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

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 ①with the increase of nitrogen gas temperature,its density decreases as dynamic viscosity increases,and the loss decreases; ②with 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.