Stationary process of dusty-gas mixtures flow in the mine workings in the presence of the heat supply zone caused by spontaneous heating centers located near the workings is considered in the article. Based on the laws of conservation of mass, impulse and energy the formulas are obtained for determining the number of characteristics (speed, density, pressure, temperature, Mach number) of the dust-gas-air mixture flow, which describe the intensity of the moving front of the dust-gas-air mixture, which crossing the zone of influence of the spontaneous heating points. These expressions contain the plus or minus sign in front of the radical, so each sought function has two significantly different meanings.
The problem is formulated on the influence of the thermal field caused by the points of spontaneous heating on the flow of dust-gas-air mixtures in the room. It was identified that for any Damkeler number representing the dimensionless amount of heat input, each of the functions found, that characterizes the stationary flow of mixtures along the working, consists of two sections. Their boundaries are two critical Mach numbers, and, moreover, the flow of mixtures in the section between them is unsteady. The larger the Damkeler number is, the longer is the section between the critical Mach numbers, and the more unsteady nature of the dust-gas mixture flow is manifested.
The conditions for the unsteady flow of mixtures are revealed. Plots are constructed that characterize the changes in the parameters of dust-gas-air mixtures crossing the zone of influence of spontaneous heating points. At critical values of heat input, the relative values of pressure and density of mixture increase monotonically with increasing the critical Mach numbers. With a Mach number equal to one, the Damkeler number assumes zero value. This indicates the impossibility of supplying heat to the dust-gas mixture when it moves in a stationary mode.
- Zakharov E.I., Kachurin N.M., Malakhova D.D. Mechanism of the process of coal spontaneous heating and its transition into spontaneous-combustion. Izvestiya TulGU. Nauki o Zemle = TulGU News. Earth sciences. 2013. № 2. pp. 42–50. (In Russ.).
- Oparin V.N., Kiryaeva T.A., Gavrilov V.Yu., Tanashev Yu.Yu., Bolotov V.A. Initiation of underground fire sources. Journal of Mining Science. 2016. Vol. 52. Iss. 3. pp. 576–592. DOI: 10.1134/S1062739116030850
- 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. Iss. 5. pp. 861–867. DOI: 10.1134/S1062739117052886
- Frank-Kamenetskiy D.A. Diffusion and Heat Transfer in the Chemical Kinetics. Moscow: Nauka, 1987. 502 p. (In Russ.).
- Kantorovich B.V. Bases of Theory of Combustion and Gasification of Solid Fuel. Moscow: Kniga po trebovaniyu, 2013. 600 p. (In Russ.).
- Chanyshev A.I. A method to determine a body’s thermal state. Journal of Mining Science. 2012. Vol. 48. Iss. 4. pp. 660–668.
- Cherdantsev S.V., Shlapakov P.A., Erastov A.Yu., Khaymin S.A., Lebedev K.S., Kolykhalov V.V., Shlapakov E.A. Investigation of the temperature field in the areas of rock and coal concentration near the self-heating zone. Available at: https://iopscience.iop.org/article/10.1088/1755-1315/206/1/012006/pdf (accessed: July 30, 2019).
- Cherdantsev S.V., Li Khi Un, Filatov Yu.M., Shlapakov P.A. Determination of the critical ignition temperature of microheterogeneous dust-gas-air mixtures in the mine workings. Gornyy informatsionno-analiticheskiy byulleten (nauchno-tekhnicheskiy zhurnal) = Mining Information and Analytical Bulletin (scientific and technical journal). 2018. №1. pp. 117–125. (In Russ.). DOI: 10.25018/0236-1493-2018-1-0-117-125
- 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. 2017. Vol. 90. Iss. 1. pp. 206–216. DOI: 10.1007/s10891-017-1557-2
- Cherdantsev S.V., Lee Khi Un, Filatov Yu.M., Shlapakov P.A. Analysis of Combustion Process of Microheterogeneous Dust and Gas Mixtures in the Mine Workings. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2017. № 11. pp. 10–15. (In Russ.). DOI: 10.24000/0409-2961-2017-11-10-15
- 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. Iss. 3. pp. 295–300.
- Levin V.A., Tunik Yu.V. Initiation of detonation combustion of coal dust in a methane-air mixture. Fizika goreniya i vzryva = Physics of Combustion and Explosion. 1987. № 1. pp. 3–8. (In Russ.).
- Bartlmä F. Gasdynamik der Verbrennung. — Stuttgart: Deutsche forschungs and versuchsanstalt «Institut fur Reaktionskinetik», 1975. 280 p. (In Germ.).
- Ovsyannikov L.V. Lectures on the basics of gas dynamics. Moscow–Izhevsk: Institut kompyuternykh issledovaniy, 2003. 336 p. (In Russ.).
- Rakhmatullin Kh.A., Sagomonyan A.Ya., Bunimovich A.I., Zverev N.N. Gas dynamics. Moscow: Vysshaja shkola, 1965. 723 p. (In Russ.).