About One Approach to the Description of Blow of Methane from the Coal Massif to the Mine Workings

N.V. Cherdantsev, Doctor of Technical Sciences, Laboratory Head, nvch2014@yandex.ru FGBNU «Federal Research Centre of Coal and Coal Chemistry of SO RAN», Kemerovo, Russia S.V. Cherdantsev, Doctor of Technical Sciences, Leading Researcher Khi Un Lee, Doctor of Technical Sciences, Professor, Deputy General Director — Academic Secretary Yu.M. Filatov, Candidate of Technical Sciences, General Director P.A. Shlapakov, Laboratory Head K.S. Lebedev, Research Engineer AO «Scientific Research Center VostNII on Safety of Work in the Mining Industry», Kemerovo, Russia

On the basis of fundamental provisions of gas dynamics the Cauchy problem was formulated for the system of the differential equations of the first order on the characteristic lines describing gas flow in the underground tank. The differential diagram and the algorithm of the approximate solution of Cauchy problem were built. Gas velocities, local sound speeds and the Mach number in the expanding part of the tank are calculated. Jet supersonic discharge of gas from the tank to the mine working was studied. Parameters of gas were calculated and the schedules of their dependences on the value of shock wave was built, some regularities of jet gas flow in the mine working were identified.
It is established that the dependence of the value of shock wave from Mach number — the monotonous slightly concaved curve indicating the nonlinear growth of shock wave value with increase in Mach number. At the same time the growth of the shock wave results in nonlinear increase in speed of the concurrent flow occurred due to different speeds of gas flow before and after the shock wave.
It is shown that at the calculated values of Mach number and the value of the shock wave the concurrent flow moves with a storm speed and is capable to damage the roadway support, injure the workers, and lift a huge number of particles of dust in the working complicating people’s breathing, and by this creating particular threat to them.
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DOI: 10.24000/0409-2961-2017-3-45-52
Year: 2017
Issue num: March
Keywords : bleeding ideal gas Euler's equations the potential of speeds sound speed March number characteristic lines the equations in final differences shock waves concurrent flow