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

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.