S.V. Cherdantsev, Dr. Sci. (Eng.), Leading Researcher Lee Khi Un, Dr. Sci. (Eng.), Prof., Deputy General Director Yu.M. Filatov, Cand. Sci. (Eng.), General Director P.A. Shlapakov, Laboratory Head AO «Scientific Research Center VostNII on Safety of Work in the Mining Industry», Kemerovo, Russia
In the course of operation of shearer and tunnelling machines, drilling rigs and other mine equipment the formation of carbon dust is inevitable, which interaction with air-gas atmosphere of excavations and development workings forms the dust-producing mixtures.
In the presence of sources of ignition emerging from the friction of operating parts of mechanisms of mining machines and tools, such dust-air-gas mixtures are prone to chemical reaction with transition to the combustion mode. Processes of inflammation, combustion, and detonation of gas suspensions of combustible disperse systems are considered in reasonable detail in the native and foreign literature. However the majority of works is devoted to combustion of coals in the power plants for the purpose of obtaining thermal energy and its further conversion. Excavations in comparison with combustion chambers and fireboxes of boiler units are one-dimensional regions of different configurations. Combustion processes of dust-air-gas mixtures in them mainly occur in a directional air-gas flow, unlike combustion in fireboxes and combustion chambers.
The purpose of this work is to detect and analyze the numerical values and functions defining the propagation conditions of combustion zone of microheterogeneous dust-air-gas mixtures in the excavations.
On the basis of the equation of thermal conductivity the stationary combustion process of microheterogeneous dust-air-gas mixtures in the excavations is considered. Cauchy problem is formulated for one-dimensional non-linear differential equation describing the process of combustion of microheterogeneous dust-air-gas mixture, and its approximate solution is framed by Gear method. It is established that the solutions of Cauchy problem are the own functions, for each of which there is own value caused by basic data of the problem.
For basic data of microheterogeneous dust-air-gas mixture the own values are found, among which the critical values are detected, below which the Cauchy problem does not have a solution, therefore, the process of combustion is impossible. It is revealed that with increase in own values the values of the required functions are also increasing.
The equation is received, which connects the temperature of the dust-air-gas mixture in the arbitrary section of the excavation and its coordinate.
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