Analysis of a sudden release of a gas-coal mixture from a conical cavity formed during the gas outburst

S. V. Cherdantsev, P. Shlapakov, K. Lebedev
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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.
分析从气体爆发时形成的锥形空腔中突然释放出的气煤混合物
地下煤矿开采中不可或缺的属性是甲烷和各种颗粒大小的煤尘。当它们混合时,就会形成煤气混合物,容易产生各种危险和极度危险的气体动力现象,主要是突然排放,同时在煤层中形成空洞,煤气混合物从这些空洞中大量释放到矿井工作面。文章讨论了瓦斯-煤混合物在突然排放时形成的地下锥形空腔中的一维静态流动问题。基本方程采用欧拉运动方程和连续性方程。对它们进行变换后,得到了一阶常微分方程,并提出了考奇问题。考奇问题的解是一个与所需马赫数有关的超越方程。超越方程的根使用 MathCAD 数学软件套件进行计算。找到马赫数后,就可以确定混合物的其余参数,即锥形区域内任意一点的气煤混合物的压力、密度和温度,包括其临界值。在此基础上,绘制了锥形区域内气煤混合物一维静态流动的一些规律性曲线。特别是,研究发现,随着马赫数的增加,气煤混合物的参数呈非线性下降;随着泊松绝热指数的增加,压力和温度降低,密度增加。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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