采空区自燃理论模型的无因次分析与应用

Dimensionless analysis and application on the mathematical model for spontaneous combustion in goaf

预测预报是采空区自燃防治的主要措施,但采空区自然发火的影响因素众多,并且各因素之间往往相互关联,这给采空区自燃的预测带来了很大困难。选取回采工作面长度作为物理模型的基准尺寸,同时选取了基准速度、基准氧气浓度和基准温度等参考值,依据这些基准参考值定义了无因次压力、无因次氧扩散系数、傅里叶准数等无因次准则。在这些无因次准则的基础上依据量纲一致原理将采空区自燃模型转换成了无因次模型。然后逐个分析模型中的无因次准则对采空区自燃的影响,将影响自燃的主要无因次准则为组合成耗氧和放热2个无因次准则。进一步分析这2个准则的取值范围,并在它们的取值范围内取2个自燃准则的不同组合进行自燃的模拟,得到采空区的最高无因次温度,并绘制成采空区自燃判别图用以对采空区自燃进行判别。

Spontaneous combustion is controlled by prediction and forecast mainly in goaf. However,it has a number of influential factors and these factors have mutual relationships,which result in a great difficulty to prediction. Therefore,the length of face was selected as reference dimension. Also,the reference value was determined such as reference velocity,reference oxygen concentration and reference temperature and so on. Then the dimensionless criteria were defined including dimensionless pressure,dimensionless oxygen diffusion coefficient and Fourier ＇s number and so on.Based on these criteria,the model of spontaneous combustion in goaf was transformed into dimensionless model by dimensional homogeneity. Subsequently,the influence of model＇s dimensionless criteria on spontaneous combustion in goaf were analyzed one by one,acquiring two dimensionless criteria：oxygen consumption and heat release. Their value ranges were further analyzed. Spontaneous combustion was modeled by various combinations in the value range of two dimensionless criteria,acquiring the maximum of dimensionless temperature. Then the discrimination diagram of spontaneous combustion in goaf was drawn for prediction. The research finding has a theoretical and practical significancefor spontaneous combustion control in mine.