基于量纲分析理论的煤尘爆炸能量预测模型

为预测煤尘爆炸能量，基于量纲分析理论建立煤尘爆炸能量预测模型。选取爆炸能量E、空气密度ρ和大气压强p的量纲为导出量纲。根据量纲分析Π定理得出含有待定参数λ的具有普适性的能量预测模型。通过小型煤尘爆炸性实验设计，测定10次爆炸最长火焰长度平均值l₀、10次最长火焰长度出现时间平均值t₀与该小型煤尘爆炸中释放能量E₀，确定模型中参数λ为0.467。对模型变量t、E、l的函数关系进行合理性检验。通过实测的15组不同时刻的火焰长度进行模型变量t、l幂指关系检验。检验结果表明:量纲选取完备，预测模型科学合理。

An energy prediction model for coal dust explosion based on dimensional analysis

To assess the coal dust explosive power,we used the dimensional analysis mathematical method to model the prediction of the energyreleased from coal dust explosion.The basic dimensions selected are those of the distance,the mass and the time,of coal dust explosion's flame propagation.The selected output dimensions are those of explosive energy,the air density and the barometric pressure.According to the dimensional analysis Ⅱ theorem,we established the energy prediction model with unknown parameters and undetermined parameters,a model that is universally applicable.By carrying out a small-scale coal dust explosion experimental design,we determined the model parameters,and obtained the average maximum flame length of ten times of coal dust explosion,the average maximum flame time,and the released energy.The undetermined parameter was calculated as 0.467.It follows that the prediction model for coal dust explosive energy and its qualification were obtained.Based on our rationality analysis of this model,the experimental measured flame length of 15 different times of coal dust explosion was used to test the power exponent relationship.The test result verifies the completeness of the selected dimensions and the scientific rationality of the prediction model.Using fewer variable parameters,this model simplifies calculations and will provide important reference for explosion hazard assessment.