov L. N., “Theoretical simulation of the closed currents near non-uniformly strongly heated surface of tungsten due to thermo-emf”, Phys. Plasmas, 29:3 (2022), 033503 | DOI

[15] Abadlia L., Gasser F., Khalouk K., Mayoufi M., Gasser J. G., “New experimental methodology, setup and LabView program for accurate absolute thermoelectric power and electrical resistivity measurements between 25 and 1600 K: Application to pure copper, platinum, tungsten, and nickel at very high temperatures”, Rev. Sci. Instrum., 85:9 (2014), 095121 | DOI

[16] Fiflis P., Kirsch L., Andruczyk D., Curreli D., Ruzic D. N., “Seebeck coefficient measurements on Li, Sn, Ta, Mo, and W”, J. Nucl. Mater., 438:1–3 (2013), 224–227 | DOI

[17] J. D. Jackson, Classical Electrodynamics, John Wiley Sons, New York—London, 1962 | MR

[18] H. Buchholz, Elektrische und magnetische Potentialfelder, Springer, Berlin—Göttingen—Heidelberg, 1957 | MR | Zbl

[19] W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill, New York—Toronto—London, 1950

[20] Walden J., “On the approximation of singular source terms in differential equations”, Numer. Methods Partial Diff. Equ., 15:4 (1999), 503–520 | 3.0.CO;2-Q class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[21] A. A. Samarskii and E. S. Nikolaev, Methods for Solving Grid Equations, Nauka, M., 1978 (in Russian)

[22] R. G. Strongin, V. P. Gergel', V. A. Grishagin, and K. A. Barkalov, Parallel Computing in Global Optimization Problems, Mosk. Gos. Univ., M., 2013 (in Russian)

[23] S. K. Godunov, S. P. Kiselev, I. M. Kulikov, and V. I. Mali, Modeling of Shock-Wave Processes in Elastic- Plastic Materials at Various (Atomic, Meso, and Thermodynamic) Structural Levels, Inst. Komp'yut. Issled., Izhevsk, 2014 (in Russian)