Comparison of heat flows in underground openings of plane and spherical symmetry

Heat flow in different-purpose underground openings is analyzed in modeling them as plane and spherical symmetry objects, with introduction of notion of an equivalent radius. The aim of the study is to determine a possible transition zone between spherical and plane symmetry in heat problem solution. The simple analytic dependences are obtained for determining heat flow at the boundary of different symmetry openings as a function of the Fourier criterion. The quantitative changes in heat flow in different symmetry openings at the first order boundary condition are compared. The rational zone is determined for possible transition from the spherical to plane symmetry at the quantitative error of heat flow prediction not higher than the permissible value in the engineering practice. The limit cross-sections of underground openings and the heat flow durations such that the spherical-to-plane symmetry transition is possible for analytical solution of heat problems are found. In particular, it is shown that at short durations of heat processes, for instance, fire in an underground structure, it is entirely admissible to use plane symmetry to predict temperature condition in rock mass for underground openings of small cross-section (less than 10 m2).

Galkin A. F., Kurta I. V., Pankov V. Yu. Comparison of heat flows in underground openings of plane and spherical symmetry. MIAB. Mining Inf. Anal. Bull. 2020;(10):133-141. [In Russ]. DOI: 10.25018/0236-1493-2020-10-0-133-141.

A.F. Galkin¹, Dr. Sci. (Eng.), Professor, Senior Researcher, e-mail: afgalkin@mail.ru,
I.V. Kurta¹, Cand. Sci. (Eng.), Assistant Professor, Vice-Rector for Research,
V.Yu. Pankov, Cand. Sci. (Geol. Mineral.), Assistant Professor,
M.K. Ammosov North-Eastern Federal University, 677000, Yakutsk, Republic of Sakha, Russia,
¹ Ukhta State Technical University, 169300, Ukhta, Republic of Komi, Russia.

A.F. Galkin, e-mail: afgalkin@mail.ru.

1. Skuba V. N. Issledovanie ustoychivosti gornykh vyrabotok v usloviyakh mnogoletney merzloty [Study of the stability of mine workings in the conditions of permafrost], Novosibirsk, Nauka, 1974, 118 p.

2. Greth A., Roghanchi P., Kocsis K. A review of cooling system practices and their applicability to deep and hot underground US mines. Proccedings of the 16th North American Mine Ventilation Symposium. Golden, 2017. Vol. 11. Pp. 1—9.

3. Danko G. Ventilation and climate control of deep mines. McGraw-Hill Yearbook of Science and Technology. 2012. Pр. 296—299.

4. Kuzmin G. P. Podzemnye sooruzheniya v kriolitozone [Underground structures in the permafrost zone], Novosibirsk, Nauka, 2002, 176 p.

5. Bondarev E.A. Krasovitsky B.A. Temperaturnyy rezhim neftyanykh i gazovykh skvazhin [The temperature regime of oil and gas wells], Novosibirsk, Nauka, 1974, 88 p.

6. Kazakov B. P., Zaitsev A. V. The study of the formation of the thermal regime of deep mines. Vestnik Permskogo natsional’nogo issledovatel’skogo politekhnicheskogo universiteta. Geologiya. Neftegazovoe i gornoe delo. 2014, no 10, pp. 91—97. [In Russ].

7. Galkin A.F., Kurt I.V., Pankov V.Yu. Estimation of the duration of the period of temporary conservation of gold mines in the permafrost zone. Gornyi Zhurnal. 2020, no 4, pp. 37—41. [In Russ].

8. Vernigor V. M., Morozov K. V., Bobrovnikov V. N. About approaches to designing the thermal regime of mines in permafrost. Journal of Mining Institute. 2013. Vol. 205, pp. 139—140. [In Russ].

9. Lapshin A.A. The effect of hardening bookmarks in treatment chambers on the microclimate of deep mines. East European Journal of Advanced Technology. 2014, no 10, pp. 3—11. [In Russ].

10. Galkin A. F. Thermal conditions of the underground town collector tunnel. Metallurgical and Mining Industry. 2015. Vol. 7. No 8. Pp. 74—77.

11. Tynyna S. V. On increasing the efficiency of local conditioning systems for dead-end preparatory workings of deep mines. Geo-Technical Mechanics. 2011, no 94, pp. 266—271. [In Russ].

12. Kazakov B. P., Levin L.Yu., Zaitsev A. V. Modern approaches to the development of methods for controlling the thermal regime of mines at high temperature of the rock mass. Gornyi Zhurnal. 2014, no 5, pp. 22—25. [In Russ].

13. Shuai Zhu, Shiyue Wu, Jianwei Cheng, Siyuan Li, Mingming Li An underground airroute temperature prediction model for ultra-deep coal mines. Minerals. 2015. Vol. 5. No 3. Pр. 527—545.

14. Khalid M. Z., Zubair M., Ali M. An analytical method for the solution of two phase Stefan problem in cylindrical geometry. Applied Mathematics and Computation. 2019. Vol. 342. Pp. 295—308.

15. McCord D., Crepeau J., Siahpush A., Brogin J. Analytical solutions to the Stefan problem with internal heat generation. Applied Thermal Engineering. 2016. Vol. 103. Pp. 443—451.

16. Bozhilov V., Petrov K. Heat and waterproofing — an effective means of improving the microclimate in mines. Doklady 9-y sessii Mezhdunarodnogo byuro po gornoy teplofizike [Reports of the 9th session of the International Bureau of Mountain Thermophysics], Poland: Gliwice, 2000, pp. 245—255.

17. Alab'ev V., Alekseenko S. N., Shaykhlislamova I. Methodological basics of gas-drainage pipeline engineering for transporting wet firedamp in winter time. Progressive technologies of coal, coalber methane and ores mining. CRC Press, London. 2014, pp. 195—200.

18. Galkin A. F. Calculation of parameters of cryolithic zone mine openings thermal protection coating. Metallurgical and Mining Industry. 2015. Vol. 7. No 8. Pp. 68—73.

19. Lapshin A.A. Mathematical modeling of microclimate normalization processes in deep ore mines. Naukovy Visnik NSU. 2014, no 3, pp. 137—144. [In Russ].

20. Goodman T. R. The use of integral methods in nonlinear problems of unsteady heat transfer. Problemy teploobmena: sbornik statey [Heat transfer problems: Collection of articles], Moscow, Atomizdat, 1967, pp. 41—95.