Geodesic
Unsteady concentration field of reacting gas in the vicinity of a burning coal particle
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 1, pp. 101-114 
S. V. Cherdantsev; P. A. Shlapakov; S. I. Goloskokov; K. S. Lebedev; A. Yu. Erastov. Unsteady concentration field of reacting gas in the vicinity of a burning coal particle. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 1, pp. 101-114. http://geodesic.mathdoc.fr/item/SJVM_2023_26_1_a7/
@article{SJVM_2023_26_1_a7,
     author = {S. V. Cherdantsev and P. A. Shlapakov and S. I. Goloskokov and K. S. Lebedev and A. Yu. Erastov},
     title = {Unsteady concentration field of reacting gas in the vicinity of a burning coal particle},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {101--114},
     year = {2023},
     volume = {26},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2023_26_1_a7/}
}
TY  - JOUR
AU  - S. V. Cherdantsev
AU  - P. A. Shlapakov
AU  - S. I. Goloskokov
AU  - K. S. Lebedev
AU  - A. Yu. Erastov
TI  - Unsteady concentration field of reacting gas in the vicinity of a burning coal particle
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2023
SP  - 101
EP  - 114
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2023_26_1_a7/
LA  - ru
ID  - SJVM_2023_26_1_a7
ER  - 
%0 Journal Article
%A S. V. Cherdantsev
%A P. A. Shlapakov
%A S. I. Goloskokov
%A K. S. Lebedev
%A A. Yu. Erastov
%T Unsteady concentration field of reacting gas in the vicinity of a burning coal particle
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2023
%P 101-114
%V 26
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2023_26_1_a7/
%G ru
%F SJVM_2023_26_1_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

The article deals with a boundary value problem of mathematical physics describing the unsteady process of diffusion of a reacting gas to a spherical coal particle located in the atmosphere of a mine. The solution of the boundary value problem is based on self-similar transformations which are a special case of group analysis. Formulas for determining the concentrations of the reacting gas in the vicinity of the coal particle and on its surface are obtained. Graphs of the dependencies of the burn-out time of the coal particle on a number of its parameters are constructed, and the fields of the reacting gas concentration at various stages of combustion of the coal particle are revealed.

[1] Frank-Kamenetskii D.A., Diffuziya i teploperedacha v khimicheskoi kinetike, Nauka, M., 1987

[2] Kantorovich B.V., Osnovy teorii goreniya i gazifikatsii tverdogo topliva, Kniga po Trebovaniyu, M., 2013

[3] Vilenskii T.V., Khzmalyan D.M., Dinamika goreniya pylevidnogo topliva, Nauka, M., 1977

[4] Lindenau N.I., Maevskaya V.M., Krylov V.F., Proiskhozhdenie, profilaktika i tushenie endogennykh pozharov v ugolnykh shakhtakh, Nedra, M., 1977

[5] Chanyshev A.I., “A method to determine a body's thermal state”, J. of Mining Science, 48:4 (2012), 660–668

[6] Cherdantsev S.V., Li Kh.U., Filatov Yu.M., Botvenko D.V., Shlapakov P.A., Kolykhalov V.V., “Gorenie melkodispersnykh pylegazovozdushnykh smesei v atmosfere gornykh vyrabotok”, FTPRPI, 2018, no. 2, 172–180 | DOI

[7] Cherdantsev S.V., Filatov Yu.M., Shlapakov P.A., “Rezhimy diffuzionnogo goreniya melkodisperstnykh pylegazovozdushnykh smesei v atmosfere gornykh vyrabotok”, Ugol, 2020, no. 2, 27–32 | DOI

[8] Shevchuk V.G., Kondrat'ev E.N., Zolotko A.N., Sidorov A.E., Oparin A.S., “Wave regimes of dust combustion”, Combustion, Explosion, and Shock Waves, 50 (2014), 80–86

[9] Sidorov A.E., Shevchuk V.G., Kondrat'ev E.N., “Conductive-radiative model of a laminar flame in dust suspensions”, Combustion, Explosion, and Shock Waves, 49 (2013), 257–263

[10] Vasilev A.A., Pinaev A.V., Trubisyn A.A., Crachev A.Y., Trotsyuk A.V., Fomin P.A., Trilis A.V., What is burning in coal mines: methane or dust?, Combustion, Explosion, and Shock Waves, 53:1 (2017), 8–14

[11] Cherdantsev S.V., Shlapakov P.A., Erastov A.Yu., Khaimin S.A., Lebedev K.S., Kolykhalov V.V., Shlapakov E.A., “Modelirovanie protsessa molekulyarnoi diffuzii reagiruyuschego gaza k pokoyascheisya grubodispersnoi ugolnoi chastitse v gornoi vyrabotke”, Vestnik Nauchnogo tsentra VostNII po promyshlennoi i ekologicheskoi bezopasnosti, 2017, no. 4, 13–21

[12] Nifantov B.F., Potapov V.P., Anferov B.A., Kuznetsova L.V., Ugli Kuzbassa: khimicheskie elementy-primesi i tekhnologii ikh izvlecheniya pri kompleksnom osvoenii mestorozhdenii, IU SO RAN, Kemerovo, 2011

[13] Denisov E.T., Sarkisov O.M., Likhtenshtein G.I., Khimicheskaya kinetika, Uchebnik dlya vuzov, Khimiya, M., 2000

[14] Koshlyakov N.S., Gliner E.B., Smirnov M.M., Uravneniya v chastnykh proizvodnykh matematicheskoi fiziki, Vysshaya shkola, M., 1970

[15] Bermant A.F., Aramanovich I.G., Kratkii kurs matematicheskogo analiza, Uchebnik dlya vuzov, 11-e izd., ster., Izd-vo «Lan», SPb., 2005

[16] Ovsyannikov L.V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978

[17] Sedov L.I., Metody podobiya i razmernosti v mekhanike, Nauka, M., 1977

[18] Pontryagin L.S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1974

[19] Alekseev E.R., Chesnokova O.V., Reshenie zadach vychislitelnoi matematiki v Mathcad 12, MATLAB 7, Maple 9, NT Press, M., 2006