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

CHEN Fangxing; HAO Xiaoli; CHEN Shiqiang; LI Yiqun; LI Shilin; LU Yi

doi:10.12438/cst.2024-0448

Volume 53 Issue 5

May 2025

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COAL SCIENCE AND TECHNOLOGY > 2025 > 53(5): 233-242. > DOI: 10.12438/cst.2024-0448

CHEN Fangxing，HAO Xiaoli，CHEN Shiqiang，et al. Spherical assembly model and prediction of pressure loss of porous media flow in goaf[J]. Coal Science and Technology，2025，53（5）：233−242. DOI: 10.12438/cst.2024-0448

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

CHEN Fangxing^1,,
HAO Xiaoli^{1, 2},
CHEN Shiqiang^{1, 2, ,},
LI Yiqun¹,
LI Shilin¹,
LU Yi¹

1.
School of Resource & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
2.
School of Civil Engineering, Hunan University of Science and Technology, Xiangtan 411201, China

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Received Date: April 09, 2024
Available Online: May 14, 2025

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Abstract

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 J_T/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 J_T/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 (R_e) is less than 10, K=2.84, and when the R_e is from 10 to 3000, K=6.56R_e^−0.334. Finally, the pseudo-three-dimensional J_T'/L model is obtained. When the R_e is below 10, the error of the predicted value is less than 6%, and when the R_e 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 R_e less than 3000, which is helpful to scientifically guide the engineering practice of accurate fire prevention in the goaf.
- pressure loss,
- porous media model,
- time specific gravity,
- boundary effect,
- correction coefficient

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

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