International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

## Mathematical Model of Ignition of Gas-Air Mixture and Fine Coal Dust Laminar Flow Y.N.Zakharov1*, D.V.Botvenko, Y.M.Filatov, Lee Hee Un2, V.A.Perminov

### Reporter: Захаров Ю.Н.

Mathematical Model of Ignition of Gas-Air Mixture and Fine Coal Dust Laminar Flow
Y.N.Zakharov1*, D.V.Botvenko, Y.M.Filatov, Lee Hee Un2, V.A.Perminov
1Kemerovo State University, Kemerovo, Russia
2 NC VostNII JSC,  Kemerovo, Russia
3 Tomsk Polytechnic University, Tomsk, Russia
Protection from methane and coal dust explosions is the key problem of mine worker safety ensuring. Modern degassing systems can extract not more than 40% of methane out of coal bed. It means that there is a high chance of methane explosive limit development in mine face areas of stope ores and development workings. Suspended particles of fine coal dust contained in airstream increase explosion power and reduce induction period. Intensity of mining activities and high performance equipment enhance the chances of frictional sparking.
Experimental study of gas suspensions which can generate heat due to chemical reactions is rather challenging. Accordingly, mathematical modeling is the main way to study oxidizing explosive atmosphere macrokinetics.  Its main goal is to analyze ignition process patterns due to different conditions and estimate prevention methods and combustion containment methods as well as combustion effects.
The article considers the problem of gas suspension laminar flow ignition in the context of exothermal oxidizing reactions regarding both vapor phase and particle surface. It is based on the heat-diffusion gas combustion model [1,2,3]. For the sake of simplicity the flow of gas mixture (methane, oxygen, unreactive part and combustion products) with uniform suspended particles of coal is supposed to be parallel flow in a semi-infinite domain. Flow velocity is considered to be constant. Dispersed phase particles like in [3] have equal size and spherical shape. Velocity of particles and gas flow velocity are equal. Oxidation process is taking part on a particle surface. Heat exchange between particles and gas follows the Newton’s law. Chemical reaction rate depends on the temperature according to the Arrhenius law. Quantity of the molecules involved into oxidation and reaction products depend on stoichiometry proportion. Thermal expansion and flow compressibility are deliberately neglected. Gas flow ignition is modelled by heat source at the boundary of solution domain x=x1.
The dynamics of temperature distribution and reacting agents and resultants of reaction depending on time, initial concentrations and flow velocity is found as a result of solving the equation system

References

[1] Zeldovich, Y.B. Mathematical theory of combustion and explosion / Y.B.Zeldovich, G.I. Barenblatt, V.B.Librovich, G.M. Makhviladze – (M; Nauka, 1980)- 478 p.
[2] Dick, I.G. “ Ignition of gas suspension in a cavity with heated radiating surfaces” /I.G.Dick, A.Y. Kraynov, A.I.Makarov.// Physics of combustion and explosion. (1990). - №5. - pp.20-24
[3] Kraynov, A.Y. “ Modelling of flame propagation  in mixture of combustible gases and particles” / A.Y.Kraynov// Physics of combustion and explosion. (2000). – V.36.-№2. - pp.3-9

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