Porous media can be seen everywhere in our production and life. It has extremely important applications in many fields such as energy, chemical industry, metallurgy, petroleum, construction, soil, materials, aerospace and nuclear reactors. However, it is difficult and hot to calculate the flow resistance. In this paper, a variable diameter tube ball model is established based on the actual porous media structure and flow characteristics. The model takes into account both the viscous and inertial resistance of the tube flow and the flow around a spherical particle, and the total flow resistance loss in the porous media is regarded as the sum of the viscous resistance loss of the tube flow, the local resistance loss of the variable diameter and the resistance loss of the flow around a sphere. Therefor a formula for calculating the resistance of porous media (variable diameter tube ball model formula) is derived. The analysis of different experimental data shows that the variable-diameter tube ball model formula can be applied well in the pre-Darcy flow, Darcy flow, Forchheimer flow and turbulent flow. Finally, through the comprehensive comparison and analysis of 45 groups of 1400 porous media resistance test data under different conditions, it is found that there are 24 groups with the maximum deviation of less than 60 % when the variable diameter tube ball model formula predicts these data, which is better than Ergun equation as a whole. The working conditions of the maximum deviation less than 60 % are the apparent velocity of 0 to 0.066 m/s, the Reynolds number of 0.005331.97 to 1101, the porosity of 0.33 to 0.4692, and the particle size of 0.375 to 1.778 mm.

中文翻译：

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基于变径管球模型的多孔介质流阻公式理论推导与分析

多孔介质在我们的生产和生活中随处可见。在能源、化工、冶金、石油、建筑、土壤、材料、航空航天、核反应堆等众多领域有着极其重要的应用。然而，流阻的计算却是一个难题和热点。本文根据实际多孔介质结构和流动特性，建立了变径管球模型。该模型同时考虑了管流的粘性阻力和惯性阻力以及球形颗粒周围的流动，多孔介质中的总流动阻力损失被视为管流的粘性阻力损失、局部流动阻力损失之和。可变直径的阻力损失和球体周围流动的阻力损失。由此推导出多孔介质阻力的计算公式（变径管球模型公式）。对不同实验数据的分析表明，变径管球模型公式可以很好地应用于预达西流、达西流、福希海默流和湍流。最后，通过对不同条件下45组1400个多孔介质阻力测试数据的综合对比分析，发现变径管球模型公式预测这些数据时最大偏差小于60%的有24组，整体优于额尔古纳方程。最大偏差小于60%的工况为表观速度0～0.066 m/s、雷诺数0.005331.97～1101、孔隙率0.33～0.4692、粒径0.375～1.778 mm。