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

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 ve- locity,reference oxygen concentration and reference temperature and so on. Then the dimensionless criteria were de- fined 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 di- mensional 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 spon- taneous combustion in goaf was drawn for prediction. The research finding has a theoretical and practical significance for spontaneous combustion control in mine.