Development of mining machinery, use of new stoping flow sheets and transition to deeper level mining govern the high intensity of gas-dynamic and thermophysical factors. For the first turn, this relates to coal and gas outbursts, bleeding, shock as well as shock and detonation waves in mine air. Of no less importance are such factors as dust–air–gas mixtures capable of oxidation and initiation of spontaneous heating sources changing temperature conditions in mine air, which promotes deflagration and detonation processes. This article attempts to construct and implement a mathematical model of gas–air flow under supersonic gas outburst in an underground excavation. The mathematical modeling assumes that the gas–air flow possesses viscosity and thermal conductivity, and is stationary when passes the shock front. In the model implementation, an autonomous equation is obtained and solved using a small parameter of the Prandtl number. The phase pattern is constructed, which reveals an isothermal jump of zero thickness at the absence of viscosity, while at the presence of viscosity, the jump has thickness and, thus, is no more isothermal. Furthermore, the formulas are obtained to find gas–air flow parameters far behind the shock front, the graphs of these parameters are plotted and the regular patterns of change in the gas–air flow parameters behind the shock front depending on the Prandtl number, initial Mach number and Poisson’s adiabatic exponent are revealed.

For citation: Cherdantsev S. V., Filatov Yu. M., Shlapakov P. A. Structure and parameters of shock front in viscous thermoconductive gas–air flow in underground excavation. MIAB. Mining Inf. Anal. Bull. 2019;(10):183-194. [In Russ]. DOI: 10.25018/0236-1493-2019-10-0-183-194.


Underground excavations, gas–air mixtures, laws of conservation of mass, momentum and energy, viscosity factor, thermal diffusivity, Mach number, Prandtl number, Poisson’s adiabatic exponent, shock front.

Issue number: 10
Year: 2019
ISBN: 0236-1493
UDK: 622.272:516.02
DOI: 10.25018/0236-1493-2019-10-0-183-194
Authors: Cherdantsev S. V., Shlapakov P. A., Filatov Yu. M.

About authors: S.V. Cherdantsev, Dr. Sci. (Eng.), Chief Researcher, e-mail:, Yu.M. Filatov, Cand. Sci. (Eng.), General Director, e-mail:, P.A. Shlapakov, Cand. Sci. (Eng.), Head of Laboratory, е–mail:, Join-stock company «Scientific Centre VOSTNII on Industrial and Ecological Safety in Mountain Industry» (JC «NC VOSTNII»), 650002, Kemerovo, Russia. Corresponding author: S.V. Cherdantsev, e-mail:


11.     Bol'shinskiy M. I., Lysikov B. A., Kaplyukhin A. A. Gazodinamicheskie yavleniya v shakhtakh [Gas dynamic phenomena in mines], Sevastopol, Veber, 2003, 284 p.

2.     Cherdantsev N. V., Cherdantsev S. V., Li Khi Un, Filatov Yu. M., Shlapakov P. A., Lebedev K. S. On one approach to the description of suflar gas emissions from the res-ervoirs of the coal massif into the mine workings. Bezopasnost' truda v promyshlennosti. 2017, no 3, pp. 45—52. [In Russ].

3.     Oparin V. N., Kiryaeva T. A., Gavrilov V.Yu., Tanashev Yu.Yu., Bolotov V. A. Initiation of underground fire sources. Journal of Mining Science, May 2016. Vol. 52, Issue 3, pp. 576—592.

4.     Chanyshev A. I. A method to determine a body’s thermal state. Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh. 2012, no 4, pp. 83—93. [In Russ].

5.     Cherdantsev S. V., Shlapakov P. A., Erastov A. Yu., Khaymin S. A., Lebedev K. S., Kolykhalov V. V., Shlapakov E. A. Study of the temperature field in Portogallo congestion in the vicinity of the center of self-heating. Naukoemkie tekhnologii razrabotki i ispol'zovaniya mineral'nykh resursov. 2018, no 4, pp. 49—55. [In Russ].

6.     Vasil'ev A. A., Vasil'ev V. A. Calculated and experimental parameters of com-bustion and detonation of mixtures based on methane and coal dust. Vestnik Nauchnogo tsentra po bezopasnosti rabot v ugol'noy promyshlennosti. 2016, no 2, pp. 8—39. [In Russ].

7.     Cherdantsev S. V., Li Hi Un, Filatov Yu. M., Botvenko D. V., Shlapakov P. A., Kolykhalov V. V. Combustion of Fine Dispersed Dust-Gas-Air Mixtures in Underground Workings. Journal of Mining Science. March 2018, vol. 54, Issue 2, pp. 339—346.

8.     Glushkov D. O., Kuznetsov G. V., Strizhak P. A. Initiation of Combustion of a Gel-Like Condensed Substance by a Local Source of Limited Power. Journal of Engineering Physics and Thermophysics, January 2017. Vol. 90, Issue 1, pp 206—216.

9.     Amelchugov S. P., Bykov V. I., Tsybenova S. B. Spontaneous Combustion of Brown-Coal Dust. Experiment, Determination of Kinetic Parameters, and Numerical Modeling. Combustion, Explosion and Shock Waves, 2002, vol. 38, Issue 3, pp. 295—300.

10.    Kurlenya M. V., Skritsky V. A. Methane Explosions and Causes of Their Origin in Highly Productive Sections of Coal Mines. Journal of Mining Science, 2017, vol. 53, no 5, pp 861—867.

11.    Fedorov A. V., Fomin P. A., Tropin D. A. Simple kinetics and detonation wave structure in a methane-air mixture. Fizika goreniya i vzryva. 2014, no 1, pp. 97—105. [In Russ].

12.    Ovsyannikov L. V. Lektsii po osnovam gazovoy dinamiki [Lectures on the basics of gas dynamics], Moskva-Izhevsk, Institut komp'yuternykh issledovaniy, 2003, 336 p.

13.    Rakhmatullin Kh. A., Sagomonyan A. Ya., Bunimovich A. I., Zverev N. N. Gazovaya dinamika [Gas dynamics], Moscow, Vysshaya shkola, 1965, 723 p.

14.    Koshlyakov N. S., Gliner E. B., Smirnov M. M. Uravneniya v chastnykh proizvodnykh matematicheskoy fiziki [Partial differential equations of mathematical physics], Moscow, Vysshaya shkola, 1970, 712 p.

15.    Kutateladze S. S. Osnovy teorii teploobmena [Fundamentals of heat transfer theory], Moscow, Atomizdat, 1979, 416 p.

Subscribe for our dispatch