Анализ внезапного выброса газоугольной смеси из полости конической формы, сформированной в процессе выброса

Abstract

Indispensable attributes in underground coal mining are methane and coal dust of various particle sizes. When they are mixed, coal-gas mixtures are formed, predisposed to various hazardous and extremely hazardous gas-dynamic phenomena, primarily to sudden emissions, accompanied by formation of cavities in the coal massif and intensive release of coal-gas mixtures from these cavities into the mine workings. The article deals with the problem of a one-dimensional stationary flow of a gas-coal mixture in an underground cone-shaped cavity formed during a sudden release. The Euler equation of motion and the continuity equation are used as the basic equations. As a result of their transformation, an ordinary differential equation of the first order is obtained, for which the Cauchy problem is formulated. The solution to the Cauchy problem is a transcendental equation with respect to the desired Mach numbers. The roots of the transcendental equation are calculated using the MathCAD mathematical software suite. Upon finding the Mach numbers, the remaining parameters of the mixture are determined, i.e. the pressure, density and temperature of the gas-coal mixture at any point in the conical region, including their critical values. Graphs are constructed that were used as the basis to establish some regularities of the one-dimensional stationary flow of a gascoal mixture in a conical region. In particular, it was found that with an increase in the Mach number, parameters of the gas-coal mixture decrease non-linearly, and with an increase in the Poisson's adiabatic index, the pressure and temperature decrease, and the density increases.