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采空区球体组装模型与多孔介质流动压损预测

Spherical assembly model and prediction of pressure loss of porous media flow in goaf

  • 摘要: 快速预测采空区内部流动损失,一直是煤矿精准防灭火的关键问题。围绕采空区多孔介质流动,提出球体组装的采空区多孔介质物理模型,结合模型几何特征,找到流动的最小体元,并划分出该流动的4个阶段。基于纳维−斯托克斯(N−S)方程,建立表观速度、球径、动力黏度、流体密度与压损的关系式,得到4个阶段的压损计算式,进一步,采用时间比重的加权方法,建立了单位长度压损模型JT/L,符合Forchheimer方程形式。应用该模型预测了压损数值,对比了数值模拟结果和Ergun方程的预测值,结果表明:对数值模拟结果的影响,相比出入口效应,发现边壁效应更大,经优化确定模型为16×7的多球组装体接枝组合;对于该接枝组合内的多孔介质流动,在层流和近层流时,Ergun预测值与数值模拟结果的相对误差小于8%;引入孔隙率为0.375的多孔介质试验数据,开展无量纲分析,验证了数值模拟结果的可靠性,但是,单位长度压损模型JT/L预测值的误差最大值达69.9%,实为将N−S方程简化成一维而引起的;定义修正系数K,表征三维流动的影响,雷诺数(Re)低于10,K=2.84,雷诺数为10~3 000时,K=6.56Re−0.334;最终,得到了拟三维的JT'/L计算模型,当雷诺数低于10,预测值的误差小于6%,在雷诺数10~3 000范围内,误差低于10%。结论表明,基于球体组装模型的采空区拟三维多孔介质流动压损计算模型,可快速预测出雷诺数不超过3 000的单位长度压损,有助于科学指导采空区精准防灭火的工程实践。

     

    Abstract: Rapid prediction of flow loss in goaf is always the key problem of accurate fire prevention in coal mines. Based on the porous media flow in goaf, a physical model of porous media in goaf assembled by spheres is proposed. Combined with the geometric characteristics of the model, the minimum volume element of the flow is found, and four stages of the flow are divided. Based on Navier−Stokes equation, the relationship between apparent velocity, diameter, dynamic viscosity, fluid density and pressure loss is established, and the pressure loss calculation formula of four stages is obtained. Further, the pressure loss model per unit length JT/L is established by using the time-specific weight method, which accords with Forchheimer equation form. The model is used to predict the pressure loss, and the simulation results are compared with the predicted values of Ergun equation. The results show that the boundary effect on the numerical simulation results is greater than that of the inlet and outlet effect. The optimal model is 16×7 multi-ball assembly unit grafting combination. For the porous media flow in the grafting combination, the relative error between Ergun predicted value and simulation result is less than 8% in laminar flow or near laminar flow. The reliability of the numerical simulation results was verified through dimensionless analysis using experimental data from porous media with a porosity of 0.375. However, the maximum error of JT/L predicted value of the unit length pressure loss model is 69.9%, which is actually caused by the simplification of N−S equation to one dimension. The correction coefficient K was defined to represent the influence of three-dimensional flow. When the Reynolds number (Re) is less than 10, K=2.84, and when the Re is from 10 to 3000, K=6.56Re−0.334. Finally, the pseudo-three-dimensional JT'/L model is obtained. When the Re is below 10, the error of the predicted value is less than 6%, and when the Re is from 10 to 3000, the error is less than 10%. It is concluded that the pseudo three-dimensional porous media flow pressure loss calculation model based on the sphere assembly model can quickly predict the pressure drop per unit length of the Re less than 3000, which is helpful to scientifically guide the engineering practice of accurate fire prevention in the goaf.

     

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