采空区瓦斯与大气两相混溶扩散模型及其求解

TWO-PHASE MISCIBLE DIFFUSION MODEL AND ITS SOLUTION BETWEEN GAS IN GOAF AND ATMOSPHERE

基于两相混溶气体渗流–扩散方程,建立了非均质采空区瓦斯涌出与风流交换的模型,用迎风式Galerkin数值方法求解,以可视化方式直观描绘了回采中采空区瓦斯的运移与分布的流体力学原理,采空区瓦斯源用负指数衰减函数描述。在力学处理上,对不透气顶、底板采空区的瓦斯涌出用可压缩两相气体混溶来考虑,流态(速度场)计算则用不可压缩气体渗流求解,由此可克服了以往采用不可压缩气体渗流–扩散模型计算瓦斯分布结果中因“超饱和”解所带来的误差和失真问题。给出增大风量后瓦斯分布的算例,由此反映出工作面风压与采空区内部瓦斯压力的动态平衡性。与单相流计算结果对比,在风流流速相对较高的情况下,两者的瓦斯分布结果基本一致,反之则差别很大,算例中开始出现差别的临界风速为0.091m/min,在采空区深部处瓦斯分布显著不同。

The model of gas effusion and air exchange in inhomogeneous goaf was established based on two-phase miscible gas seepage-diffusion equation. The model is solved by means of upwind Galerkin numerical method,and the basic fluid mechanics principle of the gas transport and distribution is described by means of visualization way. On the basis of mechanical disposal, the gas effusion in the goaf with gas-tight roof and floor is treated as two-phase gas miscible flow; but the calculation of the flow pattern （velocity field） is solved by regarding it as a seepage problem of incompressible gas. So it can avoid the error and distortion from incompressible gas seepage-diffusion model in calculating gas distribution because of super saturation solution in the result. The gas source in goaf is described by negative exponential attenuation function. An example provided in the case of wind is increased, which shows the dynamical balance feature between the air pressure in working face and gas pressure in the goaf. Compared with the result calculated as single-phase flow, the gas distribution results between them are almost the same when the speed of air is relatively high, if not, there is a large difference between the results. The critical air speed when the difference appears in the example is 0.091 m/min, but the gas distribution is significantly different in the deep part of the goaf.