采空区球−柱组装体压损预测模型及多孔介质流动特性

Prediction model for pressure loss of sphere column assembly in goaf and flow characteristics of porous media

  • 摘要: 随着煤矿向深部开采热动力灾害发生风险增大,快速预测采空区内流动损失成为煤矿精准防灭火的关键。结合采空区流动特征,提出一种孔隙率可调整的球−柱组装体采空区多孔介质物理模型,通过控制角度θ大小改变模型总体孔隙率。进一步地,划分模型流动最小体元,并将流动过程分为10个阶段,基于平均水力半径模型以及简化后的突扩−突缩并联通道局部阻力理想模型,建立单位长度压力损失表达式。通过计算模型预测压损数值,对比了试验、数值模拟以及Ergun方程计算结果,并验证了数值模拟结果可靠性。结果表明:试验数据与计算模型预测值相对误差最大不超过10%,证明计算模型方法可行;无量纲流动损失M在雷诺数Re0, 10区间内以黏性损失项为主,与总损失的偏差小于7%。在雷诺数Re0, 10区间内,计算模型与Ergun方程的预测结果对比数值模拟计算结果相对误差均小于10%;在雷诺数Re10, 1200区间内,Ergun方程结果相对误差超20%,而计算模型结果在10 < Re < 300情况下相对误差超出许可范围,最大为22%,说明计算模型可用于单位长度压损预测。多孔介质流态对压损的影响十分显著,对无量纲流动损失F的分析表明,随着雷诺数增大多孔介质流态发生转变,具体可划分4个流动区域,分别为完全层流区(0 < Re < 1)、层流主导区(1 < Re < 10)、转捩区(10 < Re < 700)以及完全湍流区(Re > 700),根据流动损失的组成划分流动形式界限,当雷诺数1 < Re < 10为达西流,当雷诺数Re > 10为非达西流。研究成果可为采空区精准防灭火的工程实践提供理论依据。

     

    Abstract: As coal mines are mined deeper, the risk of thermodynamic disasters increases, and rapid prediction of flow loss in the goaf becomes key to precise fire prevention and extinguishing in coal mines. Considering the flow characteristics of the goaf, a physical model of the goaf porous medium assembled from spheres and cylinders with adjustable porosity is proposed, where the overall porosity of the model can be changed by controlling the angle θ. Furthermore, the model’s minimum flow element is divided into 10 stages, and based on the average hydraulic radius model and a simplified ideal model of local resistance in sudden expansion-sudden contraction parallel channels, an expression for pressure loss per unit length is established. By calculating the predicted pressure loss of the model, the numerical simulation results are compared with experimental and Ergun equation calculations, and the reliability of the numerical simulation results is verified. The results show that the relative error between the experimental data and the predicted values of the calculation model does not exceed 10%, proving the feasibility of the calculation model method; the dimensionless flow loss M is mainly dominated by the viscous loss term in the Reynolds number Re0, 10 range, with a deviation from the total loss of less than 7%. Within the Reynolds number Re0, 10 range, the relative error of the predicted results of the calculation model compared to the numerical simulation calculation results is less than 10%; within the Reynolds number Re10, 1200 range, the relative error of the Ergun equation results exceeds 20%, while the calculation model results exceed the allowable range with a maximum of 22% when 10 < Re < 300, indicating that the calculation model can be used for predicting pressure loss per unit length. The flow state of the porous medium has a significant impact on pressure loss, and the analysis of the dimensionless flow loss F indicates that as the Reynolds number increases, the flow state of the porous medium changes, which can be divided into four flow regions: pure laminar flow zone (0 < Re < 1), laminar flow dominant zone (1 < Re < 10), transition zone (10 < Re < 700), and fully turbulent flow zone (Re > 700). The boundaries of flow forms are divided according to the composition of flow loss, with Darcy flow when Reynolds number 1 < Re < 10 and non-Darcy flow when Reynolds number Re > 10. The research results can provide a theoretical basis for precise fire prevention and extinguishing in goaf engineering practice.

     

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