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Analytical Solutions for Characterizing Fluid Flow through Sand-Pack in Pipes
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-08-03 , DOI: 10.1155/2020/3091402
Shichen Gao 1 , Zhixin Tian 1 , Bailu Teng 2
Affiliation  

When fluid flows through a pipe that is packed with sand particles, the fluid will bear the resistance from the sand-pack, as well as the viscous shear from the pipe wall. If the viscous shear from the pipe wall can be neglected, the fluid flow will obey Darcy’s law, and one can think the equivalent permeability of the packed-pipe equals the permeability of the sand-pack. However, if the viscous shear from the pipe wall cannot be neglected, the fluid flow will obey the Brinkman equation, and the permeability of the packed-pipe will be less than that of the sand-pack due to the additional viscous drag. In this work, on the basis of the Brinkman equation, we derived a series of analytical solutions for characterizing the fluid flow in packed-pipes. These solutions can be used to depict the velocity profiles, estimate the flux rate, and calculate the equivalent permeability of a packed-pipe. On the basis of these analytical solutions, we found that Poiseuille’s law is a special form of the derived equivalent permeability solution. We further divided the fluid flow in a packed-pipe into three regimes, including N-S flow, Brinkman flow, and Darcy flow. During the regime of Brinkman flow, the dimensionless flow velocity at the pipe center is 1, and the dimensionless flow velocity is gradually decreased to 0 at the pipe wall. We also investigated the effects of sorting, sand particle size, and sand-pack porosity on the packed-pipe permeability. The calculated results show that a more uniform size of the sand particles or a smaller mean particle diameter can lead to lower packed-pipe permeability. Compared to the sorting and mean particle diameter, the sand-pack porosity exerts a more significant effect on the packed-pipe permeability.

中文翻译:

表征通过管道沙包的流体流动的分析解决方案

当流体流过装有沙子颗粒的管道时,该流体将承受来自沙子堆的阻力以及来自管道壁的粘性剪切力。如果可以忽略管壁上的粘性剪切力,则流体流动将遵循达西定律,并且人们可以认为填料管的等效渗透率等于砂土的渗透率。但是,如果不能忽略管壁上的粘性剪切力,则流体流动将服从Brinkman方程,并且由于附加的粘性阻力,填充管的渗透率将小于砂土的渗透率。在这项工作中,基于Brinkman方程,我们推导出了一系列用于表征填充管中流体流动的解析解。这些解决方案可用于描绘速度曲线,估算通量率,并计算出填充管的等效渗透率。基于这些解析解,我们发现泊瓦依尔定律是导出的等效渗透率解的一种特殊形式。我们进一步将填充管中的流体流分为三种状态,包括NS流,Brinkman流和Darcy流。在布林克曼流态下,管中心的无量纲流速为1,管壁处的无量纲流速逐渐减小为0。我们还研究了分选,沙粒尺寸和沙堆孔隙度对填料管渗透率的影响。计算结果表明,更均匀的砂粒尺寸或较小的平均粒径会导致较低的填充管渗透性。与分选和平均粒径相比,
更新日期:2020-08-03
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