采空区气体流动:Forchheimer模型改进与压力损失预测

Gas flow in goaf: Forchheimer model improvement and pressure loss prediction

为了解决结构复杂采空区的流动阻力计算问题,提出了一种新的多孔介质物理模型。该物理模型为2×2×2大球径正方体、8个大径球、1个小径球、6个小径半球及其空腔而围成的立体结构。根据孔隙率相等和单周期流动的原则,切割该多孔介质物理模型而构建出最小流动单元。基于平均速度的假设,应用流体力学Navier-Stokes方程组,简化最小流动单元流场为一维流动,推导出最小流动单元内平均速度与惯性力、黏性力和压力梯度的4段函数表达式。采用长度比权重方法,得到了最小流动单元压力损失的计算式,建立起了单位长度压力损失与球体直径、气体流入初速度和气体密度之间量化关系。借助最普通的数值工具,预测了球体直径为15 mm工况下的压力损失值,数值计算表明:随着温度的增加,氮气密度减少,动力黏度增加,压力损失降低;随着初速度的增加,压力损失加速增加,惯性力引起的压力损失比重变大。进一步,依据现有的工程数据,利用压力损失计算方程,校验了预设防灭火控制半径,反演出了所注入氮气的初速度。所得计算结果与工程应用对比表明,采空区气体流动的压力损失满足平均速度二次关系式,并改进了Forchheimer模型,可准确预测氮气注入采空区所需表压,为防治采空区遗煤自燃提供新的方法。

In order to solve the problem on the calculation of flow resistance in a complex goaf,this paper proposes a new physical model of porous media.The physical model is a structure in which eight large balls are sandwiched by one small ball,six small diameter hemispheres,and a cavity part in 2×2×2 large diameter cubic volume.According to the principle of equal porosity and single-cycle flow,the physical model of the porous medium is cut to construct a minimum flow unit.Based on the assumption of average velocity,the Navier-Stokes equations of fluid mechanics are applied to simplify the flow field of the minimum flow unit as a one-dimensional flow,and the four-part function expressions of the average velocity and inertial force,viscous force and pressure gradient in the minimum flow unit are derived.The length-ratio weight method is used to obtain the calculation formula of the minimum flow unit pressure loss,furthermore it is constructed that the effects of a unit-length pressure loss on sphere diameter,the initial velocity of inlet airflow and gas density.By the virtue of the most common calculator,the loss values are predicted on the condition of 15 mm spherical diameter.The numerical results show that(1)with the increase of nitrogen gas temperature,its density decreases as dynamic viscosity increases,and the loss decreases;(2)with the initial velocity increase,the loss increases faster,and it is implied that the loss induced by the inertia force gradually dominates.Furthermore,based on the consisting data from engineering sites,the application of the equation checks out the radium-preset of fire extinguishing and preventing in goaf,and the initial velocity of injected nitrogen gas is inversely calculated.The comparison between the calculated results and the engineering application shows that the pressure loss of the gas flow in the goaf satisfies the quadratic relationship of the average velocity and improves the Forchheimer model.This model accurately predicts the required gauge pressure of nitrogen gas injection into a goaf,and provides a new reference for the prevention of spontaneous combustion of residual coal in goaf.