Квазистационарная задача о концентрационном поле реагирующего газа в окрестности горящей угольной частицы

Abstract

When developing coal deposit, the coal dust is formed. Mixing with the atmosphere of the mine workings, it forms the dust-gas-air mixtures that are prone to chemical reactions in various forms. As a rule, such mixtures are neutralized in the dust source area. However, in the coal mines the danger remains related to the normal combustion turning into the detonation of the coal dust. It can be both in the composition of the dust-gas-air mixture, and in the form of the settled layers suspended in the atmosphere of the workings by a methane explosion. In this case there is a risk of a multiple increase in the explosion power due to the ignition of the coal particles as and when the burning spreads through the working. Coal particles burning is considered as a stationary process. However, under certain conditions it becomes necessary to consider accounting the non-stationarity of its flow. This circumstance significantly complicates the consideration of the burning process. Quasi-stationary problem that considers the change in the concentration fields of the reacting gas around a coal particle at different time intervals is studied in the article. The formulas are obtained for determining the concentrations of the reacting gas in the vicinity of the burning coal particle and on its surface. Based on the law of mass conservation of the substances involved in the burning reaction, the formula was found for calculating the radius of the burning coal particle over time. The formula is also derived for determining the complete burning time of the coal particle. The graphs are constructed concerning the dependences of the coal particle burnout time on the number of its parameters. The concentration fields of the reacting gas around the coal particle at various stages of its burning are revealed.